PLEASE HELP

Find the leg of each isosceles right triangle if<br> hypotenuse is 5 square root 6

Mekhanik [1.2K]

Let x be the measure of both legs since the given is an isosceles right triangle. By the Pythagorean theorem we calculate for the legs,
x² + x² = (5 sqrt 6)²
The value of x from the given equation is approximately 8.66 units.

7 0

3 years ago

When Raphael solved the system below by using the method of elimination, he changed the second equation to -8x-2y=-2 what proper

galben [10]

For this case, what we are going to do is use the following property:
Multiply an equation by a scalar.
In this case, the scalar will be:
k = -2
We have then that equation 2 will be:
k * (4x + y) = k * 1
-2 * (4x + y) = - 2 * 1
-8x-2y = -2
Answer:
The property that justifies this manipulation is:
Multiply an equation by a scalar.

4 0

3 years ago

The solution to a problem is an irrational number. Which statement is true about the solution?

navik [9.2K]

Group of answer choices.

A. It can be expressed as a non repeating, non terminating decimal.

B. It can be a perfect square

C. It cannot be pie π

D. It is not possible to have a irrational number solution.

Answer:

A. It can be expressed as a non repeating, non terminating decimal.

Step-by-step explanation:

An irrational number can be defined as real numbers that cannot be expressed as a simple fraction or ratio of two integers.

Additionally, it is the opposite of a rational number and as such its decimal is continuous without having any repetition or termination. For example, pie (π) = 3.14159 is an example of an irrational number.

Assuming the solution to a mathematical problem is an irrational number. The statement which is true about the solution is that it can be expressed as a non-repeating, and non-terminating decimal.

6 0

3 years ago

Carmen spent a total of $19.50 at a concession stand on snacks for herself and her friends hamburgers cost $3.50 and hotdogs cos

Svetllana [295]

Hb=3.5, hd=2.25, hb+hd=7,

From the third, we can say hb=7-hd and we are told that:

3.5hb+2.25hd=19.5 using hb found above in this equation gives you:

3.5(7-hd)+2.25hd=19.5

24.5-3.5hd+2.25hd=19.5

-1.25hd=-5

hd=4

Carmen bought 4 hotdogs.

3 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)?

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

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.06*0.94} = 5.31$

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

(c) What is the probability that none of the 500 employees has a food allergy?

This is P(X = 0).

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

$P(X = 0) = C_{500,0}.(0.06)^{0}.(0.94)^{500} \cong 0$

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

4 0

3 years ago