Question 13<br><br> cos(546) + abs(-78) = ?

Decide if each sample is random. Explain why or why not.

julsineya [31]

Answer:

a- no they are polling

b-yes there is no point

Step-by-step explanation:

5 0

3 years ago

Expand the following. In other words, remove the parentheses (brackets):

Nina [5.8K]

Answer:

I believe that it would be A.

But answer A should be $3a + ab - a^{2}$

Step-by-step explanation:

3 0

3 years ago

Critical Thinking: Empirical/Quantitative Skills

aliya0001 [1]

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

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 combinations 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.

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

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.

This means that $p = 0.905$

Also assume that the airline sells 200 tickets

This means that $n = 200$

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

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

$P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910$

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

$\mu = E(X) = np = 200*0.905 = 181$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15$

Using continuity correction, this is $P(X \leq 180 + 0.5) = P(X \leq 180.5)$ , which is the p-value of Z when X = 180.5. Thus

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

$Z = \frac{180.5 - 181}{4.15}$

$Z = -0.12$

$Z = -0.12$ has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

$p + 0.4522 = 1$

$p = 1 - 0.4522 = 0.5478$

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

4 0

3 years ago

If the quotient of a number and 6 is added to 1/3, the result is 7/6. Find the number.

lisabon 2012 [21]

The number is 4.

<h3>What is the Quotient?</h3>

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Let n be the number in question; then, we can write the word problem as an equation like this:

⇒ (n/6) + 1/3 = 7/6

Multiply everything by the least common multiple of all the denominators (6, 3, 6), which is 6.

⇒ 6(n/6) + 9(1/3) = 6(7/6)

⇒ n + 3 = 7

Subtract 3 from both sides,

⇒ n = 4

Hence, the number is 4.

Learn more about the quotient here:

brainly.com/question/27796160

#SPJ1

3 0

1 year ago

Inventor A had 630 inventions, 600% more than the number of inventions inventor B had. How many inventions did B have?

skelet666 [1.2K]

Answer:

105 inventions

Step-by-step explanation:

Find how many inventions Inventor B had by dividing 630 by 6:

630/6

= 105

So, Inventor B had 105 inventions

6 0

3 years ago

Question 13 cos(546) + abs(-78) = ?