Brandman - Quantitative Literacy Level A
On four consecutive days, a stock price changed in the amount of +$0.99, -$0.43, +$0.06, and -$0.58. What was the average change in value over this period?
0.01
A 200-square-foot space in a warehouse is partitioned out for an office. What percentage of the total 12,000 square feet of warehouse space does this represent? Round to the nearest tenth of a percent.
0.017
The simple interest on a $2,500 loan that was made for 1.5 years was $195. What was the annual interest rate? *
0.052
The simple interest on a $3,000 loan that was made for 1 year was $300. What was the annual interest rate?
0.1
A central pivot irrigation system is designed to distribute water evenly over a circular area. The distance around the irrigated field was determined to be 125.6 meters. Find the area of the irrigated field. Use π = 3.14
1,256 square meters
If 7 tiles can cover 5 square feet of area, then how many tiles will it take to cover 1,250 square feet of space?
1,750 tiles
George finalized an investment portfolio that consisted of 5 different investment strategies. If he decides to select any 3 of them, in how many ways can the selection be made?
10
What is (1/2%) of 2,000 unique visitors to a website?
10 unique visitors
To represent the region at a sales conference, a group of 2 executives has to be chosen. If there are 15 executives in the region, in how many ways can the group be formed?
105
An ATM machine dispenses only $20 bills. How many $20 bills should be requested to have enough cash to purchase an item worth $212.20?
11
Consider the following data on the sales of books (in thousands) by two publishers in the years 2008 and 2012. 2008 2012 Publisher A 90.3 120.6 Publisher B 85.4 100.2 Assuming a constant rate of growth in sales, predict the sales (in thousands) for publisher B in the year 2016.
115
The revenue and cost, in dollars, generated from selling a particular item are modeled by the formulas R = 150x - 0.30x² and C = 1200 + 45x, respectively, where "x" represents the number of units produced and sold. What number of units must be produced and sold to break even?
12 units and 338 units
A passenger train travels on average 10 miles per hour faster than a freight train. The passenger train covered 650 miles in time "t" , whereas the freight train covered 600 miles in the same time. Calculate the average rate of the freight train.
120 Miles per hour
A retailer currently accommodates 45 shoppers a day. After a remodel, they hope to accommodate 300% of this amount. How many shoppers do they hope to accommodate each day after the remodel?
135
Consider a square plot with a length of 105 yards and an area of 2x². If a rectangular football field of the same length with an area of x² - 30x is made within the plot, find the leftover area of the plot. **
14,175 square yards
An ATM machine dispenses only $5 bills. How many $5 bills should be requested to have enough cash to purchase an item worth $72.54?
15
Find the difference between the polynomial expressions 2x² and x² + 5x, if the value of x is 15.
150
The enrollment in a management program this year is almost 200% of the enrollment last year. If 314 students enrolled this year, approximate the number of students enrolled last year.
157
The cost incurred on Day 1 for buying 15 units of Stock A and 10 units of Stock B is $1,600. On Day 2, the cost increases to $2,200 as only 20 units of Stock A and 20 units of Stock B were purchased. Which of the following systems best models this situation?
15x+10y=$1,600 20x+20y=$2,200
An apparel designer can design a dress in 24 hours. If her assistant helps her, then it will take 10 hours to complete the work. If the designer gives all of the work to the assistant, how long would it take for the assistant, working alone, to complete the dress? *
17.14 hours (1/24) * 10 + (1/x)*10 = 1 x = 17.14
A retailer received 5,000 units of a particular T-shirt in three sizes-large, small, and medium. Of the total units, 20% were large, 30% were small, and the rest were medium. How many T-shirts of medium size did the retailer receive?
2,500
One liter of a drink is made up of equal parts of apple juice and grape juice, and 125 ml of water. How many liters of apple juice would be present in 5 liters of the same drink? (1 liter = 1,000 ml; round the answer to the nearest tenth.)
2.2 liters
A particular brand of mayonnaise comes in a cylindrical container with a diameter of 10 centimeters and a height of 10 centimeters. A spoon of mayonnaise served gives the shape of a sphere with a diameter of 4 centimeters. Approximate the number of such serves per container. *
23 serves Volume of container:V = πr² h Volume of serves: V = 4πr³/3
Consider A and B take 8 hours to clean a swimming pool. If A takes twice the amount of time compared to B to complete the work, how long will it take for A to clean the swimming pool alone? *
24 hours
The average stopping distance d (in feet) on dry pavement is given by the formula: d = s²/24 where "s" represents the vehicle speed in miles per hour. Determine the stopping distance of a car traveling 25 mph on dry pavement. Round to the nearest foot.
26 feet
A salesman is on the road and has traveled 40 miles in the urban area of a city. While in the suburban area, he increased his speed by three times to cover 60 miles. If he has traveled for a total of 7 hours, calculate his average rate of speed in the suburban area. Round the rate to nearest whole number.
27 miles per hour
A megabyte consists of 2^20 bytes of information. How much information can 16 (2^4) megabytes contain?
