Math 101 Final

What is the decimal form of 1 31/36?

1.861⎯⎯⎯

Simplify the following expression. y11y19

1/y8

Simplify: 10/20 / 10/8.

10 to the 12th power

Convert 84 2/3% to a fraction in lowest terms.

127/150

Convert 17.7% to a decimal.

17.7%=0.177.

Find the reciprocal of 4/2

2/4

Divide the following. Give your answer as a reduced improper fraction if necessary. 6÷1/8

48

Which of the following is equivalent to 4 to the 7th power?

4×4×4×4×4×4×4

How many significant figures are present in the measurement 22.950g?

5. All nonzero digits are significant. The trailing zero is to the right of the decimal place, so it is also significant.

Find the volume of a sphere with radius 5

500/3π To find the volume of a sphere, use the formula: V=4/3πr3 Substitute the value for r given in the problem:

Evaluate the following expression at x=1 and y=7. 5x+9y−6

62

Find the surface area of a cylinder with radius 5 and height 4.

90π To find the surface area of a cylinder, use the formula: SA=2πr2+2πrh Substitute the values given in the problem: SASA=2π52+2π5⋅4=90π So the surface area of the cylinder is 90π units squared.

Simplify the following expression. (p−1q−3/r)3

=1/p3q9r3

Simplify: 5 squared−6squared

Following the order of operations, we should simplify powers before subtracting. Thus we have 5squared−6squared=25−36. The difference 25−36=−11 is negative because 36 is more negative than 25 is positive. -11

Find the LCM of 12 and 30.

If we list the multiples of each number, we get 12:12,24,36,48,60 30:30,60 We see that the least common multiple is 60.

Which of the following must be true about a precise measurement?

It typically contains many significant figures.

What are the two parts of an argument?

Premise(s) and conclusion

What is the result of 2.58×0.12, including correct significant figures?

Since it is a multiplication problem, we keep the lowest number of significant figures (two significant figures). 2.58×0.12=0.3096=0.31

Find the unit price of 60lbs of honey for $123.99. Round your answer to the nearest cent if necessary.

The unit price is $2.07 per pound. Each pound costs about $2.07.

What is the sum of 9, −5, and 5?

This question is asking us to add three numbers: 9+−5+5. Note that −5 and 5 are opposites, and add up to zero. So 9+−5+5=9+0=9.

What is the proper notation for the line, line segment, and ray shown below?

WZ←→, XY−→, UV⎯

What combination of lines and points in the figure below determine a plane? There may be more than one correct answer. Notice l1 and l2 are not parallel.

l2 and W V,W and Z Point W is not on l1; therefore W and l1 determine a plane. Point W is not on l2; therefore, W and l2 determine a plane. Points W,V, and Z are not collinear; hence, those points determine a plane.

Simplify the following product. x5x10

x15

If hexagons ABCDEF and GHIJKL, shown below, are similar, solve for x. Leave answer in fraction form without "x=". For example, if x=27/2, enter 27/2.

x=3/5

Simplify the following expression by expanding and collecting like terms. −(7x+6)+3(−5x−3) Give your answer in the form ax+b.

−22x−15

Translate the phrase into an algebraic expression: kdollars per 28bottles.

$k/28bottles

Which of the following equivalent to 5/4 5 over 4

10/8 10 over 8

Sean bought 3/4 of a pound of cherries and then he bought 1/3 of a pound more. When he got home, he saw that he still had 1/2 of a pound of cherries in his cupboard. How many total pounds of cherries does he have? Give your answer as an exact simplified improper fraction, not as a mixed number. Do not include units.

19/12

When calculating the CPI in the current year, the current year cost of the basket of goods is divided by what year?

a base year To calculate the CPI, the cost of the basket in the current year is divided by the cost in some base year, as this allows for easy comparisons across years.

A deck company wants to build uniquely shaped decks. How many square feet of wood would the company need to cover the deck designed below shaped like a regular pentagon and a trapezoid? The height of the trapezoid is 4.5ft. Round your answer to one decimal place. Hint: To find the area of the pentagon, divide it into 5 similar triangles. Use the fact that the radius of the pentagon (the distance from each vertex to the center) is 4.25ft.

