It is known that screws produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the screws in packages of 10 and offers a money-back guarantee that at most 1 of 10 screws are defective. That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace

Answers

Answer 1

Answer:

The company must replace 0.0042 = 0.42% of packages.

Step-by-step explanation:

For each screw, there are only two possible outcomes. Either it is defective, or it is not. The probability of an screw being defective is independent of any other screw. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

It is known that screws produced by a certain company will be defective with probability 0.01.

This means that [tex]p = 0.01[/tex]

The company sells the screws in packages of 10

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

That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace?

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.01)^{0}.(0.99)^{10} = 0.9044[/tex]

[tex]P(X = 1) = C_{10,1}.(0.01)^{1}.(0.99)^{9} = 0.0914[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.9044 + 0.0414 = 0.9958[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9958 = 0.0042[/tex]

The company must replace 0.0042 = 0.42% of packages.


Related Questions

Martha Stewart needs a total of 520 napkins for her restaurant. She currently has 234 napkins. If each package of napkins has 20 napkins, what is the minimum number of packets of napkins she should buy? Write an algebraic equation, solve, and conclude.

Answers

Answer:

520=20x+234

15 packages

Step-by-step explanation:

520-234

286

286/20

14.3, so she needs 15 packages

You are walking along a path y= 2x + 12 and your
best friend is walking along 4x + y = 6. At what point will
you cross paths?

Answers

Answer:

(-1,10)

Step-by-step explanation:

At the point when the paths cross, the respective x and y values of each equation will be equal.

Your path is y=2x+12, and your friends path is 4x+y=6. Sub 2x+12 in for y (from your path's equation) into your friends equation to find the value of x:

4x+2x+12=6

6x=-6

x=-1

y=2x+12

y=2(-1)+12=10

So you will cross paths at (-1,10)

what is (20)+(475)? I need it now​

Answers

ur answer is going to be 495

CAN SOMEONE HELP ME PLEASE ASAP

Answers

Answer:for the permieter dont you just add both sides?

Step-by-step explanation:

The premier would be y=Mx+b

Meg withdrew $300 from her account on Saturday. Then she deposited $174.83 into her account on Sunday. Meg wants to know how much would be in her brother's account if he has double her balance.
- A = -125.17
- B = -250.34
- C None of the above
Pls answer quick!!

Answers

−300 + 174.83 = -125.17. A is the answer!

if n is an integer,what is the sum of the next three consecutive even integers greater than 2n?​

Answers

Answer:

6n + 12

Step-by-step explanation:

Given an integer n, the 3 consecutive even integers greater than 2n are 2n+2, 2n+4 and 2n+6

Taking their sum;

Sum = (2n+2)+(2n+4)+(2n+6)

Sum = 2n+2n+2n+2+4+6

Sum = 6n + 12

Hence the sum of the 3 consecutive even integers greater than 2n is 6n+12

Bonus Is the point (-3, -5) inside, outside, or on the circle whose equation is (x + 7)² + (y − 2)² = 62? (SOMEONE PLEASE EXPLAIN!!)

Answers

Answer:

Outside, as the distance between the point and the center of the circle is more than the radius.

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

[tex](x-x_0)^2 + (y-y_0)^2 = r^2[/tex]

In which [tex](x_0,y_0)[/tex] is the center and r is the radius.

Testing if a point is inside the circle:

Point (x,y), we replace in the equation. If it is less than the radius squared(in this case, 62), it is in.

In this question:

Point (-3,-5). So

[tex](-3+7)^2 + (-5-2)^2 = 4^2 + (-7)^2 = 16 + 49 = 65[/tex]

The square distance of the point to the center is of 65, which is more than the square of the radius, meaning that the point is outside the circle.

Answer:

Outside

Step-by-step explanation:

Use two unit multipliers to convert 4000 square inches to square feet.

Answers

Answer:

(4000 in^2) * (1 ft/12 in)^2 = 27 7/9 ft^2

Step-by-step explanation:

4,000 Square Inches =

27.777778 Square Feet

A. 1/3
B. 1
C. 2
D. 3/1
E. 1/2
F. 2/3

Answers

Answer:

B

Step-by-step explanation:

the graph is completely proportional so the answer would be 1

C u m s t e r g o i n t r e b a r e de pe b r a i n l y?

Answers

Yes, 12345678910112121414127272771819292

Answer:rf JAMES CHARLE's?!?

Step-by-step explanation:

HELP I NEED TO DO THIS NOW

Answers

Answer: The answer is 1:2, i hope it helps.

