Question 1

A street light pole casts a shadow of length 40 ft at the same moment that a man who is 5 ft and 6 in tall has a shadow of length 12 ft. How high is the street light rounded to the nearest tenth of a foot?
A) 18.3 ft
B) 18.4 ft
C) 69.8 ft

Accepted Answer

Let the height of the street light be x.
According to the problem, we have:
(x/40) = ((5*12+6)/12)
Simplifying the equation, we get:
x = 18.48 ft
Rounding off to the nearest tenth, we get:
x ≈ 18.4 ft
Therefore, the answer is choice B.

Question 2

An  photo with its height 10 inches is to be reduced to a smaller size. The photo will now be 7.5 inches high. Find the measurement of the width of the reduced photo.
A) 5.5 in
B) 6 in
C) 6.25 in
D) 4.75 in

Accepted Answer

The answer of An  photo with its height 10...

Question 3

The distance traveled ( D ) while driving at a constant speed varies directly with the number of hours ( t ) spent driving. If the distance driven is 225 miles in 4.5 hours find how hours it takes to travel 325 miles.
A) 5.5 hours
B) 6.5 hours
C) 7.5 hours

Accepted Answer

The relationship between distance and time is given by D = rt, where r is the rate of speed. Given D1 = 225 miles in t1 = 4.5 hours, we find r = D1/t1 = 225/4.5 = 50 miles/hour. To find the time (t2) to travel D2 = 325 miles at the same rate, we use t2 = D2/r = 325/50 = 6.5 hours.

Question 4

The following is a recipe for Italian Pie that makes 8 servings.  Find the ounces of frozen spinach needed for 20 servings.
A) 20 oz
B) 25 oz
C) 30 oz

Accepted Answer

The recipe for 8 servings calls for 10 ounces of frozen spinach. To find out how much is needed for 20 servings, we can use a proportion:

10 ounces / 8 servings = x ounces / 20 servings

Cross-multiplying, we get:

8 * x = 10 * 20

Simplifying, we get:

x = 25

Therefore, the recipe for 20 servings would require 25 ounces of frozen spinach, which is option B.

Question 5

A student's tuition ( T ) at a community college varies directly with the number of credits ( c ) carried by the student. If the tuition is $1080 for 9 credits find the tuition for 15 credits.
A) $1500
B) $1750
C) $1800

Accepted Answer

We can set up a proportion:

Tuition/credits = constant

So, for the given situation:

1080/9 = k

k = 120

Now we can use this constant to find the tuition for 15 credits:

Tuition/15 = 120

Tuition = 1800

Therefore, the tuition for 15 credits is $1800, which is answer choice C.

Question 6

Solve the proportion. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the proportion. 
A) 
B) 
C) 
D)...

Question 7

In a ball the pressure of the air inside is inversely proportional to the volume of the ball. The equation that describes this relationship is  . If  psi when  find the pressure when  .
A) 1.5 psi
B) 1 psi
C) 0.8 psi

Accepted Answer

We can set up the equation as P1V1 = P2V2 and plug in the given values to solve for P2. We know that P1 = 3 psi and V1 = 2 L. We can solve for V2 by using the inverse proportionality: P1V1 = P2V2 becomes V2 = (P1V1)/P2. Plugging in the values and solving for V2, we get V2 = (3 psi x 2 L)/1.5 = 4 psi*L/3. Now we can plug in P2 = 4 psi*L/3 divided by the given volume of 3 L to get P2 = 4/9 psi. Rounding to the nearest whole number, we get 1 psi. Therefore, the answer is B) 1 psi.

Question 8

The scale on a map is 1 cm = 16 miles. How far is a distance that measures 8.25 cm on the map?
A) 132 mi
B) 128 mi
C) 0.5 mi
D) 160 mi

Accepted Answer

To find the actual distance, multiply the distance on the map (8.25 cm) by the scale factor (16 miles/cm). 8.25 cm * 16 miles/cm = 132 miles.

Question 9

A flagpole casts a shadow of length 32 ft at the same moment that a man 6 ft tall has a shadow of length 10 ft. How high is the flagpole?
A) 40 ft
B)  ft
C) 19.2 ft

Accepted Answer

We can use similar triangles to solve the problem. Let x be the height of the flagpole. Then we have the following proportion: (6/10) = (x/32). Solving for x, we get x = 19.2 ft. Therefore, the height of the flagpole is 19.2 ft, which is choice C.

Question 10

The following is the nutritional information for a breakfast sandwich.  If you eat so many of this sandwich that your sodium intake is 2825 mg what is your cholesterol intake? How many sandwiches did you eat?
A) 500 mg 3 bagels
B) 500 mg 2.5 bagels
C) 400 mg 2 bagels
D) 400 mg 3 bagels

Accepted Answer

According to the nutritional information, one breakfast sandwich contains 1190 mg of sodium and 210 mg of cholesterol. To find out how many sandwiches were eaten, we need to divide the total sodium intake (2825 mg) by the amount of sodium in one sandwich (1190 mg).

