Solve [y] = -18.<br> Help pls

When the region is rotated about y=-2, the resulting shape is a horizontal, hollow cylinder. The volume can be found with either washer method or shell method.

To use washer method, cut a thin vertical slice of the region. Rotated around y=-2, this slice becomes a washer. The width of this washer is dx. The outer radius is 2 − (-2) = 4. The inner radius is y − (-2) = y + 2. The volume of the washer is:

dV = π (4² − (y + 2)²) dx

dV = π (4² − (ln x + 2)²) dx

The total volume is the sum of the washers from x=1 to x=e².

V = ∫ dV

V = ∫₁ᵉ² π (4² − (ln x + 2)²) dx

To instead use shell method, cut a thin horizontal slice of the region. Rotated around y=-2, this slice becomes a cylindrical shell. The thickness of the shell is dy. The radius is y − (-2) = y + 2. The width is x − 1. The volume of the shell is:

dV = 2π (y + 2) (x − 1) dy

dV = 2π (y + 2) (eʸ − 1) dy

The total volume is the sum of the shells from y=0 to y=2.

V = ∫ dV

V = ∫₀² 2π (y + 2) (eʸ − 1) dy

6 0

3 years ago

Suppose a poll is taken that shows that 765 out of 1500 randomly selected, independent people believe the rich should pay more

Zanzabum

Answer:

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

$p_v =P(z>0.775)=0.219$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

Step-by-step explanation:

Data given and notation

n=1500 represent the random sample taken

X=765 represent the successes

$\hat p=\frac{765}{1500}=0.51$ estimated proportion of successes

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5:

Null hypothesis: $p \leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(z>0.775)=0.219$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly higher than 0.5

8 0

3 years ago

Solve [y] = -18. Help pls