2^24 bytes {Explanation - 16 * 2^20 = 2^4 * 2^20 = 2^(4+20) = 2^24 bytes}
Rainbow handcrafts wants to design a triangular-shaped slate with an area of 10 square centimeters and a base of 4 centimeters. Find the perimeter of the triangle if the other two sides are of the same length. *
2√29 + 4 Area : 10 = 1/2 * 4 * h h = 5 Calculation of other two sides: Connection refused - connect(2) for "localhost" port 10140 x = √29 Perimeter = 2x + 4 Perimeter = 2√29 + 4 centimeters
Anderson Toys has designed a triangular-shaped toy with an area of 20 square centimeters and base of 5 centimeters. Find the perimeter of the triangle if other two sides are of same length.
2√70.25+5 centimeters
Harold bought some books and notebooks from a stationery shop for $30. He bought three more notebooks than twice as many books. The cost of each book is $4 and each notebook is $2. Find the number of books and notebooks that Harold bought.
3 books and 9 notebooks
Given the board below with sections of different colors, if you toss a coin onto this board randomly, what is the probability that it will land on red? Red Yellow Red Green Black White Red Blue
3/8
The formula for the perimeter of a rectangle is given by P = 2l + 2w, where l represents the length and w represents the width. A small rectangular smartphone measures 9.4 centimeters by 5.8 centimeters. Determine its perimeter.
30.4 centimeters
A 1,920-pixel wide image measures 6.4 inches. Determine the number of pixels per inch (ppi) of width.
300 ppi
An executive traveled in a cab at an average speed of 25 miles per hour for 75 minutes. How far did he travel? Use the formula D = rt.
31.25 miles
11 out of 13 small-scale industries in a particular region preferred a reduction in the tax rate on sales. If 390 such industries participated in the survey, how many industries are interested in a lower sales tax rate?
330
A particular brand of ice cream comes in a cylindrical container with a diameter of 16 centimeters and a height of 20 centimeters. An ice cream scoop makes scoops in the shape of a sphere with a diameter of 6 centimeters. Approximate the number of such scoops per container. **
35 scoops Volume of container then volume of scoop
The cost function for a computer hardware supplier is -4x²y + 4xy² - 7xy - 28 for the first month and 7x²y - 5xy² - 3xy + 38 for the second month. Find the cumulative cost function for these two months.
3x²y - xy² - 10xy + 10
Consider an executive who takes 4 hours to complete a job. If his assistant helps him, then it will take 2 hours to complete the work. If the executive gives all of the work to the assistant, how long would it take for the assistant, working alone, to complete the job?
4 hours
In the year 2000, the census indicated that the population of a certain city was 36,000 people. In the 2010 census, the town grew to 78,000 people. Determine the rate at which the population changed with respect to time.
4,200 people per year
A manufacturer of processed foods set up a cylindrical facility with a conical top that is 1/3 of the total height. If the diameter of the base measures 18 meters and its height measures 24 meters at the top, estimate the volume of the facility. Round your answer to the nearest whole number.**
4,748 m³ h1 = 24/3 = 8m V = V(cone) + V (cylinder) V = πr²h/3 + πr²h2 V = 3.14(9)²(8)/3 + 3.14(9)²(16) V = 4748m³
Larry uses a submersible sump pump of 5 inch diameter to drain the water from his swimming pool and it takes 10 hours to complete. If he uses an 8 inch diameter pump, he can finish the work in 8 hours. How long will it take to drain the water using both?
4.44 hours
A particular brand of fruit preserve comes in a cylindrical container with a diameter of 14 centimeters and a height of 18 centimeters. A spoon of fruit preserve served gives the shape of a sphere with a diameter of 5 centimeters. Approximate the number of such serves per container.
42 serves
The cost of renting a car is $45 plus an additional $0.60 per mile driven. If the rental cost is not to exceed $170, what inequality will help us find out how many miles we can drive?
45 + 0.60x <= 170
A 2% glucose solution has to be combined and mixed with a 4% glucose solution to produce 62 ounces of a 2.5% glucose solution. How much of each is needed to produce the 2.5% glucose solution?
46.5 ounces of 2% glucose and 15.5 ounces of 4% glucose
A square storage yard covers an area of 144 square feet. What length of fencing is needed to enclose the yard? *
48 feet s² = 144 where s is the side of the square s = 12 The perimeter of the square is P = 4s = 4(12) = 48 feet
A quarry has an inventory of 28 tons of granite aggregate. After delivering 8 tons of aggregate to a large road construction site, the rest is to be divided equally between 4 other job sites. How many tons will each job site receive?
5 tons
A warehouse manager only has time to deliver to 4 out of the 10 retail locations requesting the product, and since she wants to deliver in the most efficient manner possible, order does matter. How many possible routes can she consider?
5,040
The area of certain cardboard packaging in square centimeters is given by the formula A = 3x² - 0.6x where "x" represents the width in centimeters. If the area is 78 square centimeters, what is the width?
5.2 centimeters
If Jonathan can build a shed in 9 hours, how much of the shed can be built in 5 hours?
5/9
The area "A" in square feet of a rectangular pool is given by the formula A = 100w - w² where "w" represents the width of the pool. Determine the width that will produce the maximum area.
