At a particular school, all students participate in at least one out of three activities: debate, music, and community service. 3 students do all three activities, 21 students do two or more activities, half of all students participate in music, and the ratio of participants in debate, music, and community service, respectively, is $5:4:3$. What is the total number of students at the school

Answers

Answer 1

Answer:

48

Step-by-step explanation:

The given parameters are;

The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services

The number of students that do all three activities = 3

The number of students that do two or more activities = 21

The number of the students that participate in music = Half of the students

The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3

Let x represent a common number factor of participants in each of the given three activities, we have;

5·x participate in debate, A

4·x participate in music, B

3·x participate in community service, C

We get;

The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C

Given that the number of students that do two or ore activities = 21, we have;

(A∩B)∪(A∩C)∪(B∩C) = 21

However, we have;

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

∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3

(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27

∴ -(A∩B) - (A∩C) - (B∩C) = -27

Therefore;

A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3

5·x + 4·x + 3·x - 27 + 3 = 12·x - 24

The total number of students = A∪B∪C = 12·x - 24

The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2

∴ 4·x = (12·x - 24)/2

8·x = 12·x - 24

12·x - 8·x = 24

4·x = 24

x = 24/4 = 6

The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48


Related Questions

Which graph represents the function f(x) = −|x − 2| − 1?

Answers

Answer:

Graph C

Step-by-step explanation:

A cannonball shot from a cannon has projectile motion.
true or false
need a answer please​

Answers

True because it makes a parabola shape it is clearly true

2 (x + 4) = 2 (-8 - x) - 2x

Answers

Answer:

x = -4

Step-by-step explanation:

Simplifying

2[x + 4] = 2[-8 + -1x] + -2x

Reorder the terms:

2[4 + x] = 2[-8 + -1x] + -2x

[4 * 2 + x * 2] = 2[-8 + -1x] + -2x

[8 + 2x] = 2[-8 + -1x] + -2x

8 + 2x = [-8 * 2 + -1x * 2] + -2x

8 + 2x = [-16 + -2x] + -2x

Combine like terms: -2x + -2x = -4x

8 + 2x = -16 + -4x

Solving

8 + 2x = -16 + -4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4x' to each side of the equation.

8 + 2x + 4x = -16 + -4x + 4x

Combine like terms: 2x + 4x = 6x

8 + 6x = -16 + -4x + 4x

Combine like terms: -4x + 4x = 0

8 + 6x = -16 + 0

8 + 6x = -16

Add '-8' to each side of the equation.

8 + -8 + 6x = -16 + -8

Combine like terms: 8 + -8 = 0

0 + 6x = -16 + -8

6x = -16 + -8

Combine like terms: -16 + -8 = -24

6x = -24

Divide each side by '6'.

x = -4

Simplifying

x = -4

2( x + 4) = 2 (-8 -x) -2x

Use the distributive property to multiply 2 by x + 4.

2x + 8 = 2 (-8 -x) - 2x

Use the distributive property to multiply 2 by -8 -x.

2x + 8 = -16 -2x - 2x

Combine -2x and 2x to get -4x.

2x + 8 = -16 - 4x

Add 4x to both sides.

2x + 8 + 4x = -16

Combine 2x and 4x to get 6x.

6x + 8 = -16

Subtract 8 from both sides.

6x = -16 - 8

Subtract 8 from -16 to get -24.

6x = -24

Divide both sides from 6.

x = [tex]\frac{-24}{6}[/tex]

Divide by -24 by 6 to get -4.

x = -4.

A virus attacked 175,245 people in city A and 1,486,964 people in city B. How many people in all were affected? Thank you in advance:)

Answers

1,662,209 is the answer. You just have to add them all up

Answer:

It's 1662209.

Step-by-step explanation:

just add them

You have 125% of the tickets required for a souvenir. What fraction of the required tickets do you have? Do you need more tickets for the souvenir? Explain. Write your answer in simplest form.

