X= {p, q, r, s, t}, Y= {1, 2, 3}. How many one-to-one function are there from Y to X.

120° angle

quester [9]

Answer:

The equation has zero solutions because the equation 2 = 3 is never true.

Hope it helps :)

6 0

2 years ago

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

2 years ago

2. The number of students in a classroom is 6 more than 4 times the number of teachers. There are 15 teachers. How many students

Alexus [3.1K]

The number of students in a classroom is 66

8 0

2 years ago

Nicole has nine dollars to spend on cards she finds friends with the same amount of money to split the cost of a set once it cos

anyanavicka [17]

Answer:

Each Friend will get $\frac{x}{3}$ cards.

Step-by-step explanation:

Let the number of cards be x.

Given:

Amount Nicole used to spend on cards = $9

Total cost of one set =$27

Also, she finds friends with the same amount of money to split the cost of a set.

So, Number of friends she finds can be calculated by dividing the Cost of 1 set with amount of money Nichole used to spend on cards.

Number of friends she finds = $\frac{27}{9} = 3$

Hence she finds 2 friends and 1 is nichole hence there are 3 persons carrying $9 to buy $27 set of card

Now, Number of cards each friend gets is equal to Total number of Cards in 1 set divided by number of people.

Number of cards each friend = $\frac{x}{3}$

Hence Each Friend will get $\frac{x}{3}$ cards.

4 0

3 years ago

According to the school survey, 12% of the students at wok wood junior high school speak Spanish. There are 36 students at the s

aivan3 [116]

The correct answer should be 300

3 0

2 years ago