A warehouse contains ten printing machines, two of which are defective. A company selects seven of the machines at random, thinking all are in working condition. What is the probability that all seven machines are nondefective?

Answers

Answer 1

Answer:

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

10 machines means that [tex]n = 10[/tex]

2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]

Seven are selected, which means that [tex]n = 7[/tex]

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]

0.0667 = 6.67% probability that all seven machines are nondefective.


Related Questions

pamela is 8 years older that jiri. the sum of their age is 102. What is jiris age?

Answers

       There are two different ways we can solve this problem. We could use brute force, or we can use some equations to solve the problem. We can start by defining Pamela and Jiri's ages differently. If Jiri is j, and Pamela is p, we can say that p = j + 8, because Jiri + 8 years is Pamela's age.

       Now, using our values for Pamela and Jiri, we can say that (j + 8) + j = 102. Now we just solve like a normal equation, so 2j = 94, and j = 47, so Jiri is 47 years old.

Answer:

J = 47

Step-by-step explanation:

P = Pamela

J = Jiris

P = 8 + J ;- Equation 1

P + J = 102 ;- Equation 2

Substitute equation 1 into 2 to get:

J + 8 + J =102

2J = 102 - 8

2J = 94

J = 47

So Jiris is 47 years old

Evaluate (657.3÷10)-(94.5÷5)

Answers

Answer:

Ans; (657.3÷10)-(94.5÷5) = 65.73 – 18.9 = 46.83

I hope I helped you^_^

Determine whether the following polygons are similar. If yes, type 'yes' in the Similar box and type in the similarity statement and scale factor. If no, type 'None' in the blanks. For the scale factor, please enter a fraction. Use the forward dash (i.e. /) to create a fraction (e.g. 1/2 is the same as 12
1
2
).

Answers

Given:

The figures of two polygons.

To find:

Whether the polygons are similar and then find the scale factor (if similar).

Solution:

From the given figures it is clear that both polygons are rectangles and their all interior angles are right angles.

The ratio of their longer sides:

[tex]\dfrac{32}{26}=\dfrac{16}{13}[/tex]

The ratio of their shorter sides:

[tex]\dfrac{18}{12}=\dfrac{3}{2}[/tex]

Since the ratio of their corresponding sides are not equal, therefore the two polygons are not similar.

Therefore the required solutions are:

Similar : No

Similarity statement : None

Scale factor : None

Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 15 adults, 8 favor capital punishment? Use a 0.05 level of significance.

Answers

Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

[tex]H_0: p = 0.4[/tex]

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

Random sample of 15 adults, 8 favor capital punishment.

This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]

[tex]z = 1.05[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

I need assistance urgent

Answers

The answer would be 173.42cm²

What is the mean of this data set?

A. 84
B. 85
C. 83
D. 88

Answers

Answer:

85

Step-by-step explanation:

Add  to get total. divide by 4.

Answer:

B. 85

Step-by-step explanation:

Sorry for this very late response. But if anyone wasn't sure if 85 is the correct answer, it is. I can confirm this because I just took the test. I hope I could help! (:

Zoe is a party planner. She orders cupcakes and sheet cakes from Creative Cakes whenever she needs beautiful cakes to serve. One sheet cake serves 24 people and 2 dozen cupcakes serve 24 people. For the Benson's bridal shower she ordered 8 dozen cupcakes and 3 sheet cakes and paid $160.81. For the Nygaard's 50th wedding anniversary she ordered 6 dozen cupcakes and 15 sheet cakes and paid $342.33. She is planning a graduation party for her niece's high school class. She wants the party to be nice but she offered to pay for the cakes herself so she wants to choose the most economical plan. Zoe estimates 250 people will attend the party.

Answers

Full question:

Zoe is a party planner. She orders cupcakes and sheet cakes from Creative Cakes whenever she needs beautiful cakes to serve. One sheet cake serves 24 people and 2 dozen cupcakes serve 24 people. For the Benson's bridal shower she ordered 10 dozen cupcakes and 4 sheet cakes and paid $186.44. For the Nygaard's 50th wedding anniversary she ordered 2 dozen cupcakes and 15 sheet cakes and paid $259.66. She is planning a graduation party for her niece's high school class. She wants the party to be nice but she offered to pay for the she wants to choose the most economical plan. Zoe estimates 250 people will attend the party

Select the most economical choice below:

Zoe should buy sheet cakes because they cost $12.38 for one sheet cake.

