MATHEMATICS COLLEGE

An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to any of the 100 students inthe school. There are 28 students in the Spanish class, 26 in the French class,and 16 in the German class. There are 12 students that are in both Spanish andFrench, 4 that are in both Spanish and German, and 6 that are in both Frenchand German. In addition, there are 2 students taking all 3 classes.(a) If a student is chosen randomly, what is the probability that he or she isnot in any of the language classes

Answers

Answer 1

Answer:

Answer:

0.5 = 50% probability that he or she is not in any of the language classes.

Step-by-step explanation:

We treat the number of students in each class as Venn sets.

I am going to say that:

Set A: Spanish class

Set B: French class

Set C: German class

We start building these sets from the intersection of the three.

In addition, there are 2 students taking all 3 classes.

This means that:

$(A \cap B \cap C) = 2$

6 that are in both French and German

This means that:

$(B \cap C) + (A \cap B \cap C) = 6$

$(B \cap C) = 4$

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

$(A \cap C) + (A \cap B \cap C) = 4$

$(A \cap C) = 2$

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

$(A \cap B) + (A \cap B \cap C) = 12$

$(A \cap B) = 10$

10 Spanish and French, but not German

16 in the German class.

This means that:

$(C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16$

$(C - B - A) + 2 + 4 + 2 = 16$

$(C - B - A) = 8$

8 in only German.

26 in the French class

$(B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26$

$(B - C - A) + 10 + 4 + 2 = 26$

$(B - C - A) = 10$

10 only French

28 students in the Spanish class

$(A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16$

$(A - B - C) + 10 + 2 + 2 = 28$

$(A - B - C) = 14$

14 only Spanish

At least one of them:

The sum of all the above values. So

$(A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50$

None of them:

100 total students, so:

$100 - (A \cup B \cup B) = 100 - 50 = 50$

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

50 out of 100. So

50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.

Related Questions

What is the sign of the product (-5)(-3)(-8)(-6)? (5 points) Positive, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is positive Positive, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is positive Negative, because the products (-5)(-3) and (-8)(-6) are negative, and the product of two negative numbers is negative Negative, because the products (-5)(-3) and (-8)(-6) are positive, and the product of two positive numbers is negative
I don’t know if it’s g(2(5)(3(5)^2-5-5
Find y from the picture plz
Brandon uses the steps below to solve the equation 15 x + 6 = 14 x + 5 using algebra tiles.Step 1 Add 14 negative x-tiles to both sides.Step 2 Add 5 negative unit tiles to both sidesStep 3 The solution is x = 1.Which explains whether Brandon is correct?Brandon is correct because he has the correct solution in step 3.Brandon is correct because he forms zero pairs to isolate the variable by using the lowest coefficient each time.Brandon is not correct because he should have performed step 2 before performing step 1.Brandon is not correct because he should have added 6 negative unit tiles to isolate the variable in step 2.
I need help on this. ive been struggling. TwTlateral areasurface areavolume

Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

Answers

Answer:

A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

Step-by-step explanation:

---Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.

Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

B. Randomization will make up for improper experimental design, data collection, and analysis.

C. Randomization makes the analysis easier since the data can be entered into the computer in any order.

D. Randomization is required by statistical consultants before they will analyze the experiment.

E. Randomization means that the experiment would not need to be replicated---

Randomization is used to ensure that the results of a trial or an experiment are actually because if the treatment or hypothesis we are trying, instead of any other external factor that we can not control, or because it just always happens that way, if all of the jellyfish are affected or not in the same way, then the Ph had little to nothing to do with it, and if only one group of them is affected we can re-try the experiment to see if the difference in the Ph had anything to do with the change.

Answer:

A.Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

Step-by-step explanation:

How long will it take for a sum of $800 attracting simple interest to become $830 if the rate is 9%? Compute the return on this investment.

