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3 years ago

Solve this system of equations to find x and y, please, and explain how you did it:

Mathematics

1 answer:

MissTica3 years ago

8 0

Answer:

Step-by-step explanation:

The system of equations is expressed as

x + y = 8 - - - - - - - - - - - - - -1

x² + y² = 34 - - - - - - - - - - - -2

From equation 1, we would make x to stand alone by subtracting y from the left hand side and the right hand side of the equation. It becomes

x + y - y = 8 - y

x = 8 - y

Substituting x = 8 - y into equation 2, it becomes

(8 - y)² + y² = 34

(8 - y)(8 - y) + y² = 34

64 - 8y - 8y + y² + y² = 34

2y² - 16y + 64 - 34 = 0

2y²- 16y + 30 = 0

Dividing through by 2, it becomes

y² - 8y + 15 = 0

y² - 5y - 3y + 15 = 0

y(y - 5) - 3(y - 5) = 0

y - 5 = 0 or y - 3 = 0

y = 5 or y = 3

Recall, x = 8 - y

x = 8 - 5. or x = 8 - 3

x = 3 or x = 5

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A square is cut into three equal rectangles. How does the area of the square compare to the sum of the areas of the three rectan

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If the square was split into 3 rectangles the 3 rectangles sum up to the square.

4 0

3 years ago

Find the area of the shaded region.

densk [106]

[1]

A1 = (h (a + b)) / 2

A1 = (21 (17 + 32)) / 2

A1 = (21 x 49) / 2

A1 = 1,029 / 2

A1 = 514.5 mm²

[2]

A2 = (b x h) / 2

A2 = (11 x 9) / 2

A2 = 99 / 2

A2 = 49.5 mm²

[3]

The area of the shaded region =

A1 - A2 =

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The answer is 465 mm².

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3 years ago

Assume that the paired data came from a population that is normally distributed. using a 0.05 significance level and dequalsxmin

Artemon [7]

"Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find $\bar{d}$ , $s_{d}$ , the t-test statistic, and the critical values to test the claim that $\mu_{d} = 0$ "

You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.

For the example, please refer to the attached picture.

A) Find $\bar{d}$
You are asked to find the mean difference between the two variables, which is given by the formula:
$\bar{d} = \frac{\sum (x - y)}{n}$

These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)

In our example:
 $\bar{d} = \frac{6}{8} = 0.75$ 

B) Find $s_{d}$
You are asked to find the standard deviation, which is given by the formula:
 $s_{d} = \sqrt{ \frac{\sum(d - \bar{d}) }{n-1} }$

These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1

In our example:
$s_{d} = \sqrt{ \frac{101.5}{8-1} }$
= √14.5
= 3.81

C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
$t = \frac{(\bar{x} - \bar{y}) - \mu_{d} }{SE}$

where SE = standard error is given by the formula:
$SE = \frac{ s_{d} }{ \sqrt{n} }$

These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract $\mu_{d}$
6) divide by the standard error

In our example:
SE = 3.81 / √8
= 1.346

The problem gives us $\mu_{d} = 0$ , therefore:
t = [(9.75 - 9) - 0] / 1.346
= 0.56

D) Find $t_{\alpha / 2}$
You are asked to find what is the t-value for a 0.05 significance level.

In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).

We find $t_{\alpha / 2} = 1.895$ 

Since our t-value is less than $t_{\alpha / 2}$ we can reject our null hypothesis!!