What is the surface area of the right rectangular prism?
1 answer:
<h3>Answer: Choice A) 252 in^2</h3>
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Explanation:
Refer to the diagram below.
The red rectangle is 6 inches by 12 inches, so its area is 6*12 = 72 square inches. There are two of these rectangles (one on top, one on the bottom). That accounts for 2*72 = 144 square inches so far.
The purple rectangles are 3 inches by 12 inches, yielding an area of 3*12 = 36 square inches each. That's another 2*36 = 72 square inches when we account for the front and back purple rectangles.
The green rectangles are 6 inches by 3 inches. Each green rectangle is 6*3 = 18 square inches. Having two of them means we'll add on 2*18 = 36 square inches.
Overall, the entire surface area is the sum of all the areas we calculated: 144+72+36 = 252 square inches, which is choice A
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Alternative Method:
- L = 12 = length
- W = 6 = width
- H = 3 = height
SA = surface area of the rectangular prism
SA = 2*(L*W + L*H + W*H)
SA = 2*(12*6 + 12*3 + 6*3)
SA = 2*(72 + 36 + 18)
SA = 2*(126)
SA = 252 in^2
So we get the same answer either way
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Answer:
The customer can conclude that the company's claim is correct
Step-by-step explanation:
The percentage of lids that has a free yogurt coupon = 20%
The number of cups a loyal customer purchases = 85 yogurt cups
The number of cups that contained a coupon = 12 (14.1%)
The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes
The interval obtained = (0.044, 0.238)
Therefore, the range of proportion within which the true proportion exists is 0.044 < < 0.238
The range of percentage within which the true percentage exist is therefore;
0.044 × 100 = 4.4% < × 100 < 0.238 × 100 = 23.8%
Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.