Which constant could each equation be multiplied by to eliminate the x variable in this system of equations? 4x + 5y = 62 5x − 3
1 answer:
Answer:
Multiply equation by 5 and
by 4
Step-by-step explanation:
Given:
Equations are
To find: constant by which each equation should be multiplied to eliminate the variable in the given system of equations
Solution:
Multiply equation (i) by 5 and (ii) by 4 to get the following equations:
On subtracting these equations, we get
So, the variable gets eliminated
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Answer:
a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.
b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.
c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.
Step-by-step explanation:
For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that 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.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?
The foreclosure rate is 1.31% for the Washington, DC area, which means that
We wanto to find, with :
In which
0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.
b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?
Foreclosure rate of 0.87% for the nation, which means that . So
0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.
c. Comment on the above findings.
The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.