Zoe should buy sheet cakes because they cost $15.66 for one sheet cake.

Zoe should buy cupcakes because they cost $12.38 for one dozen cupcakes.

Zoe should buy cupcakes because they cost $15.66 for one dozen cupcakes.

Zoe should buy cupcakes because they cost $12.38 for two dozen cupcakes.

Answer:

Zoe should buy cupcakes because they cost $12.38 for two dozen cupcakes.

Explanation:

If there are 250 people attending the high school class graduation party, then 24 people each within 250 people in total would get 2 dozen cupcakes worth $12.38 each.

Therefore there are 250/24 = 10.41 groups (10 groups approximately or 10.41×2=20.82 dozens of cupcakes required)

Zoe would need to spend 10.41×$12.38= $128.88 to buy the cupcakes for the party

In four years,George saved $540. His twin sister, Georgette, saved 10 times as much. How much did Georgette saved?

Answers

5400 dollars

540x10= 5400

Solve: 5 + n > 2

Just let me know because I am stuck and need to know the answer for this test please let me know thank you ❤️

Answers

[tex]\\ \sf\longmapsto 5+n>2[/tex]

We have to find n Take 5 to right side sign will be changed

[tex]\\ \sf\longmapsto n>2-5[/tex]

Simplify

[tex]\\ \sf\longmapsto n>-3[/tex]

Andrew buys 27 identical small cubes, each with two adjacent faces painted red. He then uses all of these cubes to build a large cube. What is the largest number of completely red faces of the large cube that he can make

Answers

Answer:

4

Step-by-step explanation:

Number of Identical small cubes = 27

Determine the largest number of completely red faces of the large cube that he can make

Given that 2 adjacent faces of each cube is painted

and the number of cubes = 27

The number of complete red face Large cube he can make = 4

Alice and Bob each choose a number uniformly (and independently) from the interval [0, 10]. What is the probability that the absolute value of the difference between their two numbers is less than 1/4

Answers

Answer:

The probability is zero (0)

Step-by-step explanation:

Given;

interval of numbers to be chosen = 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9 , 10

total possible outcome = 11

The possible numbers whose absolute difference is greater than ¹/₄ includes the following;

(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,0)

The probability of this = 11 / 11 = 1

The probability that the absolute value of the difference between their two numbers is less than 1/4

[tex]P(less \ than \ \frac{1}{4} ) = 1 - P(greater \ than \ \frac{1}{4} )\\\\P(less \ than \ \frac{1}{4} ) = 1 - 1 \\\\P(less \ than \ \frac{1}{4} ) = 0[/tex]

plz help with this:)

Answers

9514 1404 393

Answer:

  -4

Step-by-step explanation:

The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...

  x = 1, y = -4

  y/x = -4/1 = -4

The slope of the line is -4.

Find the area of Parallelogram ABCD given M< A=30° AB=10in AD=6in A=

Answers

Answer:

30 in²

Step-by-step explanation:

Parallelogram height is,

6/2 (since it's a 30°-60°-90° triangle)

= 3

Area = base × height

= 10×3 in²

= 30 in²

Answered by GAUTHMATH

8x( 5 x 2 ) Pls give answer

Answers

Answer:

80x

Step-by-step explanation:

Bracket first

5 x 2 = 10

8x x 10 = 80x

(Unless the 'x' next to the 8 is the term for multiplying:

8 x 10 = 80)

Answer:

80

Step-by-step explanation:

8 x (5 x 2)

8 x 10

Answer = 80

Companies are starting to use 360-degree surveys to evaluate the performance of their employees. This approach uses annonymous feedback from a variety of people who work closely with the employee. People who fill out the survey could be coworkers, supervisors, subordinates, or even customers. It is different from a traditional performance review, which relies only on feedback from an employee's supervisor. Many prefer the 360-degree approach because it provides a more well-rounded perspective on how the employee performs in their job role. Supervisers can be biased because they do not interact with the employee in the same way that a customer or co-worker might. However, the 360-degree survey approach still relies only on subjective feedback, which does not always give a fair representation of the employee's work?