To find the amount of wood decking needed, we calculate the area of the pentagon and the trapezoid, and add the two areas together. The area of the pentagon can be broken up into 5 similar triangles. To find the area of each triangle, first find the apothem, or the distance from the center of the pentagon to the midpoint of each side. This is the height of each triangle. h2+2.52hh=4.252=4.252−2.52‾‾‾‾‾‾‾‾‾‾‾‾√≈3.44 The area of one triangle is, A=12×b×h=12×5×3.44=8.6 Now we will multiply the area of one triangle by 5 to calculate the total area of the pentagon. A=8.6×5=43 ft2 The area of the trapezoid is, A=a+b2×h=5+82×4.5=29.25 ft2 Adding the two areas together, A=43+29.25=72.25 ft2 Rounded to one decimal place, the total square feet of wood decking needed is 72.3.

The sides of the figure below measure 11, 22, and 27 meters. Find the perimeter. Do not include units in your answer.

To find the perimeter of the figure, find the sum of the sides. PP=27+11+22=60 So the perimeter of the triangle is 60 meters.

Find the surface area of a rectangular solid with the given dimensions: length 21 feet, width 16 feet, height 7 feet. Give your answer without units.

To find the surface area of a rectangular solid, use the formula: SA=2LH+2LW+2WH Substitute the values given in the problem: SASA=2(21⋅7)+2(21⋅16)+2(16⋅7)=1190 So the surface area of the rectangular solid is 1190 square feet.

What is the measure of any angle in a regular 14-gon? Do not include the degree sign in your answer. Round to the nearest hundreth. For example, if answer is x=49.5643, enter 49.56.

154.29 We know that if S is the sum of the interior angles of a 14-gon, then S=(14−2)⋅180=12⋅180=2160 Next, since this tetradecagon is regular, we can let θ be an interior angle and obtain θ=S/n=2160/14=154.29∘

In the last 4weeks, after mowing the front and back yards, you have accumulated 90pounds of grass in the trash. What is the rate of pounds per week?

22.5pounds/week

Simplify the given expression: 5−8+3×9

24

Triangle ABC is similar to triangle XYZ. Find side a.

42 Now we can solve for a: a⋅25a=7⋅150=42

Solve the following equation for x: −5x+9=4 Enter your answer as a simplified improper fraction, if necessary. Do not include "x=" in your answer.

Subtracting 9 from both sides, we find −5x=−5 Now, dividing by −5, we find x=−5−5=1

An angle measures 76∘. Find its supplement. Do not include units in your answer

Supplementary angles are angles that add up to 180 degrees. That means the measure of the complementary angle to 76 must be 180−76=104.

Solve the following equation for x: −4(x−5)+1=−1+3(x+6) Enter your answer as a fraction if necessary. Do not include "x=" in your answer.

x=4/7

In the image below, indicate if ∠GEI, ∠EBC, ∠GAF, and ∠BDH are either acute, obtuse, straight or right angles.

∠GEI is straight. ∠EBC is obtuse. ∠BDH is acute. ∠GAF is a right angle. ∠GEI is a straight angle because the two line segments that make up the angle sides are straight lines. Straight angles always measure 180 degrees. ∠EBC is obtuse because it is larger than a right angle. Remember, obtuse angles are angles which have measurements >90 degrees. ∠GAF is a right angle because it has a square box at its vertex. The square box indicates a right angle. ∠BDH is acute because it is smaller than a right angle. Recall that acute angles have measurements <90 degrees.

Triangle DEF has one angle that measures 90∘. What are all the possible types of DEF? Select all that apply.

isosceles right scalene Triangle DEF is a right triangle since we are told one of its angles measures 90∘. DEF can also be isosceles (having angle measurements of 90∘, 45∘ and 45∘) and scalene.

Use the order of operations to simplify the given expression. 3−12⋅2+19

-2

Simplify: −7 to the 3rd power

-343

Evaluate y+(−14), when y=−33.

-47

Add or subtract: 1+7/8.

15/8

Translate and solve using proportions: What number is 25% of 64?

