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3 years ago

What measures of spread is an average distance from the mean?

Mathematics

1 answer:

MrMuchimi3 years ago

7 0

Answer:

Step-by-step explanation:

The idea behind the standard deviation is to quantify the spread of a distribution by measuring how far the observations are from their mean. The standard deviation gives the average (or typical distance) between a data point and the mean.

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Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

The measure of b is..

sladkih [1.3K]

Answer:

b =21

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

20^2 + b^2 = 29^1

400 + b^2 =841

Subtract 400 from each side

b^2 = 441

Take the square root of each side

sqrt(b^2) = sqrt(441)

b =21

7 0

3 years ago

Read 2 more answers

Jacob has a rectangular garden with an area of 56 square feet.The length of the garden is 8 feet.What is the width if the garden

blagie [28]

Answer:

The width of the garden is 7 feet.

Step-by-step explanation:

If the area is 56 feet, and the length is 8 feet, we can put this into the area equation.

Area = width * length

A = wl

Substitute variables.

56 = 8w

Divide by 8.

7 = w, or w = 7.

The width of the garden is 7 feet.

5 0

3 years ago

a vending machine takes only nickels and dimes. at the end of the day there were three times as many nickels as dimes and a tota

Ksivusya [100]

100 dimes and 300 Nickels

3 0

3 years ago

Read 2 more answers

Segment CD has point E located on it such that CE:ED = 3:5. If the endpoints are located at C(5, -6) and D(11,18) then what are

wlad13 [49]

Answer:

E(29/4,3)

Step-by-step explanation:

Given that,

Segment CD has point E located on it such that CE:ED = 3:5

The coordinates of C and D are (5, -6) and (11,18) respectively.

We need to find the coordinates of E. Let the coordinates are (x,y). Using section formula to find it as follows :

$(x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2})\\\\(x,y)=(\dfrac{3(11)+5(5)}{3+5},\dfrac{3(18)+5(-6)}{3+5})\\\\=\dfrac{29}{4},3$

So, the coordinates of E are (29/4,3).

4 0

3 years ago

What measures of spread is an average distance from the mean?￼

What measures of spread is an average distance from the mean?