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3 years ago

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Mathematics

2 answers:

mihalych1998 [28]3 years ago

8 0

The equation, y=4x+15 represents the relationship shown in the graph.

Finger [1]3 years ago

4 0

Answer:

4. $-4x+y=15$

Step-by-step explanation:

We have been given a graph of a linear function and we are asked to find the correct equation representing the relationship shown in the graph.

Since we know that the standard form of an equation is in form: $Ax+By=C$ , where A, B and C are integers.

First of all we will find the slope of our line and write equation of line in slope-intercept form. Then we will change it into standard form.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{23-15}{2-0}$

$m=\frac{8}{2}=4$

Slope of our line is 4. We can see that y-intercept (b) is 15. Now let us write equation of our line in slope-intercept form.

$y=mx+b$

$y=4x+15$

Now we will change our given equation into standard form by subtracting 4x from both sides of our equation.

$-4x+y=4x+15-4x$

$-4x+y=15$

Therefore, the equation $-4x+y=15$ represents the relationship shown in the graph in standard form and 4th option is the correct choice.

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Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Which of the following q

Ilia_Sergeevich [38]

Answer:

a) 86.73

b) 90.24

c) 10.56% scoring more than 90

d) 75.8

e) 50% probability that a randomly selected student will score more than 80.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 80, \sigma = 8$

a. Find the 80th percentile.

This is the value of X when Z has a pvalue of 0.8. So X when Z = 0.841.

$Z = \frac{X - \mu}{\sigma}$

$0.841 = \frac{X - 80}{8}$

$X - 80 = 8*0.841$

$X = 86.73$

b. Find the cutoff for the A grade if the top 10% get an A.

This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 80}{8}$

$X - 80 = 8*1.28$

$X = 90.24$

c. Find the percentage scoring more than 90.

This is 1 subtracted by the pvalue of Z when X = 90. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{90 - 80}{8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944.

1 - 0.8944 = 0.1056

10.56% scoring more than 90

d. Find the score that separates the bottom 30% from the top 70%.

This is the value of X when Z has a pvalue of 0.3. So X when Z = -0.525.

$Z = \frac{X - \mu}{\sigma}$

$-0.525 = \frac{X - 80}{8}$

$X - 80 = 8*(-0.525)$

$X = 75.8$

e. Find the probability that a randomly selected student will score more than 80.

This is 1 subtracted by the pvalue of Z when X = 80.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{80 - 80}{8}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

1 - 0.5 = 0.5

50% probability that a randomly selected student will score more than 80.

8 0

3 years ago

The CEO of a corporation has $10,000 to give as bonuses. The amount each employee receives depends on how many employees receive

crimeas [40]

Answer:

Direct proportional

Step-by-step explanation:

The direct proportional refers to the effect of one element to the other element.

In other words, when one variable is increased the other variable is also increased but the product would remain the same

y = kx

This equation represents that y is directly proportional to x

As in the given case, the bonus amount is of $10,000 and the amount earned by every employee depends on how numbers of workers are earning a bonus.

Plus, the equation is

y = 10,000

This shows the direct proportional example

8 0

4 years ago

The error term represents the vertical distance from any point to the a. value of the Y’s b. population regression line c. estim

AlladinOne [14]

Answer:

B. Population regression line

explanation:

Error term refers to the sum of deviation within regression line which provides an explanation for the difference between the results of the model and actual observed results. It represents margin of error within a statistical model.

Error term is the distance from each point to the population regression line. It includes everything that differentiates your model from reality. Therefore, factors like nonlinearities, unpredictable effects, measurement errors, and omitted variables will be reflected.

7 0

4 years ago

AD= in<br> Help me please, stuck on this question. Thankss

Hatshy [7]

Using the cosine ratio, the value of AD in the diagram is: 2√3π in.

<h3>How to Apply the Cosine Ratio?</h3>

If we have the following given in a right triangle like triangle ADC in the diagram:

AC = 4π (hypotenuse)

AD = ? (adjacent side)

The cosine ratio, CAH would be applied, which is:

Cos 30 = adjacent/hypotenuse

Cos 30 = AD/4π

AD = cos 30 × 4π = √3/2 × 4π [cos 30 = √3/2]

AD = 2√3π in.

Learn more about the cosine ratio on:

brainly.com/question/15793827

#SPJ1

6 0

2 years ago

Help!!! I will give brainiest!

Bas_tet [7]

Answer:

Option D: 38

Step-by-step explanation:

(10+5^2) ÷7 +33
35÷7+33
5+33
38 Ans

3 0

3 years ago