The 7 times the sum of a
number and 6 IS 63

Answers

Answer:

Missing number = 3

Step-by-step explanation:

Let [tex]x[/tex] be the missing number. We have the following:

[tex]7\cdot (6+x)=63,\\6+x=9,\\x=\boxed{3}[/tex]

1 mark question please answer me

Answers

Given:

The polynomial is:

[tex]P(x)=ax+b[/tex]

To find:

Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.

Solution:

We have,

[tex]P(x)=ax+b[/tex]

Putting [tex]x=-\dfrac{b}{a}[/tex], we get

[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]

[tex]P(-\dfrac{b}{a})=-b+b[/tex]

[tex]P(-\dfrac{b}{a})=0[/tex]

Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.

Plz help me well mark brainliest if correct!!.....

Answers

Answer:

9 inches

Step-by-step explanation:

9 times 6=54

find the slope intercept form (y=mx+b)

Answers

Answer:

5/9??? I think thats the answer


Si en un examen 27 preguntas son correctas el 90%, cuántas preguntas son en total?​

Answers

Respuesta:

30

Explicación paso a paso:

Número total de preguntas = 100%

Número de preguntas correctas = 27

Porcentaje de aciertos = 90%

Por eso,

Si 90% = 27

Luego ; 100% = x

Multiplicar en cruz:

0,9 veces = 27

x = 27 / 0,9

x = 30

Número de preguntas = 30

5c + 2d^2 if c = 6 and d = 3

Answers

Answer:

48

Step-by-step explanation:

Substitute c=6 and d=3 in your formulas

[tex]5*6 + 2*3^{2}\\ 30 + 18\\48[/tex]

Given a circle with a circumference of 30pi inches, solve for the exact area of a sector in terms of pi, whose central angle is one-fifth of the measure of the
circle.

Answers

30 pi inches divided by the one fifth angle is gonna be 6

simplify 1/3 : 2.5 : 3 3/4​

Answers

Answer:

1/3x3 3/4  /2.5 = 0.3

Math! Help Marking brainliest if it's correct and Explain​

Answers

Answer:

Option C : Step 3

After harvesting, she weighs each pumpkin on a scale and records its height

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What value of x satisfies this equation? 1.5(4)^2x=12 Round your answer to the nearest hundredth. The value of x is .

Answers

Answer:

O.75

Step-by-step explanation:

The value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

What is integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an equation:

[tex]\rm 1.5(4)^2^x=12[/tex]

[tex]\rm (4)^2^x=8[/tex]

[tex]\rm (2^2)^{2x}= 2^3[/tex]

[tex]\rm 2^{4x}=2^3[/tex]

4x = 3  (equating powers of same base)

x = 3/4

Thus, the value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.

Learn more about the integer exponent here:

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Sheldon spins the two spinners below one time what are the chance he will spin 3 or c ?

Answers

Answer:

[tex]P(3\ or\ c) = 0.45[/tex]

Step-by-step explanation:

Given

See attachment for spinner

Required

[tex]P(3\ or\ c)[/tex]

From the first spinner, we have:

[tex]S = \{1,2,3,4,5\}[/tex] --- Sample Space

[tex]n(S)=5[/tex]

So, P(3) is:

[tex]P(3) = \frac{n(3)}{n(S)}[/tex]

[tex]P(3) = \frac{1}{5}[/tex]

[tex]P(3) = 0.20[/tex]

From the second spinner, we have:

[tex]S = \{a,b,c,d\}[/tex]

[tex]n(S) = 4[/tex]

So, P(c) is:

[tex]P(c) = \frac{n(c)}{n(S)}[/tex]

[tex]P(c) = \frac{1}{4}[/tex]

[tex]P(c) = 0.25[/tex]

The required probability is then calculated as:

[tex]P(3\ or\ c) = P(3) + P(c)[/tex]

[tex]P(3\ or\ c) = 0.20 + 0.25[/tex]

[tex]P(3\ or\ c) = 0.45[/tex]

In the paper airplane shown , ABCD=EFGH, m

Answers

Answer:

i would think it would be the same as angle bcd so 90

Step-by-step explanation:

Ebony discovered she had $8 in quarters how many quarters are there in $8 choose the division expression you would use to find the number of quarters and $8

1. $8 ÷4
2. $8 ÷ 1/4
3. $8 ÷ 1/2​

Answers

The answer is 2. $8 divided by 1/4

HELPP ASAP DONT SEND A FILE PLS WHATS THE RULE FOR THIS TRANSFORMATION FOR ROATIONS QUESTION 5 ? I ONLY A FEW MINUTES PLZ HELP

Answers

Answer:

90-degree clockwise rotation: (x,y)⇒(y,-x)

Step-by-step explanation:

For D⇒D', (0,-3)⇒(-3,0)

For E⇒E', (2,-1)⇒(-1,-2)

For F⇒F', (5,-3)⇒(-3,5)

We can see that the pattern here is (x,y)⇒(y,-x), which is the rule for a 90-degree clockwise rotation.

