WILL GIVE BRAINLIEST

Sean’s age and Helen’s age are in the ratio of 3:5. Two years ago, Helen was twice as old as Sean was then. Find their present a

PolarNik [594]

Lets Sean's age be x
Helen's age by y
x/y=3/5
x=3/5y

Second equation
2(x-2)=y-2

on solving u get Helen as 10 and Sean as 6

3 0

4 years ago

The density of a certain material is such that it weighs 10 ounces per gallon of volume. Express this density in pounds per pint

poizon [28]

Answer:

0.08 pounds per pint.

Step-by-step explanation:

Given: The density of a certain material is such that it weighs 10 ounces per gallon.

We are to express this density in pounds per pint.

1 gallon ⇒ 10 ounces

1 pound = 16 ounces

How many pounds? = 10 ounces.

Cross-multiplying gives;

$\frac{10 * 1}{16} = 0.625$ pounds

1 gallon = 8 pints

The density in pounds per pint is;

0.625 pounds ÷ 8 pints = 0.078125 pounds per pint = 0.08 pounds per pint (answer rounded up to the nearest hundredth).

7 0

3 years ago

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)?

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