What is 3m+5-5m+14m=-13

A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb

Maksim231197 [3]

Answer:

a) $P(X = 1) = 0.38742$

b) $P(X = 3) = 0.05740$

c) $P(X = 9) = 0.00000$

d) $P(X \geq 5) = 0.00163$

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

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 combinatios 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.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

$P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742$

So

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837$

Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

3 0

3 years ago

Choose the correct slope and y-intercept of the line indicated by this linear equation.

stellarik [79]

The correct answer is m=-2 (slope) and b=4 (y-intercept).

8 0

3 years ago

A small business has 50 total employees, 15 of which are full-time. What percent of the employees are part-time?

12345 [234]

Answer:

70%

Step-by-step explanation:

50-15 =35

35/50 = 70/100

4 0

2 years ago

Solve 4 + 2 sinx= 14-8 sinx for 0° ≤ x ≤ 180

Oduvanchick [21]

<h2>Answer:</h2>

<u>x= 90°</u>.

<h2>Step-by-step explanation:</h2>

<h3>1. Write the expression.</h3>

$4 + 2 sin(x)= 14-8 sin(x)$

<h3>2. Subtract "4" from both sides of the equation.</h3>

$-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)$

<h3>3. Add "8sin(x)" to both sides of the equation.</h3>

$2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10$

<h3>4. Divide both sides by 10.</h3>

$\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1$

<h3>5. Apply the arcsin of sin^-1 to both sides of the equation.</h3>

$arcsin(sin(x))=arcsin(1)\\ \\x=90$

<h3>6. Conclude.</h3>

<u>x= 90°</u>.

3 0

1 year ago

What are the coordinates of the terminal point determined by T=20pi/3

Serga [27]

Answer:

t=5x=3049

Step-by-step explanation:

3 0

2 years ago