To expand (3 - 2x)^6 use the binomial theorem:
(x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + ...+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n
So, for x = 3, y = -2x , and n = 6 you get:
(3 - 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6
So, the sixth term is C(6,5)(3)(-2x)^5 = 6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.
The coefficient of that term is - 576.
Answer: - 576
Card P's balance increased by $3.43 more than Card Q's balance. The accumulated total on Card P over the 4 years is $1080.70 and the accumulated total of Card Q is $1,206.28. Based on the principal outlay however, Card P would have netted a higher interest over Card Q when the principal is subtracted from the accumulated value. (For eg. Card P accumulated value $1080.70 less Principal $726.19 equals $354.51).The interests over the 4 years period would be $354.51 and $351.08 respectively, hence Card P having an increase in balance of $3.43 over Card Q.
Answer:
(2.4, -1.2)
Step-by-step explanation:
Start by moving the x and the y to the same side and moving the number across the equal sign in both equations. We should now have y-0.45x=-2.3 and 2y+4.2x=7.8. We can use the elimination method by multiplying the first equation by -2 to get -2y+0.9x=4.6 and 2y+4.2x=7.8. From there, add the two equations together, eliminating y (-2+2=0). We now have 5.1x=12.4; divide both sides by 5.1 to get x=2.4. Then, in any of the two equations, let's use y-0.45x=-2.3, substitute x with 2.4. Now we have y-1.08=-2.3. Add 1.08 to both sides to get y=-1.22; round that to the nearest tenth to get -1.2.
Let r = usual driving rate
let t = usual driving time
We need to figure out t
The distance she covers in her usual time at her usual rate is r*t
The distance she covers in her new time at her new rate is:
(1+t)*((2/3)r)
Set this equal to each other and solve for t.
rt = (2/3)r + (2/3)rt
(1/3)rt = (2/3)r
(1/3)t = (2/3)
t = 2
So her usual time is 2 hours. (There's probably a faster way to do this)
Answer:
18
Step-by-step explanation:
There are 2+3 = 5 ratio units representing 45 band members, so each ratio unit represents 45/5 = 9 band members.
The 2 ratio units of sixth graders represent 2×9 = 18 sixth grade band members.
