Question 1

Late one evening, a 6 foot person is standing 16 feet from a streetlight. The streetlight is 18 feet tall. How long is the person's shadow?

Accepted Answer

A)  3 feet 
B)  9 feet 
C)  8 feet 
D)  4 feet 
E)  2 feet 
A)  3 feet 
B)  9 feet 
C)  8 feet 
D)  4 feet 
E)  2 feet C

Question 2

Solve. Round to the nearest hundredth. $\frac { 31 } { n } = \frac { 19 } { 5 }$

Accepted Answer

A)  19.00 
B)  3.80 
C)  6.20 
D)  3.06 
E)  8.16 
A)  19.00 
B)  3.80 
C)  6.20 
D)  3.06 
E)  8.16 E

Question 3

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

Accepted Answer

A)  36 $\frac { 1 } { 4 }$ % 
B)  25% 
C)  29 $\frac { 3 } { 8 }$ % 
D)  6 $\frac { 4 } { 5 }$ % 
E)  18% 
A)  36 $\frac { 1 } { 4 }$ % 
B)  25% 
C)  29 $\frac { 3 } { 8 }$ % 
D)  6 $\frac { 4 } { 5 }$ % 
E)  18% C

Question 4

At 3:00 p.m., 29-foot tree casts 36-foot shadow.A person 4 feet tall will cast how long a shadow? Round the nearest tenth.

Accepted Answer

A)  $7.0$ ft 
B)  $6.0$ ft 
C)  $5.0$ ft 
D)  $8.0$ ft 
E)  $2.0$ ft 
A)  $7.0$ ft 
B)  $6.0$ ft 
C)  $5.0$ ft 
D)  $8.0$ ft 
E)  $2.0$ ft

Question 5

An access ramp needs to rise 24 inches. If the ramp is to have a slope ratio of 1:8, what horizontal distance is needed to build the ramp? Give the answer in feet.

Accepted Answer

A)  16 feet 
B)  14 feet 
C)  3 feet 
D)  11 feet 
E)  192 feet 
A)  16 feet 
B)  14 feet 
C)  3 feet 
D)  11 feet 
E)  192 feet

Question 6

Does the phrase describe quantity or rate? 10 coins

Accepted Answer

A)  quantity 
B)  rate 
C)  neither 
D)  both 
A)  quantity 
B)  rate 
C)  neither 
D)  both

Question 7

Write the percent problems as equations or proportions and solve. Round to the nearest tenth or tenth of percent. 70% of what number is 39?

Accepted Answer

A)  $56.7$ 
B)  $54.7$ 
C)  $57.7$ 
D)  $55.7$ 
E)  $53.7$ 
A)  $56.7$ 
B)  $54.7$ 
C)  $57.7$ 
D)  $55.7$ 
E)  $53.7$

Question 8

At 5:00 p.m., a 30-foot tree casts a 134-foot shadow. How long is the shadow of a person who is 5.5 feet tall? Round your answer to one decimal place.

Accepted Answer

A)  24.0 feet 
B)  25.4 feet 
C)  23.8 feet 
D)  25.0 feet 
E)  24.6 feet 
A)  24.0 feet 
B)  25.4 feet 
C)  23.8 feet 
D)  25.0 feet 
E)  24.6 feet

Question 9

Ninety shares of Mattel stock have been purchased for $15 per share. How many shares of FedEx at $60 per share are needed to raise the average price of all shares to $50 per share? Round your answer to the nearest share if necessary.

Accepted Answer

A)  315 
B)  no solution 
C)  210 
D)  525 
E)  394 
A)  315 
B)  no solution 
C)  210 
D)  525 
E)  394

Question 10

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $$\sin \left( 30 ^ { \circ } \right)$$ .

