6. You must start with what mathematical operator to create a formula? A. + B.

Janice is creating a scrapbook page with vertices (2,1), (7,1), (7,7), and (2,7). What is the area of the page she will be cover

almond37 [142]

Answer:

The actual area of the page will be 120 square inches.

Step-by-step explanation:

Janice is creating a page of scrapbook having vertices (2,1), (7,1), (7,7), and (2,7).

If we plot the points on the coordinate plane then we will see that the page is of a rectangular shape with length (7 - 1) = 6 units which is parallel to the y-axis and width (7 - 2) = 5 units which is parallel to the x-axis.

So, the area of the page is (6 × 5) = 30 square units.

Now, given that 1 square unit is equivalent to 4 square inches.

Therefore, the actual area of the page will be (30 × 4) = 120 square inches. (Answer)

3 0

3 years ago

A tattoo enthusiast website claims that :

KATRIN_1 [288]

Answer:

The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

Step-by-step explanation:

We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.

We have a series of different probabilities that we have to distinguish one from the others:

The probability that a person has a tattoo assuming that is a Millennial is:

$\\ P(T|M) = 0.47$

The probability that a person has a tattoo assuming that is of Generation X is:

$\\ P(T|X) = 0.36$

The probability that a person has a tattoo assuming that is of Boomers is:

$\\ P(T|B) = 0.13$

The probability of being of Millennials is:

$\\ P(M) = 0.22$

The probability of being of Generation X is:

$\\ P(X) = 0.20$

The probability of being of Boomers is:

$\\ P(B) = 0.22$

Therefore, the probability of the event of having a tattoo P(T) is:

$\\ P(T) = P(T|M)*P(M) + P(T|X)*P(X) + P(T|B)*P(B)$

$\\ P(T) = 0.47*0.22 + 0.36*0.20 + 0.13*0.22$

$\\ P(T) = 0.204$

For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:

$\\ P(M \cap T) = P(M|T)*P(T)$

Or

$\\ P(T \cap M) = P(T|M)*P(M)$

But

$\\ P(M \cap T) = P(T \cap M)$

Then

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

$\\ P(M|T) = \frac{P(T|M)*P(M)}{P(T)}$