Help asap , apx algebra 1

Mathematics

1 answer:

Troyanec [42]3 years ago

5 0

D. 3
F(x) is referring to y. The question is asking what x is when y is 4.

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A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if ev

uysha [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The null hypothesis is $H_o : \beta_1 = 0$

The alternative hypothesis is $H_1 : \beta_1 \ne 1$

Step-by-step explanation:

From the question we are told that

The number observations is $n = 100$

The annual salary (in dollars) is y

The mean score on teaching evaluation is x

The the relationship between the y and x is

$y = \beta_0 + \beta _1 x + \epsilon$

Where $\beta _1$ is the mean of the equation so

The null hypothesis is $H_o : \beta_1 = 0$

The alternative hypothesis is $H_1 : \beta_1 \ne 1$

6 0

2 years ago

find the volume of a solid that is generated by rotating around the indicated axis the plane region bounded by the giveb curves:

Fofino [41]

Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.

A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)

B. By integration, using the washer method
Volume = $2\pi\int_{-1}^1(1-x^2)(2-x)dx$
$=2\pi\int_{-1}^1(x^3-2x^2-x+2)dx$
$=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}$
$=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])$
$=2\pi(8/3)$
= 16 π /3 as before