A tree is 3 ft tall casts a shadow that is 2 ft long. Find the length of the shadow that a 6 ft tree cast.

There are 7 apples on a plate. When these apples are distributed to 7 children, one for each, an apple snows on the plate. How c

blsea [12.9K]

Answer:

magic

Step-by-step explanation:

that is a magic childerns are just biting and spliting the apples

4 0

2 years ago

Read 2 more answers

Write 5 and 2/5 as a decimal

Alenkasestr [34]

Answer:

5.4.

Step-by-step explanation:

If we divide 2 by 5 we get 0.4

So 5 and 2/5 = 5.4

7 0

3 years ago

Read 2 more answers

Consider the computer output below. Fill in the missing information. Round your answers to two decimal places (e.g. 98.76). Test

slamgirl [31]

Answer:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

The 95% confidence interval would be given by (96.625;100.915)

a) $df=n-1= 19-1= 18$

b) $p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

c) The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

Step-by-step explanation:

Previous concepts and data given

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".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

$\bar X=98.77$ represent the sample mean

$s=4.77$ represent the sample standard deviation

n=19 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if we have significant difference on the mean of 100, the system of hypothesis would be:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we can calculate the Standard error for the mean like this:

$SE_{Mean}=\frac{s}{\sqrt{n}}=\frac{4.77}{\sqrt{19}}=1.094$

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

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

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 $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$98.77-1.96\frac{4.77}{\sqrt{19}}=96.625$

$98.77+1.96\frac{4.77}{\sqrt{19}}=100.915$

So on this case the 95% confidence interval would be given by (96.625;100.915)

Part a

The degree of freedom are given by:

$df=n-1= 19-1= 18$

Part b

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

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

$t=\frac{98.77-100}{\frac{4.77}{\sqrt{19}}}=-1.124$

Then since is a two sided test the p value would be:

$p_v =2*P(t_{18}$

If we compare the p value and a significance level for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Part c

If the system of hypothesis on this case are:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu > 100$

The only thing that changes is the p value and would be given by:

$p_v =P(t_{18}>-1.124)=0.862$

But again since the p value is higher than the significance level we fail to reject the null hypothesis.

7 0

3 years ago

If the length of a rectangle is 12 ft. and its area is 84 sq. ft., find the width of the rectangle.

Ket [755]

Area = LxW
84 = 12 x x
84/12 = 7

7 0

3 years ago

Kai used fabric measuring 5 yards in length to make each costume for a school play. The relationship between the number of costu

Yuki888 [10]

The best interpretation of 2 in the given context is that; 2 represents the total length of fabric in yards purchased when no costumes were made.

<h3>Slope Intercept Form</h3>

We are given the relationship between the number of costumes that Kai made, x, and the total length of fabric that he purchased y, in yards as; y - 5x = 2

Where;

x is number of costumes made
y is total length of fabrics purchased.

Now, the general slope intercept form of an equation is given by; y = mx + c

Where c is the y-intercept which is the point where x is zero.

Thus, our equation can be rewritten as;

y = 5x + 2

Comparing with y = mx + c, we can say that c = 2

This means that at x = 0, y = 2.

In conclusion, the value 2 represents the length of yards purchased when no costumes were made.

Read more about slope-intercept form at;brainly.com/question/1884491

5 0

2 years ago