Given EFGH and E=45°, what is the measure of angle F?

Mathematics

2 answers:

Ivahew [28]3 years ago

4 0

Opposite angles are congruent and adjacent angles are supplementary.

so < E + < F = 180...and < E = 45
45 + < F = 180
< F = 180 - 45
< F = 135 <==

Goryan [66]3 years ago

3 0

Remember that opposite angles are congruent.

So,

we know that <E= <G

That is 45+45= 90 degrees

We also know that consecutive angles are supplementary. E and F would equal 180 degrees.

180-45=135

<F= 135 degrees.

We can check this by seeing if all the angles add up to 360 degrees/

135+135+45+45

=360 <== this works

I hope this helps!
~kaikers

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For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5

Keith_Richards [23]

Answer:

a) $n = 50, p = \frac{1}{6}$

b) $n = 16, p = \frac{1}{100}$

c) $n = 26, p = 0.25, \mu = 6.5$

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $p$ is the probability of X happening.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so $n = 50$ .

Each roll can have 6 outcomes. So the probability that 5 is rolled is $p = \frac{1}{6}$

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so $n = 16$ .