a line in the coordinate plane has an angle of elevation of 53 degrees. Find the slope of the line correct to four decimal place
1 answer:
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Answer:
Step-by-step explanation:
So we have the expression:
To simplify, simply combine the like terms. Therefore:
Further notes:
To understand why we can combine like terms in the first place, we just need to use the distributive property. So we have the expression:
Now, factor out a y from the three terms:
Do all the operations inside the parenthesis:
And we moved the y back to the front!
This is the same result as before. When combining like terms, this is what we're essentially doing but without doing the distributive property manually. I hope you understand a bit better on how and why we can combine like terms!
Answer:
a) There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.
b) There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.
c) There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.
d) The expected number of owners who would say having a good plan is the most important advice is 2.28
Step-by-step explanation:
Questions a), b), c) are all solved as binomial distribution problems.
Question d) is a simple calculation.
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 C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
For these problems
12 business owners were contacted, so .
a. What is the probability that none of the owners would say preparing for long hours and hard work is the most important advice?
20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so .
That is P(X=0) when .
There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.
b. What is the probability that six or more owners would say preparing for long hours and hard work is the most important advice?
20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so .
This is:
So:
There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.
c. What is the probability that exactly five owners would say having good financing ready is the most important advice?
Twenty-five percent say the most important advice is to have good financing ready, so
There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.
d. What is the expected number of owners who would say having a good plan is the most important advice?
Nineteen percent say having a good plan is the most important advice, so that is
The expected number of owners who would say having a good plan is the most important advice is 2.28