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3 years ago

Use the graph of the quadratic function, g(x), to answer each question.

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

5 0

Given the graph of the function, where the vertex is the maximum point at (-5,4):

We can establish the quadratic function in vertex form:

g(x) = -(x + 5)^2 + 4

To find the value of g(-1):

Substitute -1 as the input of the function:

g(-1) = -(x + 5)^2 + 4

g(-1) = -(-1 + 5)^2 + 4

g(-1) = -(4)^2 + 4

g(-1) = -12

To find the value of g(-3):

Substitute -3 as the input of the function:

g(-3) = -(x + 5)^2 + 4

g(-3) = -(-3+ 5)^2 + 4

g(-3) = 0

To find the value of x when g(x) = 4:
Since your vertex is (-5, 4), in which the y-coordinate is 4, then its x-coordinate is -5.

Therefore, the value of x when g(x) = 4 is -5.

Please mark my answers as the Brainliest if you find my explanations helpful :)

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a) Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b) The 95% confidence interval would be given by (910.05;959.95)

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) $z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

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".

$\bar X=935$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=180$ represent the population standard deviation

n=200 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3278.222$

The sample deviation calculated $s=97.054$

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 $z_{\alpha/2}=1.96$