Relationships Between Quantities Unit Test Pmi Algebra I

1. Your lamp can fit light bulbs that have a radius of 6 cm. The box of light bulbs you have says they have a radius of two inches. Will the light bulbs fit in the lamp?

The light bulbs will fit in the lamp because their radius of two inches is equivalent to 5.08 cm, which is smaller than the maximum radius of 6 cm that the lamp can accommodate.

Explanation

The light bulbs will fit in the lamp because their radius of two inches is equivalent to 5.08 cm, which is smaller than the maximum radius of 6 cm that the lamp can accommodate.

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2. To qualify for regionals your crew team must row at a rate of 65 strokes per minute. During practice, your boat finished 7500 strokes in two hours. Will your boat qualify for regionals?

To determine if the boat will qualify for regionals, we need to calculate the average strokes per minute during practice. In two hours, there are 120 minutes. If the boat finished 7500 strokes in 120 minutes, the average strokes per minute would be 7500/120 = 62.5 strokes per minute. Since this is lower than the required rate of 65 strokes per minute, the boat will not qualify for regionals.

Explanation

To determine if the boat will qualify for regionals, we need to calculate the average strokes per minute during practice. In two hours, there are 120 minutes. If the boat finished 7500 strokes in 120 minutes, the average strokes per minute would be 7500/120 = 62.5 strokes per minute. Since this is lower than the required rate of 65 strokes per minute, the boat will not qualify for regionals.

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3. Stacy bought a tree to decorate her apartment. The tree is 4.5 feet tall. To find the price she must know how tall the tree is in inches. What is the height in inches?

2.7 inches

54 inches

23 inches

.375 inches

Stacy bought a tree that is 4.5 feet tall. To find the height in inches, we need to convert feet to inches. Since there are 12 inches in a foot, we can multiply 4.5 by 12 to get the height in inches. Therefore, the height of the tree is 54 inches.

Explanation

Stacy bought a tree that is 4.5 feet tall. To find the height in inches, we need to convert feet to inches. Since there are 12 inches in a foot, we can multiply 4.5 by 12 to get the height in inches. Therefore, the height of the tree is 54 inches.

4. Pick the most appropriate way to measure the rate of filling an Olympic sized swimming pool.

Ounces per hour

Gallons per hour

Cups per minute

Cups per hour

The most appropriate way to measure the rate of filling an Olympic sized swimming pool is in gallons per hour. This is because gallons are a commonly used unit of measurement for large volumes of liquid, and measuring the rate in gallons per hour provides a clear and practical understanding of how quickly the pool is being filled.

Explanation

The most appropriate way to measure the rate of filling an Olympic sized swimming pool is in gallons per hour. This is because gallons are a commonly used unit of measurement for large volumes of liquid, and measuring the rate in gallons per hour provides a clear and practical understanding of how quickly the pool is being filled.

5. There is a parking space that is 2.4 yards wide. Your car is 7 feet wide. Will your car fit into the parking spot?

Yes

No

Yes, the car will fit into the parking spot. To compare the width of the parking space and the car, we need to convert the measurements to the same unit. 2.4 yards is equal to 7.2 feet. Since the car is 7 feet wide, it will fit within the 7.2 feet wide parking space.

Explanation

Yes, the car will fit into the parking spot. To compare the width of the parking space and the car, we need to convert the measurements to the same unit. 2.4 yards is equal to 7.2 feet. Since the car is 7 feet wide, it will fit within the 7.2 feet wide parking space.

6. Find the cost of a tub of ice cream that holds 5 gallons if it costs $1.499 per gallon.

$8.00

$3.50

$3.33

$7.50

The cost of a tub of ice cream that holds 5 gallons can be found by multiplying the cost per gallon ($1.499) by the number of gallons (5). This gives us a total cost of $7.495. Since the cost is usually rounded up to the nearest cent, the final cost of the tub of ice cream would be $7.50.

Explanation

The cost of a tub of ice cream that holds 5 gallons can be found by multiplying the cost per gallon ($1.499) by the number of gallons (5). This gives us a total cost of $7.495. Since the cost is usually rounded up to the nearest cent, the final cost of the tub of ice cream would be $7.50.

7. A portion of the annual dog show competition is based on dog's speed. A Black Labrador Retriever runs at a rate of 8 feet per second. A Chesapeake Bay Retriever runs at a rate of 6 miles per hour. Which dog would win this portion of the competition?

