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3 years ago

What is an equation of the line that passes through the point ( 6 , − 1 ) (6,−1) and is parallel to the line x − 3 y = 3 x−3y=3?

Mathematics

1 answer:

Nataly [62]3 years ago

4 0

Answer:

y = 1

Step-by-step explanation:

Passes through (6,-1)(6,-1)

Find the slope (m)

m=(y2 - y1) / (x2 - x1)

m=(-1 - (-1) ) / (6-6)

m= 0

Parallel to x - 3y = 3

-3y = -x +3

y = 1/3 x -1

Equation of the line equation is y - y1 = m ( x - x1 )

y - ( -1 ) = 0 ( x - 6 )

y + 1 = 0

y = 1

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There is strong believe that language skills of Political science students are greater than students who study Finance. Research

BaLLatris [955]

Answer:

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

$p-value = 0.232$

The decision rule is

Fail to reject the null hypothesis

Step-by-step explanation:

From the question we are told that

The value given is

S/N

1 7 5

2 4 3

3 8 7

4 8 8

5 7 9

6 7 5

7 6 5

Generally the sample mean for the first sample is mathematically represented as

$\= x _1 = \frac{\sum x_i }{n}$

=> $\= x _1 = \frac{7 +4 + \cdots + 6}{7}$

=> $\= x _1 = 6.714$

Generally the sample mean for the second sample is mathematically represented as

$\= x _2 = \frac{\sum x_i }{n}$

=> $\= x _2 = \frac{5 + 3+ \cdots + 5}{7}$

=> $\= x _2 = 6$

Generally the sample standard deviation for the first sample is mathematically represented as

$s_1 = \sqrt{\frac{\sum (x_i - \= x_1)^2 }{n-1 } }$

=> $s_1 = \sqrt{\frac{ (7 - 6.714 )^2 +(4 - 6.714 )^2 + \cdots + (6 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 1.905$

Generally the sample standard deviation for the second sample is mathematically represented as

$s_2 = \sqrt{\frac{\sum (x_i - \= x_2)^2 }{n-1 } }$

=> $s_2 = \sqrt{\frac{ (5 - 6.714 )^2 +(3 - 6.714 )^2 + \cdots + (5 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 4.33$

Generally the pooled standard deviation is

$s = \sqrt{\frac{(n_1 - 1 )s_1^2 + (n_2 - 1 )s_2^2}{n_1 + n_2 -2 } }$

=> $s = \sqrt{\frac{(7 - 1 )1.905^2 + (7 - 1 )4.333^2}{7 + 7 -2 } }$

=> $s = 1.766$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x _1 - \= x_2 }{s * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}} }$

=> $t = \frac{6.714 - 6 }{1.766 * \sqrt{\frac{1}{7} + \frac{1}{7}} }$

=> $t = 0.757$

Generally the degree of freedom is mathematically represented as

$df = n_1 + n_2 - 2$

=> $df = 7 + 7 - 2$

=> $df = 12$

From the t distribution table the probability of $t = 0.757$ at a degree of freedom of $df = 12$ is

$t_{ 0.757 , 12} = 0.232$

Generally the p-value is

$p-value = t_{ 0.757 , 12} = 0.232$

From the values obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

8 0

3 years ago

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vodka [1.7K]

Hello!

Each time, there will be a 1/2 chance of tossing a head. Therefore, we multiply our two probabilities.

1/2(1/2)=1/4

Therefore, we have a 1/4 or 25% chance of tossing two heads in a row.

I hope this helps!

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3 years ago

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Juliette [100K]

I think the answer would be 1.8

8 0

3 years ago

Evaluate AB for A = 5, B =-2, C = 4 and D = -6.<br> 5/12<br> -5/12<br> -3/2<br> 3/2

Nezavi [6.7K]

Answer:

AB = -10

Im confused is this what you wanted?

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3 years ago

Find the height of the trapezoid. A trapezoid. The base lengths are 10 meters and 6 meters. The area is 40 square meters.

Andrew [12]

Answer:

5 meters

Step-by-step explanation:

A=a+b/2*h

40=10+6/2*h

40=8h

h=5

7 0

3 years ago

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