Determine the sign of the product of −10.4×−78.2 . Enter + for positive or – for negative
The sign of the product -10.4 × -78.2 is + (positive).
Multiply 82×(−13)
The product of 82 × (-13) is -1,066.
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 -(6/6 + 1/6), which simplifies to -7/6.
Now, we can multiply -7/6 by 7:
-7/6 × 7 = -49/6
To write this as a mixed number, we divide the numerator (-49) by the denominator (6):
-49 ÷ 6 = -8 remainder 1
Therefore, 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 the cars on the lot that are both gray and electrically powered, we multiply the fractions for each condition.
The fraction of cars that are gray is 2/5, and 1/3 of those gray cars are electrically powered.
Therefore, the fraction of cars that are both gray and electrically powered is:
(2/5) × (1/3) = 2/15
So, 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.)
To find the elevation at the bottom 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 = 70 feet
The elevation at the bottom of Lake Segundo is -70 feet, as it is below sea level.
Divide −72 by −4 . Then divide the quotient by −9 . What is th
To divide -72 by -4, we get:
-72 ÷ -4 = 18
Now, we divide the quotient 18 by -9:
18 ÷ -9 = -2
Therefore, the final quotient is -2.
What is the quotient of 100÷(−10)÷5?
To find the quotient of 100 ÷ (-10) ÷ 5, we perform the divisions in order:
First, we have 100 ÷ (-10) = -10.
Then, we have -10 ÷ 5 = -2.
Therefore, the quotient of 100 ÷ (-10) ÷ 5 is -2.
What is the quotient of 842.4 ÷ −0.6?
To find the quotient of 842.4 ÷ -0.6, we perform the division:
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
To convert 4.65 to a fraction, we can take advantage of the fact that the decimal part (0.65) can be expressed as a fraction by putting it over 100.
So, 0.65 can be written as 65/100.
Now, we can simplify this fraction by dividing the numerator and denominator by the greatest common divisor, which is 5:
65 ÷ 5 = 13
100 ÷ 5 = 20
Therefore, 4.65 as a fraction in simplest form is 465/100.
Use long division to convert 2 7/16 to a decimal.
To convert 2 7/16 to a decimal using long division, we write it as a fraction:
2 7/16 = (2 × 16 + 7) / 16 = 39/16
Now, let's perform long division:
2.4375
--------------
16 | 39.0000
-32
-----
70
-64
----
60
-48
----
120
-112
-----
80
The quotient is 2.4375.
Therefore, 2 7/16 as a decimal is approximately 2.4375.
Use long division to convert 6 7/15 to a decimal
To convert 6 7/15 to a decimal using long division, we write it as a fraction:
6 7/15 = (6 × 15 + 7) / 15 = 97/15
Now, let's perform long division:
6.46666667
--------------
15 | 97.0000000
-90
------
70
-60
-----
100
-90
-----
100
-90
-----
100
The quotient is 6.46666667 (rounded to eight decimal places).
Therefore, 6 7/15 as a decimal is approximately 6.46666667.
Use long division to convert 6715 to a decimal.(1 point)
Responses
6.715
6.715
≈6.47
≈0.46
≈6.14285
To convert 6715 to a decimal using long division:
671.5
-----------------
1 | 6715.0000
- 1
--------
51
- 50
------
10
- 10
------
0
The quotient is 671.5.
Therefore, 6715 as a decimal is 671.5.
Use long division to convert 6 7/15 to a decimal.(1 point)
Responses
6.715
6.715
≈6.47
≈0.46
≈6.14285
To convert 6 7/15 to a decimal using long division:
6.46666667
---------------
15 | 97.0000000
- 90
------
70
- 60
-----
100
- 90
-----
100
- 90
-----
100
- 90
-----
100
- 90
-----
100
- 90
-----
100
- 90
-----
100
The quotient is 6.46666667 (rounded to eight decimal places).
Therefore, 6 7/15 as a decimal is approximately 6.46666667.
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
To calculate the rate of change in the plane's altitude, we divide the change in altitude (4,000 feet) by the time taken (3.5 minutes):
Rate of change = Change in altitude / Time
Rate of change = 4,000 feet / 3.5 minutes
Rate of change ≈ 1,142.86 feet per minute
Therefore, the quotient that best represents the rate of change in the plane's altitude to the nearest hundredth is approximately 1,142.86 feet per 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

50
15
−15
−50
To calculate the change in the amount of water in gallons per minute, we divide the change in gallons (250 gallons) by the time taken (5 minutes):
Change in amount of water = Change in gallons / Time
Change in amount of water = 250 gallons / 5 minutes
Change in amount of water = 50 gallons per minute
Therefore, the change in the amount of water in gallons per 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 1/5)
First, let's simplify the given expression step by step using the properties of operations and rules for multiplying and dividing signed numbers:
(−4) × (7/5) × (−3/4) ÷ (7 1/5)
Start by simplifying the fractions:
(-4) × (7/5) × (-3/4) ÷ ((7 × 5 + 1)/5)
Next, multiply and divide:
(-4) × (7/5) × (-3/4) ÷ (36/5)
Simplify the multiplication:
(-4) × (-3) × 7 ÷ (5 × 4 × 5)
Now, calculate each operation:
(12) × (7) ÷ (100)
Multiply:
84 ÷ 100
Simplify:
0.84
Therefore, (-4) × (7/5) × (-3/4) ÷ (7 1/5) simplifies to 0.84.
−9
9

