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3 years ago

Sasha can run at an average speed of 9 3/4 min/mi. She runs at this speed for 68 1/4 min.

Mathematics

1 answer:

miv72 [106K]3 years ago

4 0

9 3/4 = 39/4 mi/m

68 1/4 = 273/4 min

39/4 mutiply by 273/4 = 10647 / 16 mi = 665.4 mi

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2 years ago

The senior class at a very small high school has 25 students. Officers need to be elected for four positions: President, Vice-Pr

kirill115 [55]

Answer:

(a) The total number of ways to select 4 officers from from 25 students is 12,650.

(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

Step-by-step explanation:

(a)

It is provided that there are a total of n = 25 students.

Officers need to be elected for four positions:

President, Vice-President, Secretary, and Treasurer.

k = 4

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

Compute the number of ways to select 4 students from from 25 as follows:

${25\choose 4}=\frac{25!}{4!(25-4)!}$

$=\frac{25!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22\times 21!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22}{4\times 3\times 2\times 1}\\\\=12650$

Thus, the total number of ways to select 4 officers from from 25 students is 12,650.

(b)

It is provided that of the 25 students, there are 13 girls and 12 boys in the class.

For the post of President and Treasurer only girls are selected.

For the post of Vice-President and Secretary only boys are selected.

Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:

${13\choose 2}=\frac{13!}{2!(13-2)!}$

$=\frac{13!}{2!\times 11!}\\\\=\frac{13\times 12\times 11!}{2!\times 11!}\\\\=\frac{13\times 12}{ 2\times 1}\\\\=78$

Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:

${12\choose 2}=\frac{12!}{2!(12-2)!}$

$=\frac{12!}{2!\times 10!}\\\\=\frac{12\times 11\times 10!}{2!\times 10!}\\\\=\frac{12\times 11}{ 2\times 1}\\\\=66$

The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:

${13\choose 2}\times {12\choose 2}=78\times 66=5148$

Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

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2 years ago

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2 years ago

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2 years ago

Read 2 more answers

The chef took out 54.8 g of butter but then found out that he took out 6.9 g of butter more than he needed. How much butter did

stira [4]

Answer:

47.9 gm

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Total butter took = 54.8 gm

Extra butter quantity = 6.9g

So, we can calculate the exact quantity of butter needed by using following formula,

Exact butter needed = Total butter - Extra butter quantity

By putting the value, we get

Exact butter needed = 54.8 gm - 6.9gm

= 47.9 gm

Hence, he need 47.9gm butter.

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2 years ago