50 ft.
A warehouse manager only has time to deliver to 2 out of the 8 retail locations requesting the product, and since she wants to deliver in the most efficient manner possible, order does matter. How many possible routes can she consider?
56
A textile manufacturer maintains a ratio of inventory to total production at 5:7. If the inventory is I units and the total production is P units, which equation should be used to calculate P for a given I?
5P = 7I
A monthly report for a company indicated that total sales for the month of April was 6 (4/5) (in thousands). The marketing supervisor needed this number in decimals and insisted on changing the report. What will be the monthly sales (in thousands) when rounded to the nearest hundredth?
6.8
A square building is constructed on an area of 225 square meters. What is the length of the four-sided boundary that needs to be painted?
60 meters
A sales team is able to convert 75% of all sales leads generated by their website to actual sales. Their website generates 23 sales leads for every 1,250 unique visitors. How many actual sales would you expect if their website was able to generate 5,000 unique visitors?
69
To represent the region at a sales conference, a group of 4 executives has to be chosen. If there are 8 executives in the region, in how many ways can the group be formed?
70
Consider an office square in shape with a length of 30 yards with an area of x². If a rectangular conference room of the same length with an area x² - 3x is made within the office, find out the area still left in the office that can be used.
90 Square Yards
Ice cream cones are in the shape of a right circular cone and have a diameter of 6 centimeters and a height of 10 centimeters. Calculate the volume of the cone. Round your answer to the nearest whole number. Use π = 3.14.
94cm³
A rectangular field is to have dimensions 7x + 7 by 5x -5 units. Which equation best models the area of the field?
A = 35x² - 35
Two bicyclists began a race at the same time, where bicyclist A set a pace 4 miles an hour faster than bicyclist B. At this pace, bicyclist A was able to cover 30 miles in the same time bicyclist B was able to cover 20 miles. What was the average speed of each bicyclist at that point?
A: 12 miles per hour; B: 8 miles per hour
The floor of an office measures 50 feet in length by 40 feet in width, and the walls are 12 feet high. Approximate the cost of paint to cover the four inner walls. Paint is sold in 5-gallon buckets for $55.50 each, and is advertised to cover 300 square feet per gallon.
$111
The value of a new house in dollars is modeled by the formula V = 250t² - 7000t + 654000 where "t" represents the number of years since it was purchased. Determine the minimum value of the house. *
$16,400 Find the vertex. T = -b/2a = -(-7,000)/2(250) = 14. That is, the minimum value occurs 14 years after purchase. V = 250(14)² - 7,000(14) + 65,400 = $16,400.
A particular stock started the week at a price of $23 and lost $2 for three consecutive days and then rallied and gained $1 a day for the next two days. At what price did the stock end the week?
$19
Brian has $6,500 to invest in stocks at the beginning of the year. Stock A gave him a return of 6% and Stock B gave him a return of 7%. If the total simple interest earned from both the stocks at the end of the year was $435, calculate the amount invested in each stock.
$2,000 was invested in Stock A and $4,500 was invested in Stock B.
Mr. Charles Way has savings worth $246,832. He decides to invest this amount, rounded off to the nearest thousands, in mutual funds. How much will Mr. Way invest?
$247,000
Jill has to pay a service tax of 12.5% on a purchase of $200. Estimate the amount to be paid without using a calculator.
$26
Mr. Charles Way has savings of $324,497. He decides to invest this amount, rounded off to the nearest thousands, in mutual funds. How much will Mr. Way invest?
$324,000
The revenue "R" in dollars from selling T-shirts at the beach is modeled by the formula R = 12.50n where "n" represents the number of T-shirts sold. Furthermore, each T-shirt costs the vendor $6.20 and the space has a fixed cost of $90 for the day. What is the profit if 72 T-shirts are sold in a day?
$363.60
The yearly profit P in dollars from MP3 player sales is estimated using the formula P=4n-16,540 where "n" represents the number of music players sold. How many music players were sold if the profit for the year was $132,400?
$37,235
The revenue R in dollars from selling n cases of a product is given by R = 90n-0.05n². Determine the revenue from selling 800 cases of the product.
$40,000
A man left half of his assets to his wife, one-third of his assets to his son, and gave the rest to charity. If the charity received $15,000, what was his wife's share?
$45,000
The profit, in thousands of dollars, is given by the formula P= 2n² - 60n + 500 where "n" represents the number of units sold, in thousands, per year. Determine the minimum profit.
$50,000
Ian and Mark are salesmen earning the same base salary. Each of them earns a bonus of $100 for each sale. What is their base salary, if the ratio of their total salaries is 5/7 after Ian sells 2 items and Mark sells 5 items?
$550
A retailer offers (1/4) off on any item. If an item is priced at $875.60, what is its price after the discount?
$656.70
The value of a new car in dollars is modeled by the formula V = 250t² - 4,500t + 28,000 where "t" represents the number of years since it was purchased. Determine the minimum value of the car.
$7,750
A retailer sells an item at $90.85, which includes 15% profit. What was the cost of the item before profit was included?
