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2 years ago

What is MEAN ABSOLUTE DEVIATION and how do you find it?

Mathematics

1 answer:

Fynjy0 [20]2 years ago

8 0

Step-by-step explanation:

Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points.

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

The dog’s leash is 60 inches long. If the dog walks back and forth with its leash pulled tight while the leash is tied to the li

labwork [276]

Answer:

150.08 inches

Step-by-step explanation:

The question simply requires that we find the length of the arc that the dog walks.

Its leash rotates through 150° and the length of the leash (radius) is 60 inches.

The length of an arc is given as:

L = α/360 * 2πR

where α = angle of arc

R =radius

Therefore:

L = 150/360 * 2 * π * 60

L = 150.08 inches

The dog walks 150.08 inches

5 0

2 years ago

The newborn weights 7 pounds and is 21 inches long. What is the ratio of weight to length?

Nikolay [14]

Answer:

1:3

Step-by-step explanation:

The required ratio will be ,

7:21

= 1 :3

4 0

2 years ago

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Find the equation in standard form of the line passing through the points (2,-3) and (4,2)

mario62 [17]

The line passes through (2,-3) and (4,2).

Calculate the slope of the line.
m = (2+3)/(4-2) = 5/2

The equation of the line is therefore
$\frac{y-2}{x-4} = \frac{5}{2}$

Cross multiply.
2(y-2) = 5(x-4)
2y - 4 = 5x - 20
2y = 5x - 16
Rewrite as
5x - 2y = 16

Answer: C. 5x - 2y = 16

8 0

3 years ago

AB is dilated by a scale factor of 3 to form A'B' . Point O, which lies on AB , is the center of dilation. The slope of AB is 3.

Anna [14]

Given that AB has been dilated by scale factor 3 to form A'B', and by laws of dilation, the image is congruent to the pre image. This implies that the image will not change in any way whatsoever apart from the size. Hence the slope will remain the same. That means the slope of A'B' will be 3

7 0

2 years ago

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