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As we move from the x-intercept (-2, 0) to the y-intercept (0, 4), x increases by 2 (this is the run) and y by 4 (this is the rise). Thus, the slope of this line is

m = rise/run = 4/2 = 2.

Given the y-intercept (0, 4) and the slope (2), the slope-intercept form of the equation of this line is y = 2x + 4.

From this we get the point-slope form:

y = 2x + 4 becomes y - 4 = 2(x - 0), or just y - 4 = 2x.

3 0

2 years ago

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelo

yawa3891 [41]

BC is the length of AD because they are parallel. Have a nice day

7 0

3 years ago

Read 2 more answers

2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nucle

DaniilM [7]

Answer:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=74$ represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$X_{2}=70$ represent the number of people suburban residents are in favor

$n_{1}=100$ sample 1 selected

$n_{2}=125$ sample 2 selected

$p_{1}=\frac{74}{100}=0.74$ represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$p_{2}=\frac{70}{125}=0.56$ represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

Statistical decision

The significance level provided is $\alpha=0.05$ ,and we can calculate the p value for this test.

Since is a two tailed test the p value would be:

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

5 0

3 years ago