$79
Rene observed that his scores in Quantitative Literacy increased with an increase in the number of daily study hours. Therefore, he believes that the scores of all students in Quantitative Literacy will increase if they spend more hours studying. What is this generalized statement called?
Conjecture/hypothesis
What is the formula for simple interest?
I=prt, "P" represents principal, amount invested at an annual interest rate "r" for "t" years.
Suppose this statement is true: If Emily gets into the doctoral program, then she will quit her job. Which of the following statements is also TRUE?
If Emily does not quit her job, then she did not get into the doctoral program.
Suppose this statement is true: If the wedding happens, then Emily will move to Europe. Which of the following statements is also TRUE?
If Emily will not move to Europe, then the wedding will not happen.
If the leading coefficient "a" is positive, how will the parabola open? Negative?
If the leading coefficient "a" is positive the parabola will open upward and if it is negative it will open downward.
What is a rectangular coordinate system?
It consists of two real number lines that intersect at a right angle.
When is an equation a contraindication?
It is an equation that is never true and thus has no solutions.
The R&D team of LS Paints has claimed that the mix of current and new automotive paint technology can paint a single charter bus in 8 hours. However, the current technology is estimated to take twice the time compared to the new technology to finish the work. Working separately, how long does it take for each automotive paint technology to paint a charter bus? New upcoming automotive paint technology takes x hours and the current technology takes 2x hours.
Current technology - 24 hours; New technology - 12 hours
The price for a particular product is determined by demand and is modeled by the linear equation p = -0.20x + 150 where "x" represents the number of units sold. What is the best interpretation of the slope?
For each unit sold, there is less demand for the product and the price drops by $0.20.
A brewer has two cylindrical containers for storing nitrogen. One has a diameter of 6 inches and a height of 8 inches. The other has a diameter of 8 inches and a height of 6 inches. Which container should be ordered in bulk in order to maximize storage capacity, if both containers are the same price? Use π = 3.14.
The second cylinder should be ordered in bulk.
What happens to the time if the distance traveled is decreased by 20 miles, keeping average rate constant? *
The time taken decreases.
Mark is trying to figure out all possible combinations for traveling between two locations using a directed graph. Which activity of the quantitative problem solving process does this scenario represent?
Visually representing the given information
When will there be a minimum y-value and maximum y-value?
When the leading coefficient "a" is positive there will be a minimum y-value and when it is negative, there will be a maximum y-value
The wholesale revenue "R" in dollars from selling x items is given by R = 0.90x - 0.05x² . The cost "C" in dollars of producing the x items is given by C = 0.32x + 48. Which equation best models the profit from producing and selling n items?
P = -0.05x² -0.58x -48
The wholesale revenue "R" in dollars from selling x items is given by R = 0.10x - 0.55x². The cost "C" in dollars of producing the "x" items is given by C = 0.15x + 400. Which equation best models the profit from producing and selling n items? **
P = -0.55x² - 0.05x - 400
Which of the following deals with the arrangement of a set of items where ordering is considered?
Permutation
What is the formula for determining Profit?
Profit = Revenue - Cost
What is the formula to determine Revenue?
Revenue equals the price "p" of a product times the number of products sold "n". R = pn
The cost of manufacturing a product is given by the formula C = 4n + 56,000 and the revenue from selling it is given by the formula R = 60n where "n" is equal to number of units. Find the number of units needed to be manufactured and sold in order to break even.
n = 1,000
A rectangular soccer field has a perimeter measuring 400 meters. The length is 40 meters less than twice the width. Find the dimensions of the rectangular soccer field. **
l = 120 meters, w = 80 meters P = 2l + 2w => 400 = 2(2w - 40) + 2w Solve for w and l.
A rectangular field has a perimeter measuring 600 meters. The length is twice the width. Find the dimensions of the rectangular field.
l = 200 meters, w= 100 meters
A rectangular bridge has an area measuring 2,000 meters. The length is 10 meters less than the width. Find the dimensions of the rectangular bridge. **
l = 50 meters, w = 40 meters
What is another way to find slope?
m = Vertical change ÷ horizontal change or rise ÷ run
What is the formula to determine the slope if given specific points?
m = y2 + y1 ÷ x2 +x1
What is an independent variable?
a variable (often denoted by x) whose variation does not depend on that of another.
It has been determined that the profit from producing and selling "x" items is given by the formula P = x² - 54x + 725. How many items must be produced and sold to break even?
x = 29 or 25 items
Profit is given by the formula P = 2x² + 180x where "x" represents the number of units sold. If the profit was $7,200, how many units were sold?
x = 30
The demand equation for a certain product is given by y=90-.05x where "x" represents the number of units sold and "y" the price in dollars. Determine the x- and y-intercepts.
x-intercept: (1,800, 0); y-intercept: (0, 90)
Write the supply curve x + 20y = 3400 in the slope-intercept form and give the slope.
y = -0.05x + 170, m = -0.05
Write the demand curve x+10y =1,200 in the slope-intercept form and give the slope. *
y = -0.1x+120 m = -0.1
Mr. Lopez changed to a new internet service provider two months ago. If the internet bill for the first month was $20 for a usage of 12Mbps and $35 for 25Mbps in the second month, find a linear equation that gives the monthly bill based on the number of units (Mbps) of internet usage.
y = 1.15x + 6.25
A lot was purchased for $20,000 in 2005 and sold for $38,000 in 2011. Which of the following linear equations best models the value of the lot since 2005?
y = 3,000x + 20,000
What is the point-slope form?
y-y1=m(x-x1)
What is the formula for distance traveled?
