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Mathematics

1 answer:

almond37 [142]3 years ago

5 0

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anything to the power of 0 is 1

1)32+10=42:1-9=-8

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Find f(g(x)) and g(f(x)) for the following functions f(x) = 2x g(x) = x + 5

Helga [31]

F(x)=2x
G(x)=x+5
Now
F(g(x))=2(x+5)
=2x+10
G(f(x))=2x+5

4 0

3 years ago

Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separat

Dmitry [639]

Answer:

Step-by-step explanation:

Hello, dividing by 0 is not defined. so

$\dfrac{2x^2}{6x}$

is defined for x different from 0

This being said, we can simplify by 2x

$\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x$

and this last expression is defined for any real number x.

Thank you

4 0

3 years ago

The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum

Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

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 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .