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2 years ago

Help meeee!! I’ll give brainliest!!!

Mathematics

1 answer:

dimulka [17.4K]2 years ago

3 0

Answer:

x = 9

y = 13

Step-by-step explanation:

Side-Side-Side or SSS means that if all three sides of one triangle are equal to all three corresponding sides of another triangle, then the two triangles are considered to be congruent (equal).

Therefore, GH = PM ⇒ 7x + 8 = 6y - 7

and, GP = HM ⇒ 8x - 10 = 5y - 3

Rewrite the first expression to make x the subject, then substitute this into the second equation, and solve for y:

GH = PM

⇒ 7x + 8 = 6y - 7

⇒ 7x = 6y - 15

⇒ x = (6/7)y - 15/7

Substituting x = (6/7)y - 15/7 into GP = HM:

GP = HM

⇒ 8x - 10 = 5y - 3

⇒ 8[(6/7)y - 15/7] - 10 = 5y - 3

⇒ (48/7)y - 120/7 - 10 = 5y - 3

⇒ (13/7)y = 169/7

⇒ y = 13

Now we have found a value for y, substitute this into one of the expressions and solve for x:

8x - 10 = 5y - 3

⇒ 8x - 10 = (5 x 13) - 3

⇒ 8x - 10 = 62

⇒ 8x = 72

⇒ x = 9

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4 years ago

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3 years ago

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and de

Naily [24]

Answer:

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

$p_v =P(Z>0.318)=0.375$

So the p value is a very high value and using the significance level provided $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona is not significantly higher than the national incident rate at 1% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=507$ represent the number of children diagnosed with Autism Spectrum Disorder (ASD) in Arizona

$n_{1}=32601$ sample elected from arizona

$\hat p_{1}=\frac{507}{32601} =0.0156$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in arizona

$p_{2}=\frac{1}{88}= 0.0114$ represent the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in the nation

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 that the incident of ASD is more in Arizona than nationally, the system of hypothesis are:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

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 $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{507+1}{32601 +88}=0.01554$

Calculate the statistic

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

$z=\frac{0.0156-0.0114}{\sqrt{0.01554(1-0.01554)(\frac{1}{32601}+\frac{1}{88})}}=0.318$

Statistical decision

The significance level provided is $\alpha=0.01$ , and we can calculate the p value for this test.

Since is a one right sided test the p value would be:

$p_v =P(Z>0.318)=0.375$

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3 years ago