All categories

3 years ago

2. A line goes through the points (8, 9) and (-2, 4).

Mathematics

1 answer:

Scrat [10]3 years ago

5 0

Answer:

Step-by-step explanation:

A line goes through the points (-2, 4) and (8, 9). We see that x increases by 10 and y increases by 5.

Thus, the slope of this line is m = rise / run = 5/10 = 1/2 (the slope)

Starting with the point slope equation y - k = m(x - h) and substituting 9 for y, 8 for x and 1/2 for m, we get:

y - 9 = (1/2)(x - 8) (point-slope form)

y = (1/2)x + 5 (slope-intercept form)

You might be interested in

Need help with number 7

Bess [88]

Answer:

$95,183.04

Step-by-step explanation:

$A = P(1 + \frac{r}{n} )^{nt}$

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

(i used a calculator but theres the formula^^ T-T)

5 0

3 years ago

Read 2 more answers

The cost of Internet access. How much do users pay for Internet service? Here are the monthly fees (in dollars) paid by a random

Ivanshal [37]

Answer:

$20.9-2.01\frac{7.65}{\sqrt{50}}=18.73$

$20.9+2.01\frac{7.65}{\sqrt{50}}=23.07$

The 95% confidence interval would be given by (18.73;23.07)

Step-by-step explanation:

Assuming these data

20 40 22 22 21 21 20 10 20 20

20 13 18 50 20 18 15 8 22 25

22 10 20 22 22 21 15 23 30 12

9 20 40 22 29 19 15 20 20 20

20 15 19 21 14 22 21 35 20 22

Previous concepts

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".

Solution to the problem

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

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

First we need to find the sample mean with the following formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{50}=20.9$

And in order to find the sample standard deviation we can use the following formula:

$s= \sqrt{\frac{\sum_{i=1}^n (x_i -\bar x)^2}{n-1}}=7.65$

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

$df=n-1=50-1=49$

Since the Confidence is 0.95or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$