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3 years ago

What is the midpoint of segment AB if A = (-2,2) and B = (4.-6)?

Mathematics

1 answer:

liraira [26]3 years ago

7 0

Answer:

$M=(1,-2)$

Step-by-step explanation:

Start with the midpoint formula:

$M=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

Identify your values:

$x_1=-2\\x_2=4\\y_1=2\\y_2=-6$

Substitute:

$M=(\frac{-2+4}{2} , \frac{2+(-6)}{2} )$

Combine terms:

$M=(\frac{2}{2},\frac{-4}{2} )$

Simplify:

$M=(1,-2)$

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If you wanted to predict the value of the y variable when the x variable is 15, you would be _____ the data.

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Extrapolation is the process by which a value is estimated by using a previously known set of numbers. Interpolation is where a value is estimated between two known values. In this case, if you wanted to predict the value of the y-variable when the x-variable is 15, you would be extrapolating beyond the known data-set.

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3 years ago

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An investment strategy has an expected return of 15 percent and a standard deviation of 9 percent. Assume investment returns are

IgorLugansk [536]

Answer:

68% of an investment earning a return between 6 percent and 24 percent.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 15

Standard deviation = 9

How likely is it to earn a return between 6 percent and 24 percent?

6 = 15 - 1*9

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By the empirical rule, there is a 68% of an investment earning a return between 6 percent and 24 percent.

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2 years ago

1000+1000= please and thank you

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Answer:

2000

Step-by-step explanation:

1+1=2

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3 years ago

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A projectile is fired at such an angle that the vertical

svetoff [14.1K]

(a) The projectile remains in the air for 10 seconds

(b) It travels a horizontal distance of 600 meters

Step-by-step explanation:

A projectile is fired at such an angle that

1. The vertical component of its velocity is 49 m/sec

2. The horizontal component of its velocity is 60 m/sec

We need to find:

(a) How long the projectile remains in the air

(b) The horizontal distance it travels

∵ The vertical distance y = $u_{y}$ t - $\frac{1}{2}$ g t², where

$u_{y}$ is the vertical component of its velocity, g is the acceleration

of gravity and t is the time

∵ y = 0 ⇒ it return to the same initial height

∵ $u_{y}$ = 49 m/s

∵ g = 9.8 m/s²

- Substitute these values in the rule above

∴ 0 = 49 t - $\frac{1}{2}$ (9.8) t²

∴ 0 = 49 t - 4.9 t²

- Take t as a common factor

∴ 0 = t (49 - 4.9 t)

- Equate each term by 0

∴ t = 0 ⇒ at initial position

∴ 49 - 4.9 t = 0

- Add 4.9 t to both side

∴ 49 = 4.9 t

- Divide both sides by 4.9

∴ t = 10 seconds

(a) The projectile remains in the air for 10 seconds

∵ The horizontal distance = $u_{x}$ t, where $u_{x}$ is the

horizontal component of its velocity

∵ $u_{x}$ = 60 m/sec

∵ t = 10 seconds

∴ x = 60 × 10 = 600 meters

(b) It travels a horizontal distance of 600 meters

Learn more:

You can learn more about the component of velocity in brainly.com/question/4464845

#LearnwithBrainly

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