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4 years ago

Find the distance between points M(-7,5) and Z(2,-3)

Mathematics

1 answer:

julsineya [31]4 years ago

8 0

Hey there! I'm happy to help!

To find the distance between two points, you find the difference between the x values, square that, find the difference between the y values, square that, add the two numbers you got, and then find the square root.

We find the difference between the x values.

-7-2=-9

Square it.

-9²=81

We find the difference between the y-values.

5--3

5+3=8

We square it.

8²=64

We add the numbers we got.

81+64=145

We square root.

√145≈12.04

This formula comes from the Pythagorean Theorem! Now you can find the distance between any two points! Have a wonderful day! :D

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2x +5 > -1 on the number line

Naya [18.7K]

Answer:

Below

Step-by-step explanation:

2x + 5 > -1

Treat the equality sign (ex. < >) as the costumary equal sign (=).

2x + 5 + (-5) > -1 + (-5) ---- -5 will cancel out the 5 on the left

2x/2 > -6/2 ------ divide by 2 to single out the x

x > -3

Remember to draw an open dot. Draw an arrow from -3 to the extreme right.

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2 years ago

If Joshua borrows $300 from his older sister to buy a bike and he promises to pay the total amount plus 5% simple interest in on

xenn [34]

Answer:

you multiply 300 by 5 % and that gives you 15

Step-by-step explanation:

5 0

3 years ago

Data on pull-off force (pounds) for connectors used in an automobile engine application are as follows:

netineya [11]

Answer:

a. A point estimate of the mean pull-force of all connectors in the population is approximately 75.7385

The point estimate for the mean used is the sample mean

b. The point estimate of the pull force that separates the weakest 50% of the connectors from the strongest 50% is 74.3131 N

c. The point estimate of the population variance is approximately 2.8577

The point estimate for the population standard deviation is approximately 1.6905

d. The standard error of the mean is approximately 0.3315

e. The point estimate of a proportion of the connectors are;

(72.7, 0.0385) , (73.8, 0.0769) , (73.9, 0.0385) , (74, 0.0385) , (74.1, 0.0385) ,(74.2, 0.0385), (74.6, 0.0385) , (74.7, 0.0385) , (74.9, 0.0385) , (75.1, 0.0769) , (75.3, 0.0385) , (75.4, 0.0385) , (75.5, 0.0385) , (75.6, 0.0385) , (75.8, 0.0385) , (76.2, 0.0385) , (76.3, 0.0385) , (76.8, 0.0385) , (77.3, 0.0385) , (77.6, 0.0385) , (78, 0.0385) , (78.1, 0.0385) , (78.2, 0.0385) , (79.6, 0.0385)

Step-by-step explanation:

The given data for the pull-force (pounds) for connectors used in an automobile engine are presented as follows;

Pull-force (pounds); 79.6, 75.1, 78.2, 74.1, 73.9, 75.6, 77.6, 77.3, 73.8, 74.6, 75.5, 74.0, 74.7, 75.8, 72.7, 73.8, 74.2, 78.1, 75.4, 76.3, 75.3, 76.2, 74.9, 78.0, 75.1, 76.8

a. A point estimate of the mean pull-force of all connectors in the population is the sample mean given as follows;

$Mean, \ \overline x = \dfrac{\Sigma x_i}{n}$

$\Sigma x_i$ = The sum of the data = 1966.6

n = The sample size = 26

Therefore, the sample mean, $\overline x$ = 1966.6/26 ≈ 75.7385

The point estimate for the mean is approximately 75.7385

The sample mean was used as the point estimate for the mean because it is simple and representative of the sample

b. The weakest 50% of the connectors are;

72.7, 73.8, 73.8, 73.9, 74, 74.1, 74.2, 74.6, 74.7, 74.9, 75.1, 75.1, 75.3

The sum of forces that separates the weakest 50%, $\Sigma x_{i}_{50 \%}$ = 966.2

The point estimate of the pull force that separates the weakest 50% of the connectors from the strongest 50% = $\Sigma x_{i}_{50 \%}$ /13 = 966.2/13 = 74.3131 N

c. The estimate of the population variance is the sample variance, given as follows;

$s^2 =\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n - 1}}$

Where;

${\sum \left (x_i-\overline x \right )^{2} }$ ≈ 71.4415

Therefore;

$s^2 =\dfrac{71.4415 }{25}} \approx 2.8577$

The point estimate of the population variance, s², is 2.8577

The point estimate for the population standard deviation, σ, is tha sample standard deviation, 's', given as follows;

s = √s² = √2.8577 ≈ 1.6905

The point estimate for the population standard deviation ≈ 1.6905

d. The standard error of the mean is given as follows;

$SE_{\mu_x} = \dfrac{s}{\sqrt{n} }$

Therefore, we have;

$SE_{\mu_x}$ = 1.6905/√(26) ≈ 0.3315

The standard error indicates the likely hood of the difference between the sample mean and the population mean

e. The point estimate of a proportion of the connectors are;

(Number of sample with a given pull-force value)/(Sample size (26))

Therefore, using Microsoft Excel, we have

8 0

3 years ago

Which statement describes the term economics?

TiliK225 [7]

C is the right answer

5 0

3 years ago

Read 2 more answers

A pro basketball player is a poorâ free-throw shooter. Consider situations in which he shoots a pair of free throws. The probabi

zlopas [31]

Answer:

The probability that he makes one of the two free throws is 0.38

Step-by-step explanation:

Hello!

Considering the situation:

A pro basketball player shoots two free throws.

The following events are determined:

A: "He makes the first free throw"

Ac: "He doesn't make the first free throw"

B: "He makes the second free throw"

Bc: "He doesn't make the second free throw"

It is known that

P(A)= 0.48

P(B/A)= 0.62

P(B/Ac)= 0.38

You need to calculate the probability that he makes one of the two free throws.

There are two possibilities, that "he makes the first throw but fails the second" or that "he fails the first throw and makes the second"

Symbolically:

P(A∩Bc) + P(Ac∩B)

P(A)= 0.48

P(Ac)= 1 - P(A)= 1 - 0.48= 0.52

P(Ac∩B) = P(Ac) * P(B/Ac)= 0.52*0.38= 0.1976≅ 0.20

P(A∩B)= P(A)*P(B/A)= 0.48*0.62= 0.2976≅ 0.30

P(A)= P(A∩B) + P(A∩Bc)

P(A∩Bc)= P(A) - P(A∩B)= 0.48 - 0.30= 0.18

Step 3

P(Ac∩B) + P(A∩Bc) = 0.20 + 0.18= 0.38

I hope this helps!

8 0

3 years ago