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10 months ago

Graph the function y=4(2^x+3)-1 and y=-2(3^x-4)+1

Mathematics

1 answer:

kondaur [170]10 months ago

4 0

The graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.

<h3>What is function?</h3>

A function is a relation between a dependent and a independent variable, such that the dependent variable depends upon the independent one for its existence.

Given are the following functions -

y = 4(2ˣ + 3) - 1

y = - 2(3ˣ - 4) + 1

We have the following functions -

y = 4(2ˣ + 3) - 1

y = - 2(3ˣ - 4) + 1

Refer to the graph attached. The graph of red color represents the function y = 4(2ˣ + 3) - 1 and the graph of blue color represents the function y = - 2(3ˣ - 4) + 1. It can be seen that the graphs are symmetrical about the line y = 10.

Therefore, the graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.

To solve more questions on plotting graphs, visit the link below-

brainly.com/question/14299685

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The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

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Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$