D=r*t, rate times the time traveled equals distance traveled
What is referred to as the process of reasoning from a premise to a logically certain conclusion?
Deductive reasoning or logical deduction
Katy observed that she could knit faster if she increased the number of daily hours she knit. What is the generalized statement that the knitting rate of all her friends will increase with an increase in the number of their daily knitting practice hours called?
Conjecture/hypothesis
Jill has to pay a service tax of 12.5% on a bill of $800. Estimate the amount to be paid without using a calculator.
$100
8 1/3 - 3 2/5
4(14/15)
In how many ways can six committee members be seated on a platform for an awards ceremony?
720
What is the quadratic formula?
x = -b ± √(b² - 4ac)/2a
What is slope intercept form?
y=mx+b
A cylindrical dustbin has a diameter of 1 meter and a height of 1 meter. Calculate the total cost to paint three-fifths of the dustbin if one cubic meter has a cost of $2. Round your answer to 2 decimal places.
$0.94
Ronald rents a banquet hall for the reception following his wedding ceremony. The rent of the banquet hall for a minimum of 6 hours is $800. Also, each additional hour will be an extra $100. Write a formula for the total rental cost incurred by Ronald and use it to determine the total rent if he needs the venue for 10 hours.
$1,200
The picture provided shows the floor plan of an office space. The diagram is not drawn to scale. The small rectangular office and one triangular room (shaded) are to be retiled at a cost of $10.25 per square foot. Estimate this cost.
$1,230
The cost, in thousands of dollars, is given by the formula C = -0.50n² + 62n - 500 where "n" represents the number of units produced, in thousands, per year. Determine the maximum cost. *
$1,422,000 Find the vertex of P = -0.50n² + 62n - 500. x-value of the vertex: -b/2a = -62/2(-0.5) = 62. Substitute x = 62 to find the maximum profit: P = -0.50(62)² + 62(62)-500 = 1422. The vertex is (62, 1422); now, interpret the results.
What is the total cost of a $124.99 item after a 6.4% sales tax is included?
$132.99
A person carries a debt of $1,850 and agrees to pay $500 and the rest in 6 equal monthly installments. What is the monthly installment?
$225
A man left half of his assets to his wife, one-third of his assets to his son, and gave the rest to charity. If the charity received $22,000, what was the son's share?*
$44,000 Explanation: The amount given to charity was one-sixth of the total assets. The son's inheritance of one-third property was twice this. Hence, the son's share = 2 *charity's share = $44,000.
The cost of a daily car rental is fixed at $35 for 20 miles with an additional $0.30 for every extra mile driven. Determine the total cost of renting the car if it is driven 80 miles in a day.
$53
Nora purchased an item that was advertised for 25% off. If she paid $400 for the item, which included the discount, what was its original price?
$533.33
What is the reduced ratio of 24 inches to 4 feet?
1 foot to 2 feet
What is the reduced ratio of 12 inches to 5 feet?
1 inch to 5 inches
It was found that 45 employees do not agree with a new company policy. What percent of the company's 1,800 employees do they represent?
2.5%
An employee worked 6(3/4) hours on Monday, 5(1/2) hours on Wednesday, and 7(3/4) for "localhost" port 10140 hours on Friday. How many hours in total did he work that week?
20 hours
A manager has to create a 5-digit personal identification number (PIN). If the first digit is not allowed to be zero and no digits are to repeat, how many PIN numbers are available for him to choose from?
27,216
A textile manufacturer maintains a ratio of inventory to total production at 2:9. If the inventory is I units and the total production is P units, which equation should be used to calculate P for a given I?
2P = 9I
A textile manufacturer has set up a cylindrical plant with a conical top that is 1/2 of the total height. If the diameter of the base measures 20 meters and its height measures 36 meters at the top, estimate its volume. Round your answer to the nearest whole number.
7,536 m³
A company's stock price and earnings per share are $23.65 and $2.89, respectively. What is the company's stock price-to-earnings ratio? Round to the nearest hundredth.
8.18
What is the definition of a counterexample?
Any example that disproves a conjecture or hypothesis.
The Profit "P" in dollars from selling pullovers at a shop is modeled by the formula P = 345n where "n" represents the number of pullovers sold. If the profit for the day was $5,647.30, how many pullovers were sold?
Approximately 16
What are premises that are self-evident or widely accepted truths?
Axioms
What is the formula for circumference and area of a circle?
C = π*d = 2πr A = πr²
A dealership in Washington, D.C. sold 50 red cars out of 250, whereas a dealership in California sold 39 red cars out of 150 total. Which dealership sells a higher percentage of red cars?
