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vekshin1
3 years ago
12

A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are

randomly selected as they come off the production line, what is the probability that both are defective (assuming that they are independent)
Mathematics
1 answer:
IRINA_888 [86]3 years ago
4 0

Answer:

0.0025 = 0.25% probability that both are defective

Step-by-step explanation:

For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution 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.

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

In which 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)!}

And p is the probability of X happening.

5 percent of these are defective.

This means that p = 0.05

If two items are randomly selected as they come off the production line, what is the probability that both are defective

This is P(X = 2) when n = 2. So

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

P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025

0.0025 = 0.25% probability that both are defective

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Radda [10]

Answer:

x = -5 , y = 1

Step-by-step explanation:

Solve the following system:

{3 x + y = -14 | (equation 1)

-2 x - y = 9 | (equation 2)

Add 2/3 × (equation 1) to equation 2:

{3 x + y = -14 | (equation 1)

0 x - y/3 = (-1)/3 | (equation 2)

Multiply equation 2 by -3:

{3 x + y = -14 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{3 x+0 y = -15 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -5 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = -5 , y = 1

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3 years ago
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Find the x and y intercepts of the quadratic equation<br> f(x)=-x^2+4x-4
earnstyle [38]
<u>X - Intercept</u>
f(x) = -x² + 4x - 4
   0 = -x² + 4x - 4
   x = <u>-(4) +/- √((4)² - 4(-1)(-4))</u>
                         2(-1)
   x = <u>-4 +/- √(16 - 16)</u>
                    -2
   x = <u>-4 +/- √(0)
</u>               -2<u>
</u>   x = <u>-4 +/- 0
</u>              -2<u>
</u>   x = <u>-4 + 0</u>      x = <u>-4 - 0</u>  
            -2                 -2
   x = <u>-4</u>             x = <u>-4</u>
         -2                   -2
   x = 2               x = 2

The solution to the problem is {2, 2}, or {2}. The x - intercept of the problem is (2, 0).

<u>Y - Intercept</u>
f(x) = -x² + 4x - 4
f(x) = -(0)² + 4(0) - 4
f(x) = -(0) + 0 - 4
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The y - intercept of the problem is (0, -4).
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8 0
3 years ago
Please help!
Gemiola [76]

The earning of the salesperson is an illustration of a linear function.

The possible functions in the two scenarios are: \mathbf{I(s) = 0.1s + 2500} and \mathbf{I(s) = 0.05s + 2000}\\

The function is given as:

\mathbf{I(s) = 0.1s + 2000}

When the base salary is increased, a possible function is:

\mathbf{I(s) = 0.1s + 2500}

This is so, because 2500 is greater than 2000

When the commission rate is decreased, a possible function is:

\mathbf{I(s) = 0.05s + 2000}\\

This is so, because 0.05 is less than 0.1

So, the possible functions in the two scenarios are:

\mathbf{I(s) = 0.1s + 2500} and \mathbf{I(s) = 0.05s + 2000}\\

See attachment for the graphs of both functions

Read more about linear equations at:

brainly.com/question/21981879

5 0
2 years ago
A rectangle has an area of 72 in². The length and the width of the rectangle are changed by a scale factor of 3.5. What is the a
kifflom [539]

Answer:

The area of the new rectangle is 882 in².

Step-by-step explanation:

Let l be the length and w be the width of the original rectangle,

So, the area of the original rectangle is,

A = l × w                  ( Area of a rectangle = Length × Width )

Given, A = 72 in²,

⇒ lw = 72 ------- (1),

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⇒ New length = 3.5 l,

And, new width = 3.5 w,

Thus, the area of the new rectangle = 3.5l × 3.5w

=(3.5)^2lw

=12.25\times 72  ( From equation (1) ),

= 882 in²

4 0
3 years ago
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