16 Identify the parts of the percent proportion. What number is 25%⏟percent of 64? Restate as a proportion. What number out of 64 is the same as 25 out of 100? Set up the proportion. Let n= the number. n64=25100 Find the cross products and set them equal. 100⋅n=64⋅25 Simplify. 100n=1,600 Divide both sides by 100. 100n100=1,600100 Simplify. n=16 Check if the answer is reasonable.Yes. 25 is a quarter of 100, and 16 is a quarter of 64.Write a complete sentence that answers the question. 16 is 25% of 64.

Convert 1.374 to a percent.

1.374=137.4%

Add the following fractions, and give your answer as a reduced improper fraction. 11/13+4/7

129/91

Round the product of 645.99 and 0.125 to the nearest tenth.

80.7

Convert the following decimal to a fraction: 0.953. Simplify when possible.

953/1000

Yesterday, James sold $29 worth of cookies and chocolate at his store. He sells cookies for $5 a box, and chocolate for $2 a bar. If he sold 7 items yesterday, how many of each item did he sell?

James sold 5 boxes of cookies and 2 chocolate bars at his store. Step 1. Understand the problem. Boxes of cookies sell for $5, and chocolate bars sell for $2. James sold a total of 7 items for $29. Step 2. Devise a plan to solve the problem. Try various combinations of the items to find which combination of 7 items results in a total of $29. For example, if James sold 6 boxes of cookies and 1 chocolate bar, calculate the total. $5(6)+$2(1)=$30+$2=$32 Step 3. Carry out the plan. Create a table of all possible combinations of boxes of cookies and chocolate bars that James could have sold. Boxes of Cookies ($5) Chocolate bars ($2) Total 0 7 $14 1 6 $17 2 5 $20 3 4 $23 4 3 $26 5 2 $29 6 1 $32 7 0 $35 In the table, there is one combination with a total of $29, namely selling 5 boxes of cookies and 2 chocolate bars. Step 4. Check your answer. $29$29$29=?$5(5)+$2(2)=?$25+$4=$29✓ James sold 5 boxes of cookies and 2 chocolate bars at his store.

Find the prime factorization of 44 using a factor tree.

The prime factorization is 2⋅2⋅11.

Find the area of the shaded region in the figure below if the radius of the outer circle is 8 and the radius of the inner circle is 2. Keep your answer in terms of π. A diagram of two concentric circles. The outer circle has radius 8, and the inner circle has radius 2. The outer region of the circle is shaded.

We are asked to find the area of the shaded region which is an outer ring within two concentric circles. To find the area, we need to find the area of the larger circle then subtract the area of the smaller circle. Remember that the area of a circle is πr2. The area of the larger circle has a radius of 8. So it's area is A=π(8)2=64π. The smaller circle has a radius of 2. So it's area is A=π(2)2=4π. Subtracting the area of the smaller circle from the area of the larger circle, we get: 64π−4π=60π So the area of the shaded region is 60π.

Divide: (−48)÷(6)

When we divide a negative by a positive number or a positive number by a negative number, the quotient will be negative. So (−48)÷(6)=−8

Multiply: (−1)(5)

When we multiply a negative times a positive number, the product will be negative. So (−1)(5)=−5

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=5, what is the area of the shaded region? Write your answer as a decimal if necessary.

25 The shaded region is comprised of two triangles inside a rectange. By finding the area of the two triangles, we can find the area of the shaded region. We already know the base of each triangle is equal to 10, the length of sides AB and DC of the rectangle. Since point E is halfway between sides AB and DC, the height of each shaded triangle is half of the height of the rectangle: 2.50. Now we can find the area of one of the shaded triangles: A=1/2⋅b⋅h A=1/2⋅10⋅2.50 A=12.50 Now that we know the area of one triangle, we can multiply by two to get the total area of the shaded region. 12.50∗2=25.00 So the area of the shaded region is 25.00.

Delaware has 25 Starbucks with a state population of 965,866. How many people does the state have per Starbucks? Round to the nearest whole number.

38635

The Centers for Medicare and Medicaid projects that consumers will spend more than $4×10 to the 12th on health care by 2017. Write 4×10 to the 12th in decimal notation.

