All categories

3 years ago

Planes X and Y and points C, D, E, and F are shown.

Mathematics

1 answer:

viva [34]3 years ago

5 0

Answer:

The answer is below

Step-by-step explanation:

The planes are shown in the image below.

From the image, points D and E are on plane Y, while point F is on plane X.

A) The line that can be drawn through points C and D is contained in plane Y.

This statement is wrong because point C is not in plane Y

B) The line that can be drawn through points D and E is contained in plane Y.

Correct. Since both points D and E are on plane Y, hence The line that can be drawn through points D and E is contained in plane Y.

C) The only point that can lie in plane X is point F.

This statement is correct because from the image only point F is on plane X.

D) The only points that can lie in plane Y are points D and E.

This statement is correct because from the image only point D and E is on plane Y.

You might be interested in

Bogdan [553]

Answer:

The present value of 10,000 if interest is paid at a rate of 6.2% compounded weekly for 8 years is 6097.56

Explanation:

We know that compound interest is given by

$A=P\left(1+\frac{r}{n}\right)^{n t}$

Where ,

Where A = final amount (which is given to be = 10000)

P = Principal amount (which is the present amount which we have to find)

r = interest rate = 6.2 = 0.062

n = no. of times interest applied per time period = it is given that the interest is applied weekly, so in one year there are 52 weeks so n = 52

t = time period = 8 years

Substituting the given values, we get

$10000=\mathrm{P}\left(1+\frac{6.2}{52}\right)^{52\times 8}$

P = 6097.5

We get, P = 6097.56 which is the present value of a sum of money

3 0

3 years ago

An article describes the chemical compositions of certain minerals in the early Archaean mantle. For a certain type of olivine a

Ket [755]

Answer:

The mean is 40.35 and the standard deviation is 0.13.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a certain type of olivine assembly, the silicon dioxide (SiO2) content (in weight percent) in a randomly chosen rock has mean 40.35 and standard deviation 0.4.

Sample of 10:

By the Central Limit Theorem, the mean is 40.35, and the standard deviation is $s = \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{10}} = 0.13$

The mean is 40.35 and the standard deviation is 0.13.

5 0

3 years ago

The Three angles of a triangle have measures 7x+6,10x-8 and 5x+3.What is the measure of the smallest angle?

g100num [7]

Answer:

43 15/22 degrees

Step-by-step explanation:

The three angles add to 180 degrees

7x+6 +10x-8 + 5x+3 = 180

Combine like terms

22x +1 = 180

Subtract 1 from each side

22x +1-1 =180-1

22x = 179

Divide each side by 22

22x/22 = 179 /22

x =179/22

The smallest angle is

5x+3

5(179/22) +3

895/22 +3

40 15/22 +3

43 15/22 degrees

8 0

3 years ago

What is the answer to this problem

daser333 [38]

I believe it is 1/2 or 2/1 but i am not positive

3 0

3 years ago

In a random sample of 25 people, the mean commute time to work was 33.9 minutes and the standard deviation was 7.2 minutes. Ass

Phoenix [80]

Answer:

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that $t_{\alpha/2}=1.32$

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

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

7 0

4 years ago