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
lara [203]
3 years ago
9

There are 360 people in my school. 15 take calculus, physics, and chemistry, and 15 don't take any of them. 180 take calculus. T

wice as many students take chemistry as take physics. 75 take both calculus and chemistry, and 75 take both physics and chemistry. Only 30 take both physics and calculus. How many students take physics?
Mathematics
1 answer:
lesantik [10]3 years ago
6 0

Answer:

150 students take physics.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the students that take calculus.

-The set B represents the students that take physics

-The set C represents the students that take chemistry.

-The set D represents the students that do not take any of them.

We have that:

A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)

In which a is the number of students that take only calculus, A \cap B is the number of students that take both calculus and physics, A \cap C is the number of students that take both calculus and chemistry and A \cap B \cap C is the number of students that take calculus, physics and chemistry.

By the same logic, we have:

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)

This diagram has the following subsets:

a,b,c,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C), D

There are 360 people in my school. This means that:

a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) + D = 360

The problem states that:

15 take calculus, physics, and chemistry, so:

A \cap B \cap C = 15

15 don't take any of them, so:

D = 15

75 take both calculus and chemistry, so:

A \cap C = 75

75 take both physics and chemistry, so:

B \cap C = 75

30 take both physics and calculus, so:

A \cap B = 30

Solution:

The problem states that 180 take calculus. So

a + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 180

a + 30 + 75 + 15 = 180

a = 180 - 120

a = 60

Twice as many students take chemistry as take physics:

It means that: C = 2B

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

B = b + 75 + 30 + 15

B = b + 120

-------------------------------

C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)

C = c + 75 + 75 + 15

C = c + 165

----------------------------------

Our interest is the number of student that take physics. We have to find B. For this we need to find b. We can write c as a function o b, and then replacing it in the equations that sums all the subsets.

C = 2B

c + 165 = 2(b+120)

c = 2b + 240 - 165

c = 2b + 75

The equation that sums all the subsets is:

a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) + D = 360

60 + b + 2b + 75 + 30 + 75 + 15 + 15 = 360

3b + 270 = 360

3b = 90

b = \frac{90}{3}

b = 30

30 students take only physics.

The number of student that take physics is:

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

B = b + 75 + 30 + 15

B = 30 + 120

B = 150

150 students take physics.

You might be interested in
Which of the following describes the following graph?
andre [41]
A. neither a function nor a relation
5 0
3 years ago
A rope 8 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a functi
shtirl [24]
<span>1st piece: x feet
2nd piece: 8-x feet
--------------------------
Use the "x" piece to form a circle:
Circumference = "x".
2(pi)*radius = x

radius = x/(2pi)
So, Area = pi[x/(2)]^2 = x^2/(4pi) = (1/4pi)x^2
=========================================================
Use the 10-x piece to form square:
side = (1/4pi)(10-x)
Area = side^2 = (1/16)(10-x)^2

Hope this helps! :)</span>
8 0
2 years ago
Nemos aquarium is filled with 2400 cm of water the base of the aquarium is 20 cm long and 12 cm wide what is the height of the w
SSSSS [86.1K]

The answer to this question is 10 cm

In this question, you asked the height and given the volume of water(2400cm3), aquarium length(20cm), and aquarium width(12cm).

Then you need to divide the volume with the length and width. The equation would be:

Aquarium height= volume / length / width

Aquarium height= 2400 cm3 / 20cm / 12 cm = 10cm.

7 0
2 years ago
Order these numbers from least to greatest.
Y_Kistochka [10]
-3,450, -0.6, 3.85, 14
Smallest to greatest --->
5 0
3 years ago
The number p and 2/3 are additive inverses.
Tpy6a [65]

Answer:

<u>The label “Sum” is located at </u><u>0</u>

<u>The label “p” is located between </u><u>0 and -1 (-2/3)</u>

<u>The label “2/3” is located between </u><u>0 and 1</u>

4 0
3 years ago
Other questions:
  • Estimates 63824+29452
    9·2 answers
  • What is the rate of change for a linear function that passes through the points (8, -10) and (-6, 14)
    13·1 answer
  • Can you help me with all of them
    13·1 answer
  • Martin is offered an investment where for $6,000 ​today, he will receive $6,180 in one year. He decides to borrow $6,000 from th
    11·1 answer
  • Please I need help I’m not good at math
    5·1 answer
  • Select the histogram that represents the given test scores
    5·1 answer
  • How many solutions does the equation 3(x-5)-7=-3x8 have
    15·1 answer
  • 6 eggs in 7 dауs what would be the answer?
    11·2 answers
  • Tim and Dan were playing football against Jason and Luke.Touchdowns are worth 7 points .Tim and Dad scored 4 touchdowns. Jason a
    9·1 answer
  • The range of f(x)=|x| is y≥0. If a&lt;0 for g(x)=a|x|, what is the range of function g?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!