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3 years ago

Angle bisectors. I need help on how to solve.

Mathematics

1 answer:

Anna [14]3 years ago

7 0

Answer:

identify if the angle is a right angle, if it is bisected it means both sides are the same, set both equations equal to each other or add them up and set them equal to 90 or 180

Step-by-step explanation:

that is the explanation.

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solniwko [45]

Answer:

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3 years ago

What is the least common denominator of<br> 5/12 and 3/8

borishaifa [10]

5/12 and 3/8 is the answer

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3 years ago

Read 2 more answers

What is the distance between -182 and 265

Cerrena [4.2K]

The distance between -182 and 265 is 83 because if you subtract 265 from-182 it will be 83. the answer is 83.

3 0

3 years ago

Two types of coins are produced at a factory: a fair coin and a biased one that comes up heads 60 percent of the time. We have o

liraira [26]

Answer:

i) 0.1% probability that if the coin is actually fair, we reach a false conclusion.

ii) 0.05% probability that if the coin is actually unfair, we reach a false conclusion

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

Fair coin:

Comes up heads 50% of the time, so $p = 0.5$

1000 trials, so $n = 1000$

$E(X) = np = 1000*0.5 = 500$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1000*0.5*0.5} = 15.81$

If the coin lands on heads 550 or more times, then we shall conclude that it is a biased coin.

(i) If the coin is actually fair, what is the probability that we shall reach a false conclusion?

This is the probability that the number of heads is 550 or more, so this is 1 subtracted by the pvalue of Z when X = 549.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{549 - 500}{15.81}$

$Z = 3.1$

$Z = 3.1$ has a pvalue of 0.9990

1 - 0.9990 = 0.001

0.1% probability that if the coin is actually fair, we reach a false conclusion.

(ii) If the coin is actually unfair, what is the probability that we shall reach a false conclusion?

Comes up heads 60% of the time, so $p = 0.6$

1000 trials, so $n = 1000$

$E(X) = np = 1000*0.6 = 600$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1000*0.6*0.4} = 15.49$

If the coin lands on less than 550 times(that is, 549 or less), then we shall conclude that it is a biased coin.

So this is the pvalue of Z when X = 549.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{549 - 600}{15.49}$

$Z = -3.29$

$Z = -3.29$ has a pvalue of 0.0005

0.05% probability that if the coin is actually unfair, we reach a false conclusion

5 0

3 years ago

Last Question PLZ HELP ASAP

rusak2 [61]

The range is all the y-values.

(1,0)
(2,2)
(-4,-2)
(-2,-3)

These points are all in the form of (x,y)

The y-coordinates make up the range.

The range is {-3, -2, 0, 2}.

Your answer is A.

3 0

3 years ago