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Volgvan
2 years ago
12

Select the correct answer. What is the solution to |x − 6| ≥ 5? A. 1 ≤ x ≤ 11 B. -11 ≤ x ≤ 1 C. x ≥ 11 or x ≤ 1 D. x ≥ 1 or x ≤

-11
Mathematics
1 answer:
diamong [38]2 years ago
5 0

The absolute value of a number <em>a</em> is written as  |a|  . And represents the distance between a and 0 on a number line.

So, Option C. x≥ 11 or x ≤ 1 is correct answer

Inequality given is,

                              |x − 6| ≥ 5

Taking <em>positive case,</em>

                               x − 6 ≥ 5

                               x − 6 + 6 ≥ 5 + 6

                                x ≥ 11

Taking <em>negative case,</em>

                                 x − 6 ≤  - 5

                                x - 6 + 6 ≤ -5 + 6

                                   x ≤ 1

So, solution of given inequality is  x ≥ 11 or   x ≤ 1

Learn more:

brainly.com/question/1779337

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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati
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Answer:

Weights of at least 340.1 are in the highest 20%.

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 = 330, \sigma = 12

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

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

0.842 = \frac{X - 330}{12}

X - 330 = 12*0.842

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Weights of at least 340.1 are in the highest 20%.

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Alexeev081 [22]

Answer:

x = 6 or x = -7

Step-by-step explanation:

Solve for x over the real numbers:

x^2 + x - 42 = 0

The left hand side factors into a product with two terms:

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Split into two equations:

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Add 6 to both sides:

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Subtract 7 from both sides:

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