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3 years ago

In the figure shown below, if line m is parallel to line n, then find the value of x

Mathematics

1 answer:

Snezhnost [94]3 years ago

8 0

Answer:

Step-by-step explanation:

The two angles shown are considered "alternate interior angles" because they lie on the INSIDE of two parallel lines, but on alternate/opposite sides of the transversal line. Alternate interior angles are congruent. You can use transformations to see that they are congruent. Therefore, you should set the two expressions equal to each other and solve for x.

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Can someone please help me with this

velikii [3]

Answer:

The answer is D.) Quadrant IV

Step-by-step explanation:

I took a quiz on this before and Quadrant IV was correct but I don't know if it's true because some of you're answers are different from mine but on my quiz D was the answer

8 0

2 years ago

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

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:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

$Z = \frac{34 - 20.76}{4.14}$

$Z = 3.2$

$Z = 3.2$ has a pvalue of 0.9993

X = 21

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

$Z = \frac{21 - 20.76}{4.14}$

$Z = 0.06$

$Z = 0.06$ has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0

3 years ago

If AA and BB are two disjoint events with P(A)=0.15P(A)=0.15 and P(B)=0.75P(B)=0.75, find the following probabilities:

zubka84 [21]

Answer:

a 0

b) 0.9

c) 0.85

d) 0.25

e) 0.1

f) 0.0375

Step-by-step explanation:

As A and B are two disjoints events, then P(A and B) is

P(A and B)=0

As A and B are two disjoints events, then P(A or B) is

P(A or B)=P(A)+P(B)

P(A or B)=0.15+0.75=0.9

P(not A)=1-P(A)

P(not A)=1-0.15=0.85

P(not B)=1-P(B)

P(not B)=1-0.75=0.25

P(not (A or B))=1-P(A or B)

P(not (A or B))=1-0.9=0.1

P(A and (not B))=P(A)*P(not B)

P(A and (not B))=0.15*0.25=0.0375

5 0

3 years ago

4 sin ^ 2 x- 4 sin x + 1 = 0

m_a_m_a [10]

$4\sin^2x-4\sin x+1=(2\sin x-1)^2=0\implies \sin x=\dfrac12$

This happens for $x=\dfrac\pi6+2n\pi$ and $x=\dfrac{5\pi}6+2n\pi$ where $n$ is any integer.

8 0

3 years ago

Ahmed an Art dealer earns 25% commission of the dollar value of the art pieces that he sells at the Gallery. Ahmed earns $10,000

Mkey [24]

Answer:

$40,000

Step-by-step explanation:

25% of x = $10,000

0.25x = 10,000

x = 10,000/0.25

x = 40,000

Answer: $40,000

3 0

3 years ago