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3 years ago

In which set are all of the numbers solutions to this inequality?

1 answer:

8 0

The answer is answer choice B,

B) {-2, -1, 0, 1}

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

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Researchers would like to test if the mean bone mineral density is different for the three different groups. Conduct an ANOVA te

laiz [17]

Answer:

H₀: μ₁ = μ₂= μ₃

Hₐ: At least one of the means is different.

Step-by-step explanation:

Analysis of variance or ANOVA test is used to determine whether the means of different groups are similar or not.

The hypothesis of an ANOVA test for n homogeneous groups is:

$H_{0}: \mu_{1}= \mu_{2}= \mu_{3}...= \mu_{n}\\H_{a}: At\ least\ one\ of\ the\ means\ is\ different$

In this case the researcher is testing whether the mean bone mineral density is different for the three different groups.

The hypothesis for this test can be defined as follows:

H₀: The mean bone mineral density is not different for the three different groups, i.e. μ₁ = μ₂= μ₃

Hₐ: The mean bone mineral density is different for the three different groups, i.e. at least one of the means is different.

3 0

3 years ago

A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

6 0

3 years ago

How many different groups of 3 movies can a person rent if there are 12 movies to choose from?

Norma-Jean [14]

If there are 12 movies and a person can rent three, then there are 220 different combinations they can be rented in.

3 0

3 years ago

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A rectangular is 8 meters long and 7 meters wide. What is its area?

Degger [83]

Answer:

56m^2

Step-by-step explanation:

The formula on getting the area of a rectangle is width x height. Therefore you just have to multiply 8 (height) to 7 (width). the answer is ^^^

8 0

2 years ago

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273 scientific notation

jeka57 [31]

Answer: 2.73 x 10 the the power of 2

Step-by-step explanation:

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3 years ago