4,000,000,000,000

Use cross multiplication to solve the following proportion: 3x+6/4=3x+1/2. Write your answer as a simplified fraction.

4/3

The pie chart below shows the number of books read each year. If the total number of people surveyed is 8000, approximately how many of them read 0 - 3 books each year? A pie chart labeled "Number of Books Read" consists of a circle divided into 5 sectors with labels and approximate sizes as a percentage of a circle as follows: 0 to 1 book, 25 percent; 2 to 3 books, 25 percent; 4 to 5 books, 28 percent; 6 to 7 books, 17 percent; 7 to 8 books, 5 percent.

4000

Add or subtract: 9/13−4/13.Enter your answer as a reduced fraction.

5/13

Multiply the following fractions, and give your answer as a reduced fraction. 2/7⋅5/6

5/21

Simplify: (5 to the 3rd power)a. Leave your answer in exponent notation.

53a

According to a survey, 59% of parents say their teens are addicted to using their cell phones. Write this percent as a ratio and do not simplify.

59/100

Ben needs to convert $500 US dollars to the Japanese Yen. One American dollar is worth 123.3 Yen. How many Yen will he have?

61650 yen y/500=123.3/1

Murphy made an art sculpture composed of 512 match sticks and 760 uncooked penne pieces. What is the ratio of match sticks to penne pieces? Simplify your answer.

64:95 or 64/95 Write as a fraction. number of match sticks/number of uncooked penne pieces Substitute the values. 512760 Simplify. 6495

Convert to scientific notation: 7,050.

7,050=7.05×10 to the 3rd power

In the following scenario, which of Polya's four steps, if any, were not performed correctly? Select all that apply. On his algebra exam, Thomas needed to solve a word problem where he was given a map that showed the lengths of several streets and needed to find the distance between two houses on the map. He wrote down all of the information provided in the word problem and decided to use the Pythagorean theorem to find the distance between the houses. After using the Pythagorean theorem, Thomas found that the distance between the houses was 150 meters. Then he looked at the map and determined that 150 meters was a reasonable distance between the two houses, so his answer was probably correct.

All of Polya's four steps were used correctly. The first step, understand the problem, was completed when Tom wrote down the information to the problem. Devise a plan was completed when he decided to use the Pythagorean theorem. Tom completed the step entitled, carry out the plan, by finding the answer using the method from the previous step. Finally, look back was completed when Tom checked his work by confirming that his answer from the previous step was reasonable.

Rowena's monthly gasoline bill dropped from $83.75 last month to $56.95 this month. Find the percent decrease.Round your answer to the nearest percent.Do NOT round until you have calculated the final answer.

It follows that the percent decrease in Rowena's monthly gasoline bill was 32%. We are asked to find the percent decrease in Rowena's monthly gasoline bill. The amount of decrease is given by initial amount−final amount=decrease 83.75−56.95=26.8. 26.8=p*83.75 p=.32

Kathy wants to buy a camera with an original price of $389. The camera is on sale with a 33% discount. What is the amount of discount?

We are asked to find the amount of discount on Cathy's camera. The amount of discount is given by discount rate×original price=amount of discount. The discount rate is in decimal form. Since the original price was $389, and it was on sale at 33%=0.33 off, we have 0.33×389=128.37. Thus, the amount of discount on Cathy's camera was $128.37.

Sue's paycheck is $1,040 for 40 hours of work. If she works 30 hours next week, what will her paycheck be?

$780 The comparison is paycheck to hours worked, so the ratios are paycheckhours worked. The unknown value is paycheck, so the x will be in the numerator. Find the cross products, set them equal, and simplify. 1040/40=x/30 40⋅x=1040⋅30 40x=31200 Divide both sides by 40 to isolate the variable x. x=780

One angle of a right triangle measures 25∘. What is the measure of the other acute angle? Give your answer without units.

