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2 years ago

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

Mathematics

2 answers:

san4es73 [151]2 years ago

7 0

Y=U
X=T
Z=V
A. ΔXYZ ≅ ΔTUV

QveST [7]2 years ago

5 0

Answer: D. No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

Here, In In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°.

In triangle TUV,

m∠T = 180° - ( m∠U +m∠V) =180° - ( 30° + 60°) = 90°

While in triangle XYZ,

m∠Z = 180° -( m∠X+m∠Y ) = 180° - ( 90° + 30°) = 60°

Hence, In the triangles XYZ and TUV,

∠ X ≅ ∠ T, ∠ Y ≅ ∠ U and ∠ Z ≅ ∠ V

Thus, By AAA similarity postulate,

Triangle XYX and TUV are similar,

Since, if two triangles are similar then they are congruent if there is at least one pair of corresponding congruent sides.

Thus, we can not prove these triangle congruent unless we have the side length.

Hence, No congruency statement can be made because the side lengths are unknown.

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Answer:

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Step-by-step explanation:

Data given and notation

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$\hat p=0.2$ estimated proportion

$p_o=0.16$ is the value that we want to test

$\alpha$ represent the significance level

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 employess are late to work is 0.16, so we need to apply a one sample proportion test:

Null hypothesis: $p=0.16$

Alternative hypothesis: $p \neq 0.16$

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

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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 requires we can replace in formula (1) like this:

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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.

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