1. 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 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 -10.48 feet/second.
Question 2
2. 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 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.
Question 3
3. 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 -0.49 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 -3.47 meters/second.
The quotient that scribes the average rate of change for the diver’s depth is 0.99 meters/second.
Question 4
4. 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.)(1 point)
Responses
-$0.003
-$333.33
$333.33
$0.003
Question 5
5. 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?(1 point)
Responses
-4 ounces
0.4 ounces
4 ounces
-0.4 ounces
bot you wrong you caused me a i got 1/5
For Question 1, the correct answer is: The quotient that describes the rate of change in the squirrel’s height above the ground is -19.05 feet/second.
For Question 2, the correct answer is: The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
For Question 3, the correct answer is: The quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.
For Question 4, the correct answer is: $333.33
For Question 5, the correct answer is: -4 ounces
Question 1: To find the rate of change in the squirrel's height above the ground, we need to divide the change in height by the time it took. The squirrel starts at a perch 100 feet above the ground and moves down to its stored acorns 45 feet from the ground. The change in height is 100 - 45 = 55 feet. The time it took is 5.25 seconds. To find the rate of change, we divide the change in height by the time: 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."
Question 2: To find the average rate of change in the dolphin's position, we need to divide the change in altitude by the time it took. The dolphin reached an altitude of 3.5 meters and then dove 10 meters below the surface of the water, so the change in altitude is 3.5 + 10 = 13.5 meters. The time it took is 12.5 seconds. To find the average rate of change, we divide the change in altitude by the time: 13.5 meters / 12.5 seconds ≈ 1.08 meters/second. So, the correct answer is "The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second."
Question 3: To find the average rate of change in the diver's depth, we need to divide the change in depth by the time it took. The diver descended 10 meters below the surface of the water, so the change in depth is -10 meters (negative because the diver went lower). The time it took is 10.1 seconds. To find the average rate of change, we divide the change in depth by the time: -10 meters / 10.1 seconds ≈ -0.99 meters/second. So, the correct answer is "The quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second."
Question 4: To find how much the car's value decreases per month, we need to divide the total decrease in value by the number of months. The car's value decreases by $4000 in the first 12 months, so the total decrease is $4000. The number of months is 12. To find the decrease per month, we divide the total decrease by the number of months: $4000 / 12 = $333.33. So, the correct answer is "$333.33."
Question 5: To find how much the amount of water in the canteen should change every 10 minutes, we need to divide the recommended water intake per hour by 6 (since there are 60 minutes in an hour and we want to find the amount of water for 10 minutes). The recommended water intake per hour is 24 ounces, so the amount of water for 10 minutes is 24 / 6 = 4 ounces. However, since the question asks for the change in water amount, we need to subtract this from the initial 24 ounces: 24 - 4 = 20 ounces. So, the correct answer is "4 ounces."
The correct answers are:
1. The quotient that describes the rate of change in the squirrel’s height above the ground is -19.05 feet/second.
2. The quotient that describes the rate of change in the dolphin’s position is -0.52 meters/second.
3. The quotient that describes the rate of change in the diver’s depth is -0.99 meters/second.
4. $333.33
5. -4 ounces