Please help me with this
please help me with this - 1

Answers

Answer 1
Answer:

Answer:

9x^2 + 12x

Step-by-step explanation:

The area of the blue

3* 3x^2 = 9x^2

The area of the pink is

3* 4x = 12x

Add them together

9x^2 + 12x


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A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that a) None of the LED light bulbs are defective? b) Exactly one of the LED light bulbs is defective? c) Two or fewer of the LED light bulbs are defective? d) Three or more of the LED light bulbs are not defective?

Answers

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.

Step-by-step explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.

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) = (n!)/(x!(n-x)!)

And p is the probability of X happening.

In this problem we have that:

n = 10, p = 0.05

a) None of the LED light bulbs are defective?

This is P(X = 0).

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

P(X = 0) = C_(10,0)*(0.05)^(0)*(0.95)^(10) = 0.5987

There is a 59.87% probability that none of the LED light bulbs are defective.

b) Exactly one of the LED light bulbs is defective?

This is P(X = 1).

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

P(X = 1) = C_(10,1)*(0.05)^(1)*(0.95)^(9) = 0.3151

There is a 31.51% probability that exactly one of the light bulbs is defective.

c) Two or fewer of the LED light bulbs are defective?

This is

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 2) = C_(10,2)*(0.05)^(2)*(0.95)^(8) = 0.0746

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5987 + 0.3151 + 0.0746 0.9884

There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) Three or more of the LED light bulbs are not defective?

Now we use p = 0.95.

Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.

So

P(X \leq 2) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X \leq 2)

In which

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C_(10,0)*(0.95)^(0)*(0.05)^(10)\cong 0

P(X = 1) = C_(10,1)*(0.95)^(1)*(0.05)^(9) \cong 0

P(X = 2) = C_(10,1)*(0.95)^(2)*(0.05)^(8) \cong 0

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0

P(X \geq 3) = 1 - P(X \leq 2) = 1

There is a 100% probability that three or more of the LED light bulbs are not defective.

Final answer:

The question relates to binomial distribution in probability theory. The probabilities calculated include those of none, one, two or less, and three or more LED bulbs being defective out of a random sample of 10.

Explanation:

This question relates to the binomial probability distribution. A binomial distribution is applicable because there are exactly two outcomes in each trial (either the LED bulb is defective or it's not) and the probability of a success remains consistent.

a) In this scenario, 'none of the bulbs being defective' means 10 successes. The formula for probability in a binomial distribution is p(x) = C(n, x) * [p^x] * [(1-p)^(n-x)]. Plugging in the values, we find p(10) = C(10, 10) * [0.95^10] * [0.05^0] = 0.5987 or 59.87%.

b) 'Exactly one of the bulbs being defective' implies 9 successes and 1 failure. Following the same formula, we get p(9) = C(10, 9) * [0.95^9] * [0.05^1] = 0.3151 or 31.51%.

c) 'Two or less bulbs being defective' means 8, 9 or 10 successes. We add the probabilities calculated in (a) and (b) with that of 8 successes to get this probability. Therefore, p(8 or 9 or 10) = p(8) + p(9) + p(10) = 0.95.

d) 'Three or more bulbs are not defective' means anywhere from 3 to 10 successes. As the failure rate is low, it's easier to calculate the case for 0, 1 and 2 successes and subtract it from 1 to find this probability. This gives us p(>=3) = 1 - p(2) - p(1) - p(0) = 0.98.

Learn more about Binomial Probability here:

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What is the upper quartile of 36 ,73,28,36,80,50

Answers

Put the numbers in order

28, 36, 36, 50, 73, 80
|. |. |
The upper quartile is 73

the upper quartile is 80

What is c in c/4 = - 9/8 ?

Answers

Answer:

c = -9/2

Step-by-step explanation:

8 and 9 pls thx guys

Answers

Number 8
the perimeter of rectangle = the perimeter of hexagon
2l + 2w = the sum of the sides on hexagon

Input what are given from the image
2l + 2w = the sum of the sides on hexagon
2(2x + 5) + 2(x) = 2x - 6 + 0.5x + 1.5x + 3x + 1 + 2.5x + 1.5x

Simplify the left side and the right side
4x + 10 + 2x = 11x - 5
6x + 10 = 11x - 5
This is the equation

Number 9
Solve the equation
6x + 10 = 11x - 5
6x - 11x = -5 - 10
-5x = -15
x = -15/-5
x = 3

The solution is x = 3

I NEED HELP WITH #5 PLZ ! Need by midnight and plz tell me how you solved it. Thank you in advance.

Answers

Answer:

Perimeter A  = 122.5

Step-by-step explanation:

Set up the following proportion

The Perimeter of B = 12 + 9 + 9 + 5

The Perimeter of B = 35

7/2 = x/PerimeterB

7/2 = x / 35                   Cross multiply

7*35 = 2x                      Combine the left side

245  = 2x                      Divide by 2

245/2 = 2x/2                Do the division

122.5 = x

The Perimeter of A = 122.5

Problem 3

If you compare the sides opposite the angle marked with a single arc, you will get the scale factor.

If these triangles are similar, and one of the sides opposite their markings will give you the scale factor

18/7.2 = x/1 where x is the scale factor going from the larger to the smaller triangle.

2.5 = x

So if you multiply the smaller triangle's sides by 2.5 you get the larger triangle.


Which letter represents the maximum of the data set on the box plot?

Answers

Answer:

Letter E represents the maximum of the data set on the box-plot.

Step-by-step explanation:

We now that in the given box-plot we have:

Letter A represents the minimum value of the data set.

Also in the given box of the whisker-box plot the lower value in the box represents the lower quartile or first quartile i.e. Q_1 i.e. letter B.

Also, the middle value in the box-plot represents the middle quartile or median of the data i.e. Q_2 i.e. letter C.

And the maximum value on the box represents the upper quartile i.e. Q_3 i.e. letter D.

The maximum value of the data set is represented by letter E.

E is your correct answer cause that's the maximum range in that data there is no other range going past it.