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3 years ago

Which graph represents the function of f(x) 9x^2 -36 / 3x + 6

Mathematics

1 answer:

Finger [1]3 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}-36}{3x+6}$

Remember that the denominator cannot be equal to zero

The value of x cannot be equal to x=-2

<em>Simplify the numerator</em>

$9x^{2}-36=(3x+6)(3x-6)$ ----> by difference of squares

substitute

$f(x)=\frac{(3x+6)(3x-6)}{3x+6}$

simplify

$f(x)=3x-6$

The domain is all real numbers except the value of x=-2

The y-intercept is the point (0,-6) ---> value of y when the value of x is equal to zero)

The x-intercept is the point (2,0) ---> value of x when the value of y is equal to zero)

therefore

The graph in the attached figure

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3 years ago

Fred flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will show tails, the

Inessa05 [86]

Answer:

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is $\frac{4}{3}$

Step-by-step explanation:

Given : Fred flips a coin, spins the spinner, and rolls a standard number cube.

To find : The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three ?

Solution :

First we find probability one by one,

1) Flips a coin - Head, Tail

Total number of outcome = 2

Favorable outcome (getting a tail) = 1

Probability that the coin will show tails is $P(T)=\frac{1}{2}$

2) Spins the spinner - yellow, green, blue

Total number of outcome = 3

Favorable outcome (land on yellow or green) = 2

Probability that the spinner will land on yellow or green $P(S)=\frac{2}{3}$

3) Rolls a standard number cube - 1,2,3,4,5,6

Total number of outcome = 6

Favorable outcome (show a three) = 1

Probability that the cube will show a three $P(C)=\frac{1}{6}$

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is

$P=P(T)+P(S)+P(C)$

$P=\frac{1}{2}+\frac{2}{3}+\frac{1}{6}$

$P=\frac{3+4+1}{6}$

$P=\frac{8}{6}$

$P=\frac{4}{3}$

Therefore, The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is $\frac{4}{3}$

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3 years ago

A random variable X with a probability density function () = {^-x > 0

Sliva [168]

The solutions to the questions are

The probability that X is between 2 and 4 is 0.314
The probability that X exceeds 3 is 0.199
The expected value of X is 2
The variance of X is 2

<h3>Find the probability that X is between 2 and 4</h3>

The probability density function is given as:

f(x)= xe^ -x for x>0

The probability is represented as:

$P(x) = \int\limits^a_b {f(x) \, dx$

So, we have:

$P(2 < x < 4) = \int\limits^4_2 {xe^{-x} \, dx$

Using an integral calculator, we have:

$P(2 < x < 4) =-(x + 1)e^{-x} |\limits^4_2$

Expand the expression

$P(2 < x < 4) =-(4 + 1)e^{-4} +(2 + 1)e^{-2}$

Evaluate the expressions

P(2 < x < 4) =-0.092 +0.406

Evaluate the sum

P(2 < x < 4) = 0.314

Hence, the probability that X is between 2 and 4 is 0.314

<h3>Find the probability that the value of X exceeds 3</h3>

This is represented as:

$P(x > 3) = \int\limits^{\infty}_3 {xe^{-x} \, dx$

Using an integral calculator, we have:

$P(x > 3) =-(x + 1)e^{-x} |\limits^{\infty}_3$

Expand the expression

$P(x > 3) =-(\infty + 1)e^{-\infty}+(3+ 1)e^{-3}$

Evaluate the expressions

P(x > 3) =0 + 0.199

Evaluate the sum

P(x > 3) = 0.199

Hence, the probability that X exceeds 3 is 0.199

<h3>Find the expected value of X</h3>

This is calculated as:

$E(x) = \int\limits^a_b {x * f(x) \, dx$

So, we have:

$E(x) = \int\limits^{\infty}_0 {x * xe^{-x} \, dx$

This gives

$E(x) = \int\limits^{\infty}_0 {x^2e^{-x} \, dx$

Using an integral calculator, we have:

$E(x) = -(x^2+2x+2)e^{-x}|\limits^{\infty}_0$

Expand the expression

$E(x) = -(\infty^2+2(\infty)+2)e^{-\infty} +(0^2+2(0)+2)e^{0}$

Evaluate the expressions

E(x) = 0 + 2

Evaluate

E(x) = 2

Hence, the expected value of X is 2

<h3>Find the Variance of X</h3>

This is calculated as:

V(x) = E(x^2) - (E(x))^2

Where:

$E(x^2) = \int\limits^{\infty}_0 {x^2 * xe^{-x} \, dx$

This gives

$E(x^2) = \int\limits^{\infty}_0 {x^3e^{-x} \, dx$

Using an integral calculator, we have:

$E(x^2) = -(x^3+3x^2 +6x+6)e^{-x}|\limits^{\infty}_0$

Expand the expression

$E(x^2) = -((\infty)^3+3(\infty)^2 +6(\infty)+6)e^{-\infty} +((0)^3+3(0)^2 +6(0)+6)e^{0}$

Evaluate the expressions

E(x^2) = -0 + 6

This gives

E(x^2) = 6

Recall that:

V(x) = E(x^2) - (E(x))^2

So, we have:

V(x) = 6 - 2^2

Evaluate

V(x) = 2

Hence, the variance of X is 2

Read more about probability density function at:

brainly.com/question/15318348

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<u>Complete question</u>

A random variable X with a probability density function f(x)= xe^ -x for x>0\\ 0& else

a. Find the probability that X is between 2 and 4

b. Find the probability that the value of X exceeds 3

c. Find the expected value of X

d. Find the Variance of X

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1 year ago

Georgia’s scores in six subjects are 89, 75, 92, 68, 78, 75, and 80. If she finds a single value that summarizes all the values

posledela

It would be mean. The mean is the average that is you are looking for, since she wants a summerization of all the values in the data set. To find the mean (average) add all the numbers and then divide by the amount of numbers.

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2 years ago