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Alex73 [517]
3 years ago
8

The recycling bin in the shape of a rectangular prism is 15.5 inches long, 8 inches wide and 7 inches high. The recycling bins n

eed to be emptied when it is 80% full. What is the total amount needed, to the nearest cubic inch, before the recycle bin is ready to empty?
Mathematics
1 answer:
Viktor [21]3 years ago
3 0

Answer:

694 cubic inches

Step-by-step explanation:

Dimension of prism

Length = 15.5 inches

width =  8 inches

height =  7 inches

Volume of regular prism is given  by area of base * height

area of base  = length * width ( as bin is rectangular)

area of base  = 15.5 * 8 square inches = 124 square inches

Volume of regular prism = area of base * height

      = 124 * 7 cubic inches = 868 cubic inches

_________________________________________________

868 cubic inches is the full capacity of the recycling bin

it is given that recycling bins need to be emptied when it is 80% full

so we need to find the 80% capacity of recycling bin

80% capacity of recycling bin = 80/100 *  full capacity of the recycling bin

                  = 0.8 * 868 cubic inches = 694.4 cubic inches

694.4 cubic inches is the amount needed before the recycle bin is ready to empty .

But question says answer should in nearest cubic inch

hence answer is 694 cubic inches

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Step-by-step explanation:

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Scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9
SVETLANKA909090 [29]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $ \pm $ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $ \frac{68}{100} \times 1200 $

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $ \pm $ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $ \frac{95}{2} \% $ of the values.

Therefore, Scores between 72 and 90 = $ \frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200  $

$ \implies 95 \times 12 $ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $ \frac{2.5}{100} \times 1200 $

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

8 0
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Answer:

Step-by-step explanation:

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If the length of a bridge on a map is 1.5 cm,then the actual length= 1.5 * 40000

= 60000.0 = 60,000 m

3 0
3 years ago
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