# Mathematics

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1. Find the circumference and area of the circle having the given diameter. d = 12 cm

The circumference is 37.7 cm.

(Round to the nearest tenth as needed.)

The area is 113.0 cm 2.

(Round to the nearest tenth as needed.)

 2. An oval track is made by erecting semicircles on each end of a 56 m by 112 m rectangle. Find the length of the track and the area enclosed by the track. The length of the track is 400 m. (Round to the nearest whole number.) The area enclosed by the track is 8734 m2. (Round to the nearest whole number.)

 3. Find the surface area and the volume of the cylinder. Surface area = 226.08 cm- Volume = 251.2 cm3 (Round to the nearest hundredth.) YOU ANSWERED: 276.0 5 cm

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4. At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins, one with radius 4 inches and the other with radius 6 inches. Compute the surface area and volume for each pumpkin. Then find the surface-area-to-volume ratio for both pumpkins. Which pumpkin has the larger ratio?

The surface area of the pumpkin with a 4-inch radius is 201 in2.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The volume of the pumpkin with a 4-inch radius is 267.9 in3.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The surface area of the pumpkin with a 6-inch radius is

452.47 in2.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

The volume of the pumpkin with a 6-inch radius is

904.3 in3.

(Do not round until the final answer. Then round to the nearest tenth as needed.)

Which pumpkin has the larger surface-area-to-volume ratio? The pumpkin with a 6-inch radius

5. Find the angular size of a circular object with a 2-inch diameter viewed from a distance of 6 yards.

The angular size of the object is 0.53

(Do not round until the final answer. Then round to the nearest hundredth as needed.)

6. A mountain peak rises from sea level to a summit elevation of 3894 ft over a horizontal distance of 15,842 ft. Find the grade of the peak.

The grade of the peak is 25 %.

(Round to the nearest percent as needed.)

7. On the map (right), the length of each 1 east-west block is — mile and the length of 5 Theater Grocery store E • •

e Library 1 4 S A L L; • • : 41 _ • •each north-south block is —4 mile. Victoria has

to walk from the library to the theater. Find the shortest walking distance. Then find the straight-line distance (‘as the crow flies’) between the two locations.

What is the shortest walking distance? 2.1 mi Bus stop — mi 5

(Round to the nearest hundredth as needed.)

What is the straight-line distance?

1.68 mi

(Round to the nearest hundredth as needed.)

8. A triangular lot is 160 ft on one side and has a

160property line of length 900 ft. Find the area of the lot in acres. (Figure not drawn to scale)

Areage, acre(s)

(Round to the nearest hundredth as needed.)

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 9. Given that the pair of triangles is similar, find the length of the side labeled n. 60 30

n = 25

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10. To get to a cabin, Dana can ride a bicycle west from a parking lot along the edge of a rectangular reservoir for 1.2 miles, and then south along the edge for 0.5 miles. Or she can row a boat directly from the parking lot. If Dana can ride 1.4 times as fast as she can row, which is the faster route?

Choose the faster route below. Rowing a boat

2_40 Riding a bicycle

11. The population of a town is increasing by 632 people per year. State whether this growth is linear or exponential. If the population is 1300 today, what will the population be in five years?

Is the population growth linear or exponential? 110 linear

exponential

 What will the population be in five years? 4460

12. 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 \$160 in one month during this period, what was it three months later?

Was the growth in inflation linear or exponential? -kV exponential

linear

What was the monthly food bill after three months? \$ 313

(Round to the nearest dollar as needed.)

13. A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 21? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)

How many grains of wheat should be placed on square 21? 1048576 grains

How many total grains of wheat should be on the board after the the grains of wheat have been placed on square 21?

2,097,151 grains

What is the total weight of all the grains of wheat on the board after the grains of wheat have been placed on square 21?

299.6 pounds

(Round to the nearest tenth as needed.)

150

14. A leprechaun places a magic penny under a girl’s pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 22 nights?

How much money will the girl have after 22 nights? \$ 41,943.04

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13. The initial population of a town is 2900, and it grows with a doubling time of 10 years. What will the population be in 8 years?

What will the population be in 8 years?

(Round to the nearest whole number as needed.)

16. An economic indicator is increasing at the rate of 4% per year. What is its doubling time? By what factor will the indicator increase in 4 years?

What is its doubling time?

years

(Type an integer or decimal rounded to the nearest tenth as needed.) By what factor will the indicator increase in 4 years?

(Type an integer or decimal rounded to the nearest hundredth as needed. Use the answer from part 1 to find this answer.)

17. The half-life of the radioactive element unobtanium-43 is 5 seconds. If 32 grams of unobtanium-43 are initially present, how many grams are present after 5 seconds? 10 seconds? 15 seconds? 20 seconds? 25 seconds?

