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3 years ago

Select the correct answer.

Mathematics

2 answers:

alexgriva [62]3 years ago

3 0

Answer:

D. 157

Step-by-step explanation:

4(x^2+3)-2y

4(6^2+3)-2(-1/2) add in given values

4(39)+1. start with parentheses

156+1. combine like terms

157. answer

anygoal [31]3 years ago

3 0

Answer:

D. 157

Step-by-step explanation:

Hi there!

We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2

Let's first simplify the expression, as that will likely make it easier

Distribute 4 to both x² and 3

4x²+12-2y

That's the expression

Substitute -6 as x into the expression

4(-6)²+12-2y

Raise (-6) to the second power

4*36+12-2y

Multiply 36 by 4

144+12-2y

Add 12 and 144 together

156-2y

Now the expression is 156-2y

But remember that we know that y=-1/2, and we haven't substituted it into the expression yet

Substitute -1/2 as y into the expression

156-2(-1/2)

Multiply

156+2/2

Simplify

156+1

Add

157

Hope this helps!

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Answer:

1) Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

For this case we see that the calculated value is higher than the critical value

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

2) Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

Step-by-step explanation:

Part 1

Data given

$\bar X=640$ represent the sample mean

$\sigma=150$ represent the population standard deviation

$n=40$ sample size

$\mu_o =500$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Step1:State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:

Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

Step 2: Calculate the statistic

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

We can replace in formula (1) the info given like this:

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

Step 3: Calculate the critical value

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

Step 4: Compare the statistic with the critical value

For this case we see that the calculated value is higher than the critical value

Step 5: Decision

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

Part 2

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

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Answer:

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Step-by-step explanation: