final
A. Create an exponential function of the form Q=Q0 x (1+r)^t
Answer:Q=5,000,000x(1-.04)^t
B. Compute each candidates percentage of the electoral winner also the winner of the popular vote?
Candidate A received _% of the electoral vote. Work: 184+183=367 184/367=.5014 Answer =50.14%
1. You arrive in Paris with $500. How much euros can you buy?
Foreign per dollar: 0.7965 x $500= $398.25 -You can but $398.25 euros with $500.
2. The sales tax rate in a city is 8.2%. Find the tax charged on a purchase of $249, and the total cost.
Sales Tax=Sales Tax Rate x Purchase Price T=8.2% x $249 T=8.2 x 0.01 x $249 T= .082 x $249 T= $20.418 (round to nearest cent would be $20.42) $249 + $20.42=$269.42
*Sid needs .7 meters of canvas material to make a carry-all bag for bis wheelchair. If canvas is $7.79 per meter, how much will Sid spend?
Sid must spend $5.45. work: .7x7.79=5.453 =5.45
Randomly meeting someone whose social security number ends in the same digit as yours.
Using the theoretical method, the probability is 1/10.
C. What is the total closing cost for choice 1?
Work: $2300+.01(110000)=3400 Answer= 3400
11. What is the probability that a 60% free-throw shooter will miss her next few throw? The probability that a 60% free throw shooter will moss her next free throw is.
Work: 1-.60=.4
B. What is the monthly payment for choice 2?
Work: 110,000x(.0425/12) /1-(1+.0425/12)^-12(30) = 389.583333333/ 0.71993890566 =541.133879931 Answer: 541.13
Candidate A received _% of the total popular vote.
Work: 4294099/8426850 = 0.50957344678 Round four decimal places = 0.5096 Answer: 50.96%
*The number of daily news paper in a country was 2533 in 1900 and 1385 in 2010.
a. The absolute change is -1148 work: 1385-2533=-1148 b. The relative change is -45% work: -1148/2533=-.45 which is then turned into a percent which is -45%.
*The main span of Bridge A (2200 feet) is__ percent shorter than the main span of Bridge B(4600 feet).
answer: 52.2 work: 2200-4600/4600 -.5217 -.522 52.2
20. During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 25% per month. State whether this increase was linear or exponential. If your food bill was $110 in one month during this period, what was it three months later?
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21. The price of a particular model car is $21,000 today and rises with time at constant rate of $890 per year. How much will a new car cost in 3.8 years?
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23. The population of a town with an initial population of 44,000 grows at a rate of 3.5% per year.
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24. A privately owned forest that had 5,000,000 acres of old growth is being clear cut at a rate of 4% per year.
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$12,000 is invested for 5 years with an APR of 3% and quarterly compounding.
$12,000 (1 + .03/4)^(5x4) = 13934.2097076 = 13934.21
$25,000 Is invested for 5 years with an APR of 4% and daily compounding. -The balance in the account after 5 years is $
$25,000 (1+ .04/365)^(365x5) = 30534.7342883 = 30534.73
C. Discuss interesting features of the data revealed by the display. Choose the correct answer below.
- the frequencies of the categories are approximately equal, though the frequency for one category is markedly less than the frequencies of the other categories. Age does not seem to be a factor in determining who receives the award.
1.Select the correct answer below.
-According to the function, the distance from home decreases by 300 miles ever 9 hours
2. (Rate of pedaling, speed of a bicycle)
-As the rate of pedaling increases, the speed of a bicycle increases.
3. (Rate of pedaling, speed of a bicycle)
-As the rate of pedaling increases, the speed of a bicycle increases.
3. Select the correct answer below.
-It is a good model if speed is constant for 9 hours.
3. Find the absolute change and the percentage change in the following case. The average sale of a house decreased from $324,000 in February 2008 to $186,000 in February 2013.
-The absolute change is -138,000 Work: Absolute change= New value- reference value =324,000-186,000 =138,000 *Turn in to a negative =-138,000 Relative change= absolute change/reference value =New value-reference value/reference value -138,000/324,000= -.426 Round to nearest thousandth place. -.426=-.426x100%= -42.6% The relative change is -42.6
1. The price of a particular model car is $23,000 today and rises with time at a constant rate of $800 per year. Houw much will a new car cost in 3.5 years?
