What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 p
4.65 can be written as 465/100. By simplifying the fraction, we divide the numerator and denominator by their greatest common divisor, which is 5.
465 ÷ 5 = 93
100 ÷ 5 = 20
Therefore, 4.65 as a fraction in simplest form is 93/20.
can u put the remender by it
When converting 4.65 to a fraction and including the remainder, we can write it as a mixed number.
To convert the decimal part 0.65 to a fraction, we observe that there are two decimal places, so we can write it as 65/100.
Now, we add the whole number part (4) to the fraction part:
4 + 65/100 = 4 65/100
To simplify this mixed number, we divide both the numerator (65) and the denominator (100) by their greatest common divisor, which is 5.
65 ÷ 5 = 13
100 ÷ 5 = 20
Therefore, 4.65 as a mixed number in simplest form is 4 13/20.
Use long division to convert 2716 to a decimal.(1 point)
Responses
2.2857
2.2857
0.4375
0.4375
2.4375
2.4375
2.716
2.716
To convert 2716 to a decimal using long division, we divide 2716 by 1000 (since there are 3 digits after the decimal point) as follows:
2.716
_______________
1000 | 2716.000
-2000
______
716.000
- 700
______
16.000
- 0
______
Therefore, 2716 as a decimal is 2.716.
Use long division to convert 6715 to a decimal.(1 point)
Responses
6.715
6.715
≈6.47
approximately equals 6.47
≈0.46
approximately equals 0.46
≈6.14285
approximately equals 6.14285
To convert 6715 to a decimal using long division, we divide 6715 by 1000 (since there are 3 digits after the decimal point) as follows:
6.715
_______________
1000 | 6715.000
-6000
______
715.000
- 700
______
15.000
- 0
______
Therefore, 6715 as a decimal 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.
To find the rate of change in the plane's altitude, we divide the change in altitude (4,000 feet) by the time it took to make the adjustment (3.5 minutes):
Rate of change = Change in altitude / Time taken
Rate of change = 4000 feet / 3.5 minutes
Calculating this quotient gives us approximately 1142.86 feet/minute.
Rounded to the nearest hundredth, 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
15
−50
negative 50
50
50
−15
To find the change in the amount of water in gallons in 1 minute, we need to calculate the rate of water being pumped out per minute.
We divide the amount of water being removed (250 gallons) by the time it takes to remove it (5 minutes):
Rate of water removal per minute = Amount of water removed / Time taken
Rate of water removal per minute = 250 gallons / 5 minutes
Calculating this quotient gives us 50 gallons per minute.
Therefore, the change in the amount of water in gallons in 1 minute 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
9
−9
negative 9
−14775
negative Start Fraction 147 over 75 End Fraction
14775
Start Fraction 147 over 75 End Fraction
To solve the expression (-4) × (75) × (-34) ÷ (715), we can follow the order of operations, which is parentheses, multiplication and division from left to right.
First, let's evaluate the multiplication:
(-4) × (75) = -300
Next, we multiply the result by (-34):
-300 × (-34) = 10,200
Finally, we divide the result by (715):
10,200 ÷ 715 = 14.265
Rounding the answer to the nearest hundredth, we get approximately 14.27.
Therefore, the solution is approximately 14.27.
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 solve the problem, we need to find the time it takes for the fish to reach a depth of -37.8 meters from its initial depth of -10.8 meters, descending at a rate of 1.5 meters every 2 minutes.
Let's calculate the change in depth:
Change in depth = Final depth - Initial depth
Change in depth = -37.8 meters - (-10.8 meters)
Change in depth = -37.8 meters + 10.8 meters
Change in depth = -27 meters
Now, we need to find how many times the fish descends 1.5 meters in order to reach a depth of 27 meters. We can set up the following equation:
1.5 meters/2 minutes = -27 meters/x minutes
Cross-multiplying, we get:
1.5 * x = -27 * 2
1.5x = -54
x = -54/1.5
x = -36
Therefore, it will take the fish 36 minutes to reach a 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.
can u make the answer shorter pls
The fish will take 36 minutes to reach a depth of -37.8 meters.
can u add a little bit of how u solved it
Certainly! Here is a slightly expanded explanation of how the problem was solved:
To find the time it takes for the fish to reach a depth of -37.8 meters, we first calculate the change in depth by finding the difference between the final depth (-37.8 meters) and the initial depth (-10.8 meters). This gives us a change in depth of -27 meters.
Next, we set up an equation using the rate of descent, which is 1.5 meters every 2 minutes. We know that in x minutes, the fish descends a total of -27 meters. Setting up the equation using the ratio of descent per minute, 1.5 meters/2 minutes = -27 meters/x minutes, allows us to solve for x.
By cross-multiplying, we get 1.5 * x = -27 * 2. Simplifying this equation, we have 1.5x = -54. Dividing both sides of the equation by 1.5, we get x = -36.
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.