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 −10.48 feet/second.
The quotient that describes the rate of change in the squirrel’s height above the ground is negative 10.48 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 negative 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.
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.
Applications of Dividing Rational Numbers Quick Check
2 of 52 of 5 Items
Question
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 negative 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/secon
The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
Applications of Dividing Rational Numbers Quick Check
3 of 53 of 5 Items
Question
A scuba diver was at a depth of 15 meters 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 describes the average rate of change for the diver’s depth is −0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.
Solve using division of rational numbers. If a car’s value decreases by $4,000 in the first 12 months, how much does the value decrease per month? (Round to the nearest hundredth.)(1 point)
Responses
0.003
0.003
−0.003
negative 0.003
−$333.33
negative 333.33 dollars
$333.33
To find the value decrease per month, we divide the total decrease of $4,000 by the number of months, which is 12.
Value decrease per month = $4,000 / 12 = $333.33
So, the value decreases by $333.33 per month.
t 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?(1 point)
Responses
4 ounces
4 ounces
−4 ounces
negative 4 ounces
0.4 ounces
0.4 ounces
−0.4 ounces
To find how much the amount of water in the canteen should change every 10 minutes, we need to calculate the amount of water consumed in 10 minutes.
Since hikers are recommended to drink 24 ounces of water per hour, we need to divide this by 6 (10 minutes is one-sixth of an hour).
Amount of water consumed in 10 minutes = 24 ounces / 6 = 4 ounces
Therefore, the amount of water in the canteen should decrease by 4 ounces every 10 minutes.
To determine the rate of change in the squirrel's height above the ground, we need to calculate the average rate at which the squirrel moves from the perch down to its stored acorns.
The squirrel starts on a perch 100 feet above the ground and moves to a hole that is 45 feet from the ground. The total change in height is 100 - 45 = 55 feet.
The time it takes for the squirrel to make this movement is given as 5.25 seconds.
To calculate the rate of change, we divide the change in height by the time taken:
Rate of change = Change in height / Time
Rate of change = 55 feet / 5.25 seconds ≈ 10.48 feet/second.
So, the correct answer is:
The quotient that describes the rate of change in the squirrel’s height above the ground is 10.48 feet/second.