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grandymaker [24]
3 years ago
6

Find the surface area of the equilateral triangular pyramid.

Mathematics
1 answer:
Alenkinab [10]3 years ago
8 0
We know that
[surface area of the triangular pyramid]=area of the base+3*[area of lateral triangles]
area of the base=12*8/2-----> 48 cm²

area of one lateral triangle=12*10/2-----> 60 cm²
[surface area of the triangular pyramid]=48+3*[60]-----> 228 cm²

the answer is the option 
<span>B) 228 cm2</span>
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How many subsets of {1, 2, 3, 4, 6, 8, 10, 15} are there for which the sum of the elements is 15?
stepladder [879]

Answer:

512

Step-by-step explanation:

Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7

.

For instance, if I divide the set into parts {1,2,4}

and {3,5}, the first part adds up to 7, and its complement adds up to 8

.

Once one makes that observation, the rest of the proof is straightforward. There are 25=32

different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.

8 0
4 years ago
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Xelga [282]
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4 0
4 years ago
The two tables below show the amount of tip, y, included on a bill charging x dollars. Restaurant B Restaurant A 10 20 30 10 25
Gala2k [10]

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The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.

Step-by-step explanation:

3 0
3 years ago
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Arada [10]

Answer:

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Step-by-step explanation:

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Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3. 5
garri49 [273]

The profit to be made when she sells the house is $103,800.

The first step is to determine the value of Tammy's house in 13 years. The formula to be used is:

  • FV = P (1 + r)^n
  • FV = Future value  
  • P = Present value  
  • R = interest rate  
  • N = number of years  

$184,000 x (1.035)^13 = $287,767.92

Profit = value of the house in 13 years - cost of the house

$287,767.92 - $184,000 = 103,767 = $103,800

To learn more about future value, please check: brainly.com/question/18760477

5 0
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