7.Solve the following system of equations:

What is the y-intercept of the line perpendicular to the line y = -x + 3 that includes the point (3, 1)?

Jlenok [28]

Slope-intercept form: y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]

For a line to be perpendicular to another line, the slope has to be the negative reciprocal of the original line's slope.

For example:

Slope(m) = $\frac{1}{2}$

Perpendicular line's slope: $-\frac{2}{1}$ or -2 [positive to negative]

m = $-\frac{3}{1}$ or -3

Perpendicular line's slope: $\frac{1}{3}$ [negative to positive]

y = -x + 3

m = -1 So the perpendicular line's slope is 1, now plug it into the equation

y = mx + b

y = x + b To find b, plug in the point (3, 1) into the equation

1 = 3 + b Subtract 3 on both sides to get b by itself

1 - 3 = 3 - 3 + b

-2 = b The y-intercept is -2

4 0

3 years ago

The yearbook committee polled 80 randomly selected students from a class of 320 ninth graders to see if they would be willing to

Anon25 [30]

Using the z-distribution, as we are working with a proportion, it is found that the margin of error for the 90% confidence interval is of 0.0524 = 5.24%.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this problem, the critical value is given as z = 1.645, and since 26 out of 80 students said they would be willing to pay extra:

$n = 80, \pi = \frac{26}{80} = 0.325$

Then, the <em>margin of error</em> is of:

$M = 1.645\sqrt{\frac{0.325(0.675)}{80}} = 0.0524$

More can be learned about the z-distribution at brainly.com/question/25890103

5 0

3 years ago

Expressed in radian measure, 390° is equivalent to?

meriva

Answer:

Step-by-step explanation:

1° = π /180° radians

390° = 390* π / 180 radians; simplify

39*π / 18 = 13 π/ 6 ≈ 6. 81 radiants

5 0

3 years ago

What is the value of arcsin (-0.18)? Use a calculator to determine the answer.

Alla [95]

The answer for the problem is A.

6 0

4 years ago

Read 2 more answers

Suppose X and Y are random variables with joint density function. f(x, y) = 0.1e−(0.5x + 0.2y) if x ≥ 0, y ≥ 0 0 otherwise (a) I

Hatshy [7]

a. $f_{X,Y}$ is a joint density function if its integral over the given support is 1:

$\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\frac1{10}\int_0^\infty\int_0^\infty e^{-x/2-y/5}\,\mathrm dx\,\mathrm dy$

$=\displaystyle\frac1{10}\left(\int_0^\infty e^{-x/2}\,\mathrm dx\right)\left(\int_0^\infty e^{-y/5}\,\mathrm dy\right)=\frac1{10}\cdot2\cdot5=1$

so the answer is yes.

b. We should first find the density of the marginal distribution, $f_Y(y)$ :

$f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\frac1{10}\int_0^\infty e^{-x/2-y/5}\,\mathrm dy$

$f_Y(y)=\begin{cases}\dfrac15e^{-y/5}&\text{for }y\ge0\\\\0&\text{otherwise}\end{cases}$

Then

$P(Y\ge8)=\displaystyle\int_8^\infty f_Y(y)\,\mathrm dy=e^{-8/5}$

or about 0.2019.

For the other probability, we can use the joint PDF directly:

$P(X\le5,Y\le8)=\displaystyle\int_0^5\int_0^8f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=1+e^{-41/10}-e^{-5/2}-e^{-8/5}$

which is about 0.7326.

c. We already know the PDF for $Y$ , so we just integrate:

$E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5$

5 0

3 years ago