Unit 5 Test On Ratios And Proportionality Math 7 Plus

1.

A parking lot contains 18 American cars and 63 foreign cars. Write the ratio of American cars to foreign cars. ( All answers should be in simplest forms)

Explanation
The ratio of American cars to foreign cars in the parking lot is 2:7 or 2 to 7. This means that for every 2 American cars, there are 7 foreign cars in the parking lot. Another way to express this ratio is 2/7, which represents the fraction of American cars out of the total number of cars in the parking lot.

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2.

During a trip, a car traveled 249.2 miles in 4 hours. How many miles per hour did the car travel?

Explanation
The car traveled 249.2 miles in 4 hours. To find the miles per hour, we divide the total distance traveled by the total time taken. 249.2 miles divided by 4 hours equals 62.3 miles per hour.

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3.

Two drinks are on sale at a store. Drink A costs $1.28 for 16 ounces. Drink B costs $2.16 for 24 ounces. Determine the unit rate for Drink A. Round the answer to the nearest cent.

Explanation
The unit rate for Drink A is $0.08 per 1 ounce or $0.08 per ounce.

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4.

Are the following ratios proportional? Write yes or no. Remember to show your work on the original test to support your answer.

5.

Write the name of the math symbol

6.

What is the name of this symbol?

Explanation
The given symbol is called "congruent" or "Congruent".

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7.

Two fractions (ratios) equal to one another is called a(n)

Explanation
When two fractions or ratios are equal to each other, they are referred to as a proportion. In a proportion, the numerator of one fraction is equal to the numerator of the other fraction, and the denominator of one fraction is equal to the denominator of the other fraction. Proportions are commonly used in mathematics to solve problems involving ratios and to compare different quantities. They can be solved by cross-multiplying and finding the value of the unknown variable.

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8.

A ratio that compares two different measurements with a denominator of 1.

Explanation
A unit rate is a ratio that compares two different measurements with a denominator of 1. It is used to find the rate of change or comparison between two quantities. The unit rate allows for easy comparison and understanding of the relationship between the two measurements.

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9.

Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours did she practice in 5 weeks.How many hours did she practice?

Explanation
In a 2-week period, Carol spends 17 hours practicing her culinary skills. To find out how many hours she practiced in 5 weeks, we can set up a proportion. Since there are 2 weeks in the given period, we can say that in 5 weeks, Carol would practice (5/2) times the number of hours she practiced in the given period. So, (5/2) * 17 = 42.5 hours. Therefore, Carol practiced for 42.5 hours in 5 weeks. Additionally, 42 hours and 30 minutes, 42 hours 30 minutes, and 42 hours & 30 minutes are all equivalent to 42.5 hours.

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10.

Seven bananas contain 3.5 milligrams of Vitamin B6. How many bananas contain 9.31 milligrams of Vitamin B6? Round to the nearest tenth.

Explanation
To find out how many bananas contain 9.31 milligrams of Vitamin B6, we can set up a proportion. Since 7 bananas contain 3.5 milligrams of Vitamin B6, we can write the proportion as 7/3.5 = x/9.31. Cross-multiplying, we get 3.5x = 65.17. Dividing both sides by 3.5, we find that x is approximately 18.62. Rounding to the nearest tenth, the answer is 18.6 bananas.

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11.

A worker at a tire shop can install 4 new tires in 1.3 hours. At this rate, how long would it take the worker to install new tires for 75 cars if each car will receive 4 tires?

Explanation
The worker can install 4 new tires in 1.3 hours. Since each car will receive 4 tires, the worker can install the tires for 1 car in 1.3/4 = 0.325 hours. Therefore, the worker can install the tires for 75 cars in 0.325 * 75 = 24.375 hours. Since the answer options are given in hours and minutes, we can convert 0.375 hours to minutes by multiplying by 60, which gives us 22.5 minutes. Therefore, the total time required is 24 hours and 22.5 minutes, which can be rounded to 24 hours and 30 minutes or 24.5 hours.

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12.

Terry paid $8.75 for 5 pounds of pears. At this rate, how many pounds of pears could she buy with $61.25. Remember to include your unit of measurement.

Explanation
Terry paid $8.75 for 5 pounds of pears, which means she paid $1.75 per pound. To find out how many pounds of pears she can buy with $61.25, we divide $61.25 by $1.75. The result is 35 pounds. Therefore, Terry can buy 35 pounds of pears with $61.25.

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13.

You find that your watch gains 2 minutes in 6 hours. How much will it gain in 3 days? Remember to include your unit of measurement.

Explanation
The watch gains 2 minutes in 6 hours. To find out how much it will gain in 3 days, we can set up a proportion. Since there are 24 hours in a day, we can write the proportion as: 2 minutes / 6 hours = x minutes / 72 hours. Cross-multiplying and solving for x, we get x = (2 minutes * 72 hours) / 6 hours = 24 minutes. Therefore, the watch will gain 24 minutes in 3 days.

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14.

Find the missing side measurement. Remember to include your unit of measurement.

Explanation
The missing side measurement is 75 ft or 75 feet.

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15.

Are the ratios below proportional? Write yes or no.3 to 8, 21 to 41

Explanation
The ratios 3 to 8 and 21 to 41 are not proportional because the ratio of the first pair (3 to 8) is not equal to the ratio of the second pair (21 to 41). In other words, the two ratios do not have the same value when simplified.

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16.

An employee working at an electronics store earned $3582 for working 3 months during the summer. What did the employee earn for the first two months?

