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3 years ago

If you vertically compress the absolute value parent function, f(x) = [ 41, by a

Mathematics

1 answer:

just olya [345]3 years ago

4 0

Answer:

$g(x) = \frac{1}{5} |x|$

Step-by-step explanation:

Given

$f(x) = |x|$

Vertically compressed

Compression Factor = 5

Required

Find the equation of the new function;

Let the new function be represented by g(x)

Let c represented the compression factor;

such that c = 5

When a function f(x) is vertically compressed by factor c, the new function becomes

$f(\frac{1}{c}x)$

From properties of functions;

$f(\frac{1}{c}x) = \frac{1}{c} *f(x)$

This implies that

$g(x) = f(\frac{1}{c}x) = \frac{1}{c} *f(x)$

$g(x) = \frac{1}{c} *f(x)$

Recall that $f(x) = |x|$ and c = 5

$g(x) = \frac{1}{5} * |x|$

$g(x) = \frac{1}{5} |x|$

Hence, the new function is  $g(x) = \frac{1}{5} |x|$ 

You might be interested in

5(2x^2-6x) - (4x^2-3x)

motikmotik

Answer:

6x^2- 27x

Step-by-step explanation:

distribute 5 through parenthesis

change - sign from in front of parenthesis

combine like terms

3 0

3 years ago

Daredevil Danny takes a practice jump as shown on the graph below. Complete the steps to determine the equation for the paraboli

Tju [1.3M]

Answer:

Step 2:

Part A

f(x) = a(x-h)^2 +k

Part B

I'm not really sure about this part

Part C

f(x)=-12/25(x-25)^2+32

Step 3:

Part A

y = ax^2 + bx + c

Part B

f(x) = -12/25(x - 25)^2 + 32

Part C

a = -12/25

b = 0

c = 32

Step-by-step explanation:

Hope This Helps!

Sorry For Taking So Long!

3 0

4 years ago

Compute the standard error for sample proportions from a population with proportion p= 0.55 for sample sizes of n=30, n=100 and

Pani-rosa [81]

Given Information:

Population proportion = p = 0.55

Sample size 1 = n₁ = 30

Sample size 2 = n₂ = 100

Sample size 3 = n₃ = 1000

Required Information:

Standard error = σ = ?

Answer:

$\sigma_1 = 0.091$

$\sigma_2 = 0.050$

$\sigma_3 = 0.016$

Step-by-step explanation:

The standard error for sample proportions from a population is given by

$\sigma = \sqrt{\frac{p(1-p)}{n} }$

Where p is the population proportion and n is the sample size.

For sample size n₁ = 30

$\sigma_1 = \sqrt{\frac{p(1-p)}{n_1} }$

$\sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} }$

$\sigma_1 = 0.091$

For sample size n₂ = 100

$\sigma_2 = \sqrt{\frac{p(1-p)}{n_2} }$

$\sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} }$

$\sigma_2 = 0.050$

For sample size n₃ = 1000

$\sigma_3 = \sqrt{\frac{p(1-p)}{n_3} }$

$\sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} }$

$\sigma_3 = 0.016$

As you can notice, the standard error decreases as the sample size increases.

Therefore, the greater the sample size lesser will be the standard error.

8 0

4 years ago

Find the slope of the line that goes through the given points.

lesya692 [45]

Answer:

Step-by-step explanation:

the formula to calculate slope is

m=( y2-y1)/(x2-x1)

here,

(9,2)= x1 ,y1

(10,6)= x2 ,y2

putting the values in formula , we get

m= (6-2)/(10-9)

=4/1

= 4

8 0

3 years ago

Read 2 more answers

A onesided test of a hypothesis, based on a sample of size 9, yields a Pvalue of .035. Which of the following best describes t

lana [24]

Answer:

1.86 < t < 2.31

Step-by-step explanation:

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean height actually is higher\lower than an specified value, the system of hypothesis would be:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

Or like this:

Null hypothesis: $\mu \geq \mu_o$

Alternative hypothesis: $\mu < \mu_o$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We don't know on this case the calculated value and with the p value we can find it.

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=9-1=8$

Since is a one side test the p value would be:

$p_v =P(t_{(8)}>t_o)=0.035$

And we can find the critical value with the following excel code:

" =T.INV(1-0.035,8)" and we got $t_p =2.09$

And cannot be a lower tail test since all the options have positive values for the statistic. So on this case the best option is:

1.86 < t < 2.31

8 0

4 years ago