Explain how to subtract the polynomial (The first attachment) from (The second attachment)

Diana worked on her science project for 6 1 3 hours. Gabe worked on his science project 1 3 4 times as long as Diana. Paula work

Vaselesa [24]

Are your numbers right? Diana worked on her project for 613 hours, Gabe worked on it for 134 times as long as Diana, and Paula worked on her science project 34 times as long as Diana? Assuming they are, It is false that Diana worked longer on her science project than Gabe worked on his. Tell me if I read the question wrong, I am happy to help.

4 0

3 years ago

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca

saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

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".

Let put some notation

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as $d_i = y_i -x_i$ and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}$

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

$\bar d=-0.7$ represent the sample mean for the difference

$\mu_d$ population mean (variable of interest)

$s_d$ =1.32 represent the sample standard deviation

n=8 represent the sample size

Confidence interval

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

$\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

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: "=-T.INV(0.025,8)".And we see that $t_(\alpha/2)=2.306$

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

$-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776$

$-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376$

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between $-1.776 \leq \mu_d \leq 0.376$ . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0

3 years ago

The plans for a shed call for a rectangular floor with a perimeter of 204 ft. The length is two times the width. Find the length

Harlamova29_29 [7]

A-length
b-width
perimeter of rectangular floor: 2a+2b=204
<span>The length is two times the width: a=2b
</span>2a + 2b = 204
2*2b + 2b = 204
6b = 204|:6
b = 34
a=2b=2*34=68

a=68->length
b=34->width

8 0

3 years ago

Read 2 more answers

A box contains 12 balls numbered 1 through 12. Two balls are drawn in succession without replacement. If the second ball has the

Nikitich [7]

<h2>Answer with explanation:</h2>

A box contains 12 balls numbered 1 through 12.

Also the ball are drawn without replacement.

a)

The probability that the first ball had a smaller number on it.

i.e. the number on the first ball could be: {1,2,3}

Hence, the probability that the first ball had a smaller number on it is: