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Dmitriy789 [7]
3 years ago
8

Solve the system of linear equations by substitution. 4x−2y=14 y=12x−1

Mathematics
1 answer:
Alexus [3.1K]3 years ago
3 0

Answer:

The answer is (-0.7, -9.4)

Step-by-step explanation:

1) Since we are using the substitution method, and we know that y = 2x-1, in the first equation, plug that into y.  It should look like this:

4x-2(12x-1) = 14

4x -24x + 2 = 14

2) Combine like terms and continue to simplify until you get a direct answer for each variable.

-20x + 2 = 14.

-20x = 12.

x = -7/10 (or -0.7)

3) Now we know what x equals, so to find our y-coordinate, we will plug this into either equation.

y = 12(-7/10) -1

y= -84/10 -1

y= -9.4

4) Now that we have our x value and y value, we know our point. The solution is (-0.7, -9.4).

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Step-by-step explanation:

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For bone density scores that are normally distributed with a mean of 0 and a standard deviation of​ 1, find the percentage of sc
gogolik [260]

Answer:

a) The percentage of bone density scores that are significantly high is 2.28%

b) The percentage of bone density scores that are significantly low is 2.28%

c) The percentage of bone density scores that are not significant is 95.44%

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.

a. significantly high​ (or at least 2 standard deviations above the​ mean).

This is 1 subtracted by the pvalue of Z = 2.

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

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b. significantly low​ (or at least 2 standard deviations below the​ mean).

pvalue of Z = -2

Z = -2 has a pvalue of 0.0228

2.28% of scores are signicantly low.

c. not significant​ (or less than 2 standard deviations away from the​ mean).

pvalue of Z = 2 subtracted by the pvalue of Z = -2.

Z = 2 has a pvalue of 0.9772

Z = -2 has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% of the scores are not significant

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Answer:

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Step-by-step explanation:

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