The number 360 is increased by 25%. The result is then decreased by 50%. What is the final number?

PLEASE HELP!!!! Only 8 of those will match up

hodyreva [135]

CARD #1: Use the number 0 to represent the yellow marbles and 1 through 9 to represent the other marbles.

Since we are only allotting one out of the 10 numbers for the yellow marbles, then we should also find a set of marbles wherein the ratio of the yellow marbles to the total marbles is 1/10. Out of the options, the situation with 30 red marbles, 40 blue marbles, 20 green marbles, and 10 yellow marbles match the ratio.

CARD #2: Use the numbers 0 through 4 to represent the yellow marbles and 5 through 9 to represent the other marbles.

We will follow the same logic as the previous pair. Since we used 5 numbers out of the 10 for yellow marbles, then we should find a situation wherein the ratio of the yellow marbles to the total marbles is 1/2. From the options, the situation with 16 red marbles, 32 blue marbles, 32 green marbles, and 80 yellow marbles satisfy the ratio.

CARD #3: Use the numbers 0 through 2 to represent the yellow marbles and 3 through 9 to represent the other marbles.

For this card, 3 out of the 10 numbers are allotted for the yellow marbles. Thus, the ratio of the yellow marbles to the total marbles should be 3/10. We can see that the only situation that satisfies this is the one with 60 red marbles, 120 blue marbles, 30 green marbles, and 90 yellow marbles.

CARD #4: Use the numbers 0 through 3 to represent the yellow marbles and 4 through 9 to represent the other marbles.

Lastly, we will apply the same logic for this card. The 4 numbers allotted for yellow marbles will tell us that the ratio of the yellow marbles to the total marbles should be 2/5. The only situation that satisfies this would be the one with 20 red marbles, 30 blue marbles, 10 green marbles, and 40 yellow marbles.

8 0

3 years ago

Solve x:<br> 6 - 6x = -24<br> -Please Help! This is homework due in for Monday! Xx

Kipish [7]

6-6x= -24

Subtract 6 from -24 = -30

divide -30 by -6= 5

x=5

3 0

3 years ago

Read 2 more answers

According to the National Institute of Allergy and Infectious Diseases, 6% of American adults have a food allergy. A large compa

Vinil7 [7]

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. 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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

6% of American adults have a food allergy

This means that $p = 0.06$

500 employees.

This means that $n = 500$

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

$E(X) = np = 500*0.06 = 30$