1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
harina [27]
3 years ago
8

A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russ

ian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2 092 students have taken at least one of Spanish, French, and Russian, how many students have taken a course in all three languages

Mathematics
1 answer:
ElenaW [278]3 years ago
3 0

Answer:

n(S\cap F \cap R)=7

Step-by-step explanation:

The Universal Set, n(U)=2092

n(S)=1232\\n(F)=879\\n(R)=114

n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14

Let the number who take all three subjects, n(S\cap F \cap R)=x

Note that in the Venn Diagram, we have subtracted n(S\cap F \cap R)=x from each of the intersection of two sets.

The next step is to determine the number of students who study only each of the courses.

n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x

These values are substituted in the second Venn diagram

Adding up all the values

2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]

2092=2085+x

x=2092-2085

x=7

The number of students who have taken courses in all three subjects, n(S\cap F \cap R)=7

You might be interested in
It’s a review please HELP ASAP I’ve been stuck on it for awhile now
AlladinOne [14]
<h3>Answer:   7 goes in the blank space</h3>

The range of values for x is 2 < x < 7

========================================

Explanation:

The hinge theorem says that the larger the opposite side is, the larger the angle will be.

AD = 11, DC = 8

Since AD > DC, this means angle ABD > angle DBC.

--------

angle ABD > angle DBC

20 > 4x-8

20+8 > 4x-8+8 ... add 8 to both sides

28 > 4x

4x < 28 ... flip both sides and the inequality sign

4x/4 < 28/4 ... divide both sides by 4

x < 7

--------

At the same time, the angle 4x-8 cannot be 0 or negative.

So we say 4x-8 > 0. Let's solve this for x.

4x-8 > 0

4x-8+8 > 0+8 ... add 8 to both sides

4x > 8

4x/4 > 8/4 ... divide both sides by 4

x > 2

2 < x ... flip both sides and the inequality sign

--------

We have 2 < x and x < 7. Both of these combine to the compound inequality 2 < x < 7

We can pick any value between 2 and 7 as long as we dont pick x = 2 or we dont pick x = 7.

6 0
2 years ago
several friends each had 2/5 of a bag of peanuts left over from the baseball game. they realized that they could had bought two
kenny6666 [7]
The answer is 5.

5 times 2/5 = 2 bags
7 0
3 years ago
Hunter is 4.52 feet tall. His sister is 0.75 times his height. How tall is Hunter's sister
Dominik [7]

Answer:

Hunter's sister is 4.53 feet tall.

Step-by-step explanation:

4.52 x 0.75 = <u>3.39 feet</u>


4 0
2 years ago
DO NOT SPAM YOU WILL BE REPORTED ANSWER QUICK PLEASE Mason bought 16 tickets to a baseball game. The group rate saved him $5.75
Wittaler [7]
Divide 296 by 16 you get 18.5 then add the 5.75 to get 24.25
So the answer is 24.25
3 0
3 years ago
- 2y + 7y + 4<br> Can someone help
sladkih [1.3K]
Hi !
the answer is 5y+4

please let me know if im wrong (:
6 0
3 years ago
Other questions:
  • If the mean if these numbers is 9 what is x ? <br><br> 16,3,x,5
    6·1 answer
  • Help me please? c: I only have 4 questions left and I'm a bit stuck
    13·1 answer
  • Which one is not a linear function?
    5·1 answer
  • After working for 24 hours,zoe made $234. After working for 40 hours, zoe made $390.predict how much she would make after 10 hou
    7·1 answer
  • a carpenter uses four nails to install each shelf. complete the table to represent the relationship between the number of nails
    5·1 answer
  • Bella is looking into getting an apartment that costs $800 per month. how much does she need to make per year in order to comfor
    9·2 answers
  • How many squares (think about the faces) are painted on a tower that is 99 cubes tall?
    14·1 answer
  • Polygon P'Q'R'S'T' shown on the grid below is an image of polygon PQRST after dilation with a scale factor of 3, keeping the ori
    9·2 answers
  • What is the difference x + 5/ x + 2 - x + 1 /x^2 + 2x
    8·2 answers
  • Nan says 21/4 is equal to 5 1/4. Dorothy says it is equal to 4 1/5. Who is correct? Show your work to prove the right answer.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!