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3 years ago

Use elimination to solve each system of equations. 1/3x-y=-1 and 1/5x-2/5y=-1

Mathematics

1 answer:

Yakvenalex [24]3 years ago

4 0

Answer:

x=−9 and y=−2

Step-by-step explanation:

Multiply the first equation by 2,and multiply the second equation by -5.

2(1/3x−y=−1)

−5(1/5x−2/5y=−1)

Becomes: 2/3x−2y=−2

−x+2y=5

Add these equations to eliminate y:

−1/3 x=3

Then solve −1/3x=3 for x:

−1/3x 3

−1/3 = −1/3

(Divide both sides by (-1)/3)

x=−9

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

1/3x−y=−1

Substitute−9 for x in 1/3x−y=−1:

1/3(−9)−y=−1

−y−3=−1(Simplify both sides of the equation)

−y−3+3=−1+3(Add 3 to both sides)

−y=2

−y

−1=

−1

(Divide both sides by -1)

y=−2

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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

The ratio of the number of boys to the number of girls in a school is 5:7.If there are 600 students in the school,how many girls

nekit [7.7K]

So,

The secret to solving problems with ratios is to find the value of one unit.

5:7 = 12 units total

To find one unit, divide the total number of students by the total number of units.
600/12 = a

Simplify
50/1 = a
50 = a

The value of each unit is 50.

Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys

50(7) = x
350 = x

There are 350 girls.

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3 years ago

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In a horse race, the odds in favor of the first horse winning in an 8-horse race are 2 to 5. The odds against the second horse w

Nataly_w [17]

The probability that the first horse wins is 2/7. The probability that the second horse wins is 3/10. Since the events that the first horse wins and the second horse wins are shared exclusive, the probability that either the first horse or the second horse will win is :

2/7 + 3/10= 41/70

Hope this is correct.

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3 years ago

Factor wheels show all the

Zielflug [23.3K]

answer: 2 × 2 × 2 × 2 × 2 = 32

Step-by-step explanation:

$32 \\ = 16 \times 2 \\ = 4 \times 4 \times 2 \\ = 2 \times 2 \times 2 \times 2 \times 2$

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2 years ago

The scale drawing of a room in a hotel is shown below. If 3 in. = 12 ft, what are the actual dimensions of the room?

rjkz [21]

Answer:

B length = 60 feet, width = 45 feet

Step-by-step explanation:

If you divide the scale drawing (15 in) by length by the scale of of the same dimension (3 in) and multiply what you get (5) by what the larger scale is (12 ft) you get the answer (60 ft)

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3 years ago