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3 years ago

10

There are 16 girls and 18 boys in a class. The teacher Chooses a students name at random to answer a question. What is the proba

bility that the teacher chooses a girl to answer the question?

1 answer:

murzikaleks [220]3 years ago

6 0

Step-by-step explanation:

girl=16

boy=18

picking a girl at random

the answer is = 1/16

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3x%5E%7B8%7D%2A7x%5E%7B3%7D%20%7D%7B3x%5E%7B6%7D%2A7%20%7D" id="TexFormula1" title="

denis23 [38]

Answer:

$a = \dfrac{x^2}{3} \quad \textsf{and} \quad b = \dfrac{x^3}{7}$

Step-by-step explanation:

Given expression:

$\dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7 }$

There are several ways this problem can be approached, and therefore many different answers. The goal is to reduce the given expression to a simple product of two terms in x, set that to the given form 3a⋅7b then solve for a and b.

$\implies \dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7}$

Cancel the common factors 3 and 7:

$\implies \dfrac{\diagup\!\!\!\!3x^{8} \cdot \diagup\!\!\!\!7x^{3} }{\diagup\!\!\!\!3x^{6} \cdot \diagup\!\!\!\!7}$

$\implies \dfrac{x^8 \cdot x^3}{x^6}$

Separate the fraction:

$\implies \dfrac{x^8}{x^6} \cdot x^3$

$\textsf{Apply the quotient rule of exponents} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies x^{8-6} \cdot x^3$

$\implies x^{2} \cdot x^3$

Now equate the simplified expression to the given form:

$\implies x^{2} \cdot x^3=3a \cdot 7b$

Therefore:

$\begin{aligned}x^{2} &=3a \:\: &\textsf{ and }\:\: \quad x^3 &=7b\\ \Rightarrow a & = \dfrac{x^2}{3} & \Rightarrow b & = \dfrac{x^3}{7}\end{aligned}$

However, we could also separate them as:

$\begin{aligned}x^{3} &=3a \:\: &\textsf{ and }\:\: \quad x^2 &=7b\\ \Rightarrow a & = \dfrac{x^3}{3} & \Rightarrow b & = \dfrac{x^2}{7}\end{aligned}$

Another way of writing them would be to go back a few steps and separate the fraction in x terms differently:

$\implies \dfrac{x^8 \cdot x^3}{x^6}=x^8 \cdot \dfrac{x^3}{x^6}=x^8 \cdot x^{-3}$

Therefore, this would give us:

$\begin{aligned}x^{8} &=3a \:\: &\textsf{ and }\:\: \quad x^{-3} &=7b\\ \Rightarrow a & = \dfrac{x^8}{3} & \Rightarrow b & = \dfrac{1}{7x^3}\end{aligned}$

As the given expression reduces to x⁵, we can separate the x term in any way we like, so long as the coefficient of a is ¹/₃ and the coefficient of b is ¹/₇. Therefore, there are many possible answers.

7 0

2 years ago

Read 2 more answers

Type the expressions as radicals 5/2

Bogdan [553]

The Radicals of y5/2 is: (y^5) = y^(5/2)

5 0

4 years ago

mr. and mrs. dobrosky are eating at friendly's. their bill is $24.79 and they are leaving a 15% tip. how much did they spend on

Sergio [31]

Answer:

Tip: $3.70

Total: $28.49

Step-by-step explanation:

1. Finding the tip:

a. tip = total cost * rate of tip

or you could do it as a proportion, which would be

b. tip percent/100 = tip/total cost

use cross products to get the tip, then add it to the total price.

I hope this helped.

4 0

3 years ago

What is the surface area of a cone, to the nearest whole number?

IgorC [24]

The answer is 240cm^2, so B.
<span>Surface Areas of Pyramids and Cones Practice: connexus
</span>1) B, 448cm^2
2) D, 209pi cm^2
3) D, 351m^2
4) B, 240cm^2
5) C, 561.1pi cm^2
Just took it so they are all correct! your welcome

3 0

3 years ago

Doug long jump was 3 yards. Jason long jump was 98. How much longer was Jason jump then Doug ?

Arisa [49]

95 yards. You'd take Jason's and subtract Dougs

7 0

3 years ago