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marusya05 [52]
2 years ago
10

5.2x-y=4.1 1.5x+y=6.7 how to solve this problem

Mathematics
2 answers:
MrRa [10]2 years ago
8 0

Answer: x=1.6

y=4.2

Step-by-step explanation:

5.2x - y = 4.1

1.5x + y = 6.7

we will add both equations and you see that the y is getting cancelled

6.7x=10.8

x=10.8/6.7= 1.6

now in any equation we will replace x with 1.6

5.2(1.6)-y=4.1

8.3-y=4.1

  -y= 4.1-8.3

-y=-4.2  multiply by -1

y=4.2

sesenic [268]2 years ago
4 0

Answer:

x = 1.61 (Estimated)

y = 4.28 (Estimated)

Step-by-step explanation:

5.2x - y = 4.1

1.5x + y = 6.7

5.2x − y = 4.1

−y = −5.2x + 4.1

y = 5.2x − 4.1

Solve for x:

1.5x + y = 6.7

1.5x + 5.2x − 4.1 = 6.7

6.7x − 4.1 = 6.7

6.7x = 10.8

x = 1.61194

Solve for y:

y = 5.2x − 4.1

y = 5.2 × 1.61194 − 4.1

y = 4.28209

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A college requires applicants to have an ACT score in the top 12% of all test scores. The ACT scores are normally distributed, w
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Answer:

a) The lowest test score that a student could get and still meet the colleges requirement is 27.0225.

b) 156 would be expected to have a test score that would meet the colleges requirement

c) The lowest score that would meet the colleges requirement would be decreased to 26.388.

Step-by-step explanation:

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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 = 21.5, \sigma = 4.7

a. Find the lowest test score that a student could get and still meet the colleges requirement.

This is the value of X when Z has a pvalue of 1 - 0.12 = 0.88. So it is X when Z = 1.175.

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

1.175 = \frac{X - 21.5}{4.7}

X - 21.5 = 1.175*4.7

X = 27.0225

The lowest test score that a student could get and still meet the colleges requirement is 27.0225.

b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the colleges requirement?

Top 12%, so 12% of them.

0.12*1300 = 156

156 would be expected to have a test score that would meet the colleges requirement

c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?

It would decrease to the value of X when Z has a pvalue of 1-0.15 = 0.85. So X when Z = 1.04.

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

1.04 = \frac{X - 21.5}{4.7}

X - 21.5 = 1.04*4.7

X = 26.388

The lowest score that would meet the colleges requirement would be decreased to 26.388.

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Answer:

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