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2 years ago

Select the correct answer. Consider the graph of the function f(x) = e^x.

Mathematics

1 answer:

patriot [66]2 years ago

6 0

Taking into account the definition of y-intercept, the y-intercept of function g is (0,3) (option C).

<h3>What is y-intercept</h3>

To find the y-intercept of a function, simply replace x with 0; and then solve the equation.

That is, to find the intersection point with the ordinate axis, f(0) is calculated by making x = 0.

<h3>The y-intercept of g(x) = 2f(x)+1</h3>

In this case, you know that:

f(x) = eˣ

g(x) = 2f(x)+1

Then, substituting the expression of the function f(x) in the function g(x), you obtain g(x)=2×eˣ + 1

The y-intercept of function g is g(0). So, g(0)=2×e⁰ + 1

Solving:

g(0)=2×1 + 1

g(0)= 2+1

Finally, the y-intercept of function g is (0,3) (option C).

Learn more about y-intercept:

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3 years ago

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Oduvanchick [21]

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a) The company should expect to replace 11.51% of its batteries.

b) 35 months.

Step-by-step explanation:

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:

$\mu = 43.8, \sigma = 6.5$

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. Then

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

$Z = \frac{36 - 43.8}{6.5}$

$Z = -1.2$

$Z = -1.2$ has a pvalue of 0.1151.

The company should expect to replace 11.51% of its batteries.

(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

$-1.28 = \frac{X - 43.8}{6.5}$