Answers

Answer:

one and one fourth

Step-by-step explanation:

I need to know this give me answer

Answers

Answer:the answer is b 10/21

Step-by-step explanation:

Answer:

B) 10/21

Step-by-step explanation:

Keep, change, flip

keep 2/7, change to multiply, flip to 5/3

2/7 x 5/3 = 10/21

Hope this helps! Pls give brainliest!

8a+3.28=46.28
solve for a please ik I already asked but I need to pass this test thank you :)

Answers

Answer:

A=5.375

Step-by-step explanation:

46.28-3.28= 43

43÷8= 5.375

I hope this helps

Part G Compare this activity tracker & with the calorie calculator you used in part A. Imagine that a company hires you to make an online tool that uses the best features of each calculator to give users an accurate sense of their physical activity and energy expenditure. What features would you use from each calculator? How would your calculator work?

Answers

Answer:

The physical activity calculator helps calculate minutes of activity and breaks down the types of activities performed every week. The calorie calculator doesn’t keep track of all activities. However, it calculates calorie expenditure. A new calculator might be a combination of the two calculators. It’d be a two-step process. People would be able to enter their age, gender, weight, height, and any medical factors so that they can ensure that their calorie calculations are accurate. Then, they’d be able to track the calories expended each day for a week by adding their activities for the whole day, from sitting to exercising. This information would give them an accurate portrayal of calorie expenditure and estimated caloric requirement.

exact answer

Step-by-step explanation:

Answer:

by seeing how the things they are doing and effecting them and then calulating them to add them up so i can see the amount of thier activity caused them to decrease or increase themselfs

Step-by-step explanation:

own explaination just incase teacher does suspect the answer

to be copied :)

100 POINTS PLEASE HELP ME 100 POINTS (make fullscreen)

Answers

Answer:

1) 64, 2) 6, 3) 26, 4) 33

Step-by-step explanation:

#1

Sum of interior angles is 180

70 + 46 + x = 180116 + x = 180x = 64#2

Sum of interior angles is 180

84 + 7x + 1 + 9x - 1 = 8416x + 84 = 18016x = 96x = 6#3

Vertical angles are same, the sum of remaining angles is same for both triangles:

35 + 25 = 34 + x60 = 34 + xx = 60 - 34x = 26#4

Exterior angle is same as the sum of non-adjacent interior angles:

5x - 7 + 6x + 3 = 8411x - 4 = 8411x = 88x = 8m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33

identicalAnswer:

1) 64, 2) 6, 3) 26, 4) 33

Step-by-step explanation:

#1

Sum of interior angles is 180

70 + 46 + x = 180

116 + x = 180

x = 64

#2

Sum of interior angles is 180

84 + 7x + 1 + 9x - 1 = 84

16x + 84 = 180

16x = 96

x = 6

#3

Vertical angles are identical, the sum of remaining angles is the same for both triangles:

35 + 25 = 34 + x

60 = 34 + x

x = 60 - 34

x = 26

#4

The exterior angle is the same as the sum of non-adjacent interior angles:

5x - 7 + 6x + 3 = 84

11x - 4 = 84

11x = 88

x = 8

m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33

Please help with this !

Answers

17+15+b = 180 so If you do 180-(15+17) =b
Well we know 15+17 is 32 so now you do 180-32 which equals 148 so b=148

When testing a claim that the majority of adult Americans are against the death penalty for a person convicted of murder, a random sample of 491 adults is obtained, and 27% of them are against the death penalty (based on data from a Gallup poll). Find the P-value. Round to 4 decimals when necessary.

Answers

Using the z-distribution, it is found that the p-value is of 1.

At the null hypothesis, it is tested that the majority is not against the death penalty, that is:

[tex]H_0: p \neq 0.5[/tex]

At the alternative hypothesis, it is tested that the majority is against the death penalty, that is:

[tex]H_1: p > 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.

In this problem, the parameters are: [tex]\overline{p} = 0.27, p = 0.5, n = 491[/tex].

Then, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.27 - 0.5}{\sqrt{\frac{0.5(0.5)}{491}}}[/tex]

[tex]z = -10.19[/tex]

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is greater than a value, the p-value is of 1.

A similar problem is given at https://brainly.com/question/16313918

answer the ones you want to. At least answer one…

I have to do 2 pages of homework I need this done I have school tomorrow..

