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Tcecarenko [31]
3 years ago
6

The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends prep

aring for the test. If a student receives 72 points on a test for which she spent 3 hours preparing, what score would she receive on the next test if she spent 4 hours preparing?
Mathematics
1 answer:
dolphi86 [110]3 years ago
8 0

Answer:

She would receive 96 points

Step-by-step explanation:

The grade (Y) received on a certain teacher's 100-point test varies in direct proportion to the amount of time(t) a student spends preparing for the test.

Mathematically

Y= kt

Where k is constant of proportionality

If y= 72 and t= 3

72=k3

72/3= k

24= k

So

Y= 24t

If t= 4

Y= kt

Y= 24(4)

Y= 96

Y = 96 points

She would receive 96 points

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(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.

The formula is given as;

nP_r=\frac{n!}{(n-r)!}

This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.

Therefore, we would have;

\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}

Therefore, if the order is relevant, this selection can be done in 6,720 ways.

(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

_nC_r=\frac{n!}{(n-r)!r!}

The formula can now be applied as follows;

\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}

If the order is not relevant, then the selection can be done in 56 ways.

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