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
aivan3 [116]
3 years ago
13

1000 households were surveyed. 275 households own a desktop computer, 455 households own a DVD player, 405 households own two ca

rs, 145 households own a desktop computer and DVD player, 195 households own a DVD player and two cars, 110 households own two cars and a desktop computer, 265 households do not own a desktop computer, do not own a DVD player, do not own two cars. Find the number of households that own: a) a desktop computer, DVD player and two cars; b) only a DVD player, no computer and no two cars; c) a desktop computer and DVD player but do not own two cars.
Mathematics
1 answer:
icang [17]3 years ago
6 0

Answer:

Step-by-step explanation:

From the given information,

Suppose

X represents the Desktop computer

Y represents the DVD Player

Z represents the Two Cars

Given that:

n(X)=275

n(Y)=455

n(Z)=405

n(XUY)=145

n(YUZ)=195

n(XUZ)=110

n((XUYUZ))=265

n(X ∩ Y ∩ Z) = 1000-265

n(X ∩ Y ∩ Z) = 735

n(X ∪ Y) = n(X)+n(Y)−n(X ∩ Y)

145 = 275+455 - n(X ∩ Y)

n(X ∩ Y) = 585

n(Y ∪ Z) = n(Y) + n(Z) − n(Y ∩ Z)

195 = 455+405-n(Y ∩ Z)

n(Y ∩ Z) = 665

n(X ∪ Z) = n(X) + n(Z) − n(X ∩ Z)

110 = 275+405-n(X ∩ Z)

n(X ∩ Z) = 570

a. n(X ∪ Y ∪ Z) = n(X) + n(Y) + n(Z) − n(X ∩ Y) − n(Y ∩ Z) − n(X ∩ Z) + n(X ∩ Y ∩ Z)

n(X ∪ Y ∪ Z) = 275+455+405-585-665-570+735

n(X ∪ Y ∪ Z) = 50

c. n(X ∪ Y ∪ C') = n(X ∪ Y)-n(X ∪ Y ∪ Z)

n(X ∪ Y ∪ C') = 145-50

n(X ∪ Y ∪ C') = 95

You might be interested in
8x+5y=24<br><br> y=-4x<br><br><br> Solve for y and x
Cloud [144]

Answer:

x= -2           and y= 8

Step-by-step explanation:

8x+5y=24-------A

y=-4x---------B

Putting the value of y from B in A

8x+5(-4x)=24

8x +(-20x)= 24

8x-20x=24

-12x=24

x= -24/12

x=-2--------C   y =-4(-2)=8

8 0
3 years ago
Heather invested $8000 in a 4- year certificate of deposit (CD) that pays 4.1 interest compound annually. What is the value of t
aliya0001 [1]
8000(1.041)x^{4}=9394.91
6 0
3 years ago
Multiple Select
lakkis [162]

Answer:

watts

Step-by-step explanation:

5 0
2 years ago
What is 1/2 ÷ 10?<br> What is 3÷ 1/6?
aev [14]
1/2 ÷10=1/20 because you multiply the bottoms

3÷1/6= 18 because it is the same as 3×6
3 0
3 years ago
Read 2 more answers
What is the volume of a cylinder with a height of 3 feet and a radius of 4 feet use 3.14 for pi
Vlad1618 [11]

Answer:

\large\boxed{V\approx150.72\ ft^3}

Step-by-step explanation:

The formula of a volume of a cylinder:

V=\pi r^2H

r - radius

H - height

We have the height H = 3ft and the radius r = 4ft. Substitute:

V=\pi(4^2)(3)=\pi(16)(3)=48\pi\ ft^3

\pi\approx3.14

V\approx48(3.14)=150.72\ ft^3

3 0
3 years ago
Read 2 more answers
Other questions:
  • Determine the value of each unknown variable
    8·1 answer
  • What is 7 less than the product of 5 and a number?
    11·1 answer
  • Please help!! I don't understand this!?!?!?
    14·2 answers
  • The dot plot shows how many swimmers are in each line at a waterpark:
    6·2 answers
  • Write a ponlynomial funstion in standard form with zeros at -2, 5 and 6
    13·1 answer
  • Line s is drawn in the xy-plane and has an equation
    13·1 answer
  • Show work for number one please!
    8·1 answer
  • Can someone answer this for me?
    13·2 answers
  • -3x+4y=7 y=3x-5 I NEED HELP PL Z HELP ME
    6·1 answer
  • The histogram shows the distribution of heights, in inches, of 100 adult men.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!