Solve using division of rational numbers. If a car’s value decreases by $2,500 in the first 6 months, how much does the value decrease per month? (Round to the nearest hundredth.)
To find out how much the value of the car decreases per month, we need to divide the total decrease in value ($2,500) by the number of months (6).
$2,500 ÷ 6 ≈ $416.67
Therefore, the value of the car decreases by approximately $416.67 per month.
. A squirrel has stored its acorns in a hole that is 45 feet from the ground in a tall tree. The squirrel starts on a perch 100 feet above the ground. The squirrel moves from the perch down to its stored acorns in 5.25 seconds. Interpret the quotient to describe the rate of change in the squirrel’s height above the ground. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the rate of change in the squirrel’s height above the ground is -19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is -10.48 feet/second.
To determine the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time it takes to make that change.
The squirrel starts at a height of 100 feet and moves down to a height of 45 feet in 5.25 seconds.
100 feet - 45 feet = 55 feet (change in height)
55 feet ÷ 5.25 seconds ≈ 10.48 feet/second
(The quotient is positive because the squirrel is moving downwards, so the rate of change is negative.)
Therefore, the quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/second.
A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin’s position. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is -1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
To determine the average rate of change in the dolphin's position, we need to divide the change in position by the time it takes to make that change.
The dolphin goes from an altitude of 3.5 meters above the water to a depth of 10 meters below the surface, which is a total change in position of 3.5 + 10 = 13.5 meters.
The time it takes for this change to occur is 12.5 seconds.
13.5 meters ÷ 12.5 seconds ≈ 1.08 meters/second
Since the dolphin is diving below the surface, the rate of change is negative.
Therefore, the quotient that describes the average rate of change in the dolphin's position is -1.08 meters/second.
The scuba diver was at a depth below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.
(1 point)
Responses
The quotient that scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -0.49 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is -3.47 meters/second.
To determine the average rate of change in the diver's depth, we need to divide the change in depth by the time it takes to make that change.
The diver descends 10 meters in 10.1 seconds.
10 meters ÷ 10.1 seconds ≈ 0.99 meters/second
Since the diver is descending, the rate of change is negative.
Therefore, the quotient that describes the average rate of change in the diver's depth is -0.99 meters/second.
Solve using division of rational numbers. If a car’s value decreases by $4000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)
To find out how much the value of the car decreases per month, we need to divide the total decrease in value ($4000) by the number of months (12).
$4000 ÷ 12 ≈ $333.33
Therefore, the value of the car decreases by approximately $333.33 per month.
. It is recommended that hikers drink 24 ounces of water an hour. If a canteen has 24 ounces of water, how much should the amount of water in the canteen change every 10 minutes?
To determine how much the amount of water in the canteen should change every 10 minutes, we need to divide the recommended water intake per hour (24 ounces) by the number of 10 minute intervals in an hour.
There are 6 sets of 10 minutes in an hour.
24 ounces ÷ 6 = 4 ounces
Therefore, the amount of water in the canteen should decrease or be consumed by approximately 4 ounces every 10 minutes.
Joshua is sharing half of a pizza with three friends. Which expression can be used to find the fraction of a whole pizza each person will get, if they sprint what they have evenly
To find the fraction of a whole pizza that each person will get, if they split it evenly, we can use the expression:
(1/2) ÷ 4
Explanation:
- The (1/2) represents the half of the pizza that Joshua is sharing.
- The ÷ 4 represents dividing that half among Joshua and his three friends.
Simplifying this expression:
(1/2) ÷ 4 = 1/2 × 1/4 = 1/8
Therefore, each person will get 1/8 of the whole pizza.
Which quotient is between -4 and -5?
Hint: Use your calculator for this problem.
(1 point)
Responses
−512÷(−112)
negative 5 and 1 half divided by open paren negative 1 and 1 half close paren
256÷(−12)
2 and 5 sixths divided by open paren negative 1 half close paren
123÷(−12)
1 and 2 thirds divided by open paren negative 1 half close paren
−913÷2
To find the quotient that is between -4 and -5, we can evaluate each expression using a calculator:
-512 ÷ (-112) ≈ 4.5714
256 ÷ (-12) ≈ -21.3333
123 ÷ (-12) ≈ -10.25
-913 ÷ 2 ≈ -456.5
The only quotient that is between -4 and -5 is -10.25.
Therefore, the correct answer is 123 ÷ (-12).
Convert 3 16/25
to a decimal.
To convert the mixed number 3 16/25 to a decimal, we can follow these steps:
1. Convert the whole number to a decimal by simply writing it down: 3.
2. Convert the fraction to a decimal by dividing the numerator (16) by the denominator (25):
16 ÷ 25 ≈ 0.64
3. Add the decimal from the fraction to the whole number:
3 + 0.64 = 3.64
Therefore, the decimal equivalent of 3 16/25 is 3.64.