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4 years ago

Find the values of x and y

Mathematics

1 answer:

Anna71 [15]4 years ago

5 0

Consecutive interior angles are supplementary (i.e. add up to 180 degrees).
2x - y + 60 = 180 and 2x + y + 40 = 180
2x - y = 180 - 60 = 120 and 2x + y = 180 - 40 = 140

2x - y = 120 . . . (1)
2x + y = 140 . . . (2)

(1) - (2) => -2y = -20 => y = -20/-2 = 10
From (1), 2x - 10 = 120 => 2x = 120 + 10 = 130 => x = 130/2 = 65

Therefore, x = 65 and y = 10.

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The amounts (in ounces) of randomly selected eight 16-ounce beverage cans are given below. See Attached Excel for Data. Assume t

motikmotik

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

Question:

The amounts (in ounces) of randomly selected eight 16-ounce beverage cans are given below.

16.5, 15.2, 15.4, 15.1, 15.3, 15.4, 16, 15.1

Assume that the amount of beverage in a randomly selected 16-ounce beverage can has a normal distribution. Compute a 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans and fill in the blanks appropriately.

A 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is ( , ) ounces. (round to 3 decimal places)

Answer:

$99\% \: \text {confidence interval} = (14.886, \: 16.113)\\\\$

Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.

Step-by-step explanation:

Let us find out the mean amount of the 16-ounce beverage cans from the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

$\bar{x} = 15.5$

Let us find out the standard deviation of the 16-ounce beverage cans from the given data.

Using Excel,

=STDEV(number1, number2,....)

The standard deviation is found to be

$s = 0.4957$

The confidence interval is given by

$\text {confidence interval} = \bar{x} \pm MoE\\\\$

Where $\bar{x}$ is the sample mean and Margin of error is given by

$$ MoE = t_{\alpha/2} \cdot (\frac{s}{\sqrt{n} } ) $ \\\\$

Where n is the sample size, s is the sample standard deviation and is the t-score corresponding to a 99% confidence level.

The t-score corresponding to a 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 8 - 1 = 7

From the t-table at α = 0.005 and DoF = 7

t-score = 3.4994

$MoE = t_{\alpha/2}\cdot (\frac{s}{\sqrt{n} } ) \\\\MoE = 3.4994 \cdot \frac{0.4957}{\sqrt{8} } \\\\MoE = 3.4994\cdot 0.1753\\\\MoE = 0.6134\\\\$

So the required 99% confidence interval is

$\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 15.5 \pm 0.6134\\\\\text {confidence interval} = 15.5 - 0.6134, \: 15.5 + 0.6134\\\\\text {confidence interval} = (14.886, \: 16.113)\\\\$

Therefore, the 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (14.886, 16.113) ounces.

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4 years ago

After examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conc

Igoryamba

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3 years ago

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C please I named it rn!! I CANT GRADUATE Without IT!

vazorg [7]

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4 years ago

I NEED HELP ASAP!!!!! How did nationalism cause contribute to the start of World War 1?

vekshin1

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These groups hoped to drive Austria Hungary from the Balkans and establish a 'Greate Serbia'

Step-by-step explanation:

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3 years ago

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padilas [110]

DE+EF=DF
8x+2=x+9
8x-x=9-2
7x=7
x=7/7
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DF=x+9
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2 years ago

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