-The equation used to model this situation is p=23,000 + (800 X t) 2. The price of a car after 3.5 years will be $26080
1. You can rent time on computers at the local copy center for a $9 setup charge and an additional $1.75 for every 5 minute. How much time can be rented for $22?
-The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r=0.35t +9 Work: 1.75/5= .35
*Diners frequently add a 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is $41.40? How much was the tip?
-The price of the meal without the tip is $36. work: 100%+.15=115% 41.40/1.15=36 -The amount of the tip is $5.4 work: 41.40-36=5.4
2. You are a music store owner and want to know how the demand of CDs (the number that you can sell) depends on the price you charge per CD.
-The situation can be described by a function. The dependent variable is the demand and the independent variable is the price.
1.You jump from an airplane with a parachute and want to know how far you have traveled at various times during your descent.
-The situation can be described by a function. The dependent variable is the distance fallen and the independent variable is the time.
You run different distance intervals on a track and want to know how your heart rate depends on the distance you rub at a fixed speed.
-The situation can be described by a function. The dependent variable is your heart rate and the independent variable is the distance run.
1. You walk through a used car lot and list the price and model year of each car you see.
-The situation cannot be described by a function.
Suppose your dog weighed 3,2 pounds at birth and weighed 14.3 pounds at birth and weighed 14.3 pounds one year later. Based on these two data points, find a linear function that describes how weight varies with age. Use this function to predict your dog's weight at 6 and 11 Yeats of age. Comment on the validity of this model.
1. The equation used to model this situation is w=3.2 +(11.1xt), where w is the weight of the dog.in pounds and t is time in years. 2. According to this model, The weight of the dog after 6 years will 69.8 pounds. 3. According to this model, the weight of the dog after 11 years will be 125.3 pounds. 4. Which statement best described the validity of this model? -The model is only accurate for small ages because the dog will eventually stop growing.
*Sharing a birthday with another person when you both have birthdays in December.
1/31
Candidate B received _% of the electoral vote.
183/367=.4986 Answer: 49.86%
2.Calculate the slope and represent it as a rate of change.
300/9=33.3333 Change it to a negative =-33.3
16. Construct a pie chart for the data set in the table to the right. The first step I'd to compute a percentage for each percentage for each category in the data set. The annual revenue (in millions of dollars) of the leading food product businesses are shown in the table.
Answer in pictures.
14. Use 5-point bins (95 to 99, 90 to 94, ect.) To make a frequency table for the set of exam scores shown below. Include columns for relative frequency and cumulative frequency. 89,86,79,85,73,87,72,91,71,96,92,88,77,91,82,88,70,75,76,73.
Answer is in picture.
15. Make a bar graph of the population of the five populous states (from census data) in a certain country, with the bars in descending order.
Answer is in picture.
-What was the monthly food bill after three months?
Answer: $215 Work: .25 x 110=27.5 110+27.5=137.5 .25 x 137.5= 34.375 34.375 + 137.5= 171.875 .25 x 171.875= 42.96875 171.875 + 42.96875=214.84375
*The wholesale price of a TV is 45% less than retail price. Therefore, the wholesale price is_ _ times the retail price.
Answer: .55 work: 100-45=55 .55
*Suppose that you arrive at a bus stop randomly, so all arrive times are equally likely. The bus arrives regularly every 40 minutes without delay. What is the expected value of your waiting time?
Answer: 20 minutes work: just divide the time by half.
What will the population be in four years?
Answer: 3552 Work: 613 x 4=2452 2452+1100=3552
A. Create an exponential function of the form Q=Q0 x (1+r)^t
Answer: 44,000 x (1+.035)^t
*What is the probability of rolling a fair die and not getting an outcome less than 2?
Answer: 5/6 work: 1-1/6 =5/6
The snowplow will be unable to move when the snow is_ inches deep.
Answer: 50 inches deep Work: 40/.8=50
Which candidate, if either, received a popular majority.
Answer: Candidate A received a popular majority.
-Was the growth in inflation linear or exponential?
Answer: Exponential growth.
E. Why might choice 1 be the better choice?
Answer: The closing costs are lower.
F. Why might choice 2 be the better choice?
Answer: The monthly payment is lower.
19. The population of a town is increasing by 613 people per year. State whether this growth is linear or exponential. If the population is 1100 today, what will the population be in four years?
Answer: linear growth
The equation used to model this situation is_ ,where p is the price of a car in dollars and t is time in years.