147/75

−147/75
Apologies, there seems to be an error in the simplification. Let's re-evaluate the expression:
(-4) × (7/5) × (-3/4) ÷ (7 1/5)
Start by simplifying the fractions:
(-4) × (7/5) × (-3/4) ÷ ((7 × 5 + 1)/5)
Next, multiply and divide:
(-4) × (7/5) × (-3/4) ÷ (36/5)
Simplify the multiplication:
(-4) × (-3) × 7 ÷ (5 × 4)
Now, calculate each operation:
12 × 7 ÷ 20
Multiply:
84 ÷ 20
Reduce the fraction:
21/5
Therefore, (-4) × (7/5) × (-3/4) ÷ (7 1/5) simplifies to 21/5.
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 can set up an equation to represent the situation.
Let's denote the time it takes for the fish to descend as "t" in minutes.
The initial depth of the fish is -10.8 meters, and every 2 minutes it descends 1.5 meters, so the equation becomes:
-10.8 + 1.5t = -37.8
To isolate "t", we subtract -10.8 from both sides:
1.5t = -37.8 - (-10.8)
1.5t = -27
Next, we divide both sides by 1.5 to solve for "t":
t = -27 / 1.5
t = -18
The fish will take 18 minutes to reach a depth of -37.8 meters.
This means that after 18 minutes, the fish will be 37.8 meters below sea level.
Mr. Imani wants to purchase paper and notebooks for his classroom. At Dollar Discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. This is modeled by 1.25p + 2.50n. Evaluate for p = 10 and n=30 to find how much it will cost Mr. Imani to purchase 10 packs of paper and 30 notebooks. (1 point)
To evaluate the cost for Mr. Imani to purchase 10 packs of paper and 30 notebooks, we substitute p = 10 and n = 30 into the expression 1.25p + 2.50n:
1.25(10) + 2.50(30)
Simplifying the expression:
12.50 + 75
Adding the numbers:
87.50
Therefore, it will cost Mr. Imani $87.50 to purchase 10 packs of paper and 30 notebooks.
The formula for finding the volume of a square prism is s2h, where s is the length of each side of the square base and h is the height of the prism. Evaluate to find the volume given values of s = 4 and h = 6.(1 point)
To evaluate the volume of a square prism with s = 4 and h = 6 using the formula s^2h, we substitute these values into the formula:
Volume = s^2h = 4^2 * 6 = 16 * 6 = 96
Therefore, the volume of the square prism with s = 4 and h = 6 is 96 cubic units.
Each month Ms. Tanaka is paid a base salary of $2,500 in addition to $100 for each television that she sells. This is modeled by 2,500 + 100t, where t represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.(1 point)
Responses
To evaluate how much Ms. Tanaka will earn for selling 12 televisions this month, we substitute t = 12 into the expression 2,500 + 100t:
2,500 + 100(12)
Simplifying the expression:
2,500 + 1,200
Adding the numbers:
3,700
Therefore, Ms. Tanaka will earn $3,700 for selling 12 televisions this month.
represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.(1 point)
Responses
To find out how much Ms. Tanaka will earn for selling 12 televisions this month, we substitute t = 12 into the expression 2,500 + 100t:
2,500 + 100(12)
Simplifying the expression:
2,500 + 1,200
Adding the numbers:
3,700
Therefore, Ms. Tanaka will earn $3,700 for selling 12 televisions this month.
Robert is preparing a poster-board presentation. He wants to make a decorative pattern with 10 squares to fill part of the poster. The area of the poster board is 720 square inches. To find how much space Robert will have left for his presentation if he uses squares with 7-inch sides, evaluate 720 − 10s2 when s = 7 .(1 point)
To find out how much space Robert will have left for his presentation if he uses squares with 7-inch sides, we substitute s = 7 into the expression 720 - 10s^2:
720 - 10(7^2)
Simplifying the expression:
720 - 10(49)
Calculating the exponent:
720 - 10 * 49
Multiplying:
720 - 490
Subtracting:
230
Therefore, if Robert uses squares with 7-inch sides, he will have 230 square inches of space left for his presentation on the poster board.
Mr. Rodriguez has a vegetable garden that borders his house. He wants to put a fence around it. It costs $7 per yard for the materials. Evaluate 7(l + 2w) , where l is the length and w is the width of his garden, to find the cost for a garden that has a length of 5 yards and a width of 2 yards.(1 point)
To find the cost for a garden that has a length of 5 yards and a width of 2 yards, we substitute l = 5 and w = 2 into the expression 7(l + 2w):
7(5 + 2*2)
Simplifying the expression:
7(5 + 4)
7(9)
Calculating:
63
Therefore, the cost for a garden with a length of 5 yards and a width of 2 yards is $63.
Simplify 4x + 8x using the properties of operations.(1 point)
To simplify 4x + 8x, we can combine the like terms, which have the same variable (x):
4x + 8x = (4 + 8) x
Simplifying the addition:
12x
Therefore, the simplified form of 4x + 8x is 12x.
Simplify 9g−7h−6g + 2h
To simplify 9g - 7h - 6g + 2h, we can combine the like terms:
9g - 6g - 7h + 2h
Simplifying the subtraction and addition:
(9g - 6g) + (-7h + 2h)
3g - 5h
Therefore, the simplified form of 9g - 7h - 6g + 2h is 3g - 5h.