Multiply (3x + 2) (4x-5)
2 answers:
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Answer:
a) 0.2581
b) 0.4148
c) 17
Step-by-step explanation:
For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. 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.
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.
In this problem we have that:
a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
. So
b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is when
So
So
c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.
The expected value of the binomial distribution is:
In this question, we have
So
The closest integer to 16.5 is 17.
Answer:
$800,500 (nearest dollar)
Step-by-step explanation:
The given scenario can be modeled as an <u>exponential equation</u>.
<u>General form of an exponential function</u>:
where:
- a is the initial value (y-intercept)
- b is the base (growth/decay factor) in decimal form
- x is the independent variable
- y is the dependent variable
If b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
The initial value (a) is the value of the investment.
Therefore, a = 1,000,000.
If the investment <u>decreases</u> by 2.2% each year, then it will be 97.8% of the previous year.
Therefore, b = 97.8% = 0.978.
Substitute these values into the formula to create a general equation for the scenario:
(where x is the time, in years).
To find the value of the investment after 10 years, substitute x = 10 into the formula:
Therefore, the value of the investment after 10 years is $800,500 (nearest dollar).
Learn more about exponential functions here: