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:

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:

[tex](A \cap B \cap C) = 2[/tex]

6 that are in both French and German

This means that:

[tex](B \cap C) + (A \cap B \cap C) = 6[/tex]

So

[tex](B \cap C) = 4[/tex]

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

[tex](A \cap C) + (A \cap B \cap C) = 4[/tex]

So

[tex](A \cap C) = 2[/tex]

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

[tex](A \cap B) + (A \cap B \cap C) = 12[/tex]

So

[tex](A \cap B) = 10[/tex]

10 Spanish and French, but not German

16 in the German class.

This means that:

[tex](C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16[/tex]

[tex](C - B - A) + 2 + 4 + 2 = 16[/tex]

[tex](C - B - A) = 8[/tex]

8 in only German.

26 in the French class

[tex](B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26[/tex]

[tex](B - C - A) + 10 + 4 + 2 = 26[/tex]

[tex](B - C - A) = 10[/tex]

10 only French

28 students in the Spanish class

[tex](A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16[/tex]

[tex](A - B - C) + 10 + 2 + 2 = 28[/tex]

[tex](A - B - C) = 14[/tex]

14 only Spanish

At least one of them:

The sum of all the above values. So

[tex](A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50[/tex]

None of them:

100 total students, so:

[tex]100 - (A \cup B \cup B) = 100 - 50 = 50[/tex]

(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

Please help!!!!!!!!!

Answers

Answer:

7.823 8.019

Step-by-step explanation:

Those two both will round up to 20 in the hundredths place and both round to 8.

What is a common denominator?

Answers

least common denominator is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.

Answer:

12

Step-by-step explanation:

Because it is the lowest number that both 4 and 6 can reach by multiplying with whole numbers

:)

The length of a rectangle is 20 inches less than twice the width. The perimeter of the rectangle is 86 inches. Find the dimensions of the rectangle.

Answers

Answer:

length=22

width=21

Step-by-step explanation:

let, length be x and width be y.

x=2y-20

2(x+y)=86

or, 2(2y-20+y)=86

or, 2(3y-20)=86

or, 6y-40=86

or, 6y= 126

or, y= 126/6

y= 21

x= 2×21-20 = 42-20 =22

In the year 2001, a company made $5.5 million in profit. For each consecutive
year after that, their profit increased by 12%. How much would the company's
profit be in the year 2003, to the nearest tenth of a million dollars?

Answers

5.5*1.12*1.12=6.9MM.......

Solve each equation by factoring ⁉️NEED THIS ASAP ⁉️

Answers

Answer:

Step-by-step explanation:

Select all multiples of the number: 9​

Answers

Answer:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Step-by-step explanation:

hi

Answer:

9,18,27,36,45,54,63,72,81,90

Step-by-step explanation:

Can someone help quick please

Answers

Answer:

PC = 4 cm

Step-by-step explanation:

AP = 4 cm

Because AB = BC, PB = PB, and we know that angle PBA = 90 degrees: triangle PBA is congruent to triangle PBC by the Side-Angle-Side theorem.

PC = AP because corresponding parts of congruent triangles are congruent.

If you borrow $3,000 at 5% simple interest for 9 months how much will you owe in 9 months? How
much interest will you pay?

Answers

Answer: $150

Step-by-step explanation:

$3,000 x 5% = 150

What is the approximate area of the circle shown below?

Answers

Answer:

A

Step-by-step explanation:

can you help me please ​

Answers

Answer:

[tex]log_372 = 3.8928[/tex]

Step-by-step explanation:

Given

[tex]log_38 = 1.8928[/tex]

Required

Evaluate [tex]log_372[/tex]

We have:

[tex]log_372 = log_3(8 *9)[/tex]

Apply law of logarithm

[tex]log_372 = log_38 +log_39[/tex]

Express 9 as 3^2

[tex]log_372 = log_38 +log_33^2[/tex]

Evaluate the exponents

[tex]log_372 = log_38 +2log_33[/tex]

[tex]log_33 = 1[/tex].

