Determine the sign of the product of −10.4×−78.2 . Enter + for positive or – for negative.(1 point)
29 answers
The product of −10.4×−78.2 is positive, so the sign is +.
Multiply 82×(−13).(1 point)
82×(−13)=-1066
Multiply −116 by 7. Write the answer as a mixed number.(1
−116 multiplied by 7 is equal to −812.
To write the answer as a mixed number, we divide −812 by 7:
−812 ÷ 7 = −116 remainder 4
Therefore, the answer is −116 4/7.
To write the answer as a mixed number, we divide −812 by 7:
−812 ÷ 7 = −116 remainder 4
Therefore, the answer is −116 4/7.
Of the cars in a used-car lot, 25 are the color gray. 13 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.(1 point)
To find the fraction of cars that are both gray and electrically powered, we need to divide the number of cars that are both gray and electrically powered by the total number of cars on the lot.
The number of cars that are both gray and electrically powered is 13.
The total number of cars on the lot is 25.
Therefore, the fraction of cars that are both gray and electrically powered is 13/25.
The number of cars that are both gray and electrically powered is 13.
The total number of cars on the lot is 25.
Therefore, the fraction of cars that are both gray and electrically powered is 13/25.
Lake Profondo has a depth of 84 feet. Lake Segundo is 56 as deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)(1 point)
To find the elevation at the bottom of Lake Segundo, we need to subtract the depth of Lake Segundo from sea level.
Sea level is typically considered to be 0 feet.
So, the elevation at the bottom of Lake Segundo is:
0 feet - 56 feet = -56 feet.
Therefore, the elevation at the bottom of Lake Segundo is -56 feet below sea level.
Sea level is typically considered to be 0 feet.
So, the elevation at the bottom of Lake Segundo is:
0 feet - 56 feet = -56 feet.
Therefore, the elevation at the bottom of Lake Segundo is -56 feet below sea level.
Divide −72 by −4. Then divide the quotient by −9. What is the final quotient? (1 point)
Dividing -72 by -4 results in a quotient of 18.
Dividing the quotient of 18 by -9 results in a final quotient of -2.
Therefore, the final quotient is -2.
Dividing the quotient of 18 by -9 results in a final quotient of -2.
Therefore, the final quotient is -2.
What is the quotient of 100÷(−10)÷5?(1 point)
Responses
−50
negative 50
−2
negative 2
−200
negative 200
2
Responses
−50
negative 50
−2
negative 2
−200
negative 200
2
The quotient of 100 ÷ (−10) ÷ 5 is -2 or negative 2.
What is the quotient of 842.4 ÷ −0.6?(1 point)
Responses
1,404
1,404
−1,404
negative 1,404
−14.04
negative 14.04
−140.4
Responses
1,404
1,404
−1,404
negative 1,404
−14.04
negative 14.04
−140.4
The quotient of 842.4 ÷ −0.6 is -1,404 or negative 1,404.
What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)
Responses
465
4 Start Fraction 6 over 5 End Fraction
465
Start Fraction 4 over 65 End Fraction
465100
4 Start Fraction 65 over 100 End Fraction
41320
Responses
465
4 Start Fraction 6 over 5 End Fraction
465
Start Fraction 4 over 65 End Fraction
465100
4 Start Fraction 65 over 100 End Fraction
41320
To convert 4.65 to a fraction, we can write 4.65 as a fraction over 1.
4.65 = 4.65/1
To simplify this fraction, we need to get rid of the decimal.
Multiplying both the numerator and denominator by 100, we get:
4.65/1 * 100/100 = 465/100
The fraction 465/100 is already simplified, so the answer is:
Start Fraction 465 over 100 End Fraction
4.65 = 4.65/1
To simplify this fraction, we need to get rid of the decimal.
