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Suppose f(x)=x^2 and g(x)=(3x)^2 which statement best compares the graph of g(x) with the graph of f(x)?

elena55 [62]

Answer:

C. The graph g(x) is horizontally compressed by a factor of 3.

Step-by-step explanation:

Given:

$f(x)=x^{2},g(x)=(3x)^{2}$

Here, the graph of $g(x)$ is a transformation of the parent function $f(x)$ .

In order to transform $f(x)=x^{2}$ to $g(x)=(3x)^{2}$ , we need to perform the following transformation:

$f(x)\rightarrow f(3x)\\x^2\rightarrow (3x)^2$

As per the transformation rules, if a positive number greater than 1 is multiplied to $x$ of the function, then the graph of the function compresses in the horizontal direction.

As 3 is multiplied to $x$ of $f(x)$ , therefore, the graph of $g(x)$ is a horizontal compression by a factor of 3.

8 0

2 years ago

A population of a particular yeast cell develops with a constant relative growth rate of 0.4425 per hour. The initial population

nalin [4]

The exponential function is often used to model the growth or decay of a population

The population size of the yeast cell after 3 hours is 6.24 million

The given parameters are:

a = 3.1M --- initial number of cells

r = 0.4425 per hour --- rate

The nth term of an exponential function is:

f(n) = a(1+r)^n-1

After 3 hours; n = 3

So, we have:

f(3) = a(1+r)^3-1

Substitute values for a and r

f(3) = 3.1 (1+0.4425)^3-1

f(3) = 3.1 ( 1.4425)^2

f(3) = 6.24

Hence, the population size of the yeast cell after 3 hours is 6.24 million.

Read more about exponential functions at: brainly.com/question/3127939

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5 0

1 year ago

Assume that you plan to use a significance level of alpha α equals =0.05 to test the claim that p1 equals = p2. Use the given sa

lara [203]

Answer:

$z=\frac{0.42-0.45}{\sqrt{\frac{0.42(1-0.42)}{100}+\frac{0.45(1-0.45)}{100}}}=-0.428$

$p_v =2*P(Z$

And we can use the following R code to find it: "2*pnorm(-0.428)"

The p value is a very high value and using any significance given $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions are not significantly different.

Step-by-step explanation:

1) Data given and notation

$X_1 =42$ people with some characteristic desired on sample 1

$X_2 =45$ people with some characteristic desired on sample 2

$n_{1}=100$ sample selected 1

$n_{2}=100$ sample selected 2

$p_{1}=\frac{42}{100}=0.42$ represent the proportion estimated for 1

$p_{2}=\frac{45}{100}=0.45$ represent the proportion estimated for 2

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion for the two samples are different , the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\frac{p_1 (1-p_1)}{n_{1}}+\frac{p_2 (1-p_2)}{n_{2}}}}$ (1)

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.42-0.45}{\sqrt{\frac{0.42(1-0.42)}{100}+\frac{0.45(1-0.45)}{100}}}=-0.428$

4) Statistical decision

We can calculate the p value for this test.

Since is a two tailed test the p value would be:

$p_v =2*P(Z$

And we can use the following R code to find it: "2*pnorm(-0.428)"

The p value is a very high value and using any significance given $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions are not significantly different.

4 0

3 years ago

Find the median of the data in the dot plot below.

Scrat [10]

Answer:

The median is 6.

Step-by-step explanation:

To find the median, put the numbers in order then find the middle number. In this data set, there are 2 numbers, so you add those 2 and divide by 2.

5+7 equals 12. 12 divided by 2 is 6.

7 0

2 years ago

Solve for y. 2(3y – 6) = 24 A. 36 B. 6 C. −6 D. −36

Juliette [100K]

Answer:

The correct answer choice would be : B.6

3 0

3 years ago

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