Black Labrador Retriever

Chesapeake Bay Retriever

The Chesapeake Bay Retriever would win this portion of the competition because it runs at a faster rate of 6 miles per hour compared to the Black Labrador Retriever's rate of 8 feet per second.

Explanation

The Chesapeake Bay Retriever would win this portion of the competition because it runs at a faster rate of 6 miles per hour compared to the Black Labrador Retriever's rate of 8 feet per second.

8. Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. When she comes back to America she needs to know how many dollars per week she was making. What is the correct amount? (1 Euro = 1.37 dollars)

$479.50/week

$357.66/week

$671.30/week

$335.65/week

Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. To find out how much she makes per week in dollars, we need to multiply her daily earnings by the number of days she works in a week. Since there are 7 days in a week, her weekly earnings in Euros would be 70 Euros/day * 7 days/week = 490 Euros/week. To convert this to dollars, we need to multiply by the exchange rate of 1.37 dollars/Euro. Therefore, her weekly earnings in dollars would be 490 Euros/week * 1.37 dollars/Euro = $671.30/week.

Explanation

Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. To find out how much she makes per week in dollars, we need to multiply her daily earnings by the number of days she works in a week. Since there are 7 days in a week, her weekly earnings in Euros would be 70 Euros/day * 7 days/week = 490 Euros/week. To convert this to dollars, we need to multiply by the exchange rate of 1.37 dollars/Euro. Therefore, her weekly earnings in dollars would be 490 Euros/week * 1.37 dollars/Euro = $671.30/week.

9. It takes 18 tablespoons of sugar to make enough brownies for all the students in your class. You have 1.5 cups in your cabinet. Will you have enough or will you need to go to the store to buy more?

You will have enough

You will have to go to the store to buy more

Since we know that 1 cup is equal to 16 tablespoons, we can calculate that 1.5 cups is equal to 24 tablespoons. Since it only takes 18 tablespoons to make enough brownies for all the students, having 24 tablespoons means that there will be enough sugar without the need to go to the store.

Explanation

Since we know that 1 cup is equal to 16 tablespoons, we can calculate that 1.5 cups is equal to 24 tablespoons. Since it only takes 18 tablespoons to make enough brownies for all the students, having 24 tablespoons means that there will be enough sugar without the need to go to the store.

10. To enter yourself into a running competition you must submit rates in feet per second. You timed yourself running 2 miles in 16.5 minutes. Which is the correct rate you should submit?

38400 feet/sec

5.3 feet/sec

19200 feet/sec

10.7 feet/sec

To find the correct rate in feet per second, we need to convert the distance and time given. Since 1 mile is equal to 5280 feet, 2 miles would be 2 * 5280 = 10560 feet. Similarly, since 1 minute is equal to 60 seconds, 16.5 minutes would be 16.5 * 60 = 990 seconds. Dividing the distance (10560 feet) by the time (990 seconds) gives us a rate of approximately 10.7 feet per second.

Explanation

To find the correct rate in feet per second, we need to convert the distance and time given. Since 1 mile is equal to 5280 feet, 2 miles would be 2 * 5280 = 10560 feet. Similarly, since 1 minute is equal to 60 seconds, 16.5 minutes would be 16.5 * 60 = 990 seconds. Dividing the distance (10560 feet) by the time (990 seconds) gives us a rate of approximately 10.7 feet per second.

11. You have a circle-shaped mirror in your bedroom. You need to figure out where to hang it, so you must find the diameter of the circle. You know the radius is 34 centimeters. How long is the diameter in inches? (Diameter=2*radius)

26.8 inches

86.4 inches

172.7 inches

13.4 inches

The diameter of a circle is calculated by multiplying the radius by 2. In this case, the radius is given as 34 centimeters. To convert centimeters to inches, we can use the conversion factor of 1 inch = 2.54 centimeters. Therefore, the diameter in inches would be 34 cm * (1 inch/2.54 cm) * 2 = 26.8 inches.

Explanation

The diameter of a circle is calculated by multiplying the radius by 2. In this case, the radius is given as 34 centimeters. To convert centimeters to inches, we can use the conversion factor of 1 inch = 2.54 centimeters. Therefore, the diameter in inches would be 34 cm * (1 inch/2.54 cm) * 2 = 26.8 inches.

12. Shawn and Corey are racing each other in gym class. The gym teacher is going to give the student who can run faster an extra credit point. Shawn runs at an average rate of 7 miles per hour. Corey runs at an average rate of 720 feet per minute. Who will receive the extra credit point?

