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2 years ago

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Sixteen students each measured the weight of 25 pennies, in grams. The list shows their measurements. 60, 62, 65, 59, 63, 63, 63

, 62, 64, 62, 60, 61, 66, 64, 61, 65 In each graph below, the mean is indicated by a solid vertical line segment while the standard deviations from the mean are indicated by dotted vertical line segments. Which graph represents the distribution of weights?

2 answers:

saveliy_v [14]2 years ago

5 0

Third one is the answer

maksim [4K]2 years ago

3 0

The correct answer is c

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Sam owes the bank a little less than $40$40. Which choice could be his balance?

tresset_1 [31]

D. because he says a little least and plus two of the other answer choices are negative so use process of elimination and D will be your answer.

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2 years ago

Read 2 more answers

ABCD is a rectangle. Trapezoid AEFB is congruent to trapezoid CFED. G is the midpoint of segment EF. Select all the ways we coul

iris [78.8K]

Answer: C, D and E

Step-by-step explanation: I'm a high school student and my teacher just went over this exact problem today. Here's somewhat how he explained it.

If you draw out trapezoid AEFB and turn it once clockwise or counterclockwise you would have only turned it 90 degrees but, turn it one more time (180) and you will see that it looks just like figure CFED. That's how I got the answers C and E. Ok, now for D its kinda the same thing Just because it say translate doesn't mean the shape would change. Even if you slide the shape and turn it two times in either direction you will still get figure CFED. Your Welcome

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2 years ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

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2 years ago

a square photo display board is made up of 60 rows of 60 photos each the area of each square photo is 4 square inches how long i

andreyandreev [35.5K]

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2 years ago

Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences. Graph showing

nika2105 [10]

Answer:

(x, y) = (1, 5)

Step-by-step explanation:

The solution is where the graphs intersect. Your problem statement says that solution point is ...

(x, y) = (1, 5)

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2 years ago