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2 years ago

Find the equation of the lines perpendicular and parallel to 2x-3y=8 line through the point (-2,-4)

Mathematics

1 answer:

marysya [2.9K]2 years ago

8 0

Answer:

y= -1.5x-7 is the equation of the perpendicular line

Here's why:

when we convert 2x-3y=8 to standard form, we get y= 2/3x-8/3. This means the perpendicular line will have a slope of the negative reciprocal of the original one, so the perpendicular slope is -1.5. When we substitute the points (-2,-4) into the equation y=-1.5x+b, we get a b value of -7. So the perpendicular line equation is y= -1.5x-7. You can't the parallel line equation with the points (-2,-4) as it is part of the line 2x-3y=8.

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Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Katena32 [7]

Answer:

A) A = 27.3°, B = 56.1°, C = 96.6°

Step-by-step explanation:

Use the Law of Cosines:

A = arccos [(b² + c² - a²)/(2bc)] = arccos [(13.2² + 15.8² - 7.3²)/(2*13.2*15.8)] = 27.3°
B = arccos [(a² + c² - b²)/(2ac)] = arccos [(7.3² + 15.8² - 13.2²)/(2*7.3*15.8)] = 56.1°
C = 180° - (A + B) = 180° - (27.3° + 56.1°) = 96.6°

Correct choice is A.

3 0

3 years ago

Number six please and thanks sm

Luda [366]

I believe the answer is C

8 0

3 years ago

A local grocery store decides to offer a free piece of fresh fruit (banana or apple) to all shoppers in the produce department.

xxMikexx [17]

The generalization that can be made from this study is that: Given the choice of a banana or an apple, twice as many shoppers will select an apple.

<h3>How to arrive at the generalization.</h3>

More of the shoppers are said to select an apple from the group of shoppers who are to but either banana or apple.

Those buying an apple are two times the people buying the banana, hence we can conclude that twice as many shoppers would choose the apple over banana.

Read more on probability here: brainly.com/question/24756209

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3 0

1 year ago

Solve for x.

Vera_Pavlovna [14]

Answer:

x=-3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

7 0

3 years ago

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (G

dezoksy [38]

Answer:

a) The mean of a sampling distribution of $\\ \overline{x}$ is $\\ \mu_{\overline{x}} = \mu = 20$ . The standard deviation is $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

b) The standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

c) The standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

d) The probability $\\ P(\overline{x}$ .

e) The probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

f) $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

Step-by-step explanation:

We are dealing here with the concept of a sampling distribution, that is, the distribution of the sample means $\\ \overline{x}$ .

We know that for this kind of distribution we need, at least, that the sample size must be $\\ n \geq 30$ observations, to establish that:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

In words, the distribution of the sample means follows, approximately, a normal distribution with mean, $\mu$ , and standard deviation (called standard error), $\\ \frac{\sigma}{\sqrt{n}}$ .

The number of observations is n = 64.

We need also to remember that the random variable Z follows a standard normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .

$\\ Z \sim N(0, 1)$

The variable Z is

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

With all this information, we can solve the questions.

Part a

The mean of a sampling distribution of $\\ \overline{x}$ is the population mean $\\ \mu = 20$ or $\\ \mu_{\overline{x}} = \mu = 20$ .

The standard deviation is the population standard deviation $\\ \sigma = 16$ divided by the root square of n, that is, the number of observations of the sample. Thus, $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

Part b

We are dealing here with a random sample. The z-score for the sampling distribution of $\\ \overline{x}$ is given by [1]. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{16 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{-4}{\frac{16}{8}}$

$\\ Z = \frac{-4}{2}$

$\\ Z = -2$

Then, the standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

Part c

We can follow the same procedure as before. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{23 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{3}{\frac{16}{8}}$

$\\ Z = \frac{3}{2}$

$\\ Z = 1.5$

As a result, the standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

Part d

Since we know from [1] that the random variable follows a standard normal distribution, we can consult the cumulative standard normal table for the corresponding $\\ \overline{x}$ already calculated. This table is available in Statistics textbooks and on the Internet. We can also use statistical packages and even spreadsheets or calculators to find this probability.

The corresponding value is Z = -2, that is, it is two standard units below the mean (because of the negative value). Then, consulting the mentioned table, the corresponding cumulative probability for Z = -2 is $\\ P(Z$ .