65* We're told that the triangle is a right triangle, which means one of the angles measures 90∘. We are also told that another angle measures 25∘. To find the third angle, we can set up an equation. Since we know all angles of a triangle must add up to 180 we can write the equation as follows: 90+25+xx=180=65 So the third angle measures 65∘. We can check by making sure our three angles add up to 180. 90+25+65=180

Convert the following mixed number to a reduced improper fraction: 9 3/7

66/7 66 over 7

Convert the following fraction to a percent: 13/50 13 over 50

26%

In a local boutique, you intend to buy a handbag with original price $38, a jacket with original price $189, and a scarf with original price $23. Currently, the store is running a promotion for 30% off the entire store. In addition, as a store loyalty card member, you are entitled to an extra 10% off all sale prices. The state charges a 5% sales tax on all purchases. What is the final purchase price of the items, including all discounts and sales tax? Round your answer to the nearest cent.

First we must find the total purchase price before any discounts or sales tax is applied. The total is $38+$189+$23=$250. Next, we find the amount of the 30% discount and subtract it from our total. Discount=(30/100)×$250=$75 Sale Price=$250−$75=$175 We must now apply the additional 10% off discount. 10% Discount=(10/100)×$175=$17.50 Subtract the second discount amount from the total after the 30% discount. Total Sale Price=$175−$17.50=$157.50 Now that we have the sale price we can calculate the sales tax. Sales Tax = % Tax×Sale Price=(5/100)×$157.50=$7.88. Finally, we add the sales tax to the sale price to find the final price, Final Price = Sale Price + Sales Tax=$157.50+$7.88=$165.38

Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $96. If the interest that was collected was simple interest, what was the annual interest rate?

If an amount of money, P, called the principal, is borrowed for a period of t years at an annual interest rate r, the amount of interest, I, is given by I=PrtwhereIPrt=interest=principal=rate=time The following information is given. IPt=$96=$1,200=2 years Substituting the given information into the simple interest formula and solving for r gives I9696=Prt=(1,200)(r)(2)=2,400r Dividing both sides by 2,400 and then converting to a percent, we have r=96/2,400=0.04=4% Thus, Kenneth's annual interest rate was 4%.

Three law firms are looking for new lawyers. There are 80 graduate students in the area. There are only 25 graduates leaving the area for work. There are 25 with a bar exam score of 257 or less. About 19 have a score of 263 and 29 with a score of 264−269. Only 7 have a bar exam score of 270 or higher. The top law firm will only consider graduates with a bar exam score of at least 270. What is the relevant information to find the percentage of students that could be considered for the top law firm? Select all that apply.

The top law firm will only consider graduates with a bar exam score of at least 270 We want to find the percentage of students that could be considered for the top law firm. So we need to find the total number of graduate students, the bar exam score accepted by the top law firm, and the number of students that got that bar exam score. The number of law firms looking, number of students leaving the area, and number of graduates with scores other than the top law firm's requirement are irrelevant. The only answer choice with relevant information is 'The top law firm will only consider graduates with a bar exam score of at least 270', which will tell us the appropriate students to count.

Vicky works in retail. Her annual gross salary is $24,000. From this, she must pay 15% income tax. In addition, she must repay a loan at a rate of $120 per month. The loan amount is taken out of her post-tax pay (i.e. after the tax has been calculated). What is Vicky's take home pay per month? Round your answer to the nearest dollar.

$1,580. Vicky's monthly pay is $24,000/12=$2,000 per month. Her monthly income tax is Income Tax=$2,000×15%=$2,000×15/100=$300, so Vicky's post-tax salary is $2,000−$300=$1,700. From this amount, Vicky must repay the loan, and therefore her take home pay is Take Home Pay=$1,700−$120=$1,580.

Mary visits the local coffee shop to use the WiFi for school projects. Mary has an English book review to write, a social studies paper, and a science presentation to complete. She first arrives and orders a coffee at $2.15 and tips 5% at the counter. Two hours later, she finishes her English review and waitress stops by. Mary decides to order a latte at $4.50, but doesn't tip. Over the next hour, the waitress returns and Mary orders another coffee and leaves a 15% tip for both the latte and coffee. An hour later, Mary completes all of her projects and leaves. What is the total tip Mary left at the coffee shop? Round the price to the nearest hundredth. Do not include $ in your answer. For example, if the price is $19.546, enter 19.55.