So:

[tex]log_372 = log_38 + 2 * 1[/tex]

[tex]log_372 = log_38 + 2[/tex]

Substitute [tex]log_38 = 1.8928[/tex]

[tex]log_372 = 1.8928 + 2[/tex]

[tex]log_372 = 3.8928[/tex]

Milo and Audrey sold tickets to the school concert. Milo sold 14 fewer tickets than Audrey. If Milo sold 32 tickets, how many tickets did Audrey sell?​

Answers

Answer:

18

Step-by-step explanation:

32-14=18

18 is the answer I think it is

Which problem can be solved with this equation?
A. Jen has 4 of a meter of ribbon. She buys 6 more meters of ribbon. How many meters of ribbon does she have in all?
B. Jen has f of a meter of ribbon, she wants to give 6 friends equal-size pleces of the ribbon. How many meters of ribbon does each
friend get?
OC. Jen has 6 meters of ribbon. She cuts
soft / of
of the ribbon. How many meters of ribbon does she have left?
OD. Jen has 6 meters of ribbon, she wants to give
of it to her friend. How many meters of ribbon does she give her friend?

Answers

Answer:

I believe the answer is B

Graphic DesignWorks ships the T-shirts it makes in boxes that measure 24 in
x 18 in x 16 in. The company rents a storage space that measures 400 ft x
240 ft x 60 ft. What is the best estimate of the number of boxes Graphic
DesignWorks is able to store?
A. 576,000 boxes
B. 1,440,000 boxes
C. 6912 boxes
D. 972,000 boxes

Answers

Answer:The answer is c

Step-by-step explanation:

The best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes.

What is volume?

Volume is the three-dimensional space enclosed by a three-dimensional object.

We have to find the volume of the box and the volume of the storage space.

The volume of the box:

Volume = length × breadth × height

= 24 × 18× 16 in³

=6912 in³

The volume of the storage space:

Volume = length × breadth × height

= 400 × 240 × 60 ft³

= 5760000 ft³

We have to convert this into inches. We know that  1 foot = 12 inches.

Therefore, 5760000 ft³ = 5760000 × (12)³ in³

We have to divide the volume of the storage space by the volume of the box to find the number of boxes that it can fit:

Number of boxes that can fit inside the storage space = (5760000 × (12)³ in³)/6912 in³

= 1440000 boxes.

Thus, the best estimate of the number of boxes Graphic DesignWorks is able to store is 1440000 boxes. The correct answer is option B.

Learn more about volume here-https://brainly.com/question/25736513

#SPJ2

The invitations to a holiday party cost a total of $31.50 if each invitation cost $0.75 cents how many invitations were sent out

Answers

Answer:

42

Step-by-step explanation:

divide the total by the cost of each invite

Which equations are equivalent to 33/x+ 4 = 12? Check all that apply.
3x + 4 = 9
43 = 3x + 4
O x + 4 = 64
U 3+ 4 = - 4
0 60 = x

Answers

Answer:

option c

x + 4 = 64

and

option e

x = 60  

Step-by-step explanation:

Given in the question an expression

3∛x+4 = 12

∛x + 4 = 12/3

∛x + 4 = 4

Take cube on both sides of the equation

∛(x + 4)³ = 4³

x + 4 = 64

x = 64 - 4

x = 60  

can someone help me? I have to turn it on by tomorrow :(

Answers

Answer:

The terms in #4 are 2500, 11t, and -3w

The terms in #5 are 17 and 4d


Solve for x.
(Round to the nearest hundredth)

Answers

Answer:

x=26.44

rounded to the nearest hundredth.

Step-by-step explanation:

Soh Cah Toa

We need opposite for x and adjacent for 44

Length × Tan (Angle)

44 × Tan (31)=26.43786724

Please helppp ASAPPP will mark brainliest

Answers

a) SR

b) QR

c) RW and RV

RT and RS

RU and RQ

Convert these mixed numbers into improper fractions.

Answers

Answer:

[tex]2\frac{2}{5}=\frac{12}{5}[/tex]

[tex]3\frac{1}{6}=\frac{19}{6}[/tex]

Step-by-step explanation:

In [tex]2\frac{2}{5}[/tex] you multiply 2x5 which equals 10 and then you add 10+2=12

2x5=10

10+2=12

=[tex]\frac{12}{5}[/tex]

You do the same thing multiply the denominator by the whole number and whatever you get when you multiply add it with the numerator.