Accepted Answer

A)  $0.600$ 
B)  $0.400$ 
C)  $0.700$ 
D)  $0.300$ 
E)  $0.500$ 
A)  $0.600$ 
B)  $0.400$ 
C)  $0.700$ 
D)  $0.300$ 
E)  $0.500$

Question 11

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

Accepted Answer

A)  $\frac { 25 } { 47 }$ 
B)  $\frac { 27 } { 47 }$ 
C)  $\frac { 23 } { 47 }$ 
D)  $\frac { 6.1 } { 11.3 }$ 
E)  $\frac { 61 } { 113 }$ 
A)  $\frac { 25 } { 47 }$ 
B)  $\frac { 27 } { 47 }$ 
C)  $\frac { 23 } { 47 }$ 
D)  $\frac { 6.1 } { 11.3 }$ 
E)  $\frac { 61 } { 113 }$

Question 12

Use proportions to find x. Round your answer to one decimal place.

Accepted Answer

A)  5.8 
B)  6.8 
C)  1.8 
D)  4.8 
E)  9.8 
A)  5.8 
B)  6.8 
C)  1.8 
D)  4.8 
E)  9.8

Question 13

Does the phrase describe quantity or rate? 5 % boric acid solution

Accepted Answer

A)  quantity 
B)  rate 
C)  neither 
D)  both 
A)  quantity 
B)  rate 
C)  neither 
D)  both

Question 14

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 111 is what percent of 60?

Accepted Answer

A)  54.1% 
B)  195% 
C)  185% 
D)  200% 
E)  66.6% 
A)  54.1% 
B)  195% 
C)  185% 
D)  200% 
E)  66.6%

Question 15

Find the given trigonometric function of the indicated angle using triangle RAW. tan R, where $$x = 26 , y = 35 , z = 46$$

Accepted Answer

A)  $\frac { 13 } { 23 }$ 
B)  $\frac { 35 } { 26 }$ 
C)  $\frac { 26 } { 35 }$ 
D)  $\frac { 23 } { 13 }$ 
E)  $\frac { 46 } { 35 }$ 
A)  $\frac { 13 } { 23 }$ 
B)  $\frac { 35 } { 26 }$ 
C)  $\frac { 26 } { 35 }$ 
D)  $\frac { 23 } { 13 }$ 
E)  $\frac { 46 } { 35 }$

Question 16

The shadow of a pole at 2 p.m. is 4 feet. The shadow of nearby 10-inch-tall squirrel is 4 inches. How tall is the pole?

Accepted Answer

A)  $11$ ft 
B)  $9$ ft 
C)  $12$ ft 
D)  $10$ ft 
E)  $8$ ft 
A)  $11$ ft 
B)  $9$ ft 
C)  $12$ ft 
D)  $10$ ft 
E)  $8$ ft

Question 17

The shadow of a flagpole at 10 a.m. is 4 feet. The shadow of a 7 foot person is 1.4 feet. How tall is the flagpole?

Accepted Answer

A)  20 feet 
B)  15 feet 
C)  18 feet 
D)  13 feet 
E)  30 feet 
A)  20 feet 
B)  15 feet 
C)  18 feet 
D)  13 feet 
E)  30 feet

Question 18

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 145 is what percent of 215?

Accepted Answer

A)  311.8% 
B)  67.4% 
C)  148.3% 
D)  68.7% 
E)  72.8% 
A)  311.8% 
B)  67.4% 
C)  148.3% 
D)  68.7% 
E)  72.8%

Question 19

Does the phrase describe quantity or rate? 10 cents per dime

Accepted Answer

A)  quantity 
B)  rate 
C)  both 
D)  neither 
A)  quantity 
B)  rate 
C)  both 
D)  neither

Question 20

Solve. $\frac { n } { 6 } = \frac { 5 } { 15 }$

Accepted Answer

A)  3 
B)  5 
C)  2 
D)  -5 
E)  6 
A)  3 
B)  5 
C)  2 
D)  -5 
E)  6

Late one evening, a 6 foot person is standing 16 feet from a streetlight. The streetlight is 18 feet tall. How long is the person's shadow?

Solve. Round to the nearest hundredth. $\frac { 31 } { n } = \frac { 19 } { 5 }$

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

At 3:00 p.m., 29-foot tree casts 36-foot shadow.A person 4 feet tall will cast how long a shadow? Round the nearest tenth.

An access ramp needs to rise 24 inches. If the ramp is to have a slope ratio of 1:8, what horizontal distance is needed to build the ramp? Give the answer in feet.

