Answer:
364ways
Step-by-step explanation
This is a problem on combination. Combination has to do with selection. For example if r objects are to be selected from a pool of n objects, this can be done in nCr ways.
nCr = n!/(n-r)!r!
If a brand has 14brands of hot sauce and he is to pick 3 to mix into a gumbo, he can select those 3 from a pool of 14brands in 14C3 number of ways.
14C3 = 14!/(14-3)!3!
14C3 = 14!/11!3!
14C3 = 14×13×12×11!/11!×6
14C3 = 14×13×12/6
14C3 = 14×26
14C3 = 364ways
Answer:
0
Step-by-step explanation:
f(x) = √(x) + 12
g(x) = 2√(x)
(f-g)(x) = √(x) + 12 - 2√(x)
(f-g)(x) = 12 - √(x)
if x = 144
(f-g)(144) = 12 - √(144) = 12 - 12 = 0
Answer:
0.75 feet per second.
Step-by-step explanation:
Please find the attachment.
We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.
So we can set a Pythagoras theorem as:


Now, we need to find the derivative of above equation with respect to time.

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: 
Let us solve for y using Pythagoras theorem.




Take positive square root:


Upon substituting our given values in derivative equation, we will get:






Therefore, the ladder is moving up at a rate of 0.75 feet per second.
<span>The lowest common factor of 7 and 18 is 126 (this is a number that both 7 and 18 multiply into, in fact by each other). This means the 126th person will be the first to get both coupons.</span>