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pochemuha
3 years ago
15

At a snack food manufacturing facility, the quality control engineer must ensure that all products feature the appropriate expir

ation date. Suppose that a box of 60 candy bars includes 12 which do not have the proper printed expiration date. The quality control engineer, in inspecting the box, grabs a handful of seven candy bars. What is the probability that there are exactly 3 faulty candy bars among the seven
Mathematics
1 answer:
Helga [31]3 years ago
5 0

Answer:

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.

Step-by-step explanation:

The bars are chosen 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:

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

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:

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

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

60 total candies means that N = 70

12 are faulty, which means that k = 12

Seven are chosen, so n = 7

What is the probability that there are exactly 3 faulty candy bars among the seven?

This is P(X = 3). So

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

P(X = 3) = h(3,70,7,12) = \frac{C_{12,3}*C_{48,4}}{C_{60,7}} = 0.1108

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.

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A recent study estimated that 68% of US adults enjoy reading a book while relaxing. How many adults are required
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Step-by-step explanation:

236, did on edge

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3 years ago
A team is excavating an archeological site. The original plan was to excavate a rectangular area 35 ft long
nikitadnepr [17]

Answer:

Part 1) The length of the new rectangle is 87.5\ ft

Part 2) The area of the new rectangle is 4,375\ ft^{2}

Step-by-step explanation:

we know that

If two rectangles are similar, then the ratio of its corresponding sides is proportional

step 1

Find the length of the new rectangle

Let

L-----> the length of the new rectangle

\frac{50}{20}=\frac{L}{35}\\ \\ L=50*35/20\\ \\L=87.5\ ft

step 2

Find the area of the new rectangle

we know that

The area of the rectangle is

A=LW

we have

L=87.5\ ft

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substitute

A=(87.5)(50)=4,375\ ft^{2}

3 0
3 years ago
What binomial do you have to add to the polynomial 2x^2+3y^2-5xy+1 to get the following?
Contact [7]

Binomial -3y^{2}+5xy when added to polynomial 2x^{2} +3y^{2} -5xy+1  gives  polynomial  that does not contain the variable y .

<h3>What is binomial?</h3>

A mathematical expression consisting of two terms connected by a plus sign or minus sign .

Example: x + 2 is a binomial, where x and 2 are two separate terms.

<h3>What is polynomial?</h3>

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer

According to the question

polynomial 2x^{2} +3y^{2} -5xy+1

when added with  -3y^{2}+5xy  

= 2x^{2}+1   (as 3y^{2} -5xy got cancelled )

that does not contain the variable y

Hence, Binomial -3y^{2}+5xy when added to polynomial 2x^{2} +3y^{2} -5xy+1  gives that does not contain the variable y .

To know more about Binomial and polynomial here :

brainly.com/question/1698358

# SPJ2

3 0
1 year ago
Read 2 more answers
Leo had $91, which is 7 times as much money as Alison had. How much
NARA [144]

Answer:

7x=91

$13.

Step-by-step explanation:

Let x represent money that Alison has.

We have been given that Leo has 7 times as much money as Alison had. So the amount of money that Leo has, would be 7x.

We are also told that Leo had $91, so we will equate 7x with 91 and solve for x as:

7x=91

To solve for x, we will divide both sides by 7:

\frac{7x}{7}=\frac{91}{7}

x=13

Therefore, Alison has $13.

8 0
3 years ago
Read 2 more answers
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DanielleElmas [232]

Answer:

B) 6

Step-by-step explanation: g = x - 9,  g = 15 - 9.   15 - 9 = 6.

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2 years ago
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