3x6=18

18+1=19

=[tex]\frac{19}{6}[/tex]

19. The formula P = a + b + cgives the perimeter P of a triangle with side
lengths a, b, and c. A triangular field has sides that measure 33 yards,
56 yards, and 65 yards. What is the perimeter of the field? (6.EE.20)

Answers

Answer:

33 + 56 + 65 = 154

cuánto es 567 + 678 es igual

Answers

Answer: 1245 :)

Step-by-step explanation:

Answer:

la respuesta es 1245

567+678=1245

Which is the volume of the solid?

Answers

Answer: the answer is A

Step-by-step explanation:

Assume that y varies inversely with x. If y = 7 when x = -2, find у when x = 7. y = ??​

Answers

Answer:

-2

Step-by-step explanation:

y=k/x

Replace y with 7 and x with -2

7=k/-2 gives you -14

Then you can replace k with -14 and x with 7

y=-14/7 gives you -2

A
9x - 40
B
3x + 20
x = [?]

Answers

Answer:

x = 10

Step-by-step explanation:

9x - 40 = 3x + 20

9x - 3x - 40 = 3x - 3x + 20

6x - 40 = 20

6x - 40 + 40 = 20 + 40

6x = 60

6x / 6 = 60 / 6

x = 10

Now plug the x value in the equation to make the statement true that A is parallel to B.

9x - 40

9(10) - 40

90 - 40

50

3x + 20

3(10) + 20

30 + 20

50

Therefore, x = 10 making the statement true that A is parallel to B. Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer: 10

Step-by-step explanation:

Help please I really need it

Answers

Answer:

40%

Step-by-step explanation:

it ads up to 90, so 50+x=90   x=40

Answer:

40° as it is a right angle

then 90 - 50= 40


HELP PLS I NEED HELP

Answers

Answer:

133

Step-by-step explanation:

180 - 47 = 133

Answer:

133°

Step-by-step explanation:

If we assume the the given to adjacent lines to be parallel then ,

The x and supplement of 47° will be equal since they will be corresponding angles .

Therefore :-

=> x = 180° - 47°

=> x = 133° .

Hence the size of angle X is 133°

Which techniques can be used to evaluate the expression 12.75 = 1.5? Select all that apply.

Answers

What is the apply??? Put all of the select all that apply so I can help you

PLEASE HELP I WILL GIVE BRAINLIEST
Given a long algebraic expression, what are some strategies that you can use to make simplifying and evaluating the expression more efficient and accurate?

How do inverse operations help solve algebraic equations? Give a real-world scenario where this might be modeled.

Answers

Answer:

See below.

Step-by-step explanation:

To simplify a long algebraic expression, you could use many methods. My personal choice is to use distribution in order to follow PEMDAS and eliminate any parenthesis within my equation. I also like to combine like terms to shorten the equation as much as possible.

Inverse operations are extremely helpful in isolating variables and simplifying equations. They can be used in many scenarios from finding the length of an object with only a formula and one side (ex. a triangle with only b and A given) to having distance and speed to figure out the time it will take to get to your destination.

Select the correct answer.

Consider this absolute value function.

f(x) = [ x + 3 ]

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3
B. x + 3, x > -3
C. -x + 3, x < -3
D. -x - 3, x < 3

Answers

Answer:

B) x + 3, x > -3

Step-by-step explanation:

I just took a test with this question on it and got it right.

Hope this helps! :)

If function f is written as a piecewise function, it will include x + 3, x > -3

The absolute value function is given as:

f(x) = | x + 3 |

Given that the function is an absolute value function, this means that:

|x + 3| > 0

Remove the absolute sign

x + 3 > 0

Subtract 3 from both sides

x > -3

Hence, if function f is written as a piecewise function, it will include x + 3, x > -3

Read more about absolute value functions at:

https://brainly.com/question/10538556

3. Given f(x)=-2(5)
Find f (4)

Answers

Answer:

f

(

x

)

=

2

, means, whatever be the value of

x

, f(x)=2#.

f

(

4

)

=

2

.

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