Solve the nonhomogeneous differential equation y′′+6y′−16y=e5x. Find the most general solution to the associated homogeneous dif
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The probability of winning a lottery by selecting the correct six integers, are
The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
Part (a); positive integers not exceeding 30.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.
Part (b); positive integers not exceeding 36.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.
Part (c); positive integers not exceeding 42.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.
Part (d); positive integers not exceeding 48.
To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.
To know more about binomial probability, here
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The complete question is-
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.
Answer:
Step-by-step explanation:
Instead of using the standard form, we can use the vertex form of a quadratic equation:
Where a is the leading coefficient, and (h, k) is our vertex.
Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:
Now, we need to determine a.
We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:
Solve for a. Subtract within the parentheses:
Add 4 to both sides:
Square:
Solve:
Thererfore, the value of a is 4.
So, our function is:
Now, let’s find our roots. Set the equation to 0 and solve for x:
So, our roots are 1 and 3.
The greater root is 3 and the lesser root is 1.
Therefore, m-n, where m>n, is 3-1 or 2.
Our final answer is 2.