Answers

Answer:

the study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural laws

45%of the total population of a village are males and there are 22000 females Find the male population of the village.​

Answers

Answer:

18000

Step-by-step explanation:

The 22000 females make up 55% of the population. So, we divide 22000 by 0.55 to get the total population.

22000 ÷ 0.55 = 40000

Now we take our total population and subtract 22000 to get the number of males in the population.

40000 - 22000 = 18000

The male population of the village is 18000.

a swift can fly at 160km/h. what is the speed in m/s? show clearly how you worked out your answer.

Answers

Answer:

[tex]\huge\boxed{\sf Speed = 44.44 \ m/s}[/tex]

Step-by-step explanation:

Speed = 160 km / hr

To convert km/hr to m/s, we multiply it by [tex]\sf \frac{10}{36}[/tex]

Hence,

[tex]\displaystyle Speed = 160 \times \frac{10}{36} \ m/s\\\\Speed = \frac{1600}{36} \ m/s\\\\Speed = 44.44 \ m/s\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!


A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?

Answers

The interest rate is about 32.045%.

The quadratic equation x^2 + 3x + 50 = 0 has roots r and s. Find a quadratic equation whose roots are r^2 and s^2.

Answers

Answer:

x^2 + 91x + 2500

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

x^2 + 3x + 50

(x-r)(x-s)

-> x^2-(r+s)x+rs

rs = 50, r + s = -3

-> (rs)^2 = 2500

(r+s)^2 = 9

-> r^2 + 2rs + s^2 = 9

-> r^2 + 2(50) + s^2 = 9

-> r^2 + s^2 + 100 = 9

-> r^2 + s^2 = -91

(x-r^2)(x-s^2)

-> x^2-(r^2+s^2)x+(rs)^2

-> x^2 - (-91)x + 2500

x^2 + 91x + 2500

Two boats are travelling at 30 miles/hr, the first going north and the second going east. The second crosses the path of the first 10 minutes after the first one was there. At what rate is their distance increasing when the second has gone 10 miles beyond the crossing point

Answers

Answer:

their distance is increasing at the rate of 41.6 miles/hr

Step-by-step explanation:

Given the data in the question;

first we determine the distance travelled by the first boat in 10 min when the second boat was crossing its path;

⇒ ( 30/60 ) × 10 = 5 miles

so as illustrated in the diagram below;

y² = x² + ( x + 5 )²

2y[tex]\frac{dy}{dt}[/tex] = 2x[tex]\frac{dx}{dt}[/tex] + 2(x+5)[tex]\frac{dx}{dt}[/tex]

y[tex]\frac{dy}{dt}[/tex] = ( 2x + 5 ) ][tex]\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]   ------ let this be equation 1

Now, given that, [tex]\frac{dx}{dt}[/tex]  = 30 miles/hr, when x = 10

so

y = √( 10² + 15² ) = √325

so from equation 1

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]

we substitute

[tex]\frac{dy}{dt}[/tex] = [( 2(10) + 5 ) / √325 ]30

[tex]\frac{dy}{dt}[/tex] = [ 25 / √325 ] × 30

[tex]\frac{dy}{dt}[/tex] = 41.6 miles/hr

Therefore, their distance is increasing at the rate of 41.6 miles/hr

Solve the following equation for
f
f. Be sure to take into account whether a letter is capitalized or not.

Answers

Answer:

q + j

Step-by-step explanation:

q = - j + f

f = q + j

q + j is the answer.

Answer:

f = q + j

Step-by-step explanation:

Rewrite the equation:

-j + f = q

Add  j  to both sides of the equation:

f = q + j

Find the area of the shaded regions:

QUICKLY!!!!!

