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3 years ago

Please help! I can't seem to figure this stuff out...

Mathematics

1 answer:

Fudgin [204]3 years ago

8 0

1: always rearrange the equation to y = mx + c so....
x - y = o

x = y

So the gradient is 1 and it intersects the y axis at (0,0)

The three points could be (1,1), (2,2), (3,3) and so on

2: -x -2y = -10
Multiply everything by -1

x + 2y = 10

2y = 10 - x

y = 5 - x/2

The y intercept is 5 so you could use the point (0,5), (2,4), (4,3) and so on

3: x + y = -2

y = -2 - x

The y intercept is -2 so you could use the points (0,-2), (2,-4), (3,-5) and so on

4: -3y =-x -7

Multiply everything by -1

3y = x + 7

y = x/3 + 7/3

The y intercept is 7/3 so you could use the points (0,7/3), (3,10/3), (6,13/3) and so o

5: -y = -x + 1

y = x - 1

The y intercept is -1 so you could use the points (0,-1), (2,1), (3,2) and so on

Hope this helps! Any questions let me know :)

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3 years ago

A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard de

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Answer:

Step-by-step explanation:

Given that:

A simple random sample n = 28

sample standard deviation S = 12.65

standard deviation $\sigma$ = 11.53

Level of significance ∝ = 0.05

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The null hypothesis and the alternative hypothesis can be computed as follows:

Null hypothesis:

$H_0: \sigma^2 = \sigma_0^2$

Alternative hypothesis:

$H_1: \sigma^2 \neq \sigma_0^2$

The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.

$X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}$

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$X_0^2 = \dfrac{(27)(160.0225)}{132.9409}$

$X_0^2 = \dfrac{4320.6075}{132.9409}$

$X_0^2 = 32.5002125$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}$

$X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.975 , 27}$ = 14.573

$X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}$

$X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}$

From the chi-square probabilities table at 0.975 and degree of freedom 27;

$X^2_{0.025 , 27}=$ 43.195

Decision Rule: To reject the null hypothesis if $X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}$ ; otherwise , do not reject the null hypothesis:

The rejection region is $X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573$

Conclusion:

We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.

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