Answer:
we divide 192 by the volume 19.5
192÷19.5=9.85 so the necklace is made of bronze
If 80% are women, then 20% are men
20% of what equals 880
0.20x = 880
x = 880/.20
x = 4400
check..
men : 20% of 4400 = 0.20(400) = 880
women : 80% of 4400 = 0.80(4400) = 3520
totaling : 3520 + 880 = 4400
so there are a total of 4400 workers
One part is 8 feet long and the other part is 17 feet long.
8+17=25
(8x2)+1=17
Answer:
Regina drank 2/4 gal. of orange juice
Step-by-step explanation:
She starts off at 3/4 which makes the equation: 3/4 - 1/4=x
3/4-1/4 equals 2/4 which gets reduced and simplified to 1/2.
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