The amount left after 5 seconds is grams.

The amount left after 10 seconds is grams.

The amount left after 15 seconds is grams.

The amount left after 20 seconds is grams.

The amount left after 25 seconds is grams.

(Round to one decimal place.)

18. Urban encroachment is causing the area of a forest to decline at the rate of 6% per year. What is the half-life of the forest? What fraction of the forest will remain in 30 years?

What is the half-life of the forest?

years

(Type an integer or decimal rounded to the nearest hundredth as needed.)

What fraction of the forest will remain in 30 years?

(Type an integer or decimal rounded to the nearest thousandth as needed. Use the answer from part 1 to find this answer.)

19. Use a growth rate of 1.4% to predict the population in 2071 of a country that in the year 2006 had a population of 400 million. Use the approximate doubling time formula.

What is the predicted population of the country in 2071? million

(Round the final answer to the nearest whole number as needed. Round the doubling time to the nearest year as needed.)

20. How many times greater is the intensity of sound from a concert speaker at a distance of 1 meter than the intensity at a distance of 15 meters?

The intensity of sound is times as strong at m as at 15 m.

21. Page 7The concentration of hydrogen ions in a liquid laboratory sample is 0.01 moles/liter. Find the pH of the sample.

 22. Plot (5, — 1) on the coordinate axes. Plot (5, — 1). iiiMMENEMEN ESEMMENNEMEN BENNENNENNEN MEMENNEMEN · i■■■■■■■■■■ MINEMENNEMEN · i■■■■■■■■■■■ EINEMENNEMEN · i■■■■■■■■■■ MMMMMMMMMNP’IMMMMMMM L9iJiJiJiai■i■iiLlLILL’ ■■■■■■■■■i■■■■■■■■■■ NENNENNENNENNENNENNE ■■■■■■■■■r■■■■■■■■■■■■■■■■■■■i■■■■■■■■■■■■■■■■■■■i■■■■■■■■■■ MENNEMENIFINEMENNEN ■■■■■■■■■i■■■■■■■■■■ np■■■■■■■■■■

23. The data table below represents a function and shows the average high temperature on certain days of the

year.

a. Identify the independent and dependent variables, and describe the domain and the range.

b. Make a clear graph of the function.

 Jan. 1 Feb. 1 Mar.! Apr. 1 May 1 June 1 July 1 Aug. 1 Sep. 1 Oct. 1 Nov. 1 Dec. 1 Dec 31 43°F 38°F 48°F 59°F 66°F 79°F 85°F 81°F 81°F 65°F 55°F 47°F 45°F

time temperature Thus, the range is temperatures between 38 and 85 43 and 45 °F. Choose the correct graph below. OA. 90 80 70 60 50 40 30 365 Average high temperature 0 B. Average high temperature 90 80 70 60 50 40 30 1 365The independent variable is

The dependent variable is

Thus, the domain is all days

certain days

over the course of a year.

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 24. The manager at a cycle repair shop has a graph displaying data from a recent day of work. Bike Repairs per Hour 144 128 112 96 80 64 48 32 16 0 MM•MMMM ••••••••••• MMMMM MM•MMMM •••••••••••• MM•MMM IMMMM1111 •••••••••Pril• MMMMWIIMM •••••••PriliM MMMPATIMM MMPIIIMMM •••••erii••••• MMIPAIMMM MPIMMMM MMPITIMM••••• MPITIMMMM Plri••••••••••• That day, the shop repaired approximately how many bikes per hour? OA. 8 OB. 0 C. 12 Repairs Completed OD. 4 2 4 6 8 10 12 Hours Past 8:00 a.m. 25. (hundreds of dollars) \$ Value Find the rate of change. 42 For every day that the time of use increases, the value decreases by hundred dollars. Time of Use 7 (days)

Distance from home in km MENEMENNEN MENNEMEMEN MEMPENEMEN 0 5 10 Number of minutes spent running26. For the graph, find the average rate of change

as a reduced fraction. Also, state the approximate units (do not abbreviate.)

The rate of change is (Do not enter the units.)

Select the appropriate units.

OA. kilometers per minute 0 B. minutes

C) C. minutes per kilometer

D. kilometers

E. None of the above.

27. You drive along the highway at a constant speed of 60 miles per hour. How far do you travel

in 4.4 hours? in 6.5 hours?

In 4.4 hours, you travel miles.

(Type an integer or a decimal.)

In 6.5 hours, you travel miles.

(Type an integer or a decimal.)

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28. The price of a particular model car is \$56,000 today and rises with time at a constant rate of

\$1,300 per year. How much will a new car cost in 4.5 years? Identify the independent and dependent variables. Write an equation for the linear function and use it to answer the given question.

