Use long division to convert 6715 to a decimal.(1 point)
To convert 6715 to a decimal using long division, divide 6715 by 100.
67.15
-------
100 | 6715
6700
----
15
The remainder is 15. Since there are no more decimal places to add, the decimal representation of 6715 is 67.15.
Use long division to convert 6 7/15 to a decimal.(1 point)
To convert 6 7/15 to a decimal using long division, follow these steps:
1. Convert the mixed number to an improper fraction:
6 7/15 = (6 * 15 + 7) / 15 = 97/15
2. Perform long division by dividing 97 by 15:
6.466666...
The remainder is 2.
Since the decimal places don't repeat, the decimal representation of 6 7/15 is 6.466666... (or rounded to a certain decimal place if desired).
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 quotient that represents the rate of change in the plane's altitude, divide the change in altitude (4,000 feet) by the time it took for the adjustment (3.5 minutes):
4000 feet ÷ 3.5 minutes ≈ 1142.86 feet/minute
Rounded to the nearest hundredth, the rate of change in the plane's altitude is approximately 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)
To find the change in the amount of water in one minute, divide the change in the amount of water (250 gallons) by the time taken (5 minutes):
250 gallons ÷ 5 minutes = 50 gallons/minute
Therefore, the change in the amount of water in 1 minute is 50 gallons.
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(7/5)×(−3/4)÷(7/15)
To solve the expression (−4) × (7/5) × (−3/4) ÷ (7/15), let's break it down step by step.
Step 1: Multiply the numbers together:
(−4) × (7/5) × (−3/4) ÷ (7/15)
= ((−4) × 7 × (−3)) / (5 × 4 × (7/15))
= 84 / 20
Step 2: Simplify the fraction:
84 / 20 = 21 / 5
Therefore, the simplified value of the expression is 21/5.
Don't simplify it.
Apologies for the confusion. Let's solve the expression without simplifying it.
(−4) × (7/5) × (−3/4) ÷ (7/15)
To solve this expression, we will follow the order of operations (PEMDAS/BODMAS).
Step 1: Multiply the numbers together:
(−4) × (7/5) × (−3/4) ÷ (7/15)
= (−4) × (7) × (−3) ÷ (5) × (4) × (7/15)
= -4 × 7 × -3 ÷ 5 × 4 × 7/15
Step 2: Apply the properties of multiplication and division:
-4 × 7 = -28
-3 ÷ 5 = -3/5
4 × 7 = 28
Therefore, the expression simplifies to:
-28 × (-3/5) × 28 / (15)
= (-28 × -3 × 28) / (5 × 15)
= (2352) / (75)
So, the expression (-4) × (7/5) × (−3/4) ÷ (7/15) simplifies to 2352/75.
What's that as a whole number?
To express 2352/75 as a whole number, we need to perform the division 2352 divided by 75:
2352 ÷ 75 = 31.36
Therefore, 2352/75 as a whole number is 31.
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 this word problem, we need to find out how many 2-minute intervals it will take for the fish to reach a depth of -37.8 meters, starting from a depth of -10.8 meters and descending at a rate of 1.5 meters every 2 minutes.
Let's calculate the difference in depth between the starting depth and the target depth:
-37.8 meters - (-10.8 meters) = -27 meters
Next, we need to divide the difference in depth by the rate of descent per 2 minutes:
-27 meters ÷ 1.5 meters = -18
It will take the fish 18 intervals of 2 minutes each to reach a depth of -37.8 meters.
To write a sentence explaining the answer:
"The fish will take 36 minutes to descend from a depth of -10.8 meters to a depth of -37.8 meters, with each interval being 2 minutes."