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BlackZzzverrR [31]
2 years ago
12

4. If TV = 14x - 8, find TU. 9x+2 5

Mathematics
1 answer:
Musya8 [376]2 years ago
5 0

<u><em>Answer:</em></u>

x = 3

<u><em>Explanation:</em></u>

The complete question is shown in the attached diagram

<u>Collinear points</u> are defined as points that lie on the same straight line

Since points U, T and V are given to be collinear, this means that these three points lie on the same straight line

Now, we are given that point U is between points T and V

This would mean that the length of segment TV can be written as the sum of the segments TU and UV

<u>Therefore:</u>

TV = TU + UV

<u>We are given that:</u>

TV = 14x - 8

TU = 9x + 2

UV = 5

<u>Substitute with the givens in the above mentioned equation and solve for x as follows:</u>

TV = TU + UV

14x - 8 = 9x + 2 + 5

14x - 8 = 9x + 7

14x - 9x = 7 + 8

5x = 15

x = 3

Hope this helps :)

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I believe the correct answer among the choice presented above is the second option. The minimum number of points needed to determine the equation of a line containing those points is two. This is because two points is also needed to make or define a line.
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A statistics practitioner in a large university is investigating the factors that affect salary of professors. He wondered if ev
Ulleksa [173]

Answer:

Step-by-step explanation:

Hello!

Given the linear regression of Y: "Annual salary" as a function of X: "Mean score on teaching evaluation" of a population of university professors. It is desired to study whether student evaluations are related to salaries.

The population equation line is

E(Y)= β₀ + β₁X

Using the information of a n= 100 sample, the following data was calculated:

R²= 0.23

                Coefficient    Standard Error  

Intercept    25675.5           11393

x                  5321                  2119

The estimated equation is

^Y= 25675.5 + 5321X

Now if the interest is to test if the teaching evaluation affects the proffesor's annual salary, the hypotheses are:

H₀: β = 0

H₁: β ≠ 0

There are two statistic you can use to make this test, a Student's t or an ANOVA F.

Since you have information about the estimation of  β you can calculate the two tailed t test using the formula:

t= \frac{b - \beta }{\frac{Sb}{\sqrt{n} } } ~t_{n-2}

t= \frac{ 5321 - 0 }{\frac{2119}{\sqrt{100} } } = 25.1109

The p-value is two-tailed, and is the probability of getting a value as extreme as the calculated t_{H_0} under the distribution t_{98}

p-value < 0.00001

I hope it helps!

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2 years ago
A web page design firm has two designs for an online hardware store. To determine which is the more effective design, the firm u
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Answer:

Explanatory variable : web page design

Response variables : Visitor's rating and amount of time visiting the site.

Kindly check explanation for the rest.

Step-by-step explanation:

The explanatory variable simply means the independent or predictor variable which is used to bring about a change in the dependent or predicted variable. The explanatory variable in the scenario above is the web page design which is used to measure the behavior and changes in the response variable which are the rating given by visitors and the number of visits on each of the two different web page designs available (explanatory variable).

The confounding factor which may affect the study is the different area assigned to test the effectiveness of each page ; designating one page for the Oakland area and the other for Miami. User preferences for each area may itself mask the actual outcome of the experiment.

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2 years ago
Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian
777dan777 [17]

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\B=30^o

Applying the law of sines

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(A)}=\frac{2}{sin(30^o)}

sin(A)=1

so

A=90^o

Find the measure of angle C

In a right triangle

we know that

B+C=90^o ----> by complementary angles

B=30^o

therefore

C=60^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{b}{sin(B)}

substitute the given values

\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}

c=2\sqrt{3}\ units

therefore

The dimensions of the triangle are

A=90^o

B=30^o

C=60^o

a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units

<em>Second case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\A=30^o

Applying the law of sines

Find the measure of angle B

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(30^o)}=\frac{2}{sin(B)}

sin(B)=0.25

so

using a calculator

B=14.48^o

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

A=30^o\\B=14.48^o

therefore

30^o+14.48^o+C=180^o

C=135.52^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{a}{sin(A)}

substitute the given values

\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}

c=5.61\ units

therefore

The dimensions of the triangle are

A=30^o

B=14.48^o

C=135.52^o

a=4\ units\\b=2\ units\\c=5.61\ units

see the attached figure to better understand the problem

4 0
2 years ago
(Ross 5.15) If X is a normal random variable with parameters µ " 10 and σ 2 " 36, compute (a) PpX ą 5q (b) Pp4 ă X ă 16q (c) PpX
pochemuha

Answer:

(a) 0.7967

(b) 0.6826

(c) 0.3707

(d) 0.9525

(e) 0.1587

Step-by-step explanation:

The random variable <em>X</em> follows a Normal distribution with mean <em>μ</em> = 10 and  variance <em>σ</em>² = 36.

(a)

Compute the value of P (X > 5) as follows:

P(X>5)=P(\frac{x-\mu}{\sigma}>\frac{5-10}{\sqrt{36}})\\=P(Z>-0.833)\\=P(Z

Thus, the value of P (X > 5) is 0.7967.

(b)

Compute the value of P (4 < X < 16) as follows:

P(4

Thus, the value of P (4 < X < 16) is 0.6826.

(c)

Compute the value of P (X < 8) as follows:

P(X

Thus, the value of P (X < 8) is 0.3707.

(d)

Compute the value of P (X < 20) as follows:

P(X

Thus, the value of P (X < 20) is 0.9525.

(e)

Compute the value of P (X > 16) as follows:

P(X>16)=P(\frac{x-\mu}{\sigma}>\frac{16-10}{\sqrt{36}})\\=P(Z>1)\\=1-P(Z

Thus, the value of P (X > 16) is 0.1587.

**Use a <em>z</em>-table for the probabilities.

8 0
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