Alicia's MP3 player contains 1,260 song. Given that 35% of the songs are rock songs and 20% of the songs are rap songs, how many
1 answer:
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Answer:
Step-by-step explanation:
When they ask you to make a variable the "subject of the formula", they're basically asking you to build a "machine" for it. In the expression , for instance, if we know what m, x, and b are, we can plug them all in and out comes a value for y! To build that machine, we need to get it by itself on one side of the equation.
So, we want to build this machine for p, and the equation we have to build it out of is
One think we can immediately say about this equation: for a fraction to be equal to one, its numerator and denominator have to be equal to each other. So we can say
Ok, what next? Well, if we want p by itself, we need to somehow peel it off of that <em>sp</em> and <em>pk</em>. Let's collect them on the right side by subtracting <em>sp </em>from both sides:
p is a <em>common factor</em> of both <em>sp </em>and <em>pk</em>, so we can peel it away using the distributive property:
And from here, we can divide both sides by and we'll have p as our subject:
or
So if we know m, k, and s, we can easily solve for p. If m = 4, k = 2, and s = 0:
Answer:
Step-by-step explanation:
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:
In order to find the expected value E(1/X) we need to find this sum:
Lets consider the following series:
And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:
(a)
On the last step we assume that and
, then the integral on the left part of equation (a) would be 1. And we have:
And for the next step we have:
And with this we have the requiered proof.
And since we have that: