Can someone please help me with this one

Which statement best describes the interquartile range of this set of weights? {120 lb, 115 lb, 135 lb, 105 lb, 80 lb, 160 lb} t

gtnhenbr [62]

i don’t really know

a
f
f
s
a

9 0

3 years ago

Need help with AP CAL

anzhelika [568]

Answer: Choice C

$\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)$

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Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve $y = e^{-x}$

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is $e^{-x}$ where 0 < x < 1

Let's compute the area of each general cross section.

$\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\$

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

$\displaystyle \int_{0}^{1}e^{-2x}dx\\\\$

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

If x = 0, then u = -2x = -2(0) = 0
If x = 1, then u = -2x = -2(1) = -2

This means,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\$

I used the rule that $\displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx$ which says swapping the limits of integration will have us swap the sign out front.

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Furthermore,

$\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

In short,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

This points us to choice C as the final answer.

5 0

1 year ago

Name a fourth point in plane UVX

sveticcg [70]

Answer:

The correct option is;

W

Step-by-step explanation:

The number of points that defines a plane in a Euclidean space in all dimensions is either three points which are not on the same line, or two colinear points and a third point not on the line

The given points of the plane are UVX, which gives the plane as being diagonal to the cube and perpendicular to the side face of the cube.

The fourth point in plane UVX is therefore W.

8 0

3 years ago

How now why would a prism beat a sphere in a competion

Lemur [1.5K]

Answer:

Because a prism travels at the speed of light . :)

3 0

2 years ago

Given: BD is a diameter m 1= 100° m BC = 30° m CD = 100 150 330

sertanlavr [38]

Answer:

150

Step-by-step explanation:

330 is to big because the diameter is 180

100 is angle 1 and CD is bigger

so it would be 150

hope i helped

4 0

2 years ago