Can y’all help me with this plzzzz

If y varies directly as x, find the constant of variation if y = 25 and x = 5.

Soloha48 [4]

Answer:

The constant of variation is 5

Step-by-step explanation:

We know direct variation is of the form

y = kx

We know y =25 and x=5

25 = k*5

Divide each side by 5

25/5 = 5k/5

5 = k

3 0

3 years ago

A salesperson earns $8 per hour plus 6% commission on her sales. In a week when she worked 40 hours, her total earnings were $69

mash [69]

Answer:

372

Step-by-step explanation:

8x40=320

692-320=372

5 0

3 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

2 years ago

recent survey found that 71% of all adults over 50 wear glasses for driving. In a random sample of 30 adults over 50, what is

valentina_108 [34]

Answer:

Mean = 21.3

Standard Deviation = 2.48

Step-by-step explanation:

We are given the following in the question:

p = 71% = 0.71

Sample size, n = 30

We have to find the mean and the standard deviation of those that wear glasses.

$\text{Mean} = np\\=30(0.71)\\=21.3$

Thus, the mean of those who wear glasses is 21.3

$\text{Standard deviation} = \sqrt{npq}\\=\sqrt{np(1-p)}\\=\sqrt{30\times 0.71\times (1-0.71)}\\=2.48$

Thus, the standard deviation of those who wear glasses is 2.48

5 0

3 years ago

Music Co charges a fee of $20 a month plus $1 per song Jams charges no monthly fee but $3 per song. How many songs would have to

NeTakaya

Answer:

10 songs

Step-by-step explanation:

20 + 1x = 3x

20 = 2x

10 = x

—

20 + 1(10) = 3(10)

20 + 10 = 30

30 = 30

4 0

3 years ago