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3 years ago

given the midpoint and one endpoint of a line segment, find the other endpoint. endpoint: (4, 10) midpoint: (5, 9)

1 answer:

4 0

The answer is (6, 8).

EXPLANATION

If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

That is:

$( \frac{x1 + x2}{2}. \frac{y1 + y2}{2} )$

But since the midpoint is given, we'll work this out in a different way.

To find the x of the other endpoint or x2, we'll have first to plug-in the given x values in the midpoint and x1.

So,

$m = \frac{x1 + x2}{2} \\ 5= \frac{4 + x2}{2}\\ 10= 4 + x2 \\ x2 = 6$

Now, let's proceed to y2.

$m = \frac{y1 + y2}{2} \\ 9= \frac{10 + y2}{2}\\ 18= 10 + y2 \\ y2 = 8$

So now you have the x and y values of the other endpoint: (6,8).

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Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at ru

valina [46]

For this study, we should use t-test and the null and alternative hypotheses would be given by H₀: μ = 7 and H₁: μ < 7.
The test statistic is -1.941 and the p-value (0.0381) is greater than α = 0.01.
Based on this, we should fail to reject the null hypothesis.
Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

<h3>What is a null hypothesis?</h3>

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

<h3>How to calculate value of the test statistic?</h3>

The test statistics can be calculated by using this formula:

$t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }$

Where:

x is the sample mean.

u is the mean.

is the standard deviation.

n is the number of hours.

For this study, we should use t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₁: μ < 7

$t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }$

t = -0.7/0.3606

t = -1.941.

For the p-value, we have:

P-value = P(t < -1.9412)

P-value = 0.0381.

Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.

Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

Read more on null hypothesis here: brainly.com/question/14913351

#SPJ1

4 0

2 years ago

Does anyone have the answers for all?

Shkiper50 [21]

Answer and Step-by-step explanation:

1-6

What you can do is plug in 6 and start by doing the first machine first, then the second. If this doesn't work, do the second machine, then the first machine.

The order that works is second machine, then first machine.

Second Machine:

y = $(6)^{2} -6$ = 36 - 6 = 30

Plug into first machine now.

First Machine:

y = $\sqrt{(30) - 5} = \sqrt{25} = 5$

We see that the result is 5.

b. If we were to do the order of second machine, then first machine, we will never get a negative result (or -5 for that matter), due to the fact that you can't algebraically square root a negative number.

However, if we were to do the order of first machine, second machine, we can get a negative number. To get -5, we plug in 6 for x in the first machine, getting an answer of 1. We plug this into the second machine, getting 1^2 - 6, which results in -5.

1-7. The absolute value of a value is the positive version of that value.

a. |54| = 54

b. $-|-7\frac{3}{5}|$ = $-7\frac{3}{5}$

c. |3| - |-1| = 3 - 1 = 2

d. |2.2 - 5.13| = |-2.93| = 2.93

1-8.

| |

| |

| || || || || |

(5 boxes on each side)

| |

| |

| || || || || || |

(6 boxes on each side)

b. The amount of squares on each side of the figure increases by 1.

c. There would be 1 square, because we know that the pattern is there is 2 squares added to the next figure, 1 at each end. If we go back a figure, we take away 2 squares.

1-9.

a. -42 - 17 = -59

b. 8 - (-9) = 8 + 9 = 17

c. 8(-9) = -72

d. -42 ÷ (-7) = 6

e. -2(-3)(-4) = 6(-4) = 24

f. -18 - 7 = -25

g. $(-5)^{2}$ = 25

h. $-5^{2} = -(5)^2 = -(25)$ = -25

i. $\sqrt{49}$ = 7

1-10. x = 2 Plug 2 in for x, then solve.

a. y = 7 - 3(2) = 7 - 6 = 1

b. y = $(2)^2 -1$ = 4 - 1 = 3

c. y = $\frac{18}{2}$ = 9

#teamtrees #PAW (Plant And Water)

I hope this helps!

8 0

3 years ago

1. Christina drew a scale model of an Olympic-size swimming pool using a

victus00 [196]

Answer: 4,5

Step-by-step explanation:

5 0

3 years ago

I need help can you help me?

Nookie1986 [14]

D - -x^2 + 3x + 7

To find this, first write out the equation:

(3x + 1) - (x^2 - 6)

Distribute the negative into x^2 and -6 so you're equation now looks like this:

3 x + 1 - x^2 + 6

Combine like terms and arrange the equation into ax^2 + bx + c to get the final answer of:

-x^2 + 3x + 7

Hope this helps!

8 0

3 years ago

If 2x^2 -2y^2 = 72 and if x+y=18 what does x-y equal

Tju [1.3M]

First factor out the 2:

x^2 - y^2 = 36

x^2 - y^2 can be factored into (x+y)(y-y) so:

(x + y)(x - y) = 36

plug in your value:

18 (x-y) = 36 and you should be able to take it from there

7 0

3 years ago

Read 2 more answers