Answer: p=21,000 + (890 x t)
The equation used to model this situation is _ ,where s is the maximum speed of the snowplow in miles per hour and s is the snow depth in inches.
Answer: s= 40-(.8 x d)
You can fill a 12-gallon tank of gas for $38.32 or buy gas for 3.35/gallon.
The better deal is to fill a 12-gallon tank for $38.32 because the price to fill a 12-gallon tank of gas for $38.32 is $3.19 per gallon. work: $38.32/12=3.19
*A boat has a top speed of 38 knots (nautical miles per hour). What is this speed in miles per hour?
The boat has a top speed of 43.73 miles per hour. work: 38(1.15077945)=43.73
In 2010, there were 39 million people over 65 years of age out of the population of 316 million. By 2050, it is estimated that there will be 88 million people over 65 years of age out of a population of 438 million. Would your chances of meeting a person over 65 at random be greater in 2010 or 2050? Explain.
The chances are greater in 2050 because the relative frequency probability of meeting a person over age 65 in 2010 is .123 and the relative frequency probability of meeting a person over age 65 in 2050 is .201. work: 39,000,000/316,000,000=.123 88,000,000/438,000,000=.201
A. State whether the data are qualitative or quantitative.
The data are quantitative.
Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences are shown below. .11,.13,.14,.16,.16,.16,.18,.18,.24,.24,.27,.29
The mean is .188 add all the numbers, divide by amount The median .17 the mode is .16 the most repeating number
Suppose that in 2008, 584,050 citizens died of a certain disease. Assuming the population of the country is 319 million, what was the mortality rate in units of deaths per 100,000 people?
The mortality rate is 186 deaths per 100,000 people. work: 594,050x(10^5) /319000000 =186.2 =186
In my data set of 10 exam scores, the mean turned out to be the score of the person with the third highest grade. No two people got the same score.
The statement makes sense because the mean of a data set can be pulled far to the left or right of the middle of the range of values by outliers.
*you return from a trip with 310 candidan dollars. How much are you candian dollars worth in U.S dollars?
U.S dollars per Canadian dollar. work: .8276x310 Answer: $256.56
12. An insurance policy sells for $600. Based on past data, an average of 1 in 100 policyholders will file a $20,000 claim, an average of 1 in 250 policyholders will file a $40,000 claim, and an average of 1 in 400 policyholders will file an $80,000 claim. Find the expected value (to the company) per policy sold. If the company sells 30,000 policies, what is the expected profit or loss?
Work: ($600 x 1) + (-20,000 x 1/100) + (-40,000 x 1/250) + (-80,000 x 1/400) (600)+(-200)+(-160)+(-200)=40 A. Answer: 40 expected value. B. Answer: 1200000 Work: 40 x 30,000= profit would be 1200000.
6. Diners frequently add a 15% tip when changing a meal to a credit card. What is the price of the meal without the tip if the amount charged is $56.35? How much was the tip? The price of the meal without tip is $
Work: 100% + .15%= 115% 56.35/1.15=49 The cost of the meal is $49 $56.35-$49=7.35 The tip is $7.35
10. The local weather forecast has been accurate for 18 of the past 34 days. Based on this fact, what is the relative frequency probability that the forecast for tomorrow will be accurate? The relative frequency probability that the forecast for tomorrow will be accurate is
Work: 18/34=.529
3. A linear model is reasonable for this situation.
Work: 22=.35t+9 22-9=13 13=.35t 13/.35=37.14 =37 minutes
A. A 100-pound person could take_ tablets in a week.
Work: 23 mg x 28 doses x 1 tablet/13.9= 46 tablets per week
B. A 100-pound person could take _ mL in a week.
Work: 23mg x 28 doses x 8mL/13.9=371 mL week
8. A hose fills a hot tub at a rate of 3.94 gallons per minute. How many hours will it take to fill a 312-gallon hot tub? It will take _ hours to fill the hot tub.
Work: 3.94 goal x 60 min =236.4 312 gal / 236.4=1.32 Answer: 1.32
Candidate B received _% of the total popular vote.
Work: 4036457/8426850 = 0.47899950752 =.4790 Answer: 47.90%
The price of a car after 3.8 years will be $
Work: P= 21,000 + (890 x t) P= 21,000 + (890 x 3.8) =24382
What is the monthly payment for choice 1?
Work: PMT= $110,000 x (.045/12) /1-(1+.045/12)^-12(30) = 412.5/ 0.74010434629 = 557.353840803 Answer=557.35
The couple owes $_.