California
To serve to employees during a two-day conference, 15 coffees and 15 doughnuts were purchased for $30. On the first day, only a few of them preferred the coffee but no doughnuts were left by the end of the day. Therefore, only 5 cups of coffee and 25 doughnuts were purchased for $20 for the second day. How much did each coffee and each doughnut cost?
Coffee: $1.50; Doughnut: $0.50
Atif observed that he scored more goals if he increased the number of daily practice hours. What is the generalized statement that the goals scored by all his team members will increase with an increase in the number of their practice hours called?
Conjecture/hypothesis
The R&D team of Premier Paints has claimed that the mix of current and new automotive paint technology can paint a single car in 3 hours. However, the current technology is estimated to take three times longer compared to the new technology to finish the work. Working separately, how long does it take for each automotive paint technology to paint a car? *
Current technology - 12 hours; New technology - 4 hours
When is an equation an identity?
It is an equation that is true for all possible values of the variable.
Mark draws a decision tree to figure out the best investment strategy out of the five investments that he believes will give relatively good returns. Which activity is he performing?
Quantitative problem solving
The price "p" of an item is modeled by the formula p = 600 - 0.8n where "n" represents the number of units sold. Revenue is the product of the price of an item and the number of units sold. Given this price model, which formula best models the revenue? **
R = 600n - 0.8n²
The price "p" of an item is modeled by the formula p = 60 - 5n where n represents the number of units sold. Revenue is the product of the price of an item and the number of units sold. Given this price model, which formula best models the revenue?
R = 60n - 5n²
The yearly demand (Q) for a product has always been in the range of 10,000 to 20,000. Find the equivalent range for the price P, given that Q=50(P-4,500)
The equivalent price range is from $4,700 to $4,900.
Jack stays at home if it rains. Today's football match was canceled due to rain. Assuming that these statements are true, what conclusion can be drawn?
Today, Jack stayed at home.
What is a dependent variable?
a variable (often denoted by y) whose value depends on that of another
What is the Pythagorean Theorem?
a² + b² = c²
Determine the slope of the given cost curve. (0,50) (20, 100)
m = 2.5
What is the formula for the line of symmetry?
x = -b/2a
The cost C in dollars of producing thumb drives is given by the formula C = 1.85x + 5,200, where x represents the number of drives produced. What is the cost of producing 3,200 thumb drives?
$11,120
The cost "y" in dollars of producing "x" products is given by the formula y = 5x + 1,200. Which statement best describes the y-intercept in this case? *
The initial fixed cost of production
A cylindrical flower vase has a diameter of 30 centimeters and a height of 60 centimeters. Calculate the total cost to fill it to two-fourths capacity if one cubic centimeter of water costs $0.0005. Round your answer to 2 decimal places. **
$10.60
Jace invested $2,500 in an account earning simple interest for a period of 6 months. If the annual interest rate is 8%, how much would he earn in interest? Use the formula for simple interest, I = prt.
$100
The cost function "C" in terms of x number of units sold is given by the formula C = -0.4 (x - 20)² + 80. What should be the expanded form of the cost function?
-0.4x² + 16x - 80
A shed covering drops 4 feet for every 12 feet forward. Determine the slope of the roof.
-1/3
Convert the temperature 25 degrees Fahrenheit to degrees Celsius. Use the formula C = 5/9 (F-32) where "F" represents degrees Fahrenheit and "C" represents degrees Celsius. Round to the nearest tenth.
-3.9° Celsius
The level of productivity decreases with an increase in the mandatory number of work hours. Which of the following conclusions is arrived at by inductive reasoning?
An office with a reasonable number of mandatory work hours has employees who are more productive.
A steel plant has been set up at a cost of $20 million with $2 million as its operating expenses per year. The expected revenue every year from this plant is $4 million. After how many years of operation will the plant recover the set up cost including the yearly operating expenses incurred? *
Approximately 10 years
An e-commerce website has been developed at a cost of $10,000 with $900 as its operating expenses per month. The expected revenue every month from the website is $1,500. After how many months of operation will the investment be recovered, including the monthly operating expenses incurred?
Approximately 17 months
An executive worked 7.75, 8.5, 7.9, 5, and 6.75 hours on 5 consecutive days. How many hours should he work on the 6th day so that his average daily hours worked will be at most 8 hours? *
At most 12.1 hours
An employee worked 5.5, 5.25, 4.9, 5, and 4.75 hours on 5 consecutive days. How many hours should he work on the 6th day so that his average daily hours worked will be at most 5 hours?
At most 4.6 hours
The cost "c" of an item is modeled by the formula c = 450 - 0.6n where "n" represents the number of units purchased. Total cost is the product of the cost of an item and the number of units purchased. Given this cost model, which formula best models the total cost? *
C = 450n - 0.6n²
If there is a one-time set-up fee of $5,280 and each item costs $62 to produce, what would be the cost function?
C = 62n + $,5280
Kenneth has used a rectangular cardboard sheet to pack his refrigerator. The area of the sheet is 15 square meters, whereas the width of the refrigerator is 2 meters less than the length. Find the length and width of the sheet.
