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Goryan [66]
3 years ago
6

Does anyone know how he got from step 1 to step 2??????????

Mathematics
1 answer:
padilas [110]3 years ago
3 0

9514 1404 393

Explanation:

Both sides of the equation are squared.

  \dfrac{x-12}{4}=\sqrt{x} \qquad\text{given}\\\\ \left(\dfrac{x-12}{4}\right)^2=x \qquad\text{square both sides}\\\\ \left(\dfrac{x}{4}-3\right)^2=x \qquad\text{divide out the fraction}\\\\ \dfrac{x^2}{4^2}-\dfrac{6}{4}x+9=x \qquad\text{$(a-b)^2=a^2-2ab+b^2$}\\\\\dfrac{x^2}{16}-\dfrac{5x}{2}+9=0 \qquad\text{subtract $x$}

I like this better without fractions, so would multiply by 16 at this point (or earlier).

  x^2 -40x +144 = 0

  (x -36)(x -4) = 0

  x = 4 or 36 . . . . . . x = 4 is extraneous

The solution is x = 36.

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Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the f
melisa1 [442]

Answer:

For the 99th percentile, we have X = 206 seconds.

Step-by-step explanation:

Problems of normally distributed samples 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:

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:

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99th percentile:

Value of X when Z has a pvalue of 0.99. So we use Z = 2.325

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For the 99th percentile, we have X = 206 seconds.

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