Answers

Answer:

[tex]41.89\ cm^2[/tex]

Step-by-step explanation:

[tex]We\ are\ given:\\In\ two\ concentric\ circles,\\OD=3\ cm\\BC=4\ cm\\\angle DOB=\angle AOC=120\\Now,\\We\ know\ that:\\Area\ of\ a\ sector\ with\ a\ central\ angle\ \theta\ and\ a\ radius\ r\ is:\\A=\frac{\theta}{360}* \pi r^2\\Here,\\Area\ between\ the\ sectors=Area\ of\ Larger\ Sector - Area\ of\ smaller\ sector=\frac{\theta}{360}*\pi(R^2-r^2),\ where\ R\ and\ r\ are\ radii\ of\ the\ respective\ circles\ and\\ \theta\ is\ the\ common\ central\ angle.\\Here,\\R=4+3=7\ cm\\r=3\ cm\\ \theta=120\\ Hence,[/tex]

[tex]Area\ of\ the\ shaded\ region=\frac{120}{360}*\pi(7^2-3^2)=\frac{1}{3}*\pi(49-9)=\frac{1}{3}*\pi(40) \approx 41.89\ cm^2[/tex]

Really need help and the answer on this one plz help.

Answers

It should be the second option I hope it’s right have a good day

Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.

Answers

Answer:

Step-by-step explanation:

in this specific case the two legs are congruent:

b = 18

For the Pythagorean theorem

a = √ 2 * 18^2 = 18√2

Write a inequality.
Question: twice a number is no more than 14
Please help

Answers

Answer:

2x[tex]\leq[/tex]14

Step-by-step explanation:

Answer:

2x ≤ 14

Step-by-step explanation:

twice a number   is no more than     14

               2x                     ≤                 14

Find the percent notation of 2.2

Answers

Answer:

2.2 x 100 = 220%

Step-by-step explanation:

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 2.2 × 100 = 220% (answer). ➥ The ease way: 1) Move the decimal point two places to the right: 2.2 → 22 → 220.

I hope this will help you

Given the following situation:
A cell phone company offers a data package by charging $20 a month plus $12 per gigabyte of data used. Write a linear equation
that relates the cost C, in dollars, to the amount of data used. Use it to determine the amount of data used if they charge you
$116.

Answers

9514 1404 393

Answer:

C = 20 +12g8 gigabytes

Step-by-step explanation:

At $12 per gigabyte, the data charge will be 12g where g is the number of gigabytes. Then the total charge is ...

  C = 12g +20

__

If C = 116, the value of g is found from ...

  116 = 12g +20

  96 = 12g . . . . . . . subtract 20

  8 = g . . . . . . . . . . divide by 12

The amount of data used is 8 gigabytes if the charge is $116.

Please help me find limit​

Answers

9514 1404 393

Answer:

  -13/11

Step-by-step explanation:

Straightforward evaluation of the expression at x=1 gives (1 -1)/(1 -1) = 0/0, an indeterminate form. So, L'Hopital's rule applies. The ratio of derivatives is ...

  [tex]\displaystyle\lim_{x\to 1}\dfrac{n}{d}=\dfrac{n'}{d'}=\left.\dfrac{\dfrac{4}{3\sqrt[3]{4x-3}}-\dfrac{7}{2\sqrt{7x-6}}}{\dfrac{5}{2\sqrt{5x-4}}-\dfrac{2}{3\sqrt[3]{2x-1}}}\right|_{x=1}=\dfrac{4/3-7/2}{5/2-2/3}=\dfrac{8-21}{15-4}\\\\=\boxed{-\dfrac{13}{11}}[/tex]

A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
meters per minute

Answers

9514 1404 393

Answer:

  2.5 m/min

Step-by-step explanation:

To find meters per minute, divide meters by minutes:

  (7.5 m)/(3 min) = 2.5 m/min

The speed of the tortoise is 2.5 meters per minute.

plz help me on this question best and right answer gets brainliest

Answers

Answer:

| - 5| 5

| 6 | 6

| - 9 | 9

the numbers will be positive when they come out from the absolute value

Answer and Step-by-step explanation:

The absolute value of a value is the positive version of that value.

| | <- Brackets are used to show that a value is being absolute.

|-5| = 5  The negative 5 with absolute brackets becomes a positive 5.

|6| = 6    A positive 6 with absolute brackets stays a positive 6.

|-9| = 9   A negative 9 with absolute brackets becomes a positive 9.

#teamtrees #PAW (Plant And Water)

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