Does the phrase describe quantity or rate? 10 coins

Write the percent problems as equations or proportions and solve. Round to the nearest tenth or tenth of percent. 70% of what number is 39?

At 5:00 p.m., a 30-foot tree casts a 134-foot shadow. How long is the shadow of a person who is 5.5 feet tall? Round your answer to one decimal place.

Ninety shares of Mattel stock have been purchased for $15 per share. How many shares of FedEx at $60 per share are needed to raise the average price of all shares to $50 per share? Round your answer to the nearest share if necessary.

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $\sin \left( 30 ^ { \circ } \right)$ .

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

Use proportions to find x. Round your answer to one decimal place.

Does the phrase describe quantity or rate? 5 % boric acid solution

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 111 is what percent of 60?

Find the given trigonometric function of the indicated angle using triangle RAW. tan R, where $x = 26 , y = 35 , z = 46$

The shadow of a pole at 2 p.m. is 4 feet. The shadow of nearby 10-inch-tall squirrel is 4 inches. How tall is the pole?

The shadow of a flagpole at 10 a.m. is 4 feet. The shadow of a 7 foot person is 1.4 feet. How tall is the flagpole?

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 145 is what percent of 215?

Does the phrase describe quantity or rate? 10 cents per dime

Solve. $\frac { n } { 6 } = \frac { 5 } { 15 }$

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Exam 4: Ratios, Rates, and Proportional Reasoning

Late one evening, a 6 foot person is standing 16 feet from a streetlight. The streetlight is 18 feet tall. How long is the person's shadow?

Solve. Round to the nearest hundredth. 31n=195\frac { 31 } { n } = \frac { 19 } { 5 }n31​=519​

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

At 3:00 p.m., 29-foot tree casts 36-foot shadow.A person 4 feet tall will cast how long a shadow? Round the nearest tenth.

An access ramp needs to rise 24 inches. If the ramp is to have a slope ratio of 1:8, what horizontal distance is needed to build the ramp? Give the answer in feet.

Does the phrase describe quantity or rate? 10 coins

Write the percent problems as equations or proportions and solve. Round to the nearest tenth or tenth of percent. 70% of what number is 39?

At 5:00 p.m., a 30-foot tree casts a 134-foot shadow. How long is the shadow of a person who is 5.5 feet tall? Round your answer to one decimal place.

Ninety shares of Mattel stock have been purchased for $15 per share. How many shares of FedEx at $60 per share are needed to raise the average price of all shares to $50 per share? Round your answer to the nearest share if necessary.

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. sin⁡(30∘)\sin \left( 30 ^ { \circ } \right)sin(30∘) .

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

Use proportions to find x. Round your answer to one decimal place.

Does the phrase describe quantity or rate? 5 % boric acid solution

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 111 is what percent of 60?

Find the given trigonometric function of the indicated angle using triangle RAW. tan R, where x=26,y=35,z=46x = 26 , y = 35 , z = 46x=26,y=35,z=46

The shadow of a pole at 2 p.m. is 4 feet. The shadow of nearby 10-inch-tall squirrel is 4 inches. How tall is the pole?

The shadow of a flagpole at 10 a.m. is 4 feet. The shadow of a 7 foot person is 1.4 feet. How tall is the flagpole?

Write the percent problem as a proportion or equation and solve. Round to the nearest tenth or tenth of a percent. 145 is what percent of 215?

Does the phrase describe quantity or rate? 10 cents per dime

Solve. n6=515\frac { n } { 6 } = \frac { 5 } { 15 }6n​=155​

Algebraic Representations

Operations With Real Numbers

Solving Equations

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Solve. Round to the nearest hundredth. $\frac { 31 } { n } = \frac { 19 } { 5 }$

Use a calculator to evaluate the given trigonometric function. Round the answer to three decimal places as needed. $\sin \left( 30 ^ { \circ } \right)$ .

Find the given trigonometric function of the indicated angle using triangle RAW. tan R, where $x = 26 , y = 35 , z = 46$

Solve. $\frac { n } { 6 } = \frac { 5 } { 15 }$