Find functions f(x) and g(x) so the given function can be expressed as

Mathematics

1 answer:

Alchen [17]3 years ago

5 0

Answer:

$f(x) = \frac{5}{x}$

$g(x) = x - 4$

Step-by-step explanation:

Composite function:

$h(x) = f(g(x)) = (f \circ g)(x)$

h(x) = 5/x-4

We have x on the denominator and not the numerator, so the outer function is given by:

$f(x) = \frac{5}{x}$

The denominator is x - 4, so this is the inner function, so:

$g(x) = x - 4$

You might be interested in

worker a earns $7.90 per widget produced, produces 14 widgets per day, and works 10 hours per day. Worker b earns $9.00 per widg

Anni [7]

What are the statements

3 0

3 years ago

Assume that foot lengths of women are normally distributed with a mean of 9.6 in and a standard deviation of 0.5 in.a. Find the

Makovka662 [10]

Answer:

a) 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b) 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c) 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

Step-by-step explanation:

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 $\frac{\sigma}{\sqrt{n}}$ .

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.

In this problem, we have that:

$\mu = 9.6, \sigma = 0.5$ .