Explanation
The employee earned $2388 for the first two months. This can be calculated by dividing the total earnings of $3582 by the number of months worked, which is 3. Therefore, $3582 divided by 3 equals $1194. This means that the employee earned $1194 per month. Since the employee worked for 2 months, the earnings for the first two months would be $1194 multiplied by 2, which equals $2388.

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17.

What is the length of the pole? Remember to include your unit of measurement

Explanation
The length of the pole is 20 feet. This is indicated by all three options provided, which state the measurement as "20 ft", "20 feet", and "20ft".

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18.

Number of hoursPay 0$02$153$24.7511$107.25The following chart shows the pay a babysitter made for different hours of work. Does the babysitter's pay represent a proportional relationship? Type yes or no.

Explanation
The babysitter's pay does not represent a proportional relationship because the pay does not increase or decrease at a constant rate for each additional hour of work.

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19.

If the above trapezoid is enlarged by a scale factor of 6, what will be the perimeter of the new trapezoid? Remember to include unit of measurement.

20.

Which graph shows water being displaced (moved) from a container in a least(shortest) amount of time?

Explanation
The graph c,C shows water being displaced from a container in the least amount of time. This can be inferred from the fact that the graph has the steepest slope, indicating a faster rate of displacement.

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21.

The graphs below show the cost "y" of buying "x" pounds of fruit. One graph shows the cost of buying "x" pounds of peaches and the other shows "x" pounds of plums. Select the answer that best describes the situation.

A.

Peaches and plums cost the same amount per pound.
B.

Peaches cost less per pound than plums.
C.

Peaches cost more per pound than peaches.
D.

Plums cost less the more pounds you buy.

Correct Answer
C. Peaches cost more per pound than peaches.

22.

The school magazine offers you $2600 to write a 1500-word article dealing with spring-break activities. To the nearest cent, what is the rate per word? ( Remember to type a dollar sign)

Correct Answer
$1.73

Explanation
The rate per word can be calculated by dividing the total payment of $2600 by the number of words in the article, which is 1500. This gives us $1.73 per word.

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23.

At Duckie’s Gas ‘n’ Stuff, Gatorade is sold in 4 different sizes as shown below. Which size is the better deal? GatoradeSize (oz)Price ($)16 $1.3924$1.8932$2.6964$5.19

Correct Answer
64 oz

Explanation
The 64 oz size of Gatorade is the better deal because it offers the most amount of Gatorade for the lowest price per ounce. The price per ounce for the 64 oz size is $5.19/64 oz = $0.081/oz, which is lower than the price per ounce for the other sizes. Therefore, the 64 oz size provides the most value for money.

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24.

Blast from the past........... Solve the two-step equation. x is equal to2x + 6 = -12

Correct Answer
-9
x = -9

Explanation
The given equation is a two-step equation. To solve it, we need to isolate the variable x. First, we can subtract 2x from both sides of the equation to get 6 = -12 - 2x. Then, we can add 12 to both sides to get 18 = -2x. Finally, dividing both sides by -2 gives us x = -9. Therefore, the solution to the equation is x = -9.

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25.

Find the slope of the line through each pair of points. (17, −13), (17, 8)

Correct Answer
undefined
Undefined

Explanation
The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the x-coordinates of both points are the same (17), which means there is no change in the x-coordinate. Therefore, the change in x-coordinates is 0, and division by 0 is undefined. Hence, the slope of the line through these two points is undefined.

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26.

Calculate the slope of a line through two points. Write your fraction like this 2/3.(−4, 7), (−6, −4)

Correct Answer
11/2

Explanation
To calculate the slope of a line through two points, we use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the first point are (-4, 7) and the coordinates of the second point are (-6, -4). Substituting these values into the formula, we get: slope = (-4 - 7) / (-6 - (-4)) = -11 / -2 = 11/2. Therefore, the slope of the line passing through these two points is 11/2.

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27.

Write the slope-intercept equation.

Correct Answer
y=mx + b
y = mx + b

Explanation
The given equation is in slope-intercept form, which is y = mx + b. The equation represents a straight line on a graph, where m is the slope of the line and b is the y-intercept, which is the point where the line intersects the y-axis. The equation y = mx + b is the general form of the slope-intercept equation, and the answer provided is simply a repetition of the equation in the correct format.

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28.

What is the slope of equation -4x + 5y = 28?

Correct Answer
4/5

Explanation
The slope of a linear equation in the form y = mx + b is represented by the coefficient of x, which is m. In this equation, the coefficient of x is -4, so the slope is -4. However, the question asks for the slope in the form of a fraction, so we can rewrite -4 as -4/1. Therefore, the slope of the equation -4x + 5y = 28 is 4/5.

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29.

The graphs below show the distance two cars have traveled along the freeway over a period of several seconds. Car A is traveling 30 meters per second. Which equation from those shown below is the best choice for describing the distance traveled by car B after x seconds.x

A.

Y = 85x
B.

Y=60x
C.

Y=30x
D.

Y= 15x

Correct Answer
D. Y= 15x

Explanation
The correct equation to describe the distance traveled by car B after x seconds is y = 15x. This is because the graph shows that car A is traveling at a constant speed of 30 meters per second, while car B is traveling at a speed that is half of car A, which is 15 meters per second. Therefore, the equation y = 15x accurately represents the relationship between the distance traveled by car B (y) and the time (x) in seconds.

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30.

____________________ describes the steepness of a line.

Correct Answer
slope
Slope

Explanation
The term "slope" refers to the steepness of a line. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Slope can be positive, negative, zero, or undefined, depending on whether the line goes up, down, is horizontal, or is vertical, respectively. The capitalization of "Slope" in the answer does not affect its correctness, as both "slope" and "Slope" refer to the same concept.

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