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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.
The quotient that best represents the rate of change in the goat’s elevation is
feet/minute.
To find the rate of change in the goat's elevation, we divide the change in elevation (50 feet) by the time taken (22 minutes):
Rate of change = Change in elevation / Time taken
Rate of change = 50 feet / 22 minutes
Calculating this gives:
Rate of change ≈ 2.27 feet/minute
So, the quotient that best represents the rate of change in the goat's elevation is 2.27 feet/minute (rounded to the nearest hundredth).
Rate of change = Change in elevation / Time taken
Rate of change = 50 feet / 22 minutes
Calculating this gives:
Rate of change ≈ 2.27 feet/minute
So, the quotient that best represents the rate of change in the goat's elevation is 2.27 feet/minute (rounded to the nearest hundredth).
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.
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 calculate the change in altitude (from 10 meters to 3 meters) and divide it by the time taken (3 seconds). Since the bird is descending, the change in altitude will be negative.
Rate of change = Change in altitude / Time taken
Rate of change = (3 meters - 10 meters) / 3 seconds
Rate of change = -7 meters / 3 seconds
Calculating this gives:
Rate of change ≈ -2.33 meters/second
Therefore, the quotient that best represents the rate of change in the bird's altitude is -2.33 meters/second (rounded to the nearest hundredth).
Rate of change = Change in altitude / Time taken
Rate of change = (3 meters - 10 meters) / 3 seconds
Rate of change = -7 meters / 3 seconds
Calculating this gives:
Rate of change ≈ -2.33 meters/second
Therefore, the quotient that best represents the rate of change in the bird's altitude is -2.33 meters/second (rounded to the nearest hundredth).
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.
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 calculate the change in depth (from 15 meters below the surface to the surface, which is 0 meters) and divide it by the time taken (9.5 seconds). Since the whale is swimming up towards the surface, the change in depth will be positive.
Rate of change = Change in depth / Time taken
Rate of change = (0 meters - (-15 meters)) / 9.5 seconds
Rate of change = 15 meters / 9.5 seconds
Calculating this gives:
Rate of change ≈ 1.58 meters/second
Therefore, the quotient that best represents the rate of change in the whale's depth is 1.58 meters/second (rounded to the nearest hundredth).
Rate of change = Change in depth / Time taken
Rate of change = (0 meters - (-15 meters)) / 9.5 seconds
Rate of change = 15 meters / 9.5 seconds
Calculating this gives:
Rate of change ≈ 1.58 meters/second
Therefore, the quotient that best represents the rate of change in the whale's depth is 1.58 meters/second (rounded to the nearest hundredth).
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 the bag changes each day, we divide the total change in weight (15 pounds) by the number of days (4 days).
Average change per day = Change in weight / Number of days
Average change per day = 15 pounds / 4 days
Calculating this gives:
Average change per day ≈ 3.75 pounds/day
Therefore, the average amount of flour in the bag changes by approximately 3.75 pounds each day (rounded to the nearest hundredth).
Average change per day = Change in weight / Number of days
Average change per day = 15 pounds / 4 days
Calculating this gives:
Average change per day ≈ 3.75 pounds/day
Therefore, the average amount of flour in the bag changes by approximately 3.75 pounds each day (rounded to the nearest hundredth).
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)
pounds
pounds
To find the average amount of flour the bag changes each day, we divide the total change in weight (15 pounds) by the number of days (4 days).
Average change per day = Change in weight / Number of days
Average change per day = 15 pounds / 4 days
Calculating this gives:
Average change per day = 3.75 pounds/day
Therefore, the average amount of flour in the bag changes by 3.75 pounds each day.
Average change per day = Change in weight / Number of days
Average change per day = 15 pounds / 4 days
Calculating this gives:
Average change per day = 3.75 pounds/day
Therefore, the average amount of flour in the bag changes by 3.75 pounds each day.
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
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
To find the rate of change in the squirrel's height above the ground, we calculate the change in height (from 100 feet to 45 feet) and divide it by the time taken (5.25 seconds). Since the squirrel is moving down towards the stored acorns, the change in height will be negative.
Rate of change = Change in height / Time taken
Rate of change = (45 feet - 100 feet) / 5.25 seconds
Rate of change = -55 feet / 5.25 seconds
Calculating this gives:
Rate of change ≈ -10.48 feet/second
Therefore, the quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/second (rounded to the nearest hundredth).
Rate of change = Change in height / Time taken
Rate of change = (45 feet - 100 feet) / 5.25 seconds
Rate of change = -55 feet / 5.25 seconds
Calculating this gives:
Rate of change ≈ -10.48 feet/second
Therefore, the quotient that describes the rate of change in the squirrel's height above the ground is -10.48 feet/second (rounded to the nearest hundredth).
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 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 negative 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
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 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 negative 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
To find the average rate of change in the dolphin's position, we calculate the change in position (from 3.5 meters above the surface to 10 meters below the surface) and divide it by the time taken (12.5 seconds). Since the dolphin is diving below the surface, the change in position will be negative.
