What is 5 to the power of 6 over 5 to the power of 2
2 answers:
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<h3>Answer: 12</h3>
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Explanation:
The two integers multiply to 36, so,
ab = 36
which solves to
a = 36/b
Then we want to add the numbers such that we get the smallest possible result.
a+b = (36/b)+b
So we want (36/b)+b to be as small as possible.
Let's say we replace b with x and we consider this function
f(x) = (36/x) + x
The goal is to find when f(x) is smallest, ie, we want to minimize the function.
If we were to graph out the function, we get the curve shown below.
To make things easier, we'll only focus on positive values of x.
The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.
So the input x = 6 leads to the smallest output f(x) = 12.
This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.
In short, a = 6 and b = 6.
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As a check,
a*b = 6*6 = 36
a+b = 6+6 = 12
We can make a table of various values to help confirm that 12 is the smallest sum.
Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.
Answer:
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:
The mean for the binomial distribution is given by:
And the variance is given by:
And the deviation is just the square root of the variance so we got: