Find the distance between the points (-2, 3) and (-7, - 7). Round your answer to the nearest tenth, if necessary.

At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a res

Ghella [55]

Answer:

a) $P(F UR) = P(F) +P(R) -P(F and R) = 0.72+0.46-0.32=0.86$

b) $P(FUR)' = 1-P(FUR)= 1-0.86 = 0.14$

Step-by-step explanation:

Let's define the following events first:

F: The event that a course has a final exam.

R: The event that a course requires a research paper

From the info provided we have that:

$P(F) = 0.72, P(R) =0.46$ P(F and R) =0.32

So then we can create a Venn diagram as we can see on the figure attached.

a. Find the probability that a course has a final exam or a research project.

For this case we can find the probability like this:

$P(F UR) = P(F) +P(R) -P(F and R) = 0.72+0.46-0.32=0.86$

b. Find the probability that a course has NEITHER of these two requirements.

For this case we can use the complement rule and we can find the probability like this:

$P(FUR)' = 1-P(FUR)= 1-0.86 = 0.14$

And that's the same value obtained with the diagram.

8 0

3 years ago

2z - 6 = 2(2 + 2) - 10

Blababa [14]

Answer:

z=2

Step-by-step explanation:

2z-6=2(2+2)-10 Distribute.

2z-6=4+4-10 Combine like terms.

2z-6=-2 Add 6 on both sides.

2z=4 Divide by 2 on both sides.

z=2

Hope this helps! Have a great day ^^

6 0

3 years ago

Solve for x!!! HELP!!!

MArishka [77]

X=22.5
I got that by writing the fraction 12/15 is equal to 18/x. To get 12 to 18 u have to multiply 12 by 1.5, so I do the same to 15 to find what x would be

6 0

3 years ago

Suppose you have 60 red marbles and 40 blue marbles in a

andrew-mc [135]

Answer: The required probability is 0.26.

Step-by-step explanation: Given that there are 60 red marbles and 40 blue marbles in a box 10 marbles are picked without replacement.

We are to find the probability of selecting 6 red marbles.

Since the marbles are picked up without replacement, so it is a situation of combination.

Let S denote the sample space of the experiment of drawing 10 marbles and E denote the event that 6 marbles are red.

So,

$n(S)=^{100}C_{10}=\dfrac{100!}{10!(100-10)!}=\dfrac{100!}{10!90!}=17310309456440,\\\\\\n(E)=^{60}C_6\times^{40}C_4=\dfrac{60!}{6!54!}\times\dfrac{40!}{4!36!}=50063860\times91390.$

Therefore, the probability of event E is given by

$P(E)=\dfrac{n(E)}{n(S)}=\dfrac{50063860\times91390}{17310309456440}=0.26.$

Thus, the required probability is 0.26.

6 0

3 years ago

You intend to draw a random sample in order to test a hypothesis about an unknown population mean. You will use a hypothesis tes

Gre4nikov [31]

Answer:

The correct order is :

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

6 0

3 years ago

Find the distance between the points (-2, 3) and (-7, - 7). Round your answer to the nearest tenth, if necessary.​

Find the distance between the points (-2, 3) and (-7, - 7). Round your answer to the nearest tenth, if necessary.