PLS HELP ME ASAP GUYS!! THANK U SM!! HELP! Thank u!!

What is the GCF of the numerator and denominator in the following fraction? 21 m to the 2nd power n/28 mn to the 2nd power

algol [13]

7m would be the GCF in this case, leaving 3mn/4n

3 0

4 years ago

I'm confused in this question. Could anyone help me please?

stepladder [879]

Answer:

I think answer is opction no. 2

Step-by-step explanation:

x = C - 5/2

3 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

4 years ago

13. Evaluate f(x) = 12 for the function f(x) = 5(x - 3) + 17. A 2 B-2 C. 62 D. -62

Alekssandra [29.7K]

Answer:

Step-by-step explanation:

First, let's rewrite the original function:

ƒ(x) = 5(x – 3) + 17

This could easily be simplified, which might make it easier:

ƒ(x) = 5x – 15 + 17 — distribute the 5 to (x – 3)

ƒ(x) = 5x + 2 — simplify

That looks easier to solve, doesn't it? Now, let's substitute 12 for x and solve for ƒ(12) [this is another way of writing x = 12]

ƒ(12) = 5(12) + 2 — substitute 12 for x

ƒ(12) = 60 + 2 — multiply and simplify

ƒ(12) = 62 — add and simplify

Now, let's prove this method works by substituting 12 for x in the original function:

ƒ(x) = 5(x – 3) + 17 — original function

ƒ(12) = 5(12 – 3) + 17 — substitute 12 for x

ƒ(12) = 5(9) + 17 — here, I subtracted the numbers in the parentheses

ƒ(12) = 45 + 17 — simplify by multiplying 5 and 9

ƒ(12) = 55 + 7 — rewriting to make mental addition easier

ƒ(12) = 60 + 2 — rewriting to make mental addition easier; does this look familiar?

ƒ(12) = 62 — simplifying to find final answer

That's just one way of breaking up the numbers so they're easier to add. You could just use a calculator, but I did this in my head, so…

There's two more ways to use the original function to solve for ƒ(12), and it's these methods:

Method 1

ƒ(x) = 5(x – 3) + 17 — original function

ƒ(12) = 5(12 – 3) + 17 — substitute 12 for x

ƒ(12) = 60 – 15 + 17 — here, I distributed 5 to each term before doing anything else

ƒ(12) = 45 + 17 — simplifying by subtracting 15 from 60

ƒ(12) = 62 — simplifying; we get the same answer

Method 2

ƒ(x) = 5(x – 3) + 17 — original function

ƒ(12) = 5(12 – 3) + 17 — substitute 12 for x

ƒ(12) = 60 – 15 + 17 — here, I distributed 5 to each term before doing anything else

ƒ(12) = 60 + 2 — simplifying by subtracting 15 from 17

ƒ(12) = 62 — simplifying; we get the same answer

What happens every time? We get the same answer, ƒ(12) = 62! To boot, sometimes you can use a rule of three to prove something true: if something happens 3 times, it will be true. Of course, you probably won't have time to do all this. I did so to help you understand the concept better. By the way, the last two methods don't follow the order of operations, P.E.M.D.A.S. (operations in parentheses; exponents; multiplication; division; addition; subtraction). That's a heads-up in case you get an order of operations question so you don't make a mistake.

I hope this helps you! Have a great day!

3 0

3 years ago

Instructions: Problem 1 ! Find the missing angle in the image below. Do not include spaces in your answers

sweet-ann [11.9K]

Answer:

40 degrees

Step-by-step explanation:

The 100 degree angle is supplementary to angle CED. This means CED will end up being 80 degrees. Since the angles in all triangles equate to 180 degrees 80 + 60 + angle D must equal 180 degrees. Therefore, angle D has to be 40 degrees.

5 0

3 years ago