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Gekata [30.6K]
3 years ago
11

Eli made a wooden box in the shape of a rectangular prism. The box has a length of 5 inches, a width of 3 1/2 inches, and a heig

ht of 7 inches.
Part A. Eli wants to paint the entire box green and give the box to his dad as a gift. What is the total area that he will paint? Explain how you found your answer.
Part B. Can the box hold 22 cubic inches of packing peanuts? Explain how you know.
Mathematics
1 answer:
levacccp [35]3 years ago
4 0

Answer:

Total surface area = 154 in²

Step-by-step explanation:

The prism has a total of 6 surfaces:  top and bottom, 2 sides, and 2 ends.

We have to find the area of each top, side, end, and then add these together, and then multiply the result by 2 to finish the job.

Area of top:  (5 in)(3.5 in) = 17.5 in²

Area of side:  (5 in)(7 in) = 35 in²

Area of end:  (3.5 in)(7 in) = 24.5 in²

Now add these three results together and multiply the sum by 2:

2( 17.5 in² + 35 in² + 24.5 in²) = total surface area = 154 in²

To answer the other part of this question:  find the volume of this prism:

V = length · width · ht = (5 in)(3.5 in)(7 in) = 122 in³.  

Yes, this box can definitely hold 22 in³ of packing peanuts.

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The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that
tekilochka [14]

Answer:

a) P(X∩Y) = 0.2

b) P_1 = 0.16

c) P = 0.47

Step-by-step explanation:

Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.

So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67

Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:

P(X∩Y) = P(X) + P(Y) - P(X∪Y)

P(X∩Y) = 0.36 + 0.51 - 0.67

P(X∩Y) = 0.2

On the other hand, the probability P_1 that he must stop at the first signal but not at the second one can be calculated as:

P_1 = P(X) - P(X∩Y)

P_1 = 0.36 - 0.2 = 0.16

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P_2 = 0.51 - 0.2 = 0.31

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