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2 years ago

-2x + y = 4

Mathematics

1 answer:

nirvana33 [79]2 years ago

3 0

Answer:

Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Tap for more steps.

Step-by-step explanation:

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A 72,000 gallon water tower is being drained. Two thousand gallons are drained in the first hour. How many hours will it take to

ololo11 [35]

Answer:

To drain the water tower it will take 36 hours.

Step-by-step explanation:

Given:

A 72,000 water tower is being drained, and in an hour 2000 gallons are drained.

Now, to calculate the hours it would take to drain total 72,000 gallons of water, we should divide the gallons of water drained in one hour by total gallons of water in the tower.

Gallons of total water in the tower ÷ Gallons of water drained per hour

$72000\div 2000$

$=\ 36$

Therefore, to drain the water tower it will take 36 hours.

6 0

3 years ago

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA ba

PSYCHO15rus [73]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

$\bar{x} = 1,465,752$

The standard deviation of mean salary is

$s = 1,346,046.2$

The confidence interval for the mean salary of all basketball coaches is given by

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } )$

Where $\bar{x}$ is the sample mean, n is the sample size, s is the sample standard deviation and $t_{\alpha/2}$ is the t-score corresponding to a 95% confidence level.

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\$

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

$\bar{x} = 1,371,191$

The standard deviation of the mean salary is

$s = 1,130,666.5$

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is

$CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\$

6 0

3 years ago

Find the area of the shape.

kaheart [24]

Answer:

36*sqrt(3)

Step-by-step explanation:

Remark

Use the Pythagorean theory to find the height. Use that height to find the area of the rectangle and the triangle Or

You can find the area of the trapezoid which requires only 1 step after you find the height.

Height

c = 8

b = 4

a = ?

a^2 + b^2 = c^2

a^2 + 4^2 = 8^2

a^2 + 16 = 64

a^2 = 64 - 16

a^2 = 48

a^2 = 16 * 3

sqrt(a^2) = sqrt(16*3)

a = 4 * sqrt(3)

That's the height

Trapezoid

b1 = 7

b2 = 7 + 4 = 11

h = 4*sqrt(3)

Area = (b1 + b2)*h / 2

Area = (7 + 11)* 4*sqrt(3)/2

Area = 18 * 2 sqrt(3)

Area = 36* sqrt(3)

6 0

3 years ago

The length of a rectangular garden is 7x + 3 feet. The width of the garden is 6x – 3 feet. Which expression represents the area

iren [92.7K]

Answer:

42x² - 3x - 9

the area of the garden is:

(7x + 3)(6x - 3)

= 42x² - 21x + 18x - 9

= 42x² - 3x - 9

4 0

2 years ago

Subject:Mathematics

Kobotan [32]

The vertex
Blah blah blah 20 characters longggggg

6 0

3 years ago