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3 years ago

5

What is the value of y? Please show work of how you solved! Thankyou

1 answer:

kap26 [50]3 years ago

6 0

$log_4(y+2)=3$
raise each side to base 4
$4^{log_4(y+2)}=4^3$
simplify
$(y+2)}=64$ using the law of logarithms $a^{log_ab}=b$
=>
y=62

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2 years ago

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,46

JulsSmile [24]

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a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

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The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

$M = \frac{50463-38737}{2} = 5863$

Relating the margin of error with the sample size:

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

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.64.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

For this problem, we have that $\sigma = 14300, M = 5863$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$5863 = 1.645\frac{14300}{\sqrt{n}}$

$5863\sqrt{n} = 1.645*14300$

$\sqrt{n} = \frac{1.645*14300}{5863}$

$(\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2$

$n = 16$

The sample size was of 16.

7 0

3 years ago

Given z=f(x,y),x=x(u,v),y=y(u,v), with x(1,3)=2 and y(1,3)=2, calculate zu(1,3) in terms of some of the values given in the tabl

stich3 [128]

The value of zu(1,3) using the data elements represented on the table of values is q + p

<h3>How to solve the calculus expression?</h3>

The given parameters are:

z = f(x, y)

x = x(u, v)

y = y(u, v)

Where

x(1, 3) = 2 and y(1, 3) = 2

To calculate zu(1,3), we make use of:

$z_u(1,3) = f_x(x,y) * x_u(1,3) + f_y(x,y) * y_u(1,3)$

The values x(1, 3) = 2 and y(1, 3) = 2 mean that:

(x,y) = (2,2).

So, we have:

$z_u(1,3) = f_x(2,2) * x_u(1,3) + f_y(2,2) * y_u(1,3)$

From the table of values, we have:

$f_x(2,2) = q$

$x_u(1,3) = 1$

$f_y(2,2) = 1$

$y_u(1,3) = p$

So, the equation becomes

$z_u(1,3) = q * 1 + 1 * p$

Evaluate the product

$z_u(1,3) = q + p$

Hence, the value of zu(1,3) is q + p

Read more about calculus at:

brainly.com/question/5313449

#SPJ1

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2 years ago