$1.11 1. Following Polya's four-step procedure, we first identify the problem that needs to be solved. We are asked what is the total tip Mary left at the coffee shop. 2. Next, we plan how to solve this problem by picking out relevant information and deciding how to use it. To find what is the total tip Mary left at the coffee shop, all we need is the price of each item purchased, and the percent tip for each item amount purchased. We solve by multiplying each tip percent by the item purchased with that tip; coffee at the count was bought with a 5% tip, and a coffee and latte were later bought with a 15% tip. Then add each tip together. 3. Coffee at the counter: 2.15⋅0.05=0.1075 Latte and coffee later: (4.50+2.15)⋅0.15=6.65⋅0.15=0.9975 Tip total: 0.1075+0.9975=1.105=$1.11 4. We were asked what is the total tip Mary left at the coffee shop, which we did by picking out the relevant information and choosing an equation to use to solve.

20,000 Leagues Under the Sea is a classic science fiction novel by French writer Jules Verne. How many kilometers are in 20,000 leagues? (Round to the nearest whole number and do not include units in your answer.) Note: There are 18,228 feet in a league and 3.28084 feet in a meter.

111,118 km

Find the area of the parallelogram in the figure below. Round your final answer to the nearest tenth.

130.4 The formula for the area of a parallelogram is A=lh where l is the length of the parallelogram and h is the height of the parallelogram. In this case, h=10.6 and l=12.3. Thus, A=12.3×10.6=130.38. Rounding the answer to the nearest tenth gives us A=130.4.

South Dakota has 25 Starbucks for a population of 868,799 while Montana has 36 Starbucks with a population of 1,052,000. If Montana was proportional to South Dakota in Starbucks to population, how many Starbucks would South Dakota have? Round to the nearest whole number.

30 starbucks x/868,799=36/1,052,000 1,052,000x=36(868,799) 1,052,000x=31,276,764 x=31,276,764/1,052,000 x=29.73... x=30

Find the area of a triangle whose base is 23 inches and whose height is 28. Write your answer as a decimal if necessary. Do not include units in your answer.

322 To find the area of a triangle, start with the formula: Area=1/2⋅b⋅h Solve for A: AA=1/2⋅23⋅28=322 So the area is equal to 322 inches squared.

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below. The figure shows a right triangle with legs marked 30 and 16.

34 Using the Pythagorean Theorem with a=30, b=16, and solving for c, we have a2+b2=c2 302+162900+256c2cc=c2=c2=c2=1,156=1,156‾‾‾‾‾√=34

While playing golf, Maurice hits the golf ball and it travels 361.87 feet. Assume the golf ball travels the same distance every time he hits it. Estimate the total amount of distance the ball will travel after 15 hits. Round the distance traveled each time the golf ball was hit to the nearest ten feet before calculating.

5400 feet Step 1. Round to numbers that are easier to calculate with. For this problem, round the amount to the nearest ten feet. The digit in the tens place in 361.87 is 6, and the digit to the right is 1. Since 1 is less than 5, do not add to the 6, and replace the digits to the right with 0. The rounded distance is 360.00 feet. Step 2. Now perform the operations. 15×360.00=5,400 The estimated distance is 5,400 feet. Since the original distance was rounded down, the estimated distance is less than the actual distance.

Solve: 4u−7/−7=u−4/4. Enter an exact answer.

56/23 Multiply each side by the LCD, 28 and simplify to get 4u−7−728(4u−7−7)−16u+28−16u+28=u−44=28(u−44)=7u−28=7u−28. Solving for u we find −16u+28−23uu=7u−28=−56=5623.

Isabelle is making a scrapbook. Each page of the scrapbook is a square with a length of 11in. If each page holds three pictures that each have an area of 15in2, what is the remaining area on each page in square inches that can be used for decoration? The area (A) of a rectangle is A=length×width.

