given a system of equations, list three ways that we can write new equations that can be used to create equivalent systems

Mathematics

1 answer:

cupoosta [38]3 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

Given a system of equations, you can

rewrite one of the equations and write the sum of two equations instead of the second equation;

rewrite one of the equations and write the difference of two equations instead of the second equation;

rewrite one of the equations and write the sum of the first equation multiplied by one nonzero number and the second equation multiplied by another nonzero number instead of the second equation.

These actions are called elementary row operations. Elementary operations with system of equations do not change the solution set.

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A triangle has sides of lengths 11 in., 59 in., and 61 in. Is the triangle a right triangle?

Evgesh-ka [11]

No No because it says a triangle has sides of length of 11 inch 59 and 61 inch is the triangle a right angle I mean triangle well no because it says 11 or side to side should be equal in once I could be wrong so it’s not

4 0

1 year ago

kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that $n = 300$

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied. So we use $p = 0.93$