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4 years ago

8

Elizabeth has two identical number cubes. Both cubes have faces numbered 1 thourgh 6. if Elizabeth rolls each cube once, what is

the probability that the sum of the two numbers on the top faces will be 10.

1 answer:

n200080 [17]4 years ago

7 0

I believe the answer is 4 out of 12.

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A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a

kow [346]

Answer:

II and III

See explanation above

Step-by-step explanation:

When all other rings remain the same, which of the following conditions would have resulted in a wider interval than the one constructed?

I. A sample size of 20 with 95 percent confidence

II. A sample size of 15 with 99 percent of confidence

III. A sample size of 12 with 95 percent confidence

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

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

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

The margin of error is given by:

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

I. A sample size of 20 with 95 percent confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new sample size n=20 the degrees of freedom for the new interval interval would be n-1=19 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.09$

And then the Margin error would be:

$ME=2.09 \frac{s}{\sqrt{20}}=0.467 s$

So then we have a lower margin of error so then we will have a shorter interval

II. A sample size of 15 with 99 percent of confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new interval the sample size n=15 the degrees of freedom for the new interval interval would be n-1=14 , the value for $\alpha=0.01$ and $\alpha/2=0.005$ and then the critical value is $t_{critc}=2.98$

And then the Margin error would be:

$ME=2.98 \frac{s}{\sqrt{15}}=0.769 s$

So then we have a greater margin of error so then we will have a wider interval. And this makes sense since with more confidence the interval needs to be wider.

III. A sample size of 12 with 95 percent confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new interval the sample size n=12 the degrees of freedom for the new interval interval would be n-1=11 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.20$

And then the Margin error would be:

$ME=2.20 \frac{s}{\sqrt{12}}=0.635 s$

So then we have a greater margin of error so then we will have a wider interval.

5 0

4 years ago

Sin^2x/cos^2 + sinxcscx = sec^2x Identify it, please explain so I know how you did it, thanks

max2010maxim [7]

$\frac{sin^2x}{cos^2x} + sin x *cscx\\ tan^2x + \frac{sin x}{sin x} \\ tan^2x + 1\\ sec^2x$

$\frac{sin^2x}{cos^2x} = tan^2x$

$csc x = \frac{1}{sinx}$

$tan^2x + 1 = sec^2x$

6 0

3 years ago

PLSSS HELP will make brainliest

RSB [31]

Answer:

151 degrees

Step-by-step explanation:

x and 29 =180

180-29=151 which equals x

3 0

4 years ago

HELP PLEASE ON 13- A, B, C<br><br>Can anyone tell me if the ones I did are right

KiRa [710]

13a.) If you're dividing and the base (in this case the base is 10) is the same, subtract the exponents.
${10}^{7} \div {10}^{5} = {10}^{7 - 5} = {10}^{2}$
13b.) If you're multiplying and the base is the same, then you add the exponents:

${s}^{2} \times {s}^{3} \times s = {s}^{2 + 3 + 1} = {s}^{6}$
13c.) This is similar to 13b:

${6}^{4} \times {6}^{3} \times 6 = {6}^{4 + 3 + 1} = {6}^{8}$

4 0

3 years ago

Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. E

Elenna [48]

Answer:

2

Step-by-step explanation:

a₃ = -2

a₇ = -10

The nth term of an arithmetic sequence is:

a = a₁ + d (n − 1)

Therefore:

-2 = a₁ + d (3 − 1) = a₁ + 2d

-10 = a₁ + d (7 − 1) = a₁ + 6d

Subtract the equations:

8 = -4d

d = -2

Plug into either equation to find the first term.

-2 = a₁ + 2(-2)

a₁ = 2

5 0

3 years ago