A mountain goat is climbing to the top of a large cliff. The cliff is 50 feet higher than its starting point. If it takes the goat 22 minutes to climb this cliff, interpret the quotient to describe the rate of change in the goat’s elevation. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the goat’s elevation is __ feet/minute.
To find the quotient that represents the rate of change in the goat's elevation, we divide the change in elevation by the time taken.
The change in elevation is 50 feet, and the time taken is 22 minutes.
Therefore, the quotient is 50 feet / 22 minutes.
To find this value to the nearest hundredth, we divide 50 by 22.
50 / 22 = 2.27 (rounded to the nearest hundredth)
So the rate of change in the goat's elevation is approximately 2.27 feet/minute.
A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth and remember that the bird is descending.(1 point)
The quotient that best represents the rate of change in the bird’s altitude is
meters/second.
To find the quotient that represents the rate of change in the bird's altitude, we divide the change in altitude by the time taken.
The change in altitude is 10 meters (initial altitude) - 3 meters (final altitude) = 7 meters (since the bird is descending).
The time taken is 3 seconds.
Therefore, the quotient is 7 meters / 3 seconds.
To find this value to the nearest hundredth, we divide 7 by 3.
7 / 3 = 2.33 (rounded to the nearest hundredth)
So the rate of change in the bird's altitude is approximately 2.33 meters/second.
A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth and remember that the bird is descending.(1 point)
The quotient that best represents the rate of change in the bird’s altitude is __ meters/second.
To find the rate of change in the bird's altitude, we need to determine the difference in altitude (in meters) before and after the 3 seconds.
The initial altitude is 10 meters above the ground, and the final altitude is 3 meters above the ground (since the bird is descending).
Therefore, the change in altitude is 10 - 3 = 7 meters.
Since the bird settles on the branch after 3 seconds, the time taken is 3 seconds.
The rate of change in the bird's altitude can be calculated by dividing the change in altitude by the time taken.
Therefore, the quotient is 7 meters / 3 seconds.
To find this value to the nearest hundredth, we divide 7 by 3.
7 / 3 = 2.33
So, the rate of change in the bird's altitude is approximately 2.33 meters/second.
A whale is swimming at a current depth of 15 meters below the surface. It swims up toward the surface and arrives there 9.5 seconds later. Find the quotient that best describes the rate of change in the whale’s depth. Give your answer to the nearest hundredth.(1 point)
The quotient that best represents the rate of change in the whale’s depth is __ meters/second.
To find the rate of change in the whale's depth, we need to determine the difference in depth (in meters) before and after the 9.5 seconds.
The initial depth is 15 meters below the surface, and the final depth is at the surface (since the whale arrives there).
Therefore, the change in depth is 15 meters (negative value since the whale is swimming up).
Since it takes the whale 9.5 seconds to swim up, the time taken is 9.5 seconds.
The rate of change in the whale's depth can be calculated by dividing the change in depth by the time taken.
Therefore, the quotient is 15 meters / 9.5 seconds.
To find this value to the nearest hundredth, we divide 15 by 9.5.
15 / 9.5 = 1.58
So, the rate of change in the whale's depth is approximately 1.58 meters/second.
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.) (1 point)
To find the amount the car's value decreases per month, we need to divide the decrease in value by the number of months.
The decrease in value is $2,500, and the number of months is 6.
Therefore, the quotient is $2,500 / 6.
To find this value to the nearest hundredth, we divide $2,500 by 6.
$2,500 / 6 ≈ $416.67
So, the value of the car decreases by approximately $416.67 per month.
A restaurant uses a 15-pound bag of flour in 4 days. Each day, the bag of flour gets lighter as more flour is used. How much does the average amount of flour in the bag change each day? (Round to the nearest hundredth.)(1 point)
To find the average amount of flour that the bag changes each day, we need to divide the total change in flour by the number of days.
The total change in flour in the bag is 15 pounds (initial amount of flour in the bag) - 0 pounds (final amount of flour in the bag after 4 days of use).
Therefore, the change in flour is 15 pounds.
Since the flour is used over a period of 4 days, the number of days is 4.
The average amount of flour that changes each day can be calculated by dividing the change in flour by the number of days.
Therefore, the quotient is 15 pounds / 4 days.
To find this value to the nearest hundredth, we divide 15 by 4.
15 / 4 ≈ 3.75
So, the average amount of flour in the bag changes by approximately 3.75 pounds each day.
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 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 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.
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 -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.
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 -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 -0.99 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.
The quotient that scribes the average rate of change for the diver’s depth is -3.47 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
$333.33
$333.33
$0.003
$0.003
-$333.33
-$333.33
-$0.003
-$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
-4 ounces
-0.4 ounces
-0.4 ounces
4 ounces
4 ounces
0.4 ounces
1. The quotient that best represents the rate of change in the squirrel’s height above the ground is 19.05 feet/second.
2. The quotient that best represents the rate of change in the dolphin’s position is -1.08 meters/second.
3. The quotient that best represents the rate of change in the diver’s depth is 0.99 meters/second.
4. The value of the car decreases by $333.33 per month.
5. The amount of water in the canteen should decrease by 4 ounces every 10 minutes.
6. 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?(1 point)
Responses
12⋅14
1 half times 1 fourth
12⋅4
1 half times 4
2⋅4
2 times 4
2⋅14
2 times 1 fourth
Question 2
7. 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
123÷(−12)
1 and 2 thirds divided by open paren negative 1 half close paren
256÷(−12)
2 and 5 sixths divided by open paren negative 1 half close paren
−913÷2
6. The expression that can be used to find the fraction of a whole pizza each person will get is 1 half times 1 fourth.
7. The quotient between -4 and -5 is −913 ÷ 2.
Convert 31625
to a decimal.(1 point)
Responses
1.92
1.92
0.64
0.64
3.64
3.64
12.64
The correct decimal conversion for the number 31625 is 31,625.
Convert 3 16/25
to a decimal.(1 point)
Responses
1.92
1.92
0.64
0.64
3.64
3.64
12.64
To convert the mixed number 3 16/25 to a decimal, we can first convert the mixed number to an improper fraction and then divide the numerator by the denominator.
The improper fraction equivalent of 3 16/25 is (3 * 25 + 16)/25 = 91/25.
To convert it to a decimal, we divide the numerator (91) by the denominator (25).
91 ÷ 25 = 3.64
So, 3 16/25 as a decimal is 3.64.