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
sveticcg [70]
3 years ago
13

A box contains four 10 nf and eight 100 nf capacitors. (a) what is the probability of obtaining at least two 10 nf capacitors if

we randomly draw four capacitors from the box with replacement? (b) what is the probability of drawing at least two 10 nf capacitors if we randomly draw four capacitors from the box without replacement?
Mathematics
2 answers:
grigory [225]3 years ago
8 0

there are 4 of the 10-nf and 8 of the 100-nf capacitors which is a total of 12 items.

the probability of drawing a 10-nf is: 4 out of 12 = \frac{1}{3}

the probability of drawing a 100-nf is: 8 out of 12 =  \frac{2}{3}

(a)  "at least two" means: 2 or 3 or 4

Probability of 2 (10's) and 2 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{2}{3} x \frac{2}{3} = \frac{4}{81}

Probability of 3 (10's) and 1 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{1}{3} x \frac{2}{3} = \frac{2}{81}

Probability of 4 (10's) and 0 (100's):  \frac{1}{3} x \frac{1}{3} x \frac{1}{3} x \frac{1}{3} = \frac{1}{81}

2 or 3 or 4: \frac{4}{81} + \frac{2}{81} + \frac{1}{81} = \frac{7}{81}

(b) without replacement

Probability of 2 (10's) and 2 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{8}{10} x \frac{7}{9} = \frac{4 x 3 x 8 x 7}{12 x 11 x 10 x 9}

Probability of 3 (10's) and 1 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{2}{10} x \frac{8}{9} = \frac{4 x 3 x 2 x 8}{12 x 11 x 10 x 9}

Probability of 4 (10's) and 0 (100's):  \frac{4}{12} x \frac{3}{11} x \frac{2}{10} x \frac{1}{9} = \frac{4 x 3 x 2 x 1}{12 x 11 x 10 x 9}

2 or 3 or 4: \frac{4 x 3 x 8 x 7}{12 x 11 x 10 x 9} + \frac{4 x 3 x 2 x 8}{12 x 11 x 10 x 9} + \frac{4 x 3 x 2 x 1}{12 x 11 x 10 x 9} = \frac{672 + 192 + 24}{12 x 11 x 10 x 9} =  \frac{888}{12 x 11 x 10 x 9}  =  \frac{111}{1485}


ladessa [460]3 years ago
4 0

Answer:

there are 4 of the 10-nf and 8 of the 100-nf capacitors which is a total of 12 items.

Step-by-step explanation:

You might be interested in
The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle m
evablogger [386]
ANSWER

x = 50.5 \degree

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


\frac{ \sin(A) }{a}  =  \frac{ \sin(B) }{b}  = \frac{ \sin(C) }{c}


From the triangle,

\frac{ \sin(x) }{60}  =  \frac{ \sin(40) }{50}

We multiply both sides of the equation by 60 to get,

sin(x)  =  \frac{ 60\sin(40 \degree) }{50}


sin(x)  = 0.7713



We solve for x to obtain,

x = arcsin(0.7713)


x = 50.475

To the nearest tenth, we round to one decimal place to get,

x = 50.5 \degree

7 0
3 years ago
Please help and show work
Eva8 [605]

Answer:

1) x(x+7)

3) (x+5)*(x+4)

4) (x-6)*(x-8)

5) x(2x+21)+11

6) 5(a-5)*(a+5)

7) (4x+3)*(2x-3)

8) 4( x²-6xy+8)

Step-by-step explanation:

4 0
3 years ago
Free points have a good week!!! Stay safe.
jeka57 [31]

Answer:

you too

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What percent of $90 = $45
Lynna [10]
45 is exactly half of 90
that means 45 is 50% of 90.
8 0
3 years ago
Which two expressions is equivalent to 8(5+x)
Natali [406]

Answer: 8(x+5) 8x + 40

40 + 8x

Step-by-step explanation:

Distribute the 8 by multiplying by each value inside the parentheses.

Commutative property in addition and multiplication allows the terms to be in reversed order.

4 0
3 years ago
Other questions:
  • Which of the following is a prime number 67 65 63 60
    15·2 answers
  • Their win percentage was 40, WICHTW hally s
    6·1 answer
  • In the given figure, what is the measure of angle CPE?
    6·1 answer
  • 1.write the slope intercept form of the equation of the line passing through (0,3) with a slope of -2....... 2.write the slope i
    6·1 answer
  • Gia’s gross annual salary is $46,392.
    8·1 answer
  • Its a math problem that I need help with.
    13·2 answers
  • In the Simple Interest Formula I=prt, what does the I stand for?
    15·2 answers
  • A ramp slopes from a warehouse door down to the street. The height of the ramp is 5 feet, and the ramp ends 10 feet from the bas
    14·2 answers
  • 7/8 greater or less than 2/4
    5·2 answers
  • Factor the GCF: 12x2y + 6x2y3 – 9xy? (4 points)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!