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4 years ago

The largest possible circle is cut out of a square whose side length is 6

Mathematics

1 answer:

AVprozaik [17]4 years ago

7 0

Answer:

7.74 feet²

Step-by-step explanation:

radius of circle r = 6/2 = 3

area of circle A = π × 3² = 9π = 28.26

area of square = 6² = 36

Remaining board area = 36-28.26 =7.74

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You need to compute the a 90% confidence interval for the population mean. How large a sample should you draw to ensure that the

RSB [31]

Answer:

The sample size required is 102.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}$

Given:

σ = 9.2

(1 - α)% = 90%

MOE = 1.5

The critical value of z for 90% confidence level is:

$z_{0.10/2}=1.645$

*Use a z-table.

Compute the value of n as follows:

$MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}$

$=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102$

Thus, the sample size required is 102.

5 0

3 years ago

A student use the sieve of Eratosthenes to find all prime numbers less than 100 create a step by step set of directions to show

nydimaria [60]

How come back home from walmart and it's called I have

5 0

3 years ago

Researchers randomly divided 500 volunteers into two equal-sized groups. One group spent 6 months on the Paleo diet. A control g

gtnhenbr [62]

Answer:

$p_v =P(t_{(498)}>1.356)=0.088$

And we can use the following excel code to find it: "=1-T.DIST(1.356,498,TRUE)"

Step-by-step explanation:

Data given and notation

$\bar X_{P}=7$ represent the mean for the sample Paleo

$\bar X_{C}=5$ represent the mean for the sample Control

$s_{P}=20$ represent the sample standard deviation for the sample Paleo

$s_{C}=12$ represent the sample standard deviation for the sample Control

$n_{P}=250$ sample size selected Paleo

$n_{C}=250$ sample size selected Control

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

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the Paleo diet provides more weight control than the control treatment, the system of hypothesis would be:

Null hypothesis: $\mu_{P}-\mu_{C}\leq 0$

Alternative hypothesis: $\mu_{P}-\mu_{C}>0$

We don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{P}-\bar X_{C})-12}{\sqrt{\frac{s^2_{P}}{n_{P}}+\frac{s^2_{C}}{n_{C}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

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

$t=\frac{(7-5)-0}{\sqrt{\frac{20^2}{250}+\frac{12^2}{250}}}}=1.356$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{P}+n_{C}-2=250+250-2=498$

Since is a one side right test the p value would be:

$p_v =P(t_{(498)}>1.356)=0.088$

And we can use the following excel code to find it: "=1-T.DIST(1.356,498,TRUE)"

8 0

3 years ago

5z2 -z-4 Whats the answer

arsen [322]

5z2-z-4
10z-z-4
9z-4

8 0

2 years ago

Solving Two -step Equations -2p-4=2

Gnesinka [82]

-2p-4=2
-2p = 2+4
-2p =6
p = 6/-2
p= -3

7 0

4 years ago