Smith chose the underlined words for a reason. What

Graph g(x), where f(x) = 4x − 2 and g(x) = f(x + 1)

BlackZzzverrR [31]

y = mx + b - it's a linear function.

Two points are enough to draw a graph of a linear function.

Step-by-step explanation:

Two different ways.

1.

g(x) = f(x + 1) → put instead of x, x + 1 into function f(x) = 4x - 2:

g(x)=4(x + 1) - 2 use the distributive property

g(x) = 4x + 4 - 2

g(x) = 4x + 2

Choose any two x values. Put them into the equation g(x) = y and calculate the values of y.

x = -1

y = 4(-1) + 2 = -4 + 2 = -2 → (-1, -2)

x = 0

y = 4(0) + 2 = 0 + 2 = 2 → (0, 2)

The graph on the picture #1.

2.

Use the transformation of a graph of a function:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x + n) - shift the graph of f(x) n units to the left

f(x - n) - shift the graph of f(x) n units to the right

f(x) = 4x - 2, g(x) = f(x + 1)

shift the graph of f(x) q unit to the left.

Plot the graph of function f(x).

Choose any two x values. Put them into the equation f(x) = y and calculate the values of y.

x = 0

y = 4(0) - 2 = 0 - 2 = -2 → (0, -2)

x = 1

y = 4(1) - 2 = 4 - 2 = 2 → (1, 2)

Plot the graph of f(x).

Shift it 1 unit to the left.

The graph on the picture #2.

3 0

2 years ago

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago

When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.

Savatey [412]

The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:

By properties of powers, if you have the same base, you can substract the exponents. Then:

=(27x^2)z/(-3x^2)(z^6)
=-9z/z^6 (As you can see: x^2-2= x^0=1)
=-9/z^5 (Then, z^6-1=z^5)

Therefore, the answer is: The exponent on the variable z is 5.

7 0

2 years ago

Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g ar

tia_tia [17]

Answer:

g(x) exceed f(x) by $10$ when $x=5$

Step-by-step explanation:

step 1

Find the equation of function f(x)

we know that

The initial value is the y-intercept of the linear function (value of y when the value of x is equal to zero)

so

$b=17$

The rate of change is equal to the slope

so

$m=-3$

therefore

$f(x)=-3x+17$

step 2

Find the equation of function g(x)

Let

$A(0,-8),B(2,0)$

Find the slope

$m=(0+8)/(2-0)=4$

$b=-8$ ----> point A

therefore

$g(x)=4x-8$

step 3

Find the value of f(x) and g(x) for $x=5$

$f(5)=-3(5)+17=2$

$g(5)=4(5)-8=12$

Find the difference

$g(5)-f(5)=12-2=10$

3 0

2 years ago

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants, the participant totals (

KengaRu [80]

Repeated measures study is when participants of the first treatment are still the participants of the second treatment either to see the effects of the variable. Thank you for your question. Please don't hesitate to ask in Brainly your queries.

8 0

2 years ago