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lana [24]
3 years ago
11

Math question down below

Mathematics
1 answer:
Kipish [7]3 years ago
3 0
Answer: 6928

----------------------------------------------------------

Explanation: 

We have two areas we need to find: The area of the trapezoid and the area of the rectangle. Let's call these areas A1 and A2.

Area of Trapezoid = (height)*(base1+base2)/2
A1 = h*(b1+b2)/2
A1 = 80*(150+100)/2
A1 = 80*250/2
A1 = 20000
A1 = 10000

Area of Rectangle = (length)*(width)
A2 = L*W
A2 = 48*64
A2 = 3072

Subtract the two areas (A1-A2) to get the difference D
D = A1 - A2
D = 10000 - 3072
D = 6928

This difference D is exactly equal to the shaded area. 


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Two angles, Angle A and Angle B are supplementary to one another. If the measure of B is 30 degrees more than the measure of A,
iVinArrow [24]

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m<A = 75 and m<B = 105.

Step-by-step explanation:

To find the two angles, we first take 180 (because supplementary angles are two angles that add up to 180) and we divide it by 2 to get 90. Then we take 30 degrees and divide that by 2 to get 15. You add 15 degrees to measure B and subtract 15 degrees to measure A. So then you get m<A = 90 - 15 = 75 and m<B = 90 + 15 = 105.

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3 years ago
The gym is 96 feet long 53 feet wide and 30 feet high. A bosketball is 28.5 inches
professor190 [17]

Answer:

21806 basketballs are needed to fill the gym

Step-by-step explanation:

We have to find both volumes in the same units, so I will use feet for the dimensions, the volume will be in cubic feet. Each feet has 12 inches.

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The volume of the gym(rectangular base with height) is given by the multiplication of its dimensions. So

V = 96*53*30 = 152640 cubic inches

Volume of the basketball:

The basketball is an sphere, so its volume is

V = \frac{4\pi r^3}{3}

In which r is the radius, which is half the diameter.

28.5 inches in diameter, so 2.375 feet in diameter, radius of 1.1875 feet. The volume of the basketball is:

V = \frac{4\pi (1.1875)^3}{3} = 7 cubic inches

How many basketballs are needed to fill the gym?

This is given dividing the volume of the gym by the volume of a basketball. So

152640/7 = 21805,7

Rouding up

21806 basketballs are needed to fill the gym

6 0
3 years ago
Write the first five terms of the sequence defined by the explicit formula.
AlexFokin [52]

Answer:

(a) 112, 28, 7, (7/4), (7/16)

Step-by-step explanation:

The sequence is given by the explicit formula

a_{n} = 112 (\frac{1}{4} )^{n-1}

The terms of the sequence are :

a_{1} = 112 (\frac{1}{4} )^{1-1} = 112  (\frac{1}{4} )^{0} =112

a_{2} = 112 (\frac{1}{4} )^{2-1} = 112(\frac{1}{4} ) =28

a_{3} = 112 (\frac{1}{4} )^{3-1} = 112(\frac{1}{4} )^{2} = 7

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a_{5} = 112 (\frac{1}{4} )^{5-1}=112 (\frac{1}{4} )^{4} = \frac{7}{16}

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