Length = 5 meters, Width = 3 meters
In order to earn a four-star rating, an employee should have an average quality score between 90 and 100 points for the last six months. If Lisa got 82, 95, 90, 90, and 105 for the first five months, how many points should she get for the sixth month to earn a four-star rating?
Lisa must earn a score of at least 78 points and at most 138 points.
The profit "y" in dollars from producing and selling "x" items is given by the formula y = x² + 90x -1750. Which statement best describes the y-intercept in this case?
Loss incurred on producing and selling the items
If the radius of a sphere is measured using inches, what is the appropriate unit for the surface area?
Square inches
An investment of $24,000 was made in two stocks. Stock A earned 6.5% and Stock B earned 8% annual interest. If the total interest was $1,777.50, how much was invested in each stock?
Stock A $9,500 and Stock B $14,500
In a survey of 240 people, 156 people said they supported the governor. What percentage supported the governor and what percentage did not?
Support: 65%; Do not support: 35%
What is referred to as a form of logical argument where two or more premises share a common term that is not in the conclusion?
Syllogism
What happens to the average rate if the distance traveled is decreased by 20 miles, keeping time constant?
The average rate decreases.
Jane is baking a cake and uses the estimation process to measure the ingredients. Why did Jane use this process?
To approximate a solution
Jane is sewing a dress for her sister and uses the estimation process to obtain the measurements. Why did Jane use this process?
To approximate a solution
Gaming laptops depreciate at a rate of $150 per year. Which linear formula best models the value of a gaming laptop that was purchased for $650?
V = 650 - 150x
A conference is to be conducted at a particular venue for 4 days. If the daily rent for the location amounts to $500, what is the total rental cost?
$2,000
A fleet vehicle uses 180 gallons of gasoline every 4 months. If gasoline costs $4.25 per gallon, what is the yearly cost of fuel?
$2,295
A manufacturing process involves a fixed cost of $1,750 and a variable cost of $1.50 per item produced. What is the total cost of producing 800 items?
$2,950
The value in dollars of a new MP3 player can be estimated by the formula V=100(t+1)^-1, where t represents the number of years after purchase. Estimate the value of the MP3 player 4 years after purchasing it.
$20
A fleet vehicle uses 300 gallons of gasoline every 6 months. If gasoline costs $5.50 per gallon, what is the yearly cost of fuel?
$3,300
Sam's base salary last month was $3,200 per month. Additionally, he earned a performance incentive of $750 and a travel allowance of $450. If his monthly contribution to income tax amounts to $550, what is his effective take-home salary last month?
$3,850
At the local discount warehouse, a set of 4 tires costs $624.75. What proportion can be used to obtain the price of 12 such tires?
$624.75/4 = x/12
A start-up reported quarterly net income in the amounts of $23,500, -$12,500, -$20,200, and -$8,200. What was the total reported net income for the year?
-$17,400
A retailer bought an item for $24 and resold it at $36. What percent increase does this markup represent?
0.5
The price of a cell phone was marked down 30% less than the initial price of C. Andrea had a coupon for an additional 10% off. In terms of C, what was the final price of the new cell phone?
0.90(0.70C)
The initial price of a motorcycle is C dollars. If you receive a 10% discount, in terms of C, what was the final price of the new motorcycle?
0.90C
A manager has to line up a presentation from a pool of eight employees. In how many ways can half of the employees present where the order matters?
1,680
A manager has to line up a presentation from a pool of 12 employees. In how many ways can one-third of the employees present where the order matters?
11,880
A manufacturer can produce 45 units of a product in 3 hours. How many units of the product can be produced in a 9-hour workday?
135 units
A 1,920-pixel wide image has a 1,080-pixel height. What is the reduced width to height ratio?
16:9
A pizzeria allows customers to choose between a thick, thin, or a medium crust and 3 types of cheese. If there are 3 different topping options, how many variations of 1-topping pizzas are available?
27
A megabyte consists of 2^20 bytes of information. How much information can 8 (2³) megabytes contain?
2^23 bytes
A gigabyte consists of 2^30 bytes of information. If a gigabyte is to be divided into 16 (2^4) sectors, how much information can be held in each sector?
2^26 bytes
A gigabyte consists of 2^30 bytes of information. If a gigabyte is to be divided into 4(2²) sectors, how much information can be held in each sector?
2^28 bytes {Explanation - Divide: 2^30/2² = 2^(30-2) = 2^28 bytes}
Google AdSense asserts that wide advertisements tend to perform better than taller ones. In particular, ads with a width to height ratio of 6:5 perform well. If your particular ad requires 420 pixels of width to display the text, what should the height be set at in order to gain the performance advantage?
350 pixels
A case of salted peanuts contains 48 individual packages. A store owner has 2 (1/4) cases of salted peanuts in stock and another 5 (1/2) cases in the warehouse. How many individual packages of salted peanuts does he have?
372 packages
A sample of 750 units from a production run were tested and 30 units were found to be defective. What is the defect ratio expressed as a percentage?
