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2 years ago

Point B has coordinates (−4, −2). The x-coordinate of point A is 5. The distance between points A and B is 15 units. What are th

e possible coordinates of point A?

Mathematics

1 answer:

GaryK [48]2 years ago

7 0

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{y})\qquad B(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{AB}{15}=\sqrt{[-4 - 5]^2 + [-2 - y]^2}\implies 15^2=(-9)^2+(-2-y)^2$

$225=81+(-2-y)(-2-y)\implies 225=81+\stackrel{F~O~I~L}{(4+4y+y^2)} \\\\\\ 144=4+4y+y^2\implies 0=y^2+4y-140\implies 0=(y-10)(y+14) \\\\\\ y= \begin{cases} 10\\ -14 \end{cases}\qquad \qquad \qquad A(5~~,~~10)\qquad A(5~~,~~-14)$

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A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

4 0

3 years ago

An airplane is preparing to land at an airport. It is 50400 feet above the ground and is descending at the rate of 3000 feet per

Dovator [93]

Answer:

let t = no of minutes when they are at the same altitude

52200 - 3300t = 2500t

52200 = 3300t + 2500t

52200 = 5800t

t = 52200/5800

t = 9 minutes they will be at the same altitude

The altitude:

9*2500 = 22500 ft

Check on other train

52200 - 9(3300) =

52200 - 29700 = 22500 ft

3 0

2 years ago

Alton had $725 for Medicare, $3000 for state income tax, and $3100 for

ella [17]

Answer:

$\$6825$

Step-by-step explanation:

Amount deducted for Medicare = $725

Amount deducted for state income tax = $3000

Amount deducted for Social security = $3100

To find: Total amount deducted from Alton's pay for FICA last year

Solution:

Total amount deducted from Alton's pay for FICA last year = Amount deducted for Medicare + Amount deducted for state income tax + Amount deducted for Social security = $725+3000+3100$

On adding 725 and 3000, we get $725+3000=3725$

On adding 3725 and 3100, we get $3725+3100=6825$

So, amount deducted = $\$6825$

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2 years ago

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A regular decagon with exterior angle 1 is shown.

vova2212 [387]

Answer:

∠1 = 36°

Step-by-step explanation:

All angles of a regular polygon are congruent, as are the sides. A regular decagon will have 10 congruent angles.

<h3>Exterior angles</h3>

The sum of the measures of the exterior angles of a convex polygon is always 360°. This decagon has 10 congruent exterior angles, so the measure of each is given by ...

10(∠1) = 360°

∠1 = 36° . . . . . . . . divide by 10

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2 years ago

What is the value of the expression? 30-5×4+2

belka [17]

30-5×4+2
30-20+2
10+2=12

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3 years ago

Read 2 more answers