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Debora [2.8K]
3 years ago
7

David received his allowance on Sunday. He spends 1/4 of his allowance on Monday and 2/3 of the remainder on Tuesday. What part

of his allowance is left for the rest of the week?
(A) 1/3(B) 1/12(C) 1/4(D) 1/2(E) 4/7
Mathematics
1 answer:
FromTheMoon [43]3 years ago
8 0

He spent 1/4 on Monday, so he had 3/4 left.

He then spent 2/3 of that, to find how much he spent you would multiply 3/4 by 2/3:

3/4 x 2/3 = 6/12 = 1/2

On Tuesday he spent 1/2 of his allowance.

So on Monday and Tuesday he spent 1/4 + 1/2 = 3/4 total.

He would have 1/4 of his allowance left.

The answer is C.

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We can use the Сosine formula to solve this problem.
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AC^2=AB^2+BC^2-2*AB*BC*cos82^o \\ AC^2=8^2+11^2-2*8*11*0.1392 \\ AC^2=64+121-24.4992= 160.508 \\ AC= \sqrt{160.508} \approx  12.67 \ cm
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The smallest angle of the triangle lies opposite the smallest side, so we need to find m</span>∠C.

cosC= \frac{AC^2+BC^2-AB^2}{2*AC*BC}  \\  \\ cosC= \frac{12.67^2+11^2-8^2}{2*12.67*11}= \frac{160.53+121-64}{278.74} = \frac{217.53}{278.74} \approx  0.7804

Now we can use Bradis's Table (I don't know the name in English, maybe Trigonometric Table?) to find m∠C:

m∠С = 38°42' = 38.7°

Answer: 38.7°


<span>I hope this helps</span>

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3 years ago
Use a whole number, a fraction, one plus sign, and four 2's to make 23.
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