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3 years ago

What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line 5x+4y=165x+4y=16?

Mathematics

1 answer:

Gnoma [55]3 years ago

6 0

Answer:

The equation of line parallel to given line passing through (8,-7) is:

$y = -\frac{5}{4}x+3$

Step-by-step explanation:

Given line is:

5x+4y=16

first of all, we have to convert the equation of given line in slope-intercept form

$4y = -5x+16$

Dividing both sides by 4

$\frac{4y}{4} = -\frac{5x}{4} + \frac{16}{4}\\y = -\frac{5}{4}x+4$

Slope intercept form is:

$y=mx+b$

The slope of given line is:

$m = -\frac{5}{4}$

Let m1 be the slope of line parallel to given line

"The slopes of two parallel lines are equal"

$m = m_1\\m_1 = -\frac{5}{4}$

The equation of line parallel to given line will be:

$y = m_1x+b$

Putting the value of slope

$y = -\frac{5}{4}x+b$

Putting the point (8,-7) in the equation

$-7 = -\frac{5}{4}(8)+b\\-7 = -(5)(2) + b\\-7 = -10+b\\b = -7 +10\\b = 3$

Putting the value of b

$y = -\frac{5}{4}x+3$

Hence,

The equation of line parallel to given line passing through (8,-7) is:

$y = -\frac{5}{4}x+3$

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On Tuesday, a local hamburger shop sold a combined total of 381 hamburgers and cheeseburgers. The number of cheeseburgers sold w

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Answer:

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Step-by-step explanation:

let c = # of cheeseburgers

let h = # of hamburgers

c = 2h (The number of cheeseburgers sold was two times the number

of hamburgers sold.)

h + c = 381 (combined total)

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3 years ago

What is (3.9 x 10 to the power of 33) times (3.25 x 10 to the power of 3)

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Answer:1.2675x10^37

Step-by-step explanation:

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3 years ago

A Statistics professor has observed that for several years students score an average of 106 points out of 150 on the semester ex

tekilochka [14]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 106

For the alternative hypothesis,

µ > 106

It is a right tailed test because of >.

Since no population standard deviation is given, the distribution is a student's t.

Since n = 241,

Degrees of freedom, df = n - 1 = 241 - 1 = 240

t = (x - µ)/(s/√n)

Where

x = sample mean = 109

µ = population mean = 106

s = samples standard deviation = 8.3

a) test statistic, t = (109 - 106)/(8.3/√241) = 5.61

We would determine the p value using the t test calculator. It becomes

p = 0.00001

Since alpha, 0.05 > than the p value, 0.00001, then we would reject the null hypothesis. Therefore, At a 5% level of significance, this improvement seem to be practicallysignificant.

b) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

n = number of samples

From the information given, the population standard deviation is unknown, hence, we would use the t distribution to find the z score

df = 240

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 1.6512

Margin of error = 1.6512 × 8.3/√241

= 0.88

Confidence interval = 109 ± 0.88

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Mamont248 [21]

Answer:

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Step-by-step explanation:

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