Rate of change = Change in position / Time taken
Rate of change = (3.5 meters - (-10 meters)) / 12.5 seconds
Rate of change = 13.5 meters / 12.5 seconds
Calculating this gives:
Rate of change ≈ 1.08 meters/second
Therefore, the quotient that describes the rate of change in the dolphin's position is 1.08 meters/second
Rate of change = Change in position / Time taken
Rate of change = (3.5 meters - (-10 meters)) / 12.5 seconds
Rate of change = 13.5 meters / 12.5 seconds
Calculating this gives:
Rate of change ≈ 1.08 meters/second
Therefore, the quotient that describes the rate of change in the dolphin's position is 1.08 meters/second
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 −0.99 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 −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 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 −0.49 meters/second.
Responses
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 −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 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 −0.49 meters/second.
To find the average rate of change in the diver's depth, we calculate the change in depth (from 15 meters below the surface to 10 meters lower) and divide it by the time taken (10.1 seconds). Since the diver is descending, the change in depth will be negative.
Rate of change = Change in depth / Time taken
Rate of change = ( -10 meters - (-15 meters)) / 10.1 seconds
Rate of change = -5 meters / 10.1 seconds
Calculating this gives:
Rate of change ≈ -0.99 meters/second
Therefore, the quotient that describes the average rate of change in the diver's depth is -0.99 meters/second (rounded to the nearest hundredth).
Rate of change = Change in depth / Time taken
Rate of change = ( -10 meters - (-15 meters)) / 10.1 seconds
Rate of change = -5 meters / 10.1 seconds
Calculating this gives:
Rate of change ≈ -0.99 meters/second
Therefore, the quotient that describes the average rate of change in the diver's depth is -0.99 meters/second (rounded to the nearest hundredth).
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
negative 0.003
−$333.33
negative 333.33 dollars
0.003
0.003
$333.33
Responses
−0.003
negative 0.003
−$333.33
negative 333.33 dollars
0.003
0.003
$333.33
To find the value decrease per month, we divide the total value decrease ($4,000) by the number of months (12).
Value decrease per month = Value decrease / Number of months
Value decrease per month = $4,000 / 12 months
Calculating this gives:
Value decrease per month ≈ $333.33
Therefore, the value decreases by approximately $333.33 per month.
Value decrease per month = Value decrease / Number of months
Value decrease per month = $4,000 / 12 months
Calculating this gives:
Value decrease per month ≈ $333.33
Therefore, the value 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?(1 point)
Responses
0.4 ounces
0.4 ounces
−4 ounces
negative 4 ounces
−0.4 ounces
negative 0.4 ounces
4 ounces
Responses
0.4 ounces
0.4 ounces
−4 ounces
negative 4 ounces
−0.4 ounces
negative 0.4 ounces
4 ounces
To find the amount of water that should change in the canteen every 10 minutes, we divide the recommended water intake per hour (24 ounces) by the number of minutes in an hour (60 minutes) and then multiply it by the number of minutes (10 minutes) in question.
Amount of water change every 10 minutes = (Recommended water intake per hour / Number of minutes in an hour) * Number of minutes
Amount of water change every 10 minutes = (24 ounces / 60 minutes) * 10 minutes
Calculating this gives:
Amount of water change every 10 minutes ≈ 4 ounces
Therefore, the amount of water in the canteen should change by approximately 4 ounces every 10 minutes.
Amount of water change every 10 minutes = (Recommended water intake per hour / Number of minutes in an hour) * Number of minutes
Amount of water change every 10 minutes = (24 ounces / 60 minutes) * 10 minutes
Calculating this gives:
Amount of water change every 10 minutes ≈ 4 ounces
Therefore, the amount of water in the canteen should change by approximately 4 ounces every 10 minutes.
_3 5/9+ 2 -4 1/9
To add the given mixed numbers: -3 5/9, 2, and -4 1/9, we can start by converting them to improper fractions.
-3 5/9 = -32/9
-4 1/9 = -37/9
Now, let's add the fractions:
-32/9 + 2 - 37/9
First, let's add the whole numbers:
2 + 0 = 2
Now, let's add the fractions:
-32/9 - 37/9 = -69/9
So, the sum of -3 5/9, 2, and -4 1/9 is:
2 - 69/9
Now, let's simplify the fraction:
2 - (69/9) = 2 - (23/3) = 2 - 7(2/3) = 2 - 2(2/3) = 1(1/3)
Therefore, the sum is 1 1/3.
-3 5/9 = -32/9
-4 1/9 = -37/9
Now, let's add the fractions:
-32/9 + 2 - 37/9
First, let's add the whole numbers:
2 + 0 = 2
Now, let's add the fractions:
-32/9 - 37/9 = -69/9
So, the sum of -3 5/9, 2, and -4 1/9 is:
2 - 69/9
Now, let's simplify the fraction:
2 - (69/9) = 2 - (23/3) = 2 - 7(2/3) = 2 - 2(2/3) = 1(1/3)
Therefore, the sum is 1 1/3.