76 square inches. Step 1. Understand the Problem. The pages of the scrapbook are squares with side lengths of 11in. Each page has three pictures on it, and each picture has an area of 15in2. You want to find the area of the remaining space in square inches. Step 2. Devise a plan to solve the problem. Draw a diagram of a page in the scrapbook to help visualize the situation. Step 3. Carry out the plan to solve the problem. Here is a diagram of what the scrapbook page could look like. A square has sides labeled 11 inches. Inside the square, there are three rectangles. The area of each rectangle is labeled 15 square inches. Use the diagram to help find the area of the remaining space. Let A be the remaining area and write an equation. Note that the area of a rectangle or square is the length times the width. AAA=11in.×11in.−3×15in2=121in2−45in2=76in2 Step 4. Check the answer. If the area of the free space in the scrapbook is 76in2, then the sum of the area of free space and the area of the three pictures should equal the area of the scrapbook page. 76in2+3×15in276in2+45in2121in2=?11in.×11in.=?121in2=121in2✓

Find the area of a circle with radius 28 cm. A circle has radius 28 connected with a line segment from the origin to the rim.

784π To find the area of a circle, use the formula: A=πr2 Substitute the value for r given in the problem: AA=π282=784π So the area of the circle is 784π centimeters squared.

Look at the pattern. Find the next number in the sequence using inductive reasoning 6,11,16,21,26,...

Add 5 to each number to get the next number. To get the next number in the sequence, take the last number and add 5, 26+5=31. The next number in the sequence is 31.

Simplify: ∣8⋅−4∣

First simplify inside the absolute value sign. ∣8⋅−4∣=∣−32∣Then take the absolute value. Remember the absolute value of a number is its distance from 0 on the number line. So ∣8∗−4∣=32

George paid $179.76 for a new lawn mower, after tax, and the tax rate is 7%. What was the original price of the lawn mower?

First, change the percentage to a decimal and write the equivalence of the sales tax amount. Let x be the original cost of the item. Sales tax amount =x⋅0.07 Next, substitute the value into the equation: Original Cost + Sales Tax Amount = Total Cost x+0.07x=179.76 Add like terms. 1.07x=179.76 Divide both sides by 1.07 to isolate the unknown value. x=$168 The original cost of the lawn mower was $168.

The sale price of a drum kit in the UK is 950 Pounds + VAT (Value Added Tax), where VAT is a sales tax of 20%. After some negotiation, the owner of the store agrees to give Bob a 12% discount on the drum kit. What is the total price that Bob pays, including VAT? Answer in Pounds and round your answer to the nearest pence (1 pence=1100Pound). Note: VAT is a sales tax that gets calculated before a discount is applied.

First, we calculate the original price of the kit including VAT. This is equivalent to increasing the price by 20%, or 100%+20%=120%. So the initial price of the kit including VAT is 950×120%=950×120/100=950×1.2=1,140. We now apply the discount of 12%, which is the same as 100%−12%=88%. So to get the final price, we take the price with VAT, and multiply by 88%, i.e. 1,140×88%=1,140×88/100=1140×0.88=1,003.2 which is 1,003.20, expressed in Pounds.

A financial instrument pays 8% simple interest (based on the purchase value) and matures after 3 years. The instrument can be purchased at any price. An investor purchases the instrument for P dollars, and calculated that the total value of the investment (i.e. P plus interest earned) will be $2,000 at maturity. Calculate P.Round your answer to the nearest cent.Do NOT round until you have calculated your final answer.

For this, we can use the formula A=P(1+rt). We know that A=2,000, r=8%=0.08 and t=3, so we can rearrange the formula for A to give P=A/1+rt, and substituting the known quantities gives P=2,000/1+(0.08)(3)=2,000/1.24≈$1,612.903 which is $1,612.90 to the nearest cent.

Find (9.86×10 to the 2nd power)(3.1×10 to the 15th power) by using a calculator. Give your answer in scientific notation and round to two decimal places.

Using a calculator, 9.86×102 and 3.1×1015 can be represented as 9.86E2 and 3.1E15, respectively. Multiplying these numbers in the calculator and rounding to two decimal places we get 3.06E18. This is equivalent to 3.06×10 to the 18th power. 3.06×10 to the 18th power.

