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WINSTONCH [101]
3 years ago
9

Solve the linear equation:

title="4^{2x+7} = 8^{2x-3}" alt="4^{2x+7} = 8^{2x-3}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
g100num [7]3 years ago
8 0

Answer:

  x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

  2(2x+7) = 3(2x -3)

  0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

  0 = 2x -23 . . . . . . . . . . . . . simplify

  0 = x - 23/2 . . . . . . . . . . . . divide by 2

  11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

_____

<em>Check</em>

This value of x makes the equation become ...

  4^(2·23/2 +7) = 8^(2·23/2 -3)

  4^30 = 8^20 . . . . . true

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A+B+C=34.5

x+1+x+x+1/2=34.5

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3 years ago
Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. If th
ioda

Answer:

The bottom cutoff heights to be eligible for this experiment is 66.1 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions 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:

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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.

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This means that \mu = 69, \sigma = 2.8

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The bottom 15% are excluded, so the bottom cutoff is the 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

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The bottom cutoff heights to be eligible for this experiment is 66.1 inches.

8 0
3 years ago
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