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2 years ago

Write the equation in point-slope form of the line that passes

Mathematics

1 answer:

mariarad [96]2 years ago

3 0

Answer:

y + 2 = 5/3(x - 4)

Step-by-step explanation:

Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)

It looks like this:

y - Y = m(x - X)

The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.

y - -2 = m(x - 4)

Fill in the slope for the m.

y - -2 = 5/3(x - 4)

Simplify if possible.

y + 2 = 5/3 (x - 4)

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Answer:

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Step-by-step explanation:

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3 years ago

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.

lawyer [7]

Using the t-distribution, it is found that the p-value of the test is 0.007.

At the null hypothesis, it is tested if the mean lifetime is not greater than 220,000 miles, that is:

$H_0: \mu \leq 220000$

At the alternative hypothesis, it is tested if the mean lifetime is greater than 220,000 miles, that is:

$H_1: \mu > 220000$ .

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.
$\mu$ is the value tested at the null hypothesis.
s is the standard deviation of the sample.
n is the sample size.

For this problem:

$\overline{x} = 226450, \mu = 220000, s = 11500, n = 23$

Then, the value of the test statistic is:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{226450 - 220000}{\frac{11500}{\sqrt{23}}}$

$t = 2.69$

We have a right-tailed test(test if the mean is greater than a value), with t = 2.69 and 23 - 1 = 22 df.

Using a t-distribution calculator, the p-value of the test is of 0.007.

A similar problem is given at brainly.com/question/13873630

8 0

3 years ago

Find sin0 where 0 is the angle shown. Give an exact value, not a decimal approximation.

otez555 [7]

Answer: Sin0 = 8/8.5

Step-by-step explanation: What we have is a right angled triangle, with two sides given and one angle which is the reference angle (unknown angle).

The Sine of the angle is calculated as

Sin0 = opposite/hypotenuse

We have the opposite side (facing the reference angle) as 8 units and the hypotenuse (facing the right angle unknown), which we shall label as X.

To calculate the hypotenuse, we shall apply the Pythagoras theorem which is,

X² = 3² + 8²

X² = 9 + 64

X² = 73

Adding the square root sign to both sides of the equation, we now have

X = √73

X = 8.5 (approximately)

Now that we have the hypotenuse as 8.5, the Sine of the angle can now be calculated as

Sin0 = opposite/hypotenuse

Sin0 = 8/8.5

7 0

3 years ago

A, B & C lie on a straight line.

bazaltina [42]

Answer:

x = 136°

Step-by-step explanation:

We can use a theorem to help us.

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For exterior angle x, the remote interior angles are z and <CBD.

From the theorem, we get this equation.

x = z + m<CBD

We know z = 52°.

We need to find m<CBD.

Angles CBD and y are a linear pair. They are supplementary, so the sum of their measures is 180°. We are given y = 96°.

m<CBD + y = 180°

m<CBD + 96° = 180°

m<CBD = 84°

x = z + m<CBD

x = 52° + 84°

x = 136°

3 0

3 years ago

Read 2 more answers

how is 0.00023 written in scientific notation? a. 23 x 10–5 b. 2.3 x 10–4 c. 2.3 x 104 d. 0.23 x 10–3

Annette [7]

Answer: $2.3\times10^{-4}$

Step-by-step explanation:

We know that Scientific notation is a way to write a very large or a very small number in the product of a decimal form of number [generally between 1 and 10] and powers of ten.

Given number : 0.00023

In scientific notation $0.00023=2.3\times\frac{1}{10000}=2.3\times10^{-4}$

Therefore, In scientific notation $0.00023=2.3\times10^{-4}$

7 0

3 years ago

Read 2 more answers