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pav-90 [236]
3 years ago
5

Penny needs 30 cubic ft of sand to fill a sandbox. She plans to buy 10 bags of sand for her sandbox. Each bag contains 2.9 cubic

feet of sand. Is this a reasonable plan? A. Yes, it is reasonable because each bag covers around 3 cubic feet. So in order to cover 30 cubic feet she would need 10 bags to be sure she has enough and end up with a little extra. B. No, it is not reasonable because each bag covers around 3 cubic feet. So in order to cover 30 cubic feet, she would need at least 30 bags to be sure she has enough sand. C. No, it is not reasonable because each bag covers a bit less than 3 cubic feet. So in order to cover 30 cubic feet, she would need to buy 11 bags to be sure she has enough sand
Mathematics
1 answer:
Romashka [77]3 years ago
4 0
The correct answer is C.

Because: 2.9 multiplied by 10 bags equals 29cubic ft and she needs 30 cubic ft. So she would need to buy 11 bags to make sure she has enough sand for the whole thing. 11 x 2.9 = 31.9 which ensures she has enough for the whole thing including extra in case. So you answer would be Answer C.
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<u>Answer: </u>

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<u>Solution: </u>

The number of combinations of n things such that m things taken together are given by:-

C_{(\boldsymbol{n}, \boldsymbol{m})}=\frac{n !}{m !(\boldsymbol{n}-\boldsymbol{m}) !}

Given Data:

A committee consisting of 4 faculty members and 5 students is to be formed.  There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to form the committee is formed given by :-

\begin{array}{l}{12 C_{4} \times 13 C_{5}} \\\\ {=\frac{12 !}{4 !(12-4) !} \times \frac{13 !}{5 !(13-5) !}} \\\\ {=\frac{12 !}{4 ! 8 !} \times \frac{13 !}{5 ! 8 !}} \\\\ {\frac{12 \times 11 \times 10 \times 9 \times 8 !}{27 \times 8 !} \times \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{120 \times 8 !}} \\\\ {=637065}\end{array}

Hence, the number of ways to form the committee is formed = 637065

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