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3 years ago

In Mr. Romero's auto shop class, the ratio

Mathematics

1 answer:

MrMuchimi3 years ago

5 0

Answer:

boys 5:2 girls

add the ratio parts together

5 + 2 = 7

divide the total number of students by the total number of parts

35/7 = 5

now multiply each part of the ratio by 5

boys 25

girls 10

there are 25 boys

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(14x-5)-(-3x+2) A. 11x-3 B. 17x-7 C. 17x-3 D. 11x-7

Vladimir [108]

The answer would be B) 17x-7

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3 years ago

How do you round 23 to the nearest thousand?

Zielflug [23.3K]

You cannot round 23 to the nearest thousand.

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3 years ago

A pizza dlivery car can travel 11 km for every gallon of gasoline it uses. If the driver's average speed is 28 km/h, how many ho

Svetlanka [38]

Answer:

13.75 hours

Step-by-step explanation:

First, find how many km the driver can travel:

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2 years ago

Complete the table and show work

Alinara [238K]

So the formula for this is for every inch of width, you multiply by 2 to get the length.

Here, I made a table for it.

2×2=4

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5 0

3 years ago

Read 2 more answers

WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"

Feliz [49]

Recall Euler's theorem: if $\gcd(a,n) = 1$ , then

$a^{\phi(n)} \equiv 1 \pmod n$

where $\phi$ is Euler's totient function.

We have $\gcd(9,32) = 1$ - in fact, $\gcd(9,32^k)=1$ for any $k\in\Bbb N$ since $9=3^2$ and $32=2^5$ share no common divisors - as well as $\phi(9) = 6$ .

Now,

$37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6$

where the $c_i$ are positive integer coefficients from the binomial expansion. By Euler's theorem,

$\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9$

so that

$32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9$

7 0

2 years ago