4
A manager has to create a 4-digit personal identification number (PIN). If the first digit is not allowed to be zero and no digits are to repeat, how many PIN numbers are available for him to choose from?
4,536
If 10 tiles can cover 3 square feet of area, then how many tiles will it take to cover 1,500 square feet of space?
5,000 tiles
For each day last week, a sales associate took orders of 42, 76, 38, 65, and 49 cases of product, respectively. What is the average number of cases ordered per day of last week?
54
George had finalized an investment portfolio that consisted of 8 different investment strategies. If he decides to select any 5 of them, in how many ways can the selection be made?
56
A project team can be formed with 3 developers, 1 test engineer, and a team lead. If there are 5 developers, 3 test engineers, and 2 team leads available, in how many ways can a project team be formed?
60
A large carton can hold 20 pounds of weight, of which there are 10 small items that weigh 1 pound each and 5 large items that weigh 2 pounds each. If 2 more larger items have to be accommodated, what would be the new ratio of smaller to larger items?
6:7
At a recycling center, a truck weighed 5,642 pounds (lbs) before unloading. After unloading, the truck weighed 4,925 lbs. What was the weight of the load?
717 lbs
A manufacturer can produce 40 units of a product in 5 hours. How many units of the product can be produced in a 9-hour workday?
72 units
Jacob has to come up with a 6-character case-sensitive password when banking online for the first time. The first 4 characters of the password must include an uppercase letter, a lowercase letter, a digit, and a special character, respectively. The last 2 characters can either take a lowercase letter, or a digit, or a special character. If the special character has to be chosen from a set of 7, in how many ways can Jacob create a password to avail online banking services?
87,494,680
A cellular phone company offered a plan costing $73.50 for 3 months of service. The company then discontinued that plan and raised the rate to $26.75 per month. What was the increase expressed as a percentage?
9.18%
The sales of mangoes have been observed to increase with the size of the fruit. Which of the following conclusions is arrived at by inductive reasoning?
A retailer's mangoes will sell well if they are large in size.
The population of a town has been observed to double every year for the last four years. The current census data on this town indicates a current population of about 10 million. Which of the following would most likely be the population of the town next year?
About 20 million
The population of a town has been observed to double every year for the last four years. The current census data on this town indicates a current population of about 3 million. Which of the following would most likely be the population of the town next year?
About 6 million
If Bob loses the election, then the healthcare reform bill will not be passed. In which of the following scenarios would the given compound statement be false?
Bob does not win the election and the healthcare reform bill is passed.
If Bob wins the competition, then he will go on a vacation. In which of the following scenarios would the given compound statement be false?
Bob wins the competition and he does not go on a vacation.
Statement 1: Eric believes that the certification program will help him secure a job. Statement 2: The organizers of the certification program claim to have secured employment for many of their students. If one of these statements is false and the other is true, which of the following statements MUST be false?
Eric believes that the certification program will help him secure a job and the organizers of the certification program claim to have secured employment for many of their students.
Jane is figuring out the list of ingredients needed to make cakes in her bakery for the following week. She rounds off the measure of the ingredients for ease. What technique is Jane using?
Estimation
Suppose this statement is true: If Emily receives more orders for cakes, then she will employ an assistant for their delivery. Which of the following statements is also TRUE?
If Emily does not employ an assistant, then she has not received more orders for cakes.
What is referred to as the process of deriving reliable generalizations from specific observations or examples?
Inductive reasoning
Which of the following statements is true of a permutation?
It deals with the arrangement of a set of items where the order does matter.
Statement 1: Jack expects that the advertising campaign will help improve sales. Statement 2: The advertising agency claims to have boosted the sales figures for many of their clients. If one of these statements is false and the other is true, which of the following statements MUST be false?
Jack expects that the advertising campaign will help improve sales and the advertising agency claims to have boosted the sales figures for many of their clients.
Jack usually walks to his office, but he takes a bus when it rains. Today's football match was canceled due to rain. Assuming that these statements are true, what conclusion can be drawn?
Jack took a bus to work today.
Statement 1: Sandra believes that her communication skills will improve after the customer orientation program. Statement 2: The organizers of the customer orientation program certify that their program is very effective. If one of these statements is false and the other is true, which of the following statements MUST be false?
Sandra believes that her communication skills will improve after the customer orientation program and the organizers certify that their program is very effective.
A webmaster runs two websites and keeps track of earnings and unique visitors. The healthcare related site earns $14 per 560 unique visitors and the automotive related website earns $14 per 350 unique visitors. Which is the more valuable site?
The automotive related site
Clara has to decide if she wants to eat Mexican or Italian food and whether she wants to order it online or over the phone. She uses the fundamental counting principle to determine the number of possible choices she has. What is the condition that is satisfied in this case that allows Clara to use the fundamental counting principle?
The choices are independent.
A bag has 20 balls, each labeled with a different letter. To find the number of ways in which 5 balls can be selected, without repetition and where order does not matter, which formula must be used?
The combination rule
A bag has 22 marbles, each labeled with a different letter. Which formula must be used in order to find out the number of ways in which 8 marbles can be selected without repetition and ignoring the order?
The combination rule