Multiplying both the numerator and denominator by 100, we get:
4.65/1 * 100/100 = 465/100
The fraction 465/100 is already simplified, so the answer is:
Start Fraction 465 over 100 End Fraction
Use long division to convert 2716 to a decimal.(1 point)
Responses
2.716
2.716
2.2857
2.2857
2.4375
2.4375
0.4375
Responses
2.716
2.716
2.2857
2.2857
2.4375
2.4375
0.4375
To convert 2716 to a decimal using long division:
2716
____________
4 | 2716.000
We start by dividing 4 into 27, which gives us 6 as the quotient:
2716
--> 24
------
7
Next, we bring down the next digit (1) and divide 4 into 71, which gives us 17 as the next digit of the quotient:
2716
--> 248
--------
71
- 68
--------
3
We bring down the next digit (6) and divide 4 into 36, which gives us 9 as the next digit of the quotient:
2716
--> 2486
--------
719
- 716
--------
33
Finally, we bring down the last digit (6) and divide 4 into 336, which gives us 84 as the next digit of the quotient:
2716
--> 24864
--------
7196
- 7160
---------
336
- 336
---------
0
Since there is no remainder and the process has ended, the quotient is the decimal representation of 2716.
Therefore, the decimal representation of 2716 is 2.716.
2716
____________
4 | 2716.000
We start by dividing 4 into 27, which gives us 6 as the quotient:
2716
--> 24
------
7
Next, we bring down the next digit (1) and divide 4 into 71, which gives us 17 as the next digit of the quotient:
2716
--> 248
--------
71
- 68
--------
3
We bring down the next digit (6) and divide 4 into 36, which gives us 9 as the next digit of the quotient:
2716
--> 2486
--------
719
- 716
--------
33
Finally, we bring down the last digit (6) and divide 4 into 336, which gives us 84 as the next digit of the quotient:
2716
--> 24864
--------
7196
- 7160
---------
336
- 336
---------
0
Since there is no remainder and the process has ended, the quotient is the decimal representation of 2716.
Therefore, the decimal representation of 2716 is 2.716.
Use long division to convert 6715 to a decimal.(1 point)
Responses
6.715
6.715
≈6.14285
approximately equals 6.14285
≈6.47
approximately equals 6.47
≈0.46
Responses
6.715
6.715
≈6.14285
approximately equals 6.14285
≈6.47
approximately equals 6.47
≈0.46
I apologize for the confusion, but it seems there has been an error in the responses provided.
To convert 6715 to a decimal using long division:
6715
____________
1 | 6715.000
We start by dividing 1 into 6, which gives us 6 as the quotient:
6715
--> 6
------
1
Next, we bring down the next digit (7) and divide 1 into 17, which gives us 17 as the next digit of the quotient:
6715
--> 67
------
17
- 17
--------
0
Finally, we bring down the last digit (5), but since it is 0, the division process ends.
Since there is no remainder and the process has ended, the quotient is the decimal representation of 6715.
Therefore, the decimal representation of 6715 is 6,715.
To convert 6715 to a decimal using long division:
6715
____________
1 | 6715.000
We start by dividing 1 into 6, which gives us 6 as the quotient:
6715
--> 6
------
1
Next, we bring down the next digit (7) and divide 1 into 17, which gives us 17 as the next digit of the quotient:
6715
--> 67
------
17
- 17
--------
0
Finally, we bring down the last digit (5), but since it is 0, the division process ends.
Since there is no remainder and the process has ended, the quotient is the decimal representation of 6715.
Therefore, the decimal representation of 6715 is 6,715.
A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth, and remember the plane is descending.(1 point)
The quotient that best represents the rate of change in the plane’s altitude is
feet/minute.
The quotient that best represents the rate of change in the plane’s altitude is
feet/minute.
To find the rate of change in the plane's altitude, we need to divide the change in altitude by the time taken.
The change in altitude is 4,000 feet (since the pilot decided to fly 4,000 feet lower).
The time taken is 3.5 minutes.
To find the rate of change, we divide the change in altitude by the time taken:
Rate of change = Change in altitude / Time taken = 4,000 feet / 3.5 minutes
Calculating this, the rate of change in the plane's altitude is approximately 1142.86 feet/minute (rounded to the nearest hundredth).
Therefore, the quotient that best represents the rate of change in the plane's altitude is 1142.86 feet/minute.
The change in altitude is 4,000 feet (since the pilot decided to fly 4,000 feet lower).
