Answer:
Ron's principal balance at the start of June was $22,909.09
Step-by-step explanation:
The simple interest formula is given by:
In which E are the earnings(interest), P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.
In this problem, we have that:
His June interest is $210, so .
The current rate of interest is 11%, so
June has 30 days, and we are assuming 360 days an year. So
We want to find P
Ron's principal balance at the start of June was $22,909.09
Answer:
17 regular popcorn bags and 23 super size bags.
Step-by-step explanation:
A group of 40 people went to the theme park. While there, each person bought popcorn.
Let the regular popcorn bags be = x
Let the super size bags be = y
................(1)
Next equation becomes:
...............(2)
Multiplying (1) by 6 :
Now subtracting this from (2) we get,
=> y = 23
And x =
=> x = 17
So, there were 17 regular popcorn bags and 23 super size bags that the group bought.
Answer:
a) Figure attached
b)
c) For the case n= 6
For the case n= 5
So then we need at least n=5 or n=6 to satisfy the condition required.
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
For this case we can use the following R code:
> x <- seq(0,9,by = 1)
> y <- dbinom(x,9,0.7)
> plot(x,y,main="Histogram",type = "h")
And we can see on the figure attached the solution.
We see that the higher probabilities are from 4 to 9
Part b
The expected value is given by:
The variance is given by:
And the standard deviation is:
Part c
First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:
We can use the complement rule and we have:
We find the indicidual probabilities:
If we use the case of n=8 and we find , we got:
For the case n= 7
For the case n= 6
For the case n= 5
So then we need at least n=5 or n=6 to satisfy the condition required.