Have no idea how to do this. Please help I beg you.

Answers

Answer:

9. First Five terms

If n=0. Then,

[tex] \frac{4(0) - 5}{2}[/tex]

[tex] \frac{0 - 5}{2} = \frac{ - 5}{2} [/tex]

If n=1. Then,

[tex] \frac{4(1) - 5}{2} [/tex]

[tex] \frac{4 - 5}{2} = \frac{ - 1}{2} [/tex]

If n=2. Then,

[tex] \frac{4(2) - 5}{2} [/tex]

[tex] \frac{8 - 5}{2} = \frac{3}{2} [/tex]

If n=3. Then,

[tex] \frac{4(3) - 5}{2} [/tex]

[tex] \frac{12 - 5}{2} = \frac{7}{2} [/tex]

If n=4. Then,

[tex] \frac{4(4) - 5}{2} [/tex]

[tex] \frac{16 - 5}{2} = \frac{11}{2} [/tex]

If n=5. Then,

[tex] \frac{4(5) - 5}{2} [/tex]

[tex] \frac{20 - 5}{2} = \frac{15}{2} [/tex]

If n=6. Then,

[tex] \frac{4(6) - 5}{2} [/tex]

[tex] \frac{24 - 5}{2} = \frac{19}{2} [/tex]

Can anybody help ASAP please?

Answers

Answer:

statement 1) similar because of the shape

theorem 2)n to m

b) statement 1)similar because of shape

2)the two are triangle but the position has been changed

Please help me (It's for a really important grade)

Answers

Answer:

4/5

Step-by-step explanation:

Sin = Opposite / Hypotenuse

Note that hypotenuse = longest side

We want to find sinФ

The opposite side length of angle "Ф" has a length of 8 and the longest side or hypotenuse has a length of 10

So sinФ would equal 8/10 which can be simplified to 4/5

For a concert, 19 boys and 22 girls bought tickets from the music club. The total cost of the tickets was $256. This total cost includes a $10 tax. What was the cost of each ticket, not including the tax?

Answers

Answer:

6

Step-by-step explanation:

19+22 =41256-10=246246-/41=6I hope this helps :)

Convert the given amount to the given unit.
3 miles; feet

Answers

Answer:

15840

Step-by-step explanation:

A canoe rental service charges a $30 transportation fee and $15 an hour to
rent a canoe. Write and equation. How long was the canoe rented if a
customer paid $105?

Answers

Answer:

5 hours

Step-by-step explanation:

Your equation is 105 = 15x + 30 subtract 30 from both sides, then divide by 15 to get x = 5 hours.

Brainliest would be apprappreciated. :-)

Mario Andretti drives his race car 500 miles in 2.5 hours. What is his speed?

Answers

Answer:

His speed was 200.

Step-by-step explanation:

500/2.5 is 200.

Answer:

The speed of Mario Andretti's race car is 200 m/h.

Step-by-step explanation:

Speed = Distance/Time=> Speed = 500 miles/2.5 hours=> Speed = 200 miles/1 hour

Conclusion:

Therefore, the speed of Mario Andretti's race car is 200 m/h.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

perform the indicated operation 3 1/2 - 1 7/10

Answers

Answer: 1 4/5

Step-by-step explanation:

3 5/10 - 1 7/10 = 1 8/10

1 8/10 = 1 4/5

help? please and thanks​

Answers

I believe it is distributive property.
None of the other ones make sense because in the first equation it isn’t either or, it has both multiplication and addition, not one or the other. Plus you are distributing the 9 into 2 and 6.

Which of the following shows the less amount from the original value?

a. Gadget of 5000 with 5% discount price

b. Mr Smith bought a leather bag for £25 and sold it for £45.

c. A calculator marked £8.50 and Mr Smith pay 15% VAT for this item.

d. Mr Smith sold of £875 for furniture with a gain of 6%.

and explain why.

Answers

Answer:

A

Step-by-step explanation:

This is because it is discounting however in the others it's increasing VAT=Value added Tax,

gain, 45-25=£20 profit therefore it's A.

