What is "$96 spent in 4 hours" written as a unit rate in minutes?

Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?

vesna_86 [32]

<h2>Hello!</h2>

The answer is:

C) They both have the same y-intercept.

In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.

So,

- Finding the equation of the g(x):

Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4$

Now, calculating the value of "b" using the first point (-1,8) and the slope of the function, we have:

$y=mx+b$

$y=-x+b$

$8=-4(-1)+b$

$b=4$

So, the equation of g(x) is:

$y=-4x+4$

- Comparing the y-intercepts of f(x) and g(x):

Finding the y-intercept of f(x), by making "x" equal to 0, we have:

$y=x+4\\\\y=4$

We have that the function f(x) has its y-intercept at "y" equal to 4.

Finding the y-intercept of g(x), by making "x" equal to 0, we have:

$y=-4x+4$

$y=-4*(0)+4$

$y=4$

We have that the function g(x) has its y-intercept at "y" equal to 4.

Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:

C) They both have the same y-intercept.

Have a nice day!

4 0

3 years ago

Read 2 more answers

Simplify 27x^7y^2/9x^6y^5

solmaris [256]

Answer: x/y^3

Step-by-step explanation:

So you divide 27/9 which is 3. Then it ix x^7-x^6=x. And then it is y^2-y^5=y3

27*x*x*x*x*x*x*x*y*y/9*x*x*x*x*x*x*y*y*y*y*y

Doing this makes it easier so you cross each variable out for each one in both sides. 3x/y^3 would be your answer.

7 0

3 years ago

Which represents the solution(s) of the equation x2 = 289?

sergeinik [125]

Answer:

B) x = +/- 17

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br

Marianna [84]

Answer:

The calculated value |Z| = |-2.5| >2.326 at 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

The manager of Publix in Clemson believes 64% is too high for his own store

Step-by-step explanation:

Step:-1

Given that the consumer Reports showed that 64% of supermarket shoppers.

Given that the population proportion

P = 0.64

Given that random sample size 'n' = 100

Given that 52 believe the supermarket brands were as good as the national brands.

sample proportion

$p^{-} = \frac{x}{n} = \frac{52}{100} = 0.52$

Step:-2

Null hypothesis: The manager of the Publix in Clemson believes 64% is too low for his own store

μ < 0.64

Alternative Hypothesis:H₁:μ > 0.64

Test statistic

$Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.52-0.64}{\sqrt{\frac{0.64 X 0.36}{100} } }$

Z = -2.5

Level of significance = 0.05

Z₀.₀₅ = 2.326

The calculated value |Z| = |-2.5| >2.326 at 0.05 level of significance

Final answer:-

The null hypothesis is rejected at a 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

3 0

3 years ago