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3 years ago

The quadrilaterals ABCD and PQRS are similar. Find the length X of SP.

Mathematics

1 answer:

BaLLatris [955]3 years ago

6 0

Answer:

$x = 3.6$

Step-by-step explanation:

Since Quadrilateral ABCD ~ PQRS, therefore:

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CD}{RS} = \frac{DA}{SP}$

Let's find the value of x by using the ratio of two corresponding sides of both quadrilaterals. Let's use:

$\frac{CD}{RS} = \frac{DA}{SP}$

CD = 5

RS = 4.5

DA = 4

SP = x

$\frac{5}{4.5} = \frac{4}{x}$

Cross multiply

$5*x = 4.5*4$

$5x = 18$

Divide both sides by 5

$x = \frac{18}{5}$

$x = 3.6$

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2 years ago

Read 2 more answers

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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:

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

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