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3 years ago

6

A teacher is randomly calling on students in a class. If there are 6 girls and 6 boys in the class, what is the theoretical prob

ability that the first 3 people called on are all girls?

1 answer:

Evgesh-ka [11]3 years ago

6 0

It would be a 50/50 chance that all of them would be girls

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Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.

vesna_86 [32]

Factorize the denominator:

$\dfrac{x^2-4}{x^3+x^2-4x-4}=\dfrac{x^2-4}{x^2(x+1)-4(x+1)}=\dfrac{x^2-4}{(x^2-4)(x+1)}$

If $x\neq\pm2$ , we can cancel the factors of $x^2-4$ , which makes $x=-2$ and $x=2$ removable discontinuities that appear as holes in the plot of $g(x)$ .

We're then left with

$\dfrac1{x+1}$

which is undefined when $x=-1$ , so this is the site of a vertical asymptote.

As $x$ gets arbitrarily large in magnitude, we find

$\displaystyle\lim_{x\to-\infty}g(x)=\lim_{x\to+\infty}g(x)=0$

since the degree of the denominator (3) is greater than the degree of the numerator (2). So $y=0$ is a horizontal asymptote.

Intercepts occur where $g(x)=0$ ( $x$ -intercepts) and the value of $g(x)$ when $x=0$ ( $y$ -intercept). There are no $x$ -intercepts because $\dfrac1{x+1}$ is never 0. On the other hand,

$g(0)=\dfrac{0-4}{0+0-0-4}=1$

so there is one $y$ -intercept at (0, 1).

The domain of $g(x)$ is the set of values that $x$ can take on for which $g(x)$ exists. We've already shown that $x$ can't be -2, 2, or -1, so the domain is the set

$\{x\in\mathbb R\mid x\neq-2,x\neq-1,x\neq2\}$

8 0

3 years ago

Y-b=m(x-a) solve for a

Leni [432]

Y-b=mx-am
y-b-mx=am
(y-b-mx)/m=a

8 0

3 years ago

Use the graph to solve the system of linear equations.<br> x+y=5<br> y – 2x = -4

Romashka [77]

Y=-x+5
Y=2x-4
X would be your slope
Y intercepts would be (0, 5) , ( 0,-4)
Formula i used was Y=Mx+B

3 0

3 years ago

StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?

scZoUnD [109]

Answer:

x= 11.25

Step-by-step explanation:

cross multiply 9 by 5 divided by 4 and that would give you x

6 0

3 years ago

A rope 13 meters long will just reach from the top of a flagpole to a point on the ground 12 meters from teh base of the flagpol

goldfiish [28.3K]

Answer:

the height of the flagpole is 5 meters

Step-by-step explanation:

The computation of the height of the flagpole is given below

Given that

the length of the rope is 13 meters

And, the ground would be 12 meters

Based on the above information, the height of the flagpole is

= √13^2 - √12^2

= √169 - √144

= √25

= 5 meters

hence the height of the flagpole is 5 meters

5 0

3 years ago