Answers

Answer:

5 months

ROI = 3.75 %

Step-by-step explanation:

Since,

The simple interest formula,

$I=P* r* t$

Where,

P = Principal amount,

r = rate per period ( in decimal )

t = number of periods,

Here, P = 800, r = 9% = 0.09,

If A is the future amount,

We have, A = 830

I = A - P = 830 - 800 = 30

By substituting the values in the above formula,

$30=800* 0.09* t$

$30=72t$

$\implies t =(30)/(72)=(5)/(12)$

Hence, it will take 5 months. ( 1 year = 12 months )

Now,

$\text{Return on investment }=(I)/(P)* 100$

$=(30)/(800)* 100$

$=3.75\%$

Solve the following quadratic equation. (x+12)^2=1 A. x = 11 and x = 13 B. x = -11 and x = -13 C. x = -11 and x = 13 D. x = 11 and x = -13Will make brainiest!!!

Answers

Answer:

Step-by-step explanation:

(x+12)^2=1

(x+12)= +or - 1

when

x+12=1

x=1-12 =-11

when

x+12=-1

x=-1-12 =-13

then

x=-11 and x= -13

Answer:

Step-by-step explanation:

Plato

Please help! Camille is saving for a laptop that costs about $850. To model her savings plan and determine how many more months it will take her to reach her goal, she recently created this equation, where y represents the total amount saved and x represents the number of months. Which statement about her work is true?'

Answers

Answer:

Camille is able to buy the laptop in 14 months.

Step-by-step explanation:

Camille is saving for her to buy new laptop. She has created equation in order to understand the savings to finance the laptop. She is saving nearly 30 percent of her salary and with this savings she will be able to buy a new laptop in 14 months. Camille should consider saving more if she wants to buy the new laptop early.

Answer:

Step-by-step explanation:

Rewrite 4+8lnx=2 without logarithms

Answers

4 + 8 ln(x) = 2

8 ln(x) = $(1)/(2) [/tex</p><p>ln (x) = [tex] (1)/(16)$

$e^(ln(x)) = e^{(1)/(16)$ by exponentiating both sides.

x = $= e^{(1)/(16)$

The table shows the number, expressed in millions, of citizens who moved in 2004, categorized by where they moved and whether they were an owner or a renter. find the probability, expressed as a decimal rounded to the nearest number of people in a certain country who moved in 2004, in millions moved to same region moved to different region moved to different country owner 11.6 11.6 2.7 2.7 0.4 0.4 renter 18.7 18.7 4.5 4.5 1.0 1.0 hundredth, that a randomly selected citizen who moved in 2004 was a person who moved to a different region to a different region.

Answers

The table is attached.
You need to find the probability, expressed as a decimal rounded to the nearest hundredth, that a randomly selected citizen who moved in 2004 was a person who moved to a different region.

What you need to calculate is the empirical probability: the number of success over the total number of outcomes.

People who moved to a different region = 2.7 + 4.5 = 7.2 millions
People who moved in 2004 = 11.6 + 2.7 + 0.4 + 18.7 + 4.5 + 1.0 = 38.9 millions

P = People who moved to a different region / People who moved in 2004
= 7.2 millions / 38.9 millions = 0.18508997

Therefore, the probability that a randomly selected citizen who moved in 2004 was a person who moved to a different region is P = 0.19

Answer:

Step-by-step explanation:

0.19

Other Questions

Stephanie was doing a science experiment to see what brand of cereal with raisinsactually had more raisins. She scooped out one cup of cereal and counted 27 raisins. Ifthere were 12 cups of cereal in the box, predict about how many raisins should therebe in the box?

Please Explain/Show your work!

A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? We would assign a probability of to the design 1 outcome, to design 2, to design 3, to design 4, and to design 5. In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Design Number of Times Preferred 1 10 2 5 3 30 4 40 5 15 Do the data confirm the belief that one design is just as likely to be selected as another? Explain. Yes, the sum of the assigned probabilities is 1. No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely. Yes, the average of the assigned probabilities is 0.20. No, a probability of about 0.50 would be assigned using the relative frequency method if selection is equally likely.

What is 783,264 rounded to the nearest ten thousand