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In circle P, EG and FH are diameters.<br> What is m EH?

zvonat [6]

Answer:

$m(\widehat{EH})$ = 130°

Step-by-step explanation:

Angles subtended at the center by the arcs $(\widehat{HG})$ and $(\widehat{EF})$ are ∠HPG and ∠EPF.

Since these angles are the vertical angles both will be equal.

m∠HPG ≅ m∠EPF

3x - 10 = 2x + 10

3x - 2x = 10 + 10

x = 20

Therefore, $m(\widehat{HG})=(3\times 20) - 10$

= 50°

Similarly $m(\widehat{EF})$ = 50°

In the same way angles subtended at the center will be equal.

m∠EPH ≅ m∠FPG

and $m(\widehat{EH})=m(\widehat{FG})$

Since $m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360$ °

$m(\widehat{EH})+m(\widehat{EH})+50+50=360$

$2m(\widehat{EH})=360-100$

$m(\widehat{EH})=130$

Therefore, measure of arc EH = 130°

3 0

3 years ago

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable

notsponge [240]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) $Z=2.45$