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3 years ago

What is the function rule for the line?

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Answer:

y =2/3x -2

Step-by-step explanation:

The y intercept is -2

The slope is

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

Using the points (0,-2) and (3,0)

m = ( 0 - -2)/(3 -0)

= (0+2)/(3-0)

= 2/3

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y =2/3x -2

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A, B, and C are collinear, and B is between A and C. The ratio of AB to AC is 1:2 If A is at (6,3) and B is at (-1,2), what are

Maksim231197 [3]

Answer:

The coordinates of C is (-8,1)

Step-by-step explanation:

Looking at the attached image, you'd see that, AB is 1 and BC is 1, that's because we are told that ratio of AB to AC is 1:2 meaning, AC is 2 and AB is 1. Therefore for that ratio to be satisfied BC has to be 1 so that AC would be 2.

Now let's assume the coordinates of C is $(x,y)$ .

To get it's coordinates, we use the section formula:

$(x,y)= (\frac{mx + nx_{1}}{m + n} , \frac{my + ny_{1}}{m + n})$

Where (m,n) is the (AB, BC)

Therefore we have

$(-1,2) = (\frac{1\times x + 1\times6}{1 + 1} , \frac{1\times y + 1\times3}{1 + 1})$

This gives:

$(-1,2) = (\frac{x + 6}{2} , \frac{y + 3}{2})$

$-1 =( \frac{x + 6}{2}$ and $2 = \frac{y + 3}{2})$

From there x = -8 and y = 1

Therefore the coordinates of C is (-8, 1).

7 0

4 years ago

The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums fo

Harrizon [31]

Using confidence interval concepts, it is found that:

a) The point estimate is the sample mean.

b) The confidence interval is: $\overline{x} \pm T\frac{s}{n}$

c) If $1411 is between the bounds of the interval yes, otherwise no.

--------------

At item a, it asks to provide a point estimate for the population mean, which is the sample mean $\overline{x}$

--------------

Item b:

In the spreadsheet, it is possible to find the <em>standard deviation for the sample</em>, thus, the t-distribution is used.
The confidence interval will be given by:

$\overline{x} \pm T\frac{s}{n}$

In which:

$\overline{x}$ is the sample mean.
T is the critical value, from the t-distribution, with a two-tailed area of $\frac{1 - 0.95}{2} = 0.025$ and n-1 degrees of freedom.
s is the standard deviation for the sample.
n is the sample size.