The volume of a cube is side length cubed (s^3)
So if you know the volume then take the cube root of 1/512... which is 1/8
So each side of the cube is 1/8.
There are 6 congruent sides on a cube (picture a “dice”). Do the area of each side would be (1/8)(1/8)= 1/64 then multiply that area by 6 and reduce ... you get 6/64 = 3/32 for the surface area
The rate of change is the slope of this line
m = (y2 - y1)/(x2 - x1) = (13 - 5)/(4 - 0) = 8/4 = 2
8x + 5(-4x) = 24
8x - 20x = 24
-12x = 24
x = -2
y = -4(-2)
y = 8
Therefore, the point of intersection is (-2,8).
-2y=11-x
-7x+11-x=-13
-8x=-24
x=3
-2y=11-3
-2y=8
y=-4
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
We solve the above questions using Combination
Combination = C(n, r) = nCr
= n!/n! ×(n - r)!
(a) How many are there to select 2 pairs of gloves?
We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2
= 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!
= 10 ways.
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
We are told to select 4 gloves out of the 10 gloves = 10C4
We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴
= 80
Hence,
10C4 - 5C4
= [10!/4! × (10 - 4)!] - 80
= 210 - 80
= 130 ways
