Answer:
Step-by-step explanation:
This is permutation, since order matters. The formula for us is
₁₈P₅ =
which simplifies to
₁₈P₅ = 
The factorial of 13 cancels out on the top and bottom leaving you with
₁₈P₅ = 18 × 17 × 16 × 15 × 14
which comes to 1,028,160 ways
Another way to look at it is: the first 5 people of 18 finish and the others you don't care about. Once the first place person is first, there are only 4 of the 18 left to finish in second place. Then there are only 3 left to finish in third place, etc. So if we use that reasoning, we don't even need to use the formula, we can just say
18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.
Answer:
F = 1.25
Step-by-step explanation:
All you would have to do is cross multiply, so our equations starts at
. We would now multiply F by 8 and 2 by 5. We now have 8F = 10. We can now divide both sides of the equation by 8 to get F = 1.25.
Answer:
a.) 
b.) therefore b = 
b is the rate of increase of number of members
c.) The club will not be able to get more than 5000 members during its first year.
Step-by-step explanation:
i) the club started with 2100 members.
so we can write
= 2100.
a.) so we can write the equation as an exponential function given by
where x is in months and b is a constant and N(x) is the number of members in the online music sharing club .
therefore 2142 = 2100
= 2100
b.) therefore b = 
b is the rate of increase of number of members
c.) Will the club have more than 5000 members during its first year? Justify your reasoning.
5000 = 2100
therefore x = 
The club will not be able to get more than 5000 members during its first year.
Answer
Length = 10 ft
Width = 5 ft
Explanation
Area of the rectangle given = 50 ft²
Let the width of the rectangle be x
So this means the length of the rectangle will be 3x - 5
What to find:
The dimensions of the rectangle.
Step-by-step solution:
Area of a rectangle = length x width
i.e A = L x W
Put A = 50, L = 3x - 5, W = x into the formula.

The quadratic equation can now be solve using factorization method:

Since the dimension can not be negative, hence the value of x will be = 5.
Therefore, the dimensions of the rectangle will be:
Answer:
$4600
Step-by-step explanation:
Write an equation to represent the problem.
Interest is calculated by multiplying the interest rate with the investment. <u>Multiplying each of the rates</u> (2%, 7% and 9%) <u>in decimal form with the investment amount is equal to the annual interest</u>, (828).
Convert a percentage to decimal form by dividing by 100:
2% ÷ 100 => 0.02
7% ÷ 100 => 0.07
9% ÷ 100 => 0.09
let "P" represent the amount of money for the total investment
0.02P + 0.07P + 0.09P = 828
Use the equation to solve for "P". Simplify by collecting like terms (numbers that have the same variable) then isolate "P" by moving the other numbers to the right side. To move a number to the other side, do it's reverse operation to both sides of the equation. (The reverse of multiplying is dividing).
0.02P + 0.07P + 0.09P = 828 Collect like terms
0.18P = 828 Isolate "P"
0.18P/0.18 = 828/0.18 Divide both sides by 0.18
P = 828/0.18 "P" is isolated because 0.18 cancelled out. Simplify.
P = 4600 Total investment
Therefore the total investment is $4600.