Solve the equation below: X+2/3x = 4/x

Find an equation, or a set of equations, to describe the set of points that are equidistant from the points p(−9, 0, 0) and q(3,

wariber [46]

X = -3.
The distance from p(-9, 0, 0) is
d = sqrt((x+9)^2 + y^2 + z^2)
The distance from q(3,0,0) is
d = sqrt((x-3)^2 + y^2 + z^2)
Let's set them equal to each other.
sqrt((x+9)^2 + y^2 + z^2) = sqrt((x-3)^2 + y^2 + z^2)
Square both sides, then simplify
(x+9)^2 + y^2 + z^2 = (x-3)^2 + y^2 + z^2
x^2 + 18x + 81 + y^2 + z^2 = x^2 - 6x + 9 + y^2 + z^2
18x + 81 = - 6x + 9
24x + 81 = 9
24x = -72
x = -3
So the desired equation is x = -3 which defines a plane.

7 0

3 years ago

If two lines intersect at a right angle, then they are perpendicular

kipiarov [429]

This is TRUE!

The definition for perpendicular only applies when the lines are at a right angle which is 90°

4 0

3 years ago

Complete the page for 15 points.

sergey [27]

Answer:

1. 15, 16, 17

2. 21, 23, 25

3. 44, 46, 48

4. -4, -3, -2

Step-by-step explanation:

1)

Step 1. Writing an equation

Let's set x as the second number in the equation.

This means that the first number is x-1, and the third number is x+1.

We know that the sum of the three numbers is 48, so:

(x-1)+x+(x+1)=48

Step 2. Solving the equation

x-1+x+x+1=48

x+x+x-1+1=48

3x=48

x=16

So the answer is 15, 16, 17

2)

Again, let's set x as the middle number.

Odd numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that the equation must be:

(x-2)+x+(x+2)=69

x+x+x=69

3x=69

x=23

The numbers are 21, 23, and 25

3)

x will be the middle number

Even numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that:

x-2+x+x+2=138

x+x+x=138

3x=138

x=46

The numbers are 44, 46, and 48.

4)

x will be the middle number.

x-1=first number, x+1=third number

x-1+x+x+1=-9

3x=-9

x=-3

The numbers are -4, -3, and -2.

3 0

3 years ago

Which statement correctly describes the diagram?

Komok [63]

Answer:

option 2

Step-by-step explanation:

6 0

3 years ago

Will improving customer service result in higher stock prices for the companies providing the better service? "When a company’s

Orlov [11]

Question:

Company 2007 Score 2008 Score

Rite Aid 73 76

Expedia 75 77

J.C. Penney 77 78

a. For Rite Aid, is the increase in the satisfaction score from 2007 to 2008 statistically significant? Use α= .05. What can you conclude?

b. Can you conclude that the 2008 score for Rite Aid is above the national average of 75.7? Use α= .05.

c. For Expedia, is the increase from 2007 to 2008 statistically significant? Use α= .05.

d. When conducting a hypothesis test with the values given for the standard deviation,

sample size, and α, how large must the increase from 2007 to 2008 be for it to be statistically significant?

e. Use the result of part (d) to state whether the increase for J.C. Penney from 2007 to 2008 is statistically significant.

Answer:

a. There is sufficient statistical evidence to suggest that the increase in satisfaction score for Rite Aid from 2007 to 2008 is statistically significant

b. There is sufficient statistical evidence to suggest that the 2008 Rite Aid score, is above the national average of 75.7

c. The statistical evidence support the claim of a significant increase from 2007 to 2008

d. 1.802 and above is significant

e. The increase of J. C. Penney from 2007 is not statistically significant.

Step-by-step explanation:

Here we have

n = 60

σ = 6

μ₁ = 73

μ₂ = 76

We put H₀ : μ₁ ≥ μ₂ and

Hₐ : μ₁ < μ₂

From which we have;

$z=\frac{(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}+\frac{\sigma _{2}^{2}}{n_{2}}}} = \frac{(\mu_{1}-\mu_{2})}{\sqrt{\frac{2\sigma_{}^{2} }{n_{}}}}}$

Plugging in the values we have

$z = \frac{(73-76)}{\sqrt{\frac{2\times 6^{2} }{60_{}}}}} = -2.7386$

The probability, P from z function computation gives;

P(Z < -2.7386) = 0.0031

Where we have P < α, we reject the null hypothesis meaning that there is sufficient statistical evidence to suggest that the increase in satisfaction score for Rite Aid from 2007 to 2008 is statistically significant

b. To test here, we have

H₀ : μ ≤ 75.7

Hₐ : μ > 75.7

The test statistic is given as follows;

$z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}} = \frac{76-75.7 }{\frac{6 }{\sqrt{60}}} = 0.3873$

Therefore, we have the probability, P given as the value for the function at z = 0.3873 that is we have;

P = P(Z > 0.3873) = P(Z < -0.3873) = 0.3493

Therefore, since P > α which is 0.05, we fail to reject the null hypothesis, that is there is sufficient statistical evidence to suggest that the 2008 Rite Aid score, is above the national average of 75.7

c. Here we put

Null hypothesis H₀ : μ₁ ≥ μ₂

Alternative hypothesis Hₐ : μ₁ < μ₂

The test statistic is given by the following equation;

$z=\frac{(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}+\frac{\sigma _{2}^{2}}{n_{2}}}} = \frac{(\mu_{1}-\mu_{2})}{\sqrt{\frac{2\sigma_{}^{2} }{n_{}}}}}$

Plugging in the values we have

$z = \frac{(75-77)}{\sqrt{\frac{2\times 6^{2} }{60_{}}}}} = -1.8257$

The probability, P from z function computation gives;

P(Z < -1.8257) = 0.03394

The statistical evidence support the claim of a significant increase

d. For statistical significance at 0.05 significant level, we have z = -1.644854

Therefore, from;

$z=\frac{(\bar{x_{1}}-\bar{x_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}$ . we have;

$z \times \sqrt{\frac{\sigma_{1}^{2} }{n_{1}}+\frac{\sigma _{2}^{2}}{n_{2}}} + (\mu_{1}-\mu _{2} )}{} ={(\bar{x_{1}}-\bar{x_{2}})$

Which gives

${(\bar{x_{1}}-\bar{x_{2}}) = z \times \sqrt{\frac{2\sigma_{}^{2} }{n_{}}}} + (\mu_{1}-\mu _{2} )}{} = -1.644854 \times \sqrt{\frac{2\times 6_{}^{2} }{60_{}}}} + 0 = -1.802$

Therefore an increase of 1.802 and above is significant

e. Based on the result of part d. we have for J.C. Penney from 2007 to 2008 an increase of 1 which is less than 1.802 at 5% significant level, is not significant.

5 0

3 years ago