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3 years ago

Find the distance and midpoint of the following points: (3, 2) and (8, 9)

Mathematics

1 answer:

azamat3 years ago

6 0

Answer:

Midpoint:

$\frac{3 + 8}{2} = 6.5 \: \: \: \: \frac{2 + 9}{2} = 6.5 \\ (6.5 \: and \: 6.5) \\ \\ distance - \sqrt{(8 - 3) {}^{2} + (9 - 2) {}^{2} } \\ \sqrt{25 + 49} = \sqrt{74}$

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In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confiden

Vlad [161]

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that $n = 2161, \pi = \frac{1214}{2161} = 0.5618$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Margin of error:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}$

$M = 0.0209$

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

4 0

3 years ago

Graph the six terms of a finite series where a1 = −3 and r = 1.5.

s344n2d4d5 [400]

We are given the first term and the common ratio, this means they belong to a geometric series.

For the given series:

$a_{1}=-3 \\ 
r=1.5$

Each term of the geometric series is obtained by multiplying the previous term by common ratio.

So the next terms will be:

-4.5, -6.75, -10.125, -15.1875, -22.78125

The general formula for the G.P would be:

$a_{n}=-3(1.5)^{n-1}$

On plotting the series, the result will be like this:

6 0

3 years ago

Read 2 more answers

QUESTION 4

ANEK [815]

(2x-1)(x+4)=0

Step-by-step explanation:

A random zero property of multiplication is taken to find the solution

(2x-1)(x+4)=0

consider a=2x-1 and b=x-4 a.b=0

either a or b or both must be 0

equating both the equations

2x-1=0 or x=4=0 x-4=0

2x-1=0 x=4

2x=1

x=1/2

substitute the values of x in the main equation

[2(1/2)-1][(1/2)+4]=0

3 0

3 years ago

Read 2 more answers

Laura created a website to create T-shirts. In the first month she put up her website she had only a single T-shirt order. Each

kiruha [24]

Laura received 144 orders over the first year

Solution:

Given function is:

f(n) = 2n - 1

Where, "n" is the month

In the first month she put up her website she had only a single T-shirt order

f(1) = 2(1) - 1 = 2 - 1

f(1) = 1

There are 12 months in a year

For the second month, and third month and so on, substitute n = 2, 3 and so on

f(2) = 2(2) - 1 = 4 - 1 = 3

f(3) = 2(3) - 1 = 6 - 1 = 5

f(4) = 2(4) - 1 = 8 - 1 = 7

f(5) = 2(5) - 1 = 10 - 1 = 9

f(6) = 2(6) - 1 = 12 - 1 = 11

f(7) = 2(7) - 1 = 14 - 1 = 13

f(8) = 2(8) - 1 = 16 - 1 = 15

f(9) = 2(9) - 1 = 18 - 1 = 17

f(10) = 2(10) - 1 = 20 - 1 = 19

f(11) = 2(11) - 1 = 22 - 1 = 21

f(12) = 2(12) - 1 = 24 - 1 = 23

Thus total orders received over first year:

Total orders = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Total orders = 144

Thus she received 144 orders over the first year

8 0

2 years ago

Is the point (2, 2 1/2) on the graph of y=x+2? How do you know?

Ksenya-84 [330]

Answer:

No, it is not on the graph.

Step-by-step explanation:

Plug in (2, 2 $\frac{1}{2}$ ) to y = x + 2

(2 $\frac{1}{2}$ ) = (2) + 2

$2\frac{1}{2} \neq 4$

6 0

3 years ago