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3 years ago

Evaluate b^2 - 4ac = -1, b = -5, and c =2. show steps pls!!

Mathematics

2 answers:

Alex Ar [27]3 years ago

6 0

B² - 4ac =
(-5)² - 4*(-1)*(2) =
25 + 8 =
33 ← answer

Alona [7]3 years ago

4 0

B^2 - 4ac =

b=-5
a=-1
c=2

So then it equals =
(-5)^2 - 4(-1)(2)

-5^2 = Equals 25

the power of 2 is multiplying the same number it's powering. Two negatives = a positive. so 5x5 = 25.

4 x -1 x 2 = -8

4 x -1 = -4 and -4 x 2 = -8.

25 - (-8) = 33

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Problems of normally distributed samples can be solved using the z-score formula.

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

This Zscore is how many standard deviations the value of the measure X 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) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

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

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

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