Multiply −1 1/6 by 7. Write the answer as a mixed number.(1 point)
To multiply -1 1/6 by 7, first convert -1 1/6 to an improper fraction.
-1 1/6 = -(6/6 + 1/6) = -7/6
Then, multiply -7/6 by 7:
-7/6 * 7 = -49/6
Now, convert -49/6 back to a mixed number:
-49/6 = -8 1/6
Of the cars in a used-car lot, 2/5 are the color gray. 1/3 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 find the product of the two fractions.
The fraction of cars that are gray is 2/5, and the fraction of gray cars that are electrically powered is 1/3.
Multiplying these fractions, we get:
2/5 * 1/3 = 2/15
Therefore, 2/15 of the cars on the lot are both gray and electrically powered.
Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 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 depth of Lake Segundo, which is 5/6 as deep as Lake Profondo, we need to multiply the depth of Lake Profondo by 5/6.
84 feet * 5/6 = (84 * 5)/(6) = 420/6 = 70
Therefore, Lake Segundo has a depth of 70 feet.
Since the elevation at the bottom of Lake Profondo is below sea level, we can infer that the elevation at the bottom of Lake Segundo would also be below sea level.
Divide −72 by −4. Then divide the quotient by −9. What is the final quotient? (1 point)
The division of -72 by -4 is:
-72 ÷ -4 = 18
Then, if we divide the quotient 18 by -9, the final quotient is:
18 ÷ -9 = -2
Therefore, the final quotient is -2.
What is the quotient of 100÷(−10)÷5?(1 point)
To solve this expression, we need to perform the division in the given order: 100 ÷ (-10) ÷ 5.
First, divide 100 by -10:
100 ÷ (-10) = -10
Then, divide the result (-10) by 5:
-10 ÷ 5 = -2
Therefore, the quotient of 100 ÷ (-10) ÷ 5 is -2.
What is the quotient of 842.4 ÷ −0.6?(1 point)
Responses
To find the quotient of 842.4 ÷ -0.6, we can divide 842.4 by -0.6:
842.4 ÷ -0.6 = -1404
Therefore, the quotient is -1404.
What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)
Responses
To convert 4.65 to a fraction, we can write it as a fraction with the decimal part as the numerator and the place value of the decimal part as the denominator.
In this case, the decimal part of 4.65 is 0.65. The decimal has 2 decimal places, so the denominator should be 10^2, which is 100.
Therefore, 4.65 as a fraction is:
4.65 = 465/100
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5:
465/100 = (465 ÷ 5) / (100 ÷ 5) = 93/20
Therefore, 4.65 as a fraction in simplest form is 93/20.
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)
To determine the rate of change in the plane's altitude, we need to divide the change in altitude (4,000 feet) by the time it takes to make the adjustment (3.5 minutes).
The quotient is given by:
Rate of change = Change in altitude / Time
Plugging in the values:
Rate of change = 4,000 feet / 3.5 minutes
Calculating this, we find:
Rate of change ≈ 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 1 minute, we can divide the change in water (250 gallons) by the time it takes to remove the water (5 minutes).
The quotient is given by:
Change in water per minute = Change in water / Time
Plugging in the values:
Change in water per minute = 250 gallons / 5 minutes
Calculating this, we find:
Change in water per minute = 50 gallons/minute
Therefore, the change in the amount of water in 1 minute is 50 gallons.