CPhill

P = 11t     where t is the number of teams and P is the number of players.....here's  a graph......

https://www.desmos.com/calculator/3ht5qqwls0

[4*30+5]/[17+8]  =

[120 + 5] / [25]  =

125/ 25

5

Here's another approach

16^2*(16^-3)^2*4^38

--------------------------- = 16^x                 what is x

(16^(-1)*2^12)  

Notice that    2^12   = (2^2)^6  = 4^6   

And   4^38 / 2^12 =   4^38 / 4^6   =  4^32 =  (4^2)^16  =   16^16 .....  so we have

[16^2  * [ (16)^(-3)]^2 * 16^16]  /  16^(-1)   =

[16^(2) [16^(-6) * 16^16] / 16^(-1)  =

16^(12) / 16^(-1)  =

16^13     so  x must = 13

u/5=-26   multiply both sides by 5

u = -26(5)   = -130

(6) A garden is 300 metres wide and 400 metres long. There is a pathway that runs along the perimeter inside the garden. The area of the pathway is half of the area of the park. What is the  width of the pathway?

Let x be the width of the pathway......then.....we have an inner rectangle whose area is defined as:

(300 - 2x) (400 - 2x)  = 60,000m^2  simplify

120000 - 1400x + 4x^2  = 60000   subtract 60000 from each side

4x^2 - 1400x  + 60000  = 0

x^2 - 350x + 15000  = 0 ........factor

(x - 50) (x - 300)  = 0  setting each factor to 0, x= 300m (reject) or x = 50m......which is correct

(3) Solve the following using the standard identity (a+b) (a-b) = a 2 - b 2 A) 109 × 91 B) 1002 × 998 C) 103 × 97 D) 109 × 91

B is the answer ......  a = 1000 and b = 2

(1) If the volume of a cube is 8000 m^3 , then what is the surface area of the cube?

The side of the cube = (8003m^3)^(1/3)  = 29 m

The surface area is given by   6*(side)^2   =  6*(20m)^2 =  6 *400m^2  = 2400m^2

(5) Sara and Iqbal run a hundred metres race. Sara wins by 20 metres. For the next race, Sara starts from 20 metres behind the original starting line, and Iqbal starts from the original starting line. If they both run at the same speed in which they ran the original race, who will win this race, and by how many metres?

Assuming that the reach their top speeds instantaneously, for every meter that  Sara runs, Iqbal runs 4/5 of a meter

Then.......Sara will run 120m in the second race and Iqbal will run  (120)(4/5)m  = 96m....

Therefore.....Sara will win by 4 m

There are 625 students in all

The number of seniors proportioned would be : (90/625) * 30 = 4.32  → round to 4

The number of juniors would be  (142/625) * (30)   = 6.8  →  round to 7

The number of soph. would be  (175/625) * (30)   = 8.4  →  round to 8

The number of freshmen would be (218/625) * 30  = 10.4 →  round to 10

This leaves 1 seat, which could be assigned to any of the classes.