Square WXYZ dilates by a factor of 1/3 with respect to the origin to create W'X'Y'Z'. If W'X' is 6 units, what is WX? *

Tina conducted a survey to find the favorite weekend activity of the people in her state. She asked 10 of her neighbors what the

sattari [20]

Answer:

Tina conducted a survey to find the favorite weekend activity of the people in her state. She asked 10 of her neighbors what their favorite weekend activity is. Tina concludes that boating is the favorite weekend activity of the people in her state because 70% of her neighbors like to go boating on weekends.

Use at least two sentences to explain why Tina's sample may not be valid. Make sure to use facts to support your answe

5 0

2 years ago

Read 2 more answers

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the bl

trapecia [35]

Answer:

About 99.74% of the area is between z = -3 and z = 3

Step-by-step explanation:

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.

Area between z = 3 and z = -3

pvalue of z = 3 subtracted by the pvalue of z = -3

z = 3 has a pvalue of 0.9987

z = -3 has a pvalue of 0.0013

0.9987 - 0.0013 = 0.9974

0.9974*100 = 99.74%

About 99.74% of the area is between z = -3 and z = 3

8 0

3 years ago

Ramon invested a total $9,700 into two accounts, account 1 earns 6% simple interest and account 2 earns 4% simple interest. Afte

jarptica [38.1K]

Answer:

In the account that paid 3% Ramon put $800

In the account that paid 6% Ramon put $1,600

Step-by-step explanation:

5 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

2 years ago

The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of 2 2 . what is the measure of the angle

creativ13 [48]

The correct question is
The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of √2/2 .
What is the measure of the angle?

Let
∅--------> the angle
cos ∅=√2/2
cos ∅=[distance of one of the leg/hypotenuse]
[distance of one of the leg/hypotenuse]=√2/2

I could say that
distance of one of the leg=√2
and
hypotenuse=2
so
applying the Pythagorean theorem
c=hypotenuse=2
a=√2
b=?
c²=a²+b²-------> b²=c²-a²------> b²=2²-(√2)²-----> b²=2-----> b=√2

therefore
if a=b
then
the angle ∅=45°

the answer is the option
b.45 degrees

7 0

3 years ago