How do you solve for x in 7 x = 21 ?

Find the equation of the linear function passing through (2,3) and (5,12)

Elis [28]

y = 3x - 3 is the equation of the linear function passing through (2, 3) and (5, 12)

Solution:

Given that we have to find the equation of linear function passing through (2, 3) and (5, 12)

The formula y = mx + b is said to be a linear function

Where "m" is the slope of line and "b" is the y - intercept

Let us first find the slope of line

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=2 ; y_{1}=3 ; x_{2}=5 ; y_{2}=12$

Substituting values we get,

$m=\frac{12-3}{5-2}=\frac{9}{3}=3$

Thus slope of line is m = 3

To find the y - intercept, substitute m = 3 and (x, y) = (2, 3) in y = mx + b

3 = 3(2) + b

3 = 6 + b

b = 3 - 6

b = -3

Thus the required equation of linear function is:

Substitute m = 3 and b = -3 in formula

y = mx + b

y = 3x - 3

Thus the equation of linear function is found

6 0

3 years ago

In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time coll

algol13

Answer:

(a) The sample size required is 2401.

(b) The sample size required is 2377.

(c) Yes, on increasing the proportion value the sample size decreased.

Step-by-step explanation:

The confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hatp(1-\hat p)}{n}}$

The margin of error in this interval is:

$MOE=z_{\alpha/2}\sqrt{\frac{\hatp(1-\hat p)}{n}}$

The information provided is:

MOE = 0.02

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

(a)

Assume that the proportion value is 0.50.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.50(1-0.50)}{n}}\\n=\frac{1.96^{2}\times0.50(1-0.50)}{0.02^{2}}\\=2401$

Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows:

$MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.55(1-0.55)}{n}}\\n=\frac{1.96^{2}\times0.55(1-0.55)}{0.02^{2}}\\=2376.99\\\approx2377$

Thus, the sample size required is 2377.

(c)

On increasing the proportion value the sample size decreased.

8 0

4 years ago

The cost of producing key chains with the company logo printed on them consists of a onetime setup fee of $205.00 plus $0.70 fo

Elena-2011 [213]

Simply add in the known information. To find the cost of 1700 key chains, substitute it for p in the equation, like this: C=205.00+0.70(1700) and solve.

7 0

4 years ago

Read 2 more answers

How to find the mean of a probability distribution?

e-lub [12.9K]

That depends. If you have a finite data set, you would add up all the points you have and divide by the total count.

Or, if you are working with pure distributions, the mean is the same as the expected value of the corresponding random variable.

Suppose you have a discrete random variable $X$ with a given probability mass function $f_X(x)$ , then the mean is given by

$\mathbb E(X)=\displaystyle\sum_xxf_X(x)$

which would mean you take all the possible probability for the event that $X=x$ , multiply each by that $x$ , and add them together.

If the distribution is continuous, say a random variable $Y$ that has probability distribution function $f_Y(y)$ over some support $S$ , then the mean is

$\mathbb E(Y)=\displaystyle\int_Syf_Y(y)\,\mathrm dy$

3 0

3 years ago

Which of the x-values are solutions to the following inequality

Gnom [1K]

4(2-x) > -2x-3(4x+1)

5 0

3 years ago