6 members of the Benton family are going to their school's Community Day. They have a coupon for $4.50 off their total. If they pay $40.50 for all their tickets, how much does one ticket cost without the coupon? ​

Answers

Answer:

$7.50

Step-by-step explanation:

you add 40.50 + 4.50 which then equals 45 and you divide that by 6 and you get 7.50

One ticket costs $7.50 without the coupon this we obtained by dividing total cost before discount  by Number of tickets

Let us find the total cost of the tickets before the coupon is applied. We can do this by adding the discount amount ($4.50) to the final cost ($40.50):

Total cost before discount = Final cost + Discount amount

Total cost before discount = $40.50 + $4.50

Total cost before discount = $45.00

Now we can divide the total cost before discount by the number of tickets

(6) to find the cost of one ticket:

Cost of one ticket = Total cost before discount / Number of tickets

Cost of one ticket = $45.00 / 6

Cost of one ticket = $7.50

Therefore, one ticket costs $7.50 without the coupon.

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3 x 1/2 in fraction form

Answers

Answer:

3*1/2= 3/2

Step-by-step explanation:

[tex]\frac{3}{1}[/tex]*[tex]\frac{1}{2}[/tex] = 3/2

3*1/2= 3/2

3 is equal to 3/1

we then directly multiply

equation: (3/1)(1/2)

(3/1)(1/2)

3*1 = 3

1*2= 2

3/2 or 1 1/2.

How do you write in fraction form?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenth place, so we place 6 over 10 to create the equivalent fraction, 6/10.

Learn more about fraction form at

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On Tuesday, 14 students handed in a permission slip for a field trip. On Thursday, twice as many students handed in their permission slip than on Tuesday. On Friday, an additional 7 students turned in their permission slip. What expression could be used to find the total number of permission slips handed in?
14 x 2 + 7
14 + (2 x 14) + 7
14 + (2 x 7)
14 ÷ (2 x 7) + 14

Answers

14+(2x14)+7 is the correct answer.

LE
11. The diagram shows two night-angled triangles, joined together along a common side
AB = 10-8 cm, BC = 14 4 om and CD = 24 cm.
24 am
10-8 cm
B
14-4 cm
Diagram noi drawn to scale
Calculate the area of triangle ACD.
You must show all your working.

Answers

Answer:

216 cm²

Step-by-step explanation:

Area of ∆ACD = ½*CD*CA

CD = 24 cm

CA = ?

Use pythagorean theorem to find CA.

Thus:

CA² = AB² + BC²

Substitute

CA² = 10.8² + 14.4² = 324

CA = √324

CA = 18 cm

Area of ∆ACD = ½*CD*CA

Substitute

Area = ½*24*18

= 216 cm²

The answer to the above question

Answers

Answer:

Step-by-step explanation:

Since our interval is given as it is, we are in QIII. That interval is equivalent to 270 degrees to 360 degrees, which is QIII. If we draw this right triangle in QIII and label it accordingly, the side adjacent to the reference angle is sqrt2 and the hypotenuse is 2. We know this because the cosine ratio is defined as the side adjacent to the reference angle over the hypotenuse of the right triangle. That means that we have to find the missing side in order to determine the other 2 main trig ratios. Using Pythagorean's Theorem, we have

[tex]2^2=\sqrt{2}^2+b^2[/tex] and

[tex]4=2+b^2[/tex] so

[tex]b=\sqrt{2}[/tex]. But since it is for a value that, in QIII is negative, it is [tex]-\sqrt{2}[/tex]

Now we can find the sin and tan of that reference angle. Sin is defined as the side opposite the reference angle over the hypotenuse, so

[tex]sin\theta=\frac{-\sqrt{2} }{2}[/tex] and tan, which is defined as side opposite the reference angle over the side adjacent to the reference angle, then

[tex]tan\theta=\frac{-\sqrt{2} }{\sqrt{2} }=-1[/tex]

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