Answer:
Step-by-step explanation:
Answer:
The number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
Step-by-step explanation:
There are 100 tickets that are distributed among 100 different people.
Four different prizes are awarded, including a grand prize.
The selection of the four wining tickets can be done using permutations.
Permutation is an arrangement of all the data set in a specific order.
The formula to compute the permutation of <em>k</em> objects from <em>n</em> different objects is:
In this case we need to compute the number of selection of the 4 winning tickets accordingly from 100 tickets.
Compute the number of ways to select 4 winning tickets as follows:
Thus, the number of ways to award the prizes if it satisfies the given conditions is 94,109,400.
Answer:
Width = ft
Step-by-step explanation:
The tank holds 150 gallons of water.
7.5 gallons holds 1 ft³ of water.
So 150 gallons will hold;
× 1 ft³ = 20 ft³
The volume of the tank = Length(l) × Width(w) × Height(h) = 20 ft³
i.e 5 ft × w × 3 ft = 20 ft³
15w ft² = 20 ft³
w = = ft
Answer:
The laplace transform is
Step-by-step explanation:
We will solve this problem by applying the laplace transform properties (their proofs are beyond the scope of this explanation).
Consider first the function f(t) = 1. By definition of the laplace transform, we have
when f(t) = 1 we get
We will apply the following properties: Define L(f) as applying the laplace transform
(this means, multiplying by an exponential corresponds to a shift in the s parameter of the transform of f)
(this is, multypling by is equivalent to taking the n-th derivative of the transform.
We are given the function . Since the transform of the constant function 1 is 1/s, by applying the first property we get
By applying the second property we get
Answer:
Degree: 9
Coefficient: -1
Step-by-step explanation:
The degree of a polynomial is equivalent to the highest degree of all its terms.
The term with the highest degree in this polynomial is y^9