1. a @ b=c means a= (3+3c)(8-2b). If 36 @ 3= c, find the value of c in simplest form.

2. Fifty-four (54) marbles were divided among 3 boys in the ratio 1: 2/3: 1/3. The boy receiving the most marbles received ____marbles.

3. If m is 500% of n, then n divided by ____will yield m.

4. Two number cubes each have 6 faces and each is labeled 1, 2, 4, 6, 7, 8. If the two number cubes are rolled and the numbers showing on the upper faces are added, what is the probability of rolling a sum of 10?

5. Let N_{6 }mean 1+2+3+4+5+6. Let O_{6 }mean 1+3+5+7+9+11=36. Note O_{N }=N^{2 };

meaning O_{2 }= 2^{2} ; O_{3}=3^{2 }- - -; O_{6}= 6^{2} - - - . Let E_{6} mean 2+4+6+8+10+12= 42.

Furthermore, N_{12}= O_{6}+E_{6}. If N_{401}= 80, 601, find the value of E_{200}.

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...

5.05.0(3 lesson ratings)(3)

0

1. a @ b=c means a= (3+3c)(8-2b). If 36 @ 3= c, find the value of c in simplest form.

a @ b = c ==> a = (3+3c)(8-2b)
36 @ 3= c ==> 36 = (3+3c)(8-2*3) and solve for c.

2. Fifty-four (54) marbles were divided among 3 boys in the ratio 1: 2/3: 1/3. The boy receiving the most marbles received ____marbles.

x(1: 2/3: 1/3) = x : 2/3 x : 1/3 x

x + 2/3 x + 1/3 x = 54 and solve for x.

3. If m is 500% of n, then n divided by ____will yield m.

(m)(is)(500%)(of)(n)
m = (500/100)*n where * means multiply
m = 5n = n*(5/1) = n/?

4. Two number cubes each have 6 faces and each is labeled 1, 2, 4, 6, 7, 8. If the two number cubes are rolled and the numbers showing on the upper faces are added, what is the probability of rolling a sum of 10?

10 = 2 + 8 or 8 + 4
10 = 4 + 6 or 6 + 4

probability = 4/?

5. Let N6 mean 1+2+3+4+5+6.
Let O6 mean 1+3+5+7+9+11=36. ON = N^2: O2=2^2, O3=3^2, …, O6=6^2, ….
Let E6 mean 2+4+6+8+10+12= 42.
Furthermore, N12= O6+E6. If N401=80601, find the value of E200.

N400+401 = N401 = 80601; and
N400=O200+E200=200^2 + E200