Determine the sign of the product of −10.4×−78.2 . Enter + for positive or – for negative.(1 poi
The sign of the product of -10.4 and -78.2 is + (positive).
Multiply −1 1/6 by 7. Write the answer as a mixed number.
To multiply -1 1/6 by 7, we first need to convert -1 1/6 to an improper fraction.
-1 1/6 can be written as -7/6.
Multiplying -7/6 by 7, we get: -7/6 * 7 = -49/6.
To write the answer as a mixed number, we divide the numerator (-49) by the denominator (6).
49 divided by 6 is 8 with a remainder of 1.
So the answer is -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 on the lot that are both gray and electrically powered, we need to multiply the fractions representing the proportion of gray cars and the proportion of electrically powered gray cars.
Given that 2/5 of the cars on the lot are gray and 1/3 of the gray cars are electrically powered, we have:
(2/5) * (1/3) = (2 * 1) / (5 * 3) = 2/15
Therefore, 2/15 of the cars on the lot are both gray and electrically powered.
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
To find out how long it will take for the fish to reach a depth of -37.8 meters, we can set up an equation.
Let t represent the time it takes in minutes.
The initial depth of the fish is -10.8 meters.
The fish descends another 1.5 meters every 2 minutes.
So, the equation can be written as -10.8 + 1.5t = -37.8.
Now we can solve for t.
Subtracting -10.8 from both sides of the equation, we have 1.5t = -37.8 + 10.8.
Simplifying, we get 1.5t = -27.
To isolate t, we divide both sides of the equation by 1.5.
t = -27 / 1.5.
Simplifying further, we have t = -18.
Since time cannot be negative in this context, we disregard the negative sign and consider the magnitude of the time. So, it will take the fish 18 minutes to reach a depth of -37.8 meters.
This means that it will take the fish 18 minutes to descend 37.8 meters below sea level from its initial depth of -10.8 meters.
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), we will apply the rules for multiplying and dividing signed numbers.
First, let's simplify the multiplication:
(-4) × (7/5) × (-3/4) = (-4 × 7 × -3) / (5 × 4)
Multiplying the numerators and denominators, we have:
= 84 / 20
Next, let's simplify the division:
(84 / 20) ÷ (7/15) = (84 / 20) × (15/7)
Multiplying the numerators and denominators, we have:
= (84 × 15) / (20 × 7)
Simplifying further, we get:
= 1260 / 140
Finally, let's simplify the fraction:
= 9
Therefore, (-4)×(7/5)×(-3/4)÷(7/15) equals 9.
ilot 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.