C) Quartile 3 (q3) minus Quartile 1 (q1)
Let 
be the inital number of Timmy's marbles, and 
be the inital number of Ben's marbles.
At the beginning, "Timmy had 3/4 of what Ben had", which means
(I wrote the equation in an equivalent form to avoid denominators)
Then, Ben gives 36 marbles to Timmy. So, now Ben has 
marbles, and Timmy has 
marbles. The new ratio is 1 to 3 in Timmy's favour, so we have
(same as before)
So, we have the following linear system:
From the first equation we know that 
, so the second equation becomes
Now that we know the value for , we can simply plug it into the first equation to get
Answer:
120 different ways
Step-by-step explanation:
The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.
1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.
5P5 = 5! / (5 - 5)!
5P5 = 5! / 0!
Zero factorial (0!) is always 1.
So, 5P5 = 5! / 1
5! = 5 × 4 × 3 × 2 × 1
5! = 120
Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.
Answer:
f(x)= x2 -4
Step-by-step explanation:
it is because it has no complex roots