Corey will receive the extra credit point because his average speed of 720 feet per minute is faster than Shawn's average speed of 7 miles per hour. Since Corey's speed is given in feet per minute and Shawn's speed is given in miles per hour, we need to convert the units to compare them. There are 5,280 feet in a mile and 60 minutes in an hour. Converting Corey's speed to miles per hour, we get 720 feet per minute * 60 minutes per hour / 5,280 feet per mile = 8 miles per hour. Since 8 miles per hour is faster than 7 miles per hour, Corey will receive the extra credit point.

Explanation

Corey will receive the extra credit point because his average speed of 720 feet per minute is faster than Shawn's average speed of 7 miles per hour. Since Corey's speed is given in feet per minute and Shawn's speed is given in miles per hour, we need to convert the units to compare them. There are 5,280 feet in a mile and 60 minutes in an hour. Converting Corey's speed to miles per hour, we get 720 feet per minute * 60 minutes per hour / 5,280 feet per mile = 8 miles per hour. Since 8 miles per hour is faster than 7 miles per hour, Corey will receive the extra credit point.

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13. You are measuring your feet at the shoe store to determine what shoe size to buy. On the measurement device there are centimeters, inches, and millimeters. Which unit would you pick? Explain why.

When measuring something, it is generally preferred to use the smallest unit available in order to achieve the highest level of precision. In this case, millimeters are the smallest unit on the measurement device, so using them would provide the most precise measurement of the feet. Centimeters and inches are larger units and would result in a less precise measurement. Therefore, choosing millimeters would be the best option for determining the shoe size accurately.

Explanation

When measuring something, it is generally preferred to use the smallest unit available in order to achieve the highest level of precision. In this case, millimeters are the smallest unit on the measurement device, so using them would provide the most precise measurement of the feet. Centimeters and inches are larger units and would result in a less precise measurement. Therefore, choosing millimeters would be the best option for determining the shoe size accurately.

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14. You have $15 in your wallet. You want to buy a package of chicken that costs $4.999 per pound. The package weighs 4 pounds. Estimate the cost, and then decide if you have enough money.

Based on the given information, the package of chicken costs $4.999 per pound and weighs 4 pounds. To estimate the cost, we can multiply the cost per pound by the weight of the package: $4.999 x 4 = $19.996. Since $19.996 is greater than the $15 you have in your wallet, it can be concluded that you will not have enough money to buy the package of chicken.

Explanation

Based on the given information, the package of chicken costs $4.999 per pound and weighs 4 pounds. To estimate the cost, we can multiply the cost per pound by the weight of the package: $4.999 x 4 = $19.996. Since $19.996 is greater than the $15 you have in your wallet, it can be concluded that you will not have enough money to buy the package of chicken.

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15. Explain what you think the most appropriate way to measure the speed at which you can ride a bike is. Why?

The most appropriate way to measure the speed at which you can ride a bike is in miles per hour. This is because miles per hour is a standard unit of measurement for speed and is commonly used in transportation. It allows for easy comparison and understanding of how fast you can travel on a bike. Additionally, measuring speed in miles per hour is useful for assessing your performance and progress over time, especially if you are riding for extended periods or long distances.

Explanation

The most appropriate way to measure the speed at which you can ride a bike is in miles per hour. This is because miles per hour is a standard unit of measurement for speed and is commonly used in transportation. It allows for easy comparison and understanding of how fast you can travel on a bike. Additionally, measuring speed in miles per hour is useful for assessing your performance and progress over time, especially if you are riding for extended periods or long distances.

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16. Rachel is spending 5 Pesos everyday on pubic transportation while she studies abroad. Her mother would like to know how much she is spending in dollars per week. What is the cost? (1 dollar = 12.92 Pesos)

Rachel is spending 5 Pesos on public transportation every day. To find out how much she is spending in dollars per week, we need to convert the daily cost from Pesos to dollars. Given that 1 dollar is equal to 12.92 Pesos, we can calculate the weekly cost by multiplying the daily cost by the conversion rate and the number of days in a week. Therefore, the cost is $2.71 per week.

Explanation

Rachel is spending 5 Pesos on public transportation every day. To find out how much she is spending in dollars per week, we need to convert the daily cost from Pesos to dollars. Given that 1 dollar is equal to 12.92 Pesos, we can calculate the weekly cost by multiplying the daily cost by the conversion rate and the number of days in a week. Therefore, the cost is $2.71 per week.

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