Answer:

Gadget of 5000 with 5% discount price

Step-by-step explanation:

This is the only option with a discount, not an additional extra on top.

I desperately need help !

Answers

Answer:

t = 9.57

Step-by-step explanation:

We can use trig functions to solve for the t

Recall the 3 main trig ratios

Sin = opposite / hypotenuse

Cos = adjacent / hypotenuse

Tan = opposite / adjacent.

( note hypotenuse = longest side , opposite = side opposite of angle and adjacent = other side )

We are given an angle as well as its opposite side length ( which has a measure of 18 ) and we need to find its adjacent "t"

When dealing with the opposite and adjacent we use trig ratio tan.

Tan = opp / adj

angle measure = 62 , opposite side length = 18 and adjacent = t

Tan(62) = 18/t

we now solve for t

Tan(62) = 18/t

multiply both sides by t

Tan(62)t = 18

divide both sides by tan(62)

t = 18/tan(62)

t = 9.57

And we are done!

T= 9.57 do the math it’s not hard

Which is greater? -4.84 or -8.48

Answers

Answer:

-4.84

Step-by-step explanation:

the -4.84 is closest to the positive side of a number line. meaning -4.84 is greater

Answer:

-4.84

Step-by-step explanation:

Becuase the smaller the minus number the greater Becuase its the reverse of positive numbers

What is the percent of increase from 80 to 95?

Answers

Amount of increase = 95-80 = 15

Percent increase = (15/80) x 100

Percent increase = 18.75%

You can retry this question below
The sum of two numbers is 71. The difference of the two numbers is 41. What are the two numbers.
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 71."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 41."
Solve the system you have written above.
The larger number, x is
The smaller number, y is
Calculator

Answers

Answer:

x = 56

y = 15

Step-by-step explanation:

"The sum of two numbers is 71."

x + y = 71

"The difference of the two  numbers is 41."

x - y = 41

Solve the system:

From the first eq.

x = 71 - y

Replacing this value in the second eq.

(71-y) - y = 41

71 - 2y = 41

71 - 41 = 2y

30 = 2y

y = 30/2

y = 15

From the second eq.

x - y = 41

x - 15 = 41

x = 41 + 15

x = 56

Check:

from the first eq.

x + y = 71

56 + 15 = 71

please help asap !!
Solve the system of equations 2x + 3y = 40 and -2x + 2y = 20 A.x = 10 , y = 20 B. x=-10 , y = 20 C. x = -6 , y = 4 D. x = 2 , y = 12

Answers

Answer:

D is answer

Step-by-step explanation:

-2x + 2y = 20

2x = 40-3y

so -(40-3y)+2y =20

-40+3y+2y = 20

5y = 60

y = 12

2x = 40-3y

2x = 40-3(12)

2x = 40-36

2x = 4

x = 2

so x = 2 , y = 12

YES OR NOOO PLEASEE ANSWER

Answers

Answer:

Not a Function.... hope you pass!

9,3,1, what is the sequence and what is it equal to?

Answers

Answer: the sequence is to divide by 3 and it gets smaller and smaller by dividing by three I don't think there is an end to it.

Step-by-step explanation:

9/3=3

3/3=1

1/3=1/3

1/3/3=1/9

1/9/3=1/27

1/27/3=1/81

and I think you know what I mean by now right?

Can you please help me with this question

Answers

Answer:

  B

Step-by-step explanation:

The table that represents a function will have no x-values repeated.

  A. 4 is repeated -- not a function

  B. all x-values are unique -- this is a function

  C. 2 is repeated -- not a function

  D. 3 is repeated -- not a function

is (-a + b)² = a² - 2ab + b² right or wrong, and why?

Answers

Answer:

[tex]\huge\boxed{\sf Right.}[/tex]

Step-by-step explanation:

[tex](-a+b)^2[/tex]

Let's apply the formula (x+y)² = x² + 2xy + y²

Here, x = -a and y = b

So,

= (-a)² + 2(-a)(b) + (b)²

= a² - 2ab + b²

Hence, it has been proved that (-a + b)² = a² - 2ab + b².

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807
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