What is the slope intercept form of a linear function

Adrian is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:

VikaD [51]

If we start with the assumption that segment DE is parallel to segment BC, then we the similarity condition that:
triangle ABC is similar to triangle ADE
For this to be true, the ratio corresponding sides of the two triangles must be equal. So:
5/8 =? 6/10
But
5/8 =/= 6/10

So, DE is not parallel to BC

4 0

3 years ago

Solve for W. 4w-4+2(5w+8)=-2(w+3) Simplify your answer as much as possible.

gayaneshka [121]

Answer:

w = $-\frac{9}{8}$

Step-by-step explanation:

The question is $4w-4+2(5w+8)=-2(w+3)$

We can first use distributive property to simplify, the distributive property is $a(b+c)=ab+ac$

Thus we have:

$4w-4+2(5w+8)=-2(w+3)\\4w-4+10w+16=-2w-6$

Now we combine like terms and simplify to get the final answer for w.

$4w-4+10w+16=-2w-6\\14w+12=-2w-6\\14w+2w=-6-12\\16w=-18\\w=\frac{-18}{16}\\w=-\frac{9}{8}$

Thus, w = $-\frac{9}{8}$

8 0

3 years ago

Read 2 more answers

Find the sum. (adding and subtracting polynomials)

OverLord2011 [107]

Answer:

(-8x - 12) + (9x + 4)= x-8

(-3p^3 + 5p^2 - 2p) + (3r^2 - 3r)= -3p^3+5p^2-2p+3r^2-3r

( -3p^3 + 5p^2 - 2p) + (-p^3 - 8p^2 -15p)= -4p^3-3p^2-17p

. ( 9r^2+4r-7) + (3r^2-3r)= 12r^2+r-7

7 0

3 years ago

Given: W (-4, 2) and Z (7, 5). What is the slope of the line parallel to WZ?

Tatiana [17]

Answer:

$\frac{3}{11}$

Step-by-step explanation:

$\frac{5-2}{7- (-4)}$ = $\frac{3}{11}$

3 0

3 years ago

Last year, a comprehensive report stated that 28% of businesses in the northeast of Ohio were considered highly profitable. This

Alik [6]

Answer:

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

Step-by-step explanation:

Data given and notation

n=50 represent the random sample taken

X=19 represent the businesses were highly profitable

$\hat p=\frac{19}{50}=0.38$ estimated proportion of businesses were highly profitable

$p_o=0.28$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of businesses were highly profitable is different from 0.28 or no, the system of hypothesis is.:

Null hypothesis: $p=0.28$

Alternative hypothesis: $p \neq 0.28$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info required we can replace in formula (1) like this:

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

4 0

4 years ago