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
bekas [8.4K]
3 years ago
13

There were 29 students available for the woodwind section of the school orchestra. 11 students could play the flute, 15 could pl

ay the clarinet and 12 could play the saxophone. four could play the flute and the saxophone, four could play the flute and the clarinet, and 6 could play the clarinet and the saxophone. 3 students can play none of the three instruments. Find the number of students who could play: a. All the instruments b. Only the saxophone c. The saxophone and clarinet, but not the flute d. Only one of the clarinet, saxophone, or flute.
Mathematics
1 answer:
Dafna11 [192]3 years ago
6 0

Answer:

a. The number of students who can play all three instruments = 2 students

b. The number of students who can play only the saxophone is 0

c. The number of students who can play the saxophone and the clarinet but not the flute = 4 students

d. The number of students who can play only one of the clarinet, saxophone, or flute = 4

Step-by-step explanation:

The total number of students available = 29

The number of students that can play flute = 11 students

The number of students that can play clarinet = 15 students

The number of students that can play saxophone = 12 students

The number of students that can play flute and saxophone = 4 students

The number of students that can play flute and clarinet = 4 students

The number of students that can play clarinet and saxophone = 6 students

Let the number of students who could play flute = n(F) = 11

The number of students who could play clarinet = n(C) = 15

The number of students who could play saxophone = n(S) = 12

We have;

a. Total = n(F) + n(C) + n(S) - n(F∩C) - n(F∩S) - n(C∩S) + n(F∩C∩S) + n(non)

Therefore, we have;

29 = 11 + 15 + 12 - 4 - 4 - 6 + n(F∩C∩S) + 3

29 = 24 + n(F∩C∩S) + 3

n(F∩C∩S) = 29 - (24 + 3) = 2

The number of students who can play all = 2

b. The number of students who can play only the saxophone = n(S) - n(F∩S) - n(C∩S) - n(F∩C∩S)

The number of students who can play only the saxophone = 12 - 4 - 6 - 2 = 0

The number of students who can play only the saxophone = 0

c. The number of students who can play the saxophone and the clarinet but not the flute = n(C∩S) - n(F∩C∩S) = 6 - 2 = 4

The number of students who can play the saxophone and the clarinet but not the flute = 4 students

d. The number of students who can play only the saxophone = 0

The number of students who can play only the clarinet = n(C) - n(F∩C) - n(C∩S) - n(F∩C∩S) = 15 - 4 - 6 - 2 = 3

The number of students who can play only the clarinet = 3

The number of students who can play only the flute = n(F) - n(F∩C) - n(F∩S) - n(F∩C∩S) = 11 - 4 - 4 - 2 = 1

The number of students who can play only the flute = 1

Therefore, the number of students who can play only one of the clarinet, saxophone, or flute = 1 + 3 + 0 = 4

The number of students who can play only one of the clarinet, saxophone, or flute = 4.

You might be interested in
Jessica is organizing a guided tour of the rain forest. The average profit per person that the touring company makes is given by
Allushta [10]

As a practical equation, this one doesn't make much sense -- why would the profit per person have a term proportional to the number of people?  Let's just go with it.

18x + \dfrac{35}{x}

= \dfrac{18x^2}{x} + \dfrac{35}{x}

= \dfrac{18x^2 + 35}{x}

That's the answer to the first part.

35/x represents a portion of the profit that's 35/x per person, or a constant $35 per tour.

4 0
3 years ago
Does anyone know the answer to this like I don't understand how to do this?
victus00 [196]

Answer:

The m∠5 (measure of angle 5) is 135°.

Step-by-step explanation:

The m∠1 is equal to 135°. Since ∠1 and ∠5 are alternate exterior angles, they will be congruent.

5 0
2 years ago
CAN SOMEONE HELP ME​
ANTONII [103]

Answer:

C is the answer

you can also see

7 0
3 years ago
10 less than 5 times a number is less than 6 times the number decreased by eight
-BARSIC- [3]

Answer:

The Answer is: the Number is -2

Step-by-step explanation:

Let n = the number.

Five times the number minus 10 is less than 6 times the number minus eight:

5n - 10 = 6n - 8

-1n = -8 + 10

-n = 2

n = -2, the value of the number is -2.

Proof:

5(-2) - 10 = 6(-2) - 8

-10 - 10 = -12 - 8

-20 = -20

Hope this helps! Have an Awesome Day!! :-)

8 0
3 years ago
Estimating Areas and Areas of Circles
umka21 [38]

Answer:

1)84 yd

2)63 in

3)7853.98 mm (round as you want)

4)153.94 ft

5)201.06 m

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • Angelo reads 1&1/2 pages in 3 minutes. Find his reading speed in pages per hour
    13·2 answers
  • Chris earns $10.00 each time he washes his neighbor’s car. The expression 10x represents Chris' earnings. What does the variable
    7·2 answers
  • What is the ladder diagram of 27
    13·1 answer
  • How do you use a number line to add integers?
    7·1 answer
  • Round 3,004 to the nearest whole number HELPPPP
    11·2 answers
  • Evaluate the combination.<br> 5C4 <br><br> A.) 1<br> B.) 4<br> C.) 5<br> D.) 10
    13·1 answer
  • The formula v = square root of 64h gives the velocity v in feet per second of an object that has fallen h feet. find the velocit
    5·1 answer
  • −6 = x8+4<br> what is x?
    6·1 answer
  • SOMEONE PLEASE HELP ME...
    11·1 answer
  • Solve for y: -20x + 10y = 30
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!