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anyanavicka [17]
1 year ago
12

Write an equation in slope-intercept form of the line containing the points (3,-1) and (6, 7).

Mathematics
1 answer:
umka2103 [35]1 year ago
7 0

The equation in slope-intercept form of the line containing the points (3,-1) and (6, 7) is; y = ⁸/₃x - 7

<h3>What is the equation in Slope Intercept form?</h3>

We are given the coordinates of two points as;

(3,-1) and (6, 7).

Now, the formula for the equation of the line containing the two points in slope intercept form is;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Thus, we have;

(y + 1)/(x - 3) = (7 + 1)/(6 - 3)

(y + 1)/(x - 3) = = 8/3

y + 1 = (8/3)(x - 3)

y + 1 = ⁸/₃x - 8

y = ⁸/₃x - 7

Read more about Slope intercept form at; brainly.com/question/1884491

#SPJ1

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MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)  

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=30.9 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size  

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=174-1=173

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that t_{\alpha/2}=1.97, this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.  

Now we have everything in order to replace into formula (1):

30.9-1.97\frac{7.5}{\sqrt{174}}=29.780    

30.9+1.97\frac{7.5}{\sqrt{174}}=32.020

So on this case the 95% confidence interval would be given by (29.780;32.020)    

The value 29.6 is not contained on the interval calculated.

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One month Tammy rented 2 movies and 6 video games for a total of $ 42 . The next month she rented 5 movies and 3 video games for
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Answer:

The rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

Step-by-step explanation:

Let the rental cost of 1 movie be m.

Let the rental cost of 1 video game be v.

One month, Tammy rented 2 movies and 6 video games for a total of $42. This means that:

2m + 6v = 42 ________ (1)

The next month she rented 5 movies and 3 video games for a total of $30. This means that:

5m + 3v = 30 _________(2)

We now have two simultaneous equations:

2m + 6v = 42 ________ (1)

5m + 3v = 30 _________(2)

Multiply (2) by 2, and we have:

2m + 6v = 42 __________ (1)

10m + 6v = 60 _________ (3)

Subtract (1) from (3):

 10m + 6v = 60

-<u> 2m + 6v = 42</u>

 <u>  8m     =     18</u>

=> m = 18 / 8

m = $2.25

Put the value of m back in (1):

2(2.25) + 6v = 42

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=> 6v = 42 - 4.5 = 37.5

v = 37.5 / 6

v = $6.25

Therefore, the rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

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