answer.
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
svet-max
2 months ago
14

In a group of Explore students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. O

f these, 8 students like all three activities, while 30 like only one of them.
How many students like only two of the three activities?
Mathematics
1 answer:
Zina [12.3K]2 months ago
8 0

Answer:

34 students appreciate just two of the activities.

Step-by-step breakdown:

The number of students who enjoy video games is A = 38

The count of students fond of movies is B = 12

The students who thrive on solving math problems is C = 24

A∩B∩C = 8

Using the formula:

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)

= 38 + 12 + 24 - n(A∩B) - n(B∩C) - n(A∩C) + 8

Moreover, the count of students that enjoy exclusively one activity can be derived from the following equation:

n(A) - n(A∩B) - n(A∩C) + n(A∩B∩C) + n(B) - n(A∩B) - n(B∩C) + n(A∩B∩C) + n(C) - n(C∩B) - n(A∩C) + n(A∩B∩C) = 30

n(A) + n(B) + n(C) - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 3·n(A∩B∩C) = 30

38 + 12 + 24 - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 24 = 30

- 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) = -68

Thus, n(A∩B) + n(B∩C) + n(A∩C) = 34.

Consequently, the total of students who enjoy just two of the activities equals 34.

You might be interested in
A skydiver is 960 meters above the ground when she opens her parachute. After opening the parachute, she descends at a constant
Inessa [12570]

Response:

The equation of the linear function can be represented as:

H(S) = 960 - 3.2*S


0 0
20 days ago
The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of
PIT_PIT [12445]
A. Mean and standard deviation.

The sampling distribution’s mean closely matches the population mean. Since the population mean is 174.5, the sampling distribution’s mean equals this value.

The standard deviation of the sampling distribution is:

            σₓ̄ = σ / √n

Plugging in values:

            σₓ̄ = 6.9 / √25 = 1.38

b. Calculate z-scores for both values:
         
      z = (value - mean) / standard deviation

For 172.5:
     z = (172.5 - 174.5) / 1.38 = -1.49
Corresponding probability ≈ 0.068

For 175.8:
   z = (175.8 - 174.5) / 1.38 = 0.94
Corresponding probability ≈ 0.83

The difference between these probabilities is 0.762.

Approximately 0.762 × 200 = 152 sample means lie between 172.5 and 175.8.

c. Z-score for 172 cm:

    z = (172 - 174.5) / 1.38 = -1.81
Probability ≈ 0.03

Hence, samples with means below 172 cm equal 0.03 × 200 = 6.
8 0
2 months ago
A quarterback looks downfield at a receiver who is 14 yards away. The receiver is covered, so the quarterback turns 30° to his r
Zina [12379]
Your answer will be C.
8 0
1 month ago
Read 3 more answers
If BD = 7x – 10, BC = 4x – 29, and CD = 5x – 9, find each value.
babunello [11817]
BD=7x-10
Solution: x=bd/7 + 10/7

BC=4x-29
Solution: x=Bc/4 + 29/4

CD=5x - 9
Solution: x= cd/5 + 9/5
4 0
2 months ago
The value of x in logx(9/63)=1/2 is​
lawyer [12517]

Answer: x = 7/2

Step-by-step explanation: You can simplify 1/2 x 7 to reach 7/2, therefore x is equal to 7/2.

8 0
2 months ago
Other questions:
  • I JUST NEED THESE 3 QUESTIONS
    6·1 answer
  • Data were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data reveal
    15·1 answer
  • Why wouldn't the man stand in line to step on the scale ? <br><br> answer ?
    10·1 answer
  • 1.4 puzzle time Why was the geometry book so sad? It had
    11·2 answers
  • Explain what it means to have a correlation in a scatterplot.
    9·2 answers
  • Susan and Jim own a lawn care business. The amount Susan charges for a lawn care by the hour is shown in the table.
    6·1 answer
  • Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the b
    12·2 answers
  • A used car dealer has 30 cars and 10 of them are lemons (i.e.~ mechanically faulty used cars), and you don't know which is which
    12·1 answer
  • Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord
    9·1 answer
  • Raphael can finish his math project in 3 hours. It takes Jai to do the same project in 4 hours. If they will work together as pa
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!