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Alex73 [517]
2 years ago
10

Write the equation of the line for a line that passes through (4, 4) and (1, -2).

Mathematics
2 answers:
Vesna [10]2 years ago
7 0

Step-by-step explanation:

(4, 4) and (1, -2).

(x1,y1) and (x2,y2)

slope=(y2-y1/x2-x1)

m= -2-4/1-4

m=2

slopeintercept form

y=2x-4

point slope form

y-4=2(x-4)

pshichka [43]2 years ago
6 0

(\stackrel{x_1}{4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}}\implies \cfrac{-6}{-3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{4}) \\\\\\ y-4=2x-8\implies y=2x-4

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Read 2 more answers
Suppose that the population mean for income is $50,000, while the population standard deviation is 25,000. If we select a random
Fudgin [204]

Answer:

Probability that the sample will have a mean that is greater than $52,000 is 0.0057.

Step-by-step explanation:

We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

We select a random sample of 1,000 people.

<em>Let </em>\bar X<em> = sample mean</em>

The z-score probability distribution for sample mean is given by;

               Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean = $50,000

            \sigma = population standard deviation = $25,000

            n = sample of people = 1,000

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P(\bar X > $52,000)

  P(\bar X > $52,000) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } } ) = P(Z > 2.53) = 1 - P(Z \leq 2.53)

                                                                    = 1 - 0.9943 = 0.0057

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>

Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

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2 years ago
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