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Mathematics

2 answers:

Harlamova29_29 [7]2 years ago

5 0

The correct answer is C

mars1129 [50]2 years ago

3 0

Answer:

Step-by-step explanation:

(3- $\sqrt{2$ )(3+ $\sqrt{2$ )

=(3)^2-( $\sqrt{2$ )^2

=9-2

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Suppose that a department contains 7 men and 15 women. How many ways are there to form a committee with six members if it must h

Anna [14]

Answer:

7502040

Step-by-step explanation:

you can have 6 women,5 women and 1 men,4 women and 2 men,

in first case,you can place women in 15*14*13*12*11*10 ways

in second case

15*14*13*12*11*7

and in third case

15*14*13*12*7*6

and you need to sum all this numbers

3 0

2 years ago

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation

Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .