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3 years ago

Which of the pairs of angles are complementary?

Mathematics

2 answers:

kolezko [41]3 years ago

8 0

Complementary pairs = APW and ZPW

NikAS [45]3 years ago

3 0

Answer:

∠APW and ∠ZPW

Step-by-step explanation:

Pair of complementary angles : A pair of angles whose sum is 90° is said to be the pair of complementary angles.

Option 1 : ∠APB and ∠ZPB

Since APB is straight line

So, ∠APB = 180°

∠ZPB = 90°(Given)

So, ∠APB +∠ZPB=180°+ 90°= 270°

Since the sum of angles is not 90°.

Thus Option 1 is not a pair of complementary angles.

Option 2: ∠APZ and ∠BPZ

∠APZ = 90°

∠BPZ = 90°

So, ∠APZ +∠BPZ =90°+90° =180°

Since the sum of angles is not 90°.

Thus Option 2 is not a pair of complementary angles.

Option 3 : ∠APW and ∠ZPW

∠APW+∠ZPW=∠APZ

∠APZ =90°(Given)

So,∠APW+∠ZPW=90°

Since the sum of angles is 90°.

Thus Option 3 is a pair of complementary angles.

Option 4: ∠WPZ and ∠BPZ

∠WPZ + ∠BPZ = ∠WPZ + 90°

Since the sum of angles must be greater than 90°.

Thus Option 4 is not a pair of complementary angles.

Hence ∠APW and ∠ZPW are the pair of complementary angles.

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3 years ago

A report indicated that 37% of adults had received a bogus email intended to steal personal information. Suppose a random sample

fiasKO [112]

Answer:

5.05% probability that no more than 34% had received such an email.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this problem.

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .