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2 years ago

A 30−60−90 triangle has a longer leg with length 53√4 and a hypotenuse with length 5/2 . What is the length of the shorter leg?

Mathematics

1 answer:

Vlad1618 [11]2 years ago

8 0

The length of the shorter leg is √2

<h3>Pythagoras theroem</h3>

To get the length of the shorter leg, we will use the Pythagoras theorem. According to the theorem:

hyp^2 = opp^2 + adj^2

Given the following

Hyp = √4

Opposite = √2

Required

Adjacent side

Substitute into the formula

(√4 )^2 = 2 + adj^2

4 - 2 = adj^2

adj^2 = 2

adj = √2

Hence the length of the shorter leg is √2

Learn more on Pythagoras theorem here: brainly.com/question/343682

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If measure FG = 120° and measure EH = 94, what is measure angle EPH?

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Answer:

∠EPH = 107°

Step-by-step explanation:

∠EPH is an angle formed by two intersecting chords.

arc FG and arc EH are the arcs ∠EPH intercepts.

The relationship between an angle formed by intersecting chords and their intercepted arcs is that the angle is equal to half the sum of its intercepted arcs.

Which means that ∠EPH = 1/2 ( arc FG + arc EH )

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A genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 174 yellow peas. Use a 0.01

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Answer:

a) $z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649$

b) For this case we need to find a critical value that accumulates $\alpha/2$ of the area on each tail, we know that $\alpha=0.01$ , so then $\alpha/2 =0.005$ , using the normal standard table or excel we see that:

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Step-by-step explanation:

Data given and notation

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X=174 represent the number of yellow peas

$\hat p=\frac{174}{594}=0.293$ estimated proportion of yellow peas

$p_o=0.23$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

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 yellow peas is 0.23:

Null hypothesis: $p=0.23$

Alternative hypothesis: $p \neq 0.23$

When we conduct a proportion test we need to use the z statisitc, 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 requires we can replace in formula (1) like this:

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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 $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>3.649)=0.00026$

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