Work: Taxable income: $47,300-(3900+6100)=37300 Amount taxed at 15% = $36,250-$8925=$27,325 Amount taxed at 25%= $37300 -$36,250=$1050 Income tax= (10% x 8,925) +(15% x $27,325) + (25% x $1050 ) = (.10 x 8,925) +(.15x $27,325) + (.25x $1050 ) =$ 5253.75 Mia owes $ 5253.75 in taxes $32,500-(3900+6100)=$22500 Amount taxed at 15%= $22500-$8925=$13,575 Income tax= (10% x $8925) + (15% x $13575) = (.10 x $8925) + (.15 x $13575) Steve owes =2928.75 Total tax= $ 5253.75+ 2928.75= 8182.5 Round to nearest dollar Answer: The couple owes $8183
The couple owes $_.
Work: Total adjusted gross income: $47300+32500= $79800 Taxable income= $79800-(2x3900)+12200 = 59800 Amount taxed at 15%= 59800 -17850= 41950 Income tax= (10% x 17850)+(15% x 41950 ) =(.10 x 17850)+(.15 x 41950 ) = 8077.5 Answer=8078
9. Sid needs. 8 meters of canvas material to make a carry-all bag for his wheelchair. If canvas is $10.16 per minute, How much will Sid spend? (Note that $10.16 per meter is the same as $10.16 for one meter.) Sid must spend $
Work: Treat them as whole numbers .8 x 10.16=8.128 nearest cent would be 8.13
D. What is the total closing cost for choice 2?
Work: 2300+.03(110000)=5600 Answer:5600
4. The gestation of horses (336 days) Is percent longer than the gestation of pigs (115 days).
Work: Relative difference= compared value-reference value/ reference value =336-115/115 =1.922 1.922x100%=192.2 Answer:192.2
Her taxable income was $_.
Work: $42300-(2900+5180)=$34200 Answer: 34220
-Her gross income was $_.
Work: $43,000+1900=44900 Answer: 44900.
Her adjusted income was $_.
Work: $44900-$2600=$42300 Answer: 42300
5. The population of city A is 28% less than the population of city B, so city A's population is % of city B's. City A's population is 72% of city B's
Work: (100-28)%=72 Answer: 72%
*An allergy drug is tested by giving 130 people the drug and 100 people a placebo. A control group consists of 80 people who were given no treatment. The number of people in each group who showed improvement appears in the table.
http://www.justanswer.com/math-homework/6apzt-allergy-drug-tested-giving-120-people-drug.html
Use the frequency table for the ages of recent award-winning male actors at the time when they won their award to construct the corresponding histogram.
in pictures. just look at the table and then match it with the chart.
Deposits of $350 per month are put into an investment plan that pays an APR of 4.9%. How much money will be in the plan after 24 years?
include work fix answer: A total of $100,800.00 will have been paid into the account over 24 years and after the 24 years, the account will have a balance of $191,454.05.
C. Does the couple's face a "marriage penalty" if they marry before the end of the year?
no
7. A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 23 mg every six hours. A. Following this dosage, how many 13.9 mg chewable tablets would be taken in a week? B. This antihistamine also comes in a liquid form with a concentration of zzz 13.9 mg/8 no. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take a week?
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13. The frequency table categorizes winners of a prestigious award from 1990 through 2012 by their age at the time they received the award. Complete parts (a) through (c) below.
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A woman earned wages of $43,000, recieved $1900 in interests from a savings account, and contributed $2600 to a tax-deferred retirement plan. She was entitled to a personal exemption of $2900 and had deductions totaling $5180. Find her gross income, adjusted gross income, and taxable income.
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Compute each candidates percentage of the total popular vote. Did either candidate receive a popular majority.
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Consider the following pair of loan options for a $110,000 mortgage. Calculate the monthly payments total closing costs for each option. Explain which is the better option and why. Choice 1: 30 -year fixed rate at 4.5% with closing costs of $2300 and 1 point. Choice 2: 30 -year fixed rate at 4.25% with closing costs of $2300 and 3 point.
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Mia and Steve have adjusted gross incomes of $48,800 and $33,200, respectively. Assume that each person takes one exemption and the standard deduction.
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22. A snowplow has maximum speed of 40 miles per hour on a dry highway. Its maximum speed decreases by. 8 moles per hour for every inch of snow on the highway. According to this model, at what show depth will the snow plow be unable to move?
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