What is the converse of the statement?

Mathematics

2 answers:

likoan [24]3 years ago

7 0

Answer:

(A)If lines have negative reciprocal slopes, then they are perpendicular.

Step-by-step explanation:

The given statement is:

Perpendicular lines have negative reciprocal slopes.

To get the converse of the conditional statement, interchange the hypothesis and the conclusion.

Then the converse of the above given statement will be given as:

If the lines have negative reciprocal slopes, then they are perpendicular.

Hence, option A is correct.

user100 [1]3 years ago

3 0

Not 100% sure:
If lines have negative reciprocal slopes, then they are perpendicular.

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skad [1K]

Answer:

The probability is 70% that the sample mean amount of juice will be contained between 4.9168 ounces and 5.0832 ounces.

Step-by-step explanation:

To solve this question, the Normal probability distribution and the Central Limit Theorem are important.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 5, \sigma = 0.4, n = 25, s = \frac{0.4}{\sqrt{25}} = 0.08$

The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

The lower end of this interval is the value of X when Z has a pvalue of 0.5 - 0.7/2 = 0.15

The upper end of this interval is the value of X when Z has a pvalue of 0.5 + 0.7/2 = 0.85

Lower end

X when Z has a pvalue of 0.15. So X when $Z = -1.04$ .