write the equation of a line that is parallel to y = -7/5x + 6 and that passes through the point (2, -6)

Answers

Answer 1
Answer:

Answer:

y = -7/5x - 6.7

Step-by-step

y = -7/5x + 6. A Line that is parallel will always have the same slope. The slope is m. m in this situation = -7/5x. A lines equation is y = mx + b. m = -7/5. y = -7/5x + b. Now to find b we can substitute the given point which goes through the new line, (2, -6). In this point x =2 and y = -6. Now substitute the x and y values into our equation. y = -7/5x + b is now -6 = -7/5(2) + b. -7/5(2) = -7/10. -6 = 7/10 + b. Subtract 7/10 from -6. Its -6 and 7/10 or -6.7 . -6.7 = b. b = -6.7. Now substitute the b value into the equation. y = -7/5x -6.7.


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Which value is needed to determine a confidence interval for a sample mean?
OA
the margin of error for the proportion
ов.
the population size
OC.
the sample proportion
OD
the standard error of the mean

Answers

The value needed to determine a confidence interval for a sample mean is the standard error of the mean option (D) is correct.

What is a confidence interval for population standard deviation?

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follows:

\rm s\sqrt{(n-1)/(\chi^2_(\alpha/2, \ n-1))} < \sigma < s\sqrt{(n-1)/(\chi^2_(1-\alpha/2, \ n-1))}

Where s is the standard deviation.

n is the sample size.

\chi^2_(\alpha/2, \ n-1) and \chi^2_(1-\alpha/2, \ n-1) are the constant based on the Chi-Square distribution table:

α is the significance level.

σ is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

 

It is given that:

The value needed to determine a confidence interval for a sample mean is the standard error of the mean.

CI = X + Z(s/√n)

Here CI is the confidence interval

Z is the confidence level

X is the sample mean

Thus, the value needed to determine a confidence interval for a sample mean is the standard error of the mean option (D) is correct.

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Answer:

D.thestandarderrorofthemean

Step-by-step explanation:

trust me i got it right Plato

At a given time, the length, L, of the shadow of an object varies directlyas the height of the object, H. If the shadow is 27 ft when the height of
the object is 12 ft, what is the height of the object if the shadow is 18 ft?

Answers

Answer:

8 ft

Step-by-step explanation:

Use the direct variation equation, y = kx, where k is a constant.

Change the equation to fit the variables: L = kH

Plug in the given length of the shadow and the height of the object, then solve for k:

L = kH

27 = k(12)

2.25 = k

So, the equation is L = 2.25H

Then, plug in 18 as L, and solve for H:

L = 2.25H

18 = 2.25H

8 = H

So, when the shadow is 18 feet, the height of the object is 8 ft

Final answer:

Using the concept of direct variation, we find that the constant of variation is 2.25. Subsequent substitution in the equation reveals that the object's height when the shadow is 18ft is 8ft.

Explanation:

The question involves the concept of direct variation in mathematics. In direct variation, two quantities increase or decrease together to keep their ratio constant. This concept is given by the equation Y = kX, where Y and X are the quantities and k is a constant.

In our situation, the length of the shadow (L) varies directly with the object's height (H), i.e., L = kt. We are given that L=27ft when H=12ft, we can find the constant k by solving the equation 27ft = k * 12ft. This will get us k = 27ft/12ft = 2.25.

Now, we can determine the object's height if the shadow is 18ft. By substituting the values into the equation, we get 18ft = k * H. Substituting the value of k (2.25) will yield H = 18ft /2.25 = 8ft. Hence, the object's height when the shadow is 18ft is 8ft.

Learn more about Direct Variation here:

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Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

Answers

Answer:

e^(3t)(2t+5t^(2))

Step-by-step explanation:

L^(-1)[(2s+4)/((s-3)^(3)) ]=

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem:L^(1) [F(s-a)=L^(-1)[F(s)|_(s \to s-a)\n L^(1) [F(s-a)=e^(at) f(t)

L^(-1)[(2s+4)/((s-3)^(3)) ]=e^(3t) L^(-1)[(2(s+3)+4)/(s^(3)) ]

Separate the fraction in a sum:

e^(3t) L^(-1)[(2s+10)/(s^(3)) ]=e^(3t) L^(-1)[(2s)/(s^(3))+(10)/(s^(3)) ]=e^(3t) (L^(-1)[(2)/(s^(2))]+ L^(-1)[(10)/(s^(3))])

The formula for this is:

L^(-1)[(n!)/(s^(n+1)) ]=t^(n)

Modify the expression to match the formula.

e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ (10)/(2) L^(-1)[(2)/(s^(2+1))])=e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])

Solve

e^(3t) (2L^(-1)[(1)/(s^(1+1))]+ 5 L^(-1)[(2)/(s^(2+1))])=e^(3t)(2t+5t^(2) )

Billy wants to buy 657 mugs. The mugs are sold for a price of 3 for $4. How much must Billy pay for all the mugs?

Answers

(657mugs)/(3) = 219
219 * $4 = $876
875 is the answer to your question so have a nice day

One basketball team played 30 games throughout their entire season. If this team won 80% of those games, how many games did they win? Enter a numerical answer only.

Answers

the team won 24 games out of 30

What is the simplified form of this expression?

(5x2 + 2x + 11) − (7 + 4x − 2x2)

Answers

Answer:

7x² - 2x + 4

Step-by-step explanation:

(5x² + 2x + 11) - (7 + 4x - 2x²) = 5x² + 2x + 11 - 7 - 4x + 2x² =

(5x² + 2x²) + (2x - 4x) + (11 - 7) = 7x² - 2x + 4