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Semenov [28]
3 years ago
10

Use the equation of the circle centered at the origin and

Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer:

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+(y-k)^2=r^2

If we are given x and y as 0 and 5 respectively, and we are also told that the center is (0, 0), our h and k are both 0. Filling in x, y, h, and k we can find the radius. So let's do that:

(0-0)^2+(5-0)^2=r^2 and

0^2+5^2=r^2 so

r^2=25  Our circle's equation is

x^2+y^2=25

Since the point in question, (4, 4), lies in the first quadrant, we will concentrate on that quadrant only. To fall within the circle, we can set up an inequality and test the point (4, 4). If it lies ON the circle then the equality would be true. Let's try that first:

4^2+4^2=25

Obviously, 16 + 16 does not equal 25, so that point (4, 4) does not lie ON the circle. In fact from that statement alone, we can determine that the point lies outside the circle because

4^2+4^2>25

If the inequality < were true then the point would lie inside.

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The Lylian is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be an
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Answer:

p_v =P(z>z_{calc})

In order to establishing the success of the method we need to obtain a p value very low in order to reject the null hypothesis because we need  enough evidence in favor of the alternative hypothesis, so then the best option would be:

f. 0.001

Step-by-step explanation:

We need to conduct a hypothesis in order to test the claim that one of several methods claimed to increase the likelihood of a baby girl so then the system of hypothesis are:  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p > 0.5  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The p value for this case is given by:

p_v =P(z>z_{calc})

In order to establishing the success of the method we need to obtain a p value very low in order to reject the null hypothesis because we need  enough evidence in favor of the alternative hypothesis, so then the best option would be:

f. 0.001

3 0
3 years ago
9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?
ZanzabumX [31]
<h3>Answer:  17,280</h3>

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

=========================================================

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

-------------

Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.

6 0
3 years ago
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