The table shows the price for different numbers of pens: Does this table of numbers represent a proportional relationship?

A sequence of Bernoulli trials consists of choosing components at random from a batch of components. A selected component is eit

Drupady [299]

Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial 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 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.

The probability that a selected component is non-defective is 0.8

This means that $p = 0.8$

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

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

$P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287$

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

$p = (0.8)^8*0.2 = 0.0336$

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

4 0

3 years ago

A puppy and kitten are 180 meters apart when they see each other. The puppy can run at a speed of 25 meters per second, while th

Gnom [1K]

It seems it should be the other way... . How soon will the puppy catch up with the kitten.

The way you have it the kitten will never catch the pup. There is already 180m between them so, the distance will only increase because the puppy runs faster than the cat.

If the puppy runs after the cat, will eventually catch up with it and can be calculated. Not the other way around.

If the pup runs after the cat, the distance between them will decrease and the pup will catch the cat.

RT = D kitten

RT = D+180 puppy

20T = D

25T = D + 180

Substitution

25T = 20T +180

5T = 180

T = 36s

7 0

3 years ago

6:20=9:x=x:10=x:60=16:x=12:x

ivolga24 [154]

6:20=9:30=3:10=18:60=16:160/3=12:40

Step-by-step explanation:

The question requires you to find value of x in the ratios given;

Start with the first pair

6:20 = 9:x

6/20 =9/x

6x=20*9

6x=180

x=180/6=30 ⇒⇒ 6:20 = 9:30

The second pair after replacing the value of x=30 will be

9:30 = x:10

9/30=x/10

90=30x

90/30 =x

3=x⇒⇒ 9:30 = 3:10

The third pair after replacing value of x=3 will be

3:10 =x:60

3/10 =x/60

180=10x

180/10 =x

18=x ⇒⇒ 3:10 = 18:60

The fourth pair after replacing value of x=18 will be;

18:60 = 16:x

18/60 = 16/x

18x=16*60

x= (16*60)/18 =160/3

x= 160/3 ⇒⇒⇒ 18:60 = 16: 160/3

The firth pair after replacing value of x=160/3 will be;

16: 160/3 =12:x

16x= 160/3 *12

16x = 160 * 4

x= (160 *4 )/16

x=40

⇒⇒ 16: 160/3 = 12: 40

Learn More

Ratios and proportions :brainly.com/question/9512748

Keywords : ratio, value of x, proportion

#LearnwithBrainly

6 0

3 years ago

Two communications companies offer calling plans. With Company X, it costs 30¢ to connect and then

tensa zangetsu [6.8K]

<h3>Answer: n+15</h3>

=======================================================

Explanation:

n = number of minutes
cost of company X = 3n+30
cost of company Y = 2n+15

To find out how much more company X charges, we subtract the two cost expressions

CompanyX - CompanyY = (3n+30)-(2n+15) = 3n+30-2n-15 = n+15 which is the final answer.

--------------

An example:

Let's say you talk on the phone for n = 20 minutes.

Company X would charge you 3n+30 = 3*20+30 = 90 cents

Company Y would charge you 2n+15 = 2*20+15 = 55 cents

The difference of which is 90-55 = 35 cents.

If you plugged n = 20 into the n+15 expression we got, then n+15 = 20+15 = 35 matches up with the previous 35 cents.

This example helps confirm the answer. I'll let you try out other examples.

8 0

2 years ago

Use the following function rule to find

Vera_Pavlovna [14]

Answer:

what rule my screen is white

3 0

2 years ago