Glen is told that the absolute change in his pretest to post-test scores is 14 points and the relative change in his scores is 21.88%. Interpret the absolute and relative change from Glen's pretest to his post-test score.

Glen's score increased 14 points or 21.88% from his pretest to his post-test. The pretest score is indicated to be the from test, or initial value. Therefore, the post-test is the final test, or final value. We are told that the absolute change in test scores is 14 points. Since it is a positive value, this tells us we have an increase in test scores. We are told that the relative change is 21.88%. Therefore, Glen's score increased 14 points or 21.88% from his pretest to his post-test.

On AE←→, which of the statements must be true? I. CA−→−∪CD⎯is a ray. II. CA−→−∩CE−→− is a line. III. CA−→−∩CD⎯ is a point.

I and III only As shown in the figure below, I) CA−→− is a ray, and the union of a ray with any collinear segment is a ray. In this case, we add CD⎯ to CA−→−to form DA−→−. III) CA−→− comprises point C and all points to the left of point C. Thus, only point C is in common with CD⎯(all points between point C and point D, inclusive)

Using deductive reasoning, which statement is true given the following information? Mia eats only green foods. Chicken is not green.

Mia does not eat chicken.

Stacy is calculating the inflation rate between 2004 and 2005. The price index in 2004 is 90. The price index in 2005 is 87. She calculates the inflation rate as 87/90∗100%. Is Stacy's calculation of the inflation rate correct?

No, the numerator should be (87 - 90). The numerator should be (Final Index - Initial Index), so here it should be (87 - 90). The denominator should be (Initial Index), so here it should be 90. To calculate the inflation rate the equation should read 87−90/90∗100%

A right triangle has side 7 and hypotenuse 25. Use the Pythagorean Theorem to find the length of the third side.

The Pythagorean Theorem tells us that the sum of the squares of the two legs, a and b is equal to the square of the hypotenuse, c: a2+b2=c2 We are given one side, a, and the hypotenuse, c. To find b, we plug in our values for a and c and solve for b. 72+b249+b2b224‾‾‾√b=252=625=576=b=24

Colin is an employee who has gross earnings of $50,000 per year. He wants to know the total amount that will be deducted from his paycheck for the Medicare portion of the FICA tax for the year. Calculate this value.Round your answer to the nearest cent.Do NOT round until you calculate the final answer.

The entirety of Colin's gross pay is subject to the 1.45% Medicare tax. $50,000×0.0145=$725 Thus, the Colin is subject to $725 in deductions for the FICA Medicare tax.

The city of Richmond is conducting a feasibility study to determine if a high-speed commuter rail system should be added. The number of people commuting into Richmond to work each morning for the past six months are given below: January 2,749,876 February 3,293,874 March 4,923,940 April 3,531,890 May 2,309,870 June 3,103,210 The city will round each month's commuter numbers to the nearest million before finding the total. What is the estimated commuter traffic over the past 6 months?

The problem tells us that the city will round each day's commuter traffic to the nearest millions place. Following the rules of rounding, 2,749,876 will round to 3,000,000; then 3,293,874 will round to 3,000,000; then 4,923,940 will round to 5,000,000; then 3,531,890 will round to 4,000,000; then 2,309,870 will round to 2,000,00; and 3,103,210 will round to 3,000,000. We then add up the rounded amounts, 3,000,000+3,000,000+5,000,000+4,000,000+2,000,000+3,000,000=20,000,000. Richmond's estimated 6 month total commuter traffic is 20,000,000 people.

The length of a rectangle is 97 meters and the width is 14 meters. Find the area. Give your answer without units.

To find the area of a rectangle, we multiply the length times the width. When we multiply these numbers we find 97×14=1358 So the area of the rectangle is 1358 meters squared.

Write the ratio as a fraction: 630kilometers in 5hours. Simplify your answer.

Write as a fraction with 630kilometers in the numerator and 5hours in the denominator. 630kilometers/5hours Simplify by dividing the numerator and denominator by the GCF, 5. 126kilometers/1hour So, 630kilometers in 5hours is equivalent to 126kilometers/1hour.

If triangles ABC and XYZ are similar, what is the length of side b?

b=12