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2 years ago

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .

1 answer:

6 0

First we need to find the volume of the prism without the dilated factor:

The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5 $ft^{2}$
Height of the prism = 10f

Volume(without dilated) = 5*10 = 50 $ft^{3}$

Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.

Volume of the dilated prism = $d^{3}$ * (Volume of the prism without dilation)

Where d = dilated factor. Therefore,

$v = (\frac{6}{5} )^{3} * 50$

v = 86.4 $ft^{3}$

So the correct answer: 86.4 $ft^{3}$

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Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The

Harlamova29_29 [7]

Answer:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

We have the following data given:

$n_1 =20$ represent the sample size for group 1

$n_2 =20$ represent the sample size for group 2

$\bar X_1 =43.5$ represent the sample mean for the group 1

$\bar X_2 =40.1$ represent the sample mean for the group 2

$s_1=4.1$ represent the sample standard deviation for group 1

$s_2=3.2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525$

And the deviation would be just the square root of the variance:

$S_p=3.678$

The statistic is givne by:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

6 0

2 years ago

Ron and amie opened an educational savings account for their daughter when she was born making a $5,000 initial investment. They

Arlecino [84]

Interest rate= 0.083%

Step-by-step explanation:

Principal= $5000 Amount= $10000 Time period= 12 years

A=Amount, P= Principal, I= Simple Interest r= Rate of interest t= Time period

$A= P+ I\\10000= 5000+ I\\I=10000-5000=5000\\I=Prt\\5000=5000*r*12\\r=5000/5000*12\\r=5000/60000\\r=0.083$

6 0

2 years ago

A(2, 5), B(2, -3), and D(-6, 5) are three vertices of square ABCD. What are the coordinates of the fourth vertex, C?

drek231 [11]

Since we know this figure is a square, we also know that all sides are the same. Therefore, we must figure out one side length and then use that math to find the other point. A simple way to do this is to graph the points and match them up for the missing corner.

In the graph below, you will see that (-6, -3) is circles in red, showing that it is the correct answer. The red dots show how we could match up the corners to find the answer.