The time taken is 3.5 minutes.
To find the rate of change, we divide the change in altitude by the time taken:
Rate of change = Change in altitude / Time taken = 4,000 feet / 3.5 minutes
Calculating this, the rate of change in the plane's altitude is approximately 1142.86 feet/minute (rounded to the nearest hundredth).
Therefore, the quotient that best represents the rate of change in the plane's altitude is 1142.86 feet/minute.
A fire engine’s water tank holds 750 gallons of water. If the pump removes 250 gallons of water in 5 minutes, what is the change in the amount of water in gallons in 1 minute?(1 point)
Responses
−15
negative 15
50
50
15
15
−50
Responses
−15
negative 15
50
50
15
15
−50
To find the change in the amount of water in gallons in 1 minute, we need to divide the change in water (250 gallons) by the time taken (5 minutes).
The change in water is 250 gallons.
The time taken is 5 minutes.
To find the change in the amount of water in 1 minute, we divide the change in water by the time taken:
Change in water per minute = Change in water / Time taken = 250 gallons / 5 minutes
Calculating this, the change in the amount of water in 1 minute is 50 gallons.
Therefore, the correct response is 50 gallons.
The change in water is 250 gallons.
The time taken is 5 minutes.
To find the change in the amount of water in 1 minute, we divide the change in water by the time taken:
Change in water per minute = Change in water / Time taken = 250 gallons / 5 minutes
Calculating this, the change in the amount of water in 1 minute is 50 gallons.
Therefore, the correct response is 50 gallons.
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(75)×(−34)÷(715)
(1 point)
Responses
−9
negative 9
9
9
14775
Start Fraction 147 over 75 End Fraction
−14775
(−4)×(75)×(−34)÷(715)
(1 point)
Responses
−9
negative 9
9
9
14775
Start Fraction 147 over 75 End Fraction
−14775
To solve the expression (-4) × (75) × (-34) ÷ (715), we can perform the operations step by step:
First, we multiply -4 and 75: (-4) × (75) = -300.
Next, we multiply -300 and -34: -300 × (-34) = 10200.
Finally, we divide 10200 by 715: 10200 ÷ 715 = 14.25.
Since the original expression involves negative numbers, the final result is negative.
Therefore, the correct response is -14.25.
First, we multiply -4 and 75: (-4) × (75) = -300.
Next, we multiply -300 and -34: -300 × (-34) = 10200.
Finally, we divide 10200 by 715: 10200 ÷ 715 = 14.25.
Since the original expression involves negative numbers, the final result is negative.
Therefore, the correct response is -14.25.
Solve the following word problem. A fish is swimming at −10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of −37.8 meters? Show your work and write a sentence to explain what your answer means.(4 points)
To find out how long it will take for the fish to reach a depth of -37.8 meters, we need to calculate the number of 2-minute intervals needed for the fish to descend from -10.8 meters to -37.8 meters.
The difference in depth from the starting depth to the target depth is calculated as:
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
Next, we need to calculate the number of 2-minute intervals needed to descend 27 meters, with the fish descending 1.5 meters every 2 minutes:
27 meters ÷ 1.5 meters = 18
Therefore, it will take the fish 18 intervals of 2 minutes each to reach a depth of -37.8 meters.
In total, the fish will take 18 x 2 = 36 minutes to reach the depth of -37.8 meters.
This means that after 36 minutes of descending at a rate of 1.5 meters every 2 minutes, the fish will reach a depth of -37.8 meters.
The difference in depth from the starting depth to the target depth is calculated as:
-37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
Next, we need to calculate the number of 2-minute intervals needed to descend 27 meters, with the fish descending 1.5 meters every 2 minutes:
27 meters ÷ 1.5 meters = 18
Therefore, it will take the fish 18 intervals of 2 minutes each to reach a depth of -37.8 meters.
In total, the fish will take 18 x 2 = 36 minutes to reach the depth of -37.8 meters.
This means that after 36 minutes of descending at a rate of 1.5 meters every 2 minutes, the fish will reach a depth of -37.8 meters.