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3 years ago

What is the y-intercept of the function, represented by the table of values below

Mathematics

1 answer:

Basile [38]3 years ago

5 0

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope- formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, 15) and (x₂, y₂ ) = (1, 6) ← 2 ordered pairs from the table

m = $\frac{6-15}{1-(-2)}$ = $\frac{-9}{1+2}$ = $\frac{-9}{3}$ = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (2, - 3 ) , then

- 3 = - 6 + c ⇒ c = - 3 + 6 = 3

The y- intercept c = 3 → D

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You paint 1/2 wall in 1/4 hour. At that rate, how long will it take you to paint one wall?

Mnenie [13.5K]

(1/2) / (1/4) = 1 / x......1/2 wall to 1/4 hr = 1 whole wall to x hrs
cross multiply
(1/2)(x) = (1/4)(1)
1/2x = 1/4
x = 1/4 * 2
x = 2/4 reduces to 1/2....so it will take 1/2 hr (or 30 minutes) to paint the whole wall.

6 0

4 years ago

Read 2 more answers

A manufacturer needs to pay $300 to start making a certain new product. Besides the initial costs of $300, this product will als

maw [93]

Answer:

$\displaystyle \frac{300+18x}{x}\le 24$

Step-by-step explanation:

Average Cost

Making a certain new product costs $300 plus $18 per product.

The total cost for x products is given by:

300 + 18x

To get the average cost, we divide the total cost by the number of products manufactured:

$\displaystyle A=\frac{300+18x}{x}$

If the manufacturer wants to keep the average cost at $24 or less:

$\mathbf{\displaystyle \frac{300+18x}{x}\le 24}$

This is the required inequality

6 0

3 years ago

True or false? show how do you know: 57×2×5=10×57

gtnhenbr [62]

Answer:

true

Step-by-step explanation:

because If you multiply the 2 by 5 you will get 10

4 0

3 years ago

ASK YOUR TEACHER An article reported that for a sample of 42 kitchens with gas cooking appliances monitored during a one-week pe

xxMikexx [17]

Answer:

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

Step-by-step explanation:

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".

$\bar X=654.16$ represent the sample mean

$\mu$ population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 represent the sample size

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)

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

$df=n-1=42-1=41$

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that $t_{\alpha/2}=2.02$