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3 years ago

What is the equation of a line perpendicular to the line y=(4/9)x-2 that passes through the point (4,3)?

1 answer:

3 0

y=(4/9)x-2
This is in slope intercept form (y=mx+b), where m is the slope.
A perpendicular line will have the opposite reciprocal of the slope.
So if the slope here is 4/9, then the perpendicular line's slope will be -9/4.

Now that you have the slope (-9/4) and a point (4, 3), you can use the point-slope formula to find the equation.
y - y₁ = m(x - x₁)
y - 3 = (-9/4)(x - 4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12

So the answer will be:
C. y= -(9/4)x+12

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In a simple random sample of 14001400 young people, 9090% had earned a high school diploma. Complete parts a through d below.

ratelena [41]

Answer:

(a) The standard error is 0.0080.

(b) The margin of error is 1.6%.

(c) The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d) The percentage of young people who earn high school diplomas has increased.

Step-by-step explanation:

Let p = proportion of young people who had earned a high school diploma.

A sample of n = 1400 young people are selected.

The sample proportion of young people who had earned a high school diploma is:

$\hat p=0.90$

(a)

The standard error for the estimate of the percentage of all young people who earned a high school diploma is given by:

$SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Compute the standard error value as follows:

$SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=\sqrt{\frac{0.90(1-0.90)}{1400}}\\$

$=0.008$

Thus, the standard error for the estimate of the percentage of all young people who earned a high school diploma is 0.0080.

(b)

The margin of error for (1 - α)% confidence interval for population proportion is:

$MOE=z_{\alpha/2}\times SE_{\hat p}$

Compute the critical value of z for 95% confidence level as follows:

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

Compute the margin of error as follows:

$MOE=z_{\alpha/2}\times SE_{\hat p}$

$=1.96\times 0.0080\\=0.01568\\\approx1.6\%$

Thus, the margin of error is 1.6%.

(c)

Compute the 95% confidence interval for population proportion as follows:

$CI=\hat p\pm MOE\\=0.90\pm 0.016\\=(0.884, 0.916)\\\approx (88.4\%,\ 91.6\%)$

Thus, the 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d)

To test whether the percentage of young people who earn high school diplomas has increased, the hypothesis is defined as:

H₀: The percentage of young people who earn high school diplomas has not increased, i.e. p = 0.80.

Hₐ: The percentage of young people who earn high school diplomas has not increased, i.e. p > 0.80.

Decision rule:

If the 95% confidence interval for proportions consists the null value, i.e. 0.80, then the null hypothesis will not be rejected and vice-versa.

The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

The confidence interval does not consist the null value of p, i.e. 0.80.

Thus, the null hypothesis is rejected.

Hence, it can be concluded that the percentage of young people who earn high school diplomas has increased.

8 0

3 years ago

ASAP PLS HELP DUE TODAY. WILL GIVE BRAINLIEST IF A GOOD ANSWER EXPLENATION AND CORRECT ANSWER

aniked [119]

Answer:

$7 + (-8)$

Step-by-step explanation:

Given

$7 - 8$

(a): Write as additive inverse.

An additive inverse is of the form a + (-b)

In this case:

$a = 7$

$b = -8$

So, the expression can be represented as:

$7 + (-8)$

(b): Number line representation

When the expression in (a) is solved.

The result is:

$7 - 8 = 7 + (-8) = -1$

This means that the number line must accommodate 7 and -1.

Having said that, options (b) and (c) are out because their range is 0 to 15 and this excludes -1.

Option (d) is a wrong representation of $7 - 8$

Hence, (a) is correct

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3 years ago

You ride your skateboard to school and tell all your friends you rode at a speed of 25 mph. They know this cannot he true becaus

andrew-mc [135]

The distance between your house and school and how long it took you to get there

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3 years ago

First discovered more than 30 years ago, Lina’s sunbird, a four-and-a-half-inch animal found in the Philippines and that resembl

Arlecino [84]

Answer: the correct one is C) found in the Philippines and resembling

Step-by-step explanation:

To maintain parallelism, you must list items with equal grammatical structure.

"Found" is just an adjective that modifies the animal, and so is "resembling." Sure, they don't sound the same, but they're both adjectives.

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3 years ago

Please need help for question number 26

kherson [118]

(8,12)(14,3)

Use midpoint formula

(X1+x2/2, y1+y2/2)

Substitute with your points

(8+14/2, 12+3/2)

Solve each

(22/2,15/2)

Cancel common factor 2

(2×(4+7)/2(1),15/2)

Simplify

(4+7/1,15/2)

This is your midpoint

(11, 15/2)

3 0

3 years ago