 The independent variable is time in years the car cost the car maker

 The dependent variable is the car cost the car maker time in years

The equation for the price function is p =

(Type your answer in slope-intercept form. Type an expression using x as the variable. Do not include the \$ symbol in your answer.)

The price of the car in 4.5 years will be \$ (Type an integer or a decimal.)

29. Tidy Cab charges \$5 per ride plus 300 per quarter-mile traveled. Use a graph to estimate how

far someone can ride for \$8.30.

Choose the approximate length of a \$ 8.30 cab ride.

CIA. 0.75 miles 0B. 3.75 miles

C. 11 miles 0 a 2.75 miles

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30. A \$700 washing machine in a Laundromat is depreciated for tax purposes at a rate of \$70 per

year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach \$0?

The equation of the line in slope-intercept form is V =

(Type your answer in slope-intercept form. Type an expression using t as the variable. Do not include the \$ symbol in your answer.)

It takes years for the machine to depreciate to \$0.

A 12 y x 2 10 8 6 2 U -8 -4 8 U 2 1 6 4 12 31. Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation. y=2x+8 What is the slope? Select the correct choice below and fill in any answer boxes within your choice. CA. The slope is (Simplify your answer.) OB. The slope is undefined.

What is the y-intercept? Select the correct choice below and fill in any answer boxes within your choice.

OA. The y-intercept is

(Type an integer or a simplified fraction.)

OB. There is no y-intercept.

Graph the equation. 1

Click to enlarge graph

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32. Find the slope and the y-intercept. Then graph the equation. y= — 7x — 3 What is the slope? (Type an integer or a fraction.) 20 A 16 12 a y 4 x

Page 130 6 2 -8 -44 4 8 r2 6 20

a 12 16 23Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.

eiglel f at§ 00. go –

 33. Use the slope and the y-intercept to graph the line. y = 3x— 8 What is the slope? (Type an integer or a fraction.) 0 8 6 4 y 0 -8 -6 -4 2 -22 2 4 6 8 x 0

Use the graphing tool to graph the line. Use 4

the slope and y-intercept when drawing the 6

line.

80 70 60 50 40 30 20 10 I I I I34. Kara’s Custom Tees experienced fixed costs

C= Cost of producing 50 shirts = \$ Use the graphing tool on the right to graph the equation. Click to -) enlarge graph 2M1 E■of \$500 and variable costs of \$2 per shirt. Write an equation that can be used to determine the total expenses, find the cost, C, of producing 50 shirts, and graph the equation. Let x equal the total number of shirts.

MMEMEMMEMM •••■•••••■•• ■■■■■■■■■■■■ •••■•••••■••

I

MEMMEMMEM ••••••••••• MEMMEMMEM ■■■■■■■■■■■

I

MEMMEMMEM ••••••••••• MEMMEMMEM ••••••••••• MEMMEMMEM MENNEMENNEN MEMMEMMEM ••••••••

10 20 30 40 50 60

121SEMOOM=

35. Solve for x. = 16

The solution is x =

(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

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36. Answer the questions for the problem given below.

The average price of a home in a town was \$176,000 in 2007 but home prices are rising by 6% per year.

a. Find an exponential function of the form Q = Qo x (1 + t (where r > 0) for growth to model the situation described.

Q=\$ x (1+ )t

(Type an integer or a decimal.)

b. Fill the table showing the value of the average price of a home for the following five years.

 Year = t Average price 0 \$176,000 1 \$ 2 \$ 3 \$ 4 \$ 5 \$

(Do not round until the final answer. Then round to the nearest dollar as needed.)

37. The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36

hours. Suppose that a patient receives an initial dose of 40 milligrams of Valium at midnight.

a. How much Valium is in the patient’s blood at noon on the first day?

b. Estimate when the Valium concentration will reach 35% of its initial level.

a. How much Valium is in the patient’s blood at noon on the first day?

There is approximately mg of Valium in the patient’s blood at noon on the first day.

(Round to the nearest tenth as needed.)

b. Estimate when the Valium concentration will reach 35% of its initial level.

After approximately hours the Valium concentration will reach 35% of its initial level.

(Round to the nearest hour.)

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38. A toxic radioactive substance with a density of 2 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 45 years ago. If the half-life of the substance is 20 years, what was the density of the substance when it was deposited 45 years ago?

The density of the radioactive substance when it was deposited 45 years ago

was approximately mg / cm2.

(Round to the nearest tenth as needed.)

39. Solve for x. 11x= 121

The solution is x =

(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

40. Use a calculator to solve the following equation. 7X_ 59

x=

(Round to the nearest hundredth as needed.)

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