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kykrilka [37]
3 years ago
10

Mark is solving the following system.

Mathematics
2 answers:
fredd [130]3 years ago
6 0
I think its he didnt eliminate the same variables
miskamm [114]3 years ago
6 0

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3)  4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

Answer: correct choice is C

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Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t
svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

Problems of normally distributed samples are 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 = 450, \sigma = 100

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

Z = \frac{550 - 450}{100}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 350

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

Z = \frac{350 - 450}{100}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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

1.88 = \frac{X - 450}{100}

X - 450 = 1.88*100

X = 638

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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

0.253 = \frac{X - 450}{100}

X - 450 = 0.253*100

X = 475.3

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

-0.385 = \frac{X - 450}{100}

X - 450 = -0.385*100

X = 411.5

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

0.385 = \frac{X - 450}{100}

X - 450 = 0.385*100

X = 488.5

The middle 30% of the test scores is between 411.5 and 488.5.

7 0
3 years ago
I need help with this
jeka57 [31]

Answer:

A

Step-by-step explanation:

supplementary agles add up to 180 degrees, so when you subtract 162 from 180, you get 18. Hope this helped :D

6 0
3 years ago
Read 2 more answers
A box plot is known as a box-and-mustache plot?<br> <br><br>True<br>or <br>False<br>??
vladimir1956 [14]
This will be false a box plot is also known as quantile plots
6 0
3 years ago
Read 2 more answers
A national study reported that 75% of high school graduates pursue a college education immediately after graduation. A private h
Verdich [7]

Answer:

The % students going to higher education is 79.60 % which is higher than the reported value.

Step-by-step explanation:

According to national study report the students going to college for higher education = 75 %

Given that

156 of their 196 graduates last year went on to college.

% students going to higher education is

(\frac{156}{196}) 100 = 79.60

Thus the % students going to higher education is 79.60 % which is higher than the reported value.

4 0
3 years ago
You borrow $18,000 to buy a new car. You will pay $3,240 in simple interest at the end of 6 years. What is the annual interest r
mixer [17]
Simple Interest, I = PRT/100

3240 = 18 000 * R * 6 /100

3240 = 180*R*6

3240 / (180*6) = R          Use your calculator

3 = R

The annual interest rate is 3%.
5 0
3 years ago
Read 2 more answers
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