2825 mg ÷ 1190 mg per sandwich = 2.37 (rounded)

Therefore, the person ate about 2.37 sandwiches. Since they cannot eat a fraction of a sandwich, we need to round to the nearest option. Option B) is the closest choice, with 500 mg of cholesterol for 2.5 bagels. Therefore, the answer is:

Answer: B)
 500 mg 2.5 bagels

Question 11

The pair of triangles are similar. Find the value of the unknown side x .

Accepted Answer

The answer of The pair of triangles are similar. Find...

Question 12

The box below lists the nutritional information for a wrap. 
  What is the ratio of sugars to total carbohydrate?

Accepted Answer

The answer of The box below lists the nutritional information...

Question 13

The box below lists the nutritional information for a wrap. 
  How many mg of sodium would wraps contain? What percent of the % Daily Value would that be?

Accepted Answer

The answer of The box below lists the nutritional information...

Question 14

Solve the proportion. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the proportion. 
A) 
B) 
C) 
D)...

Question 15

The pair of triangles are similar. Find the value of the unknown side x .

Accepted Answer

The answer of The pair of triangles are similar. Find...

Question 16

The following is a recipe for Italian Pie that makes 8 servings.  Find the number of cups of pepperoni needed for 24 servings.
A) 1 cup
B)  cups
C)  cups

Accepted Answer

The answer of The following is a recipe for Italian...

Question 17

A flagpole casts a shadow of length 30.8 ft at the same moment that a woman 5 ft tall has a shadow of length 7 ft. How high is the flagpole?

Accepted Answer

The answer of A flagpole casts a shadow of length...

Question 18

The box below lists the nutritional information for a wrap. 
  If you eat so many of this wrap that your sodium intake is 3150 mg what is your cholesterol intake? How many wraps did you eat?

Accepted Answer

The answer of The box below lists the nutritional information...

Question 19

A map has a scale of  . A distance along Dixie Highway on the map measures 8.5 cm. How many miles is that distance?

Accepted Answer

The answer of A map has a scale of ...

Question 20

A map has a scale of  . A distance along Dixie Highway is 19 miles. How many cm is that distance on the map?

Accepted Answer

The answer of A map has a scale of ...

Quiz 7: Rational Expressions and Equations

A street light pole casts a shadow of length 40 ft at the same moment that a man who is 5 ft and 6 in tall has a shadow of length 12 ft. How high is the street light rounded to the nearest tenth of a foot?

An photo with its height 10 inches is to be reduced to a smaller size. The photo will now be 7.5 inches high. Find the measurement of the width of the reduced photo.

The distance traveled ( D ) while driving at a constant speed varies directly with the number of hours ( t ) spent driving. If the distance driven is 225 miles in 4.5 hours find how hours it takes to travel 325 miles.

The following is a recipe for Italian Pie that makes 8 servings. Find the ounces of frozen spinach needed for 20 servings.

A student's tuition ( T ) at a community college varies directly with the number of credits ( c ) carried by the student. If the tuition is $1080 for 9 credits find the tuition for 15 credits.

Solve the proportion.

In a ball the pressure of the air inside is inversely proportional to the volume of the ball. The equation that describes this relationship is . If psi when find the pressure when .

The scale on a map is 1 cm = 16 miles. How far is a distance that measures 8.25 cm on the map?

A flagpole casts a shadow of length 32 ft at the same moment that a man 6 ft tall has a shadow of length 10 ft. How high is the flagpole?

The following is the nutritional information for a breakfast sandwich. If you eat so many of this sandwich that your sodium intake is 2825 mg what is your cholesterol intake? How many sandwiches did you eat?

The pair of triangles are similar. Find the value of the unknown side x .

The box below lists the nutritional information for a wrap. What is the ratio of sugars to total carbohydrate?

The box below lists the nutritional information for a wrap. How many mg of sodium would wraps contain? What percent of the % Daily Value would that be?

Solve the proportion.

The pair of triangles are similar. Find the value of the unknown side x .

The following is a recipe for Italian Pie that makes 8 servings. Find the number of cups of pepperoni needed for 24 servings.

A flagpole casts a shadow of length 30.8 ft at the same moment that a woman 5 ft tall has a shadow of length 7 ft. How high is the flagpole?

The box below lists the nutritional information for a wrap. If you eat so many of this wrap that your sodium intake is 3150 mg what is your cholesterol intake? How many wraps did you eat?

A map has a scale of . A distance along Dixie Highway on the map measures 8.5 cm. How many miles is that distance?

A map has a scale of . A distance along Dixie Highway is 19 miles. How many cm is that distance on the map?