Which is larger 1 or 2

Which is the length of the hypotenuse of the triangle?

Pepsi [2]

Since this is a right triangle, we can use the Pythagorean Theorem, which states a² + b² = c² in a right triangle.

Plugging our numbers in, we get:

(12)² + (35)² = c²

From there, we can square the numbers.

(144) + (1225) = c²

Then, we can add them together to find the sum;

(1369) = c²

And finally, we can find the square root of both sides.

(37) = c

Therefore, 37 is the answer and your answer choice is correct.

5 0

3 years ago

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A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

Zina [86]

Answer:

The number of ways to form the committee is formed = 637065

Solution:

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 :-

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