The equivalence

means that n-5 is a multiple of 12.
that is
n-5=12k, for some integer k
and so
n=12k+5
for k=-1, n=-12+5=-7
for k= 0, n=0+5=5 (the first positive integer n, is for k=0)
we solve 5000=12k+5 to find the last k
12k=5000-5=4995
k=4995/12=416.25
so check k = 415, 416, 417 to be sure we have the right k:
n=12k+5=12*415+5=4985
n=12k+5=12*416+5=4997
n=12k+5=12*417+5=5009
The last k which produces n<5000 is 416
For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,
thus there are 417 integers n satisfying the congruence.
Answer: 417
Answer:
basically multiplication, (that quantity) times 5
Step-by-step explanation:
Answer:
<u>radius = √13</u>
Step-by-step explanation:
Forming the equation :
<u>(x - h)² + (y - k)² = r²</u>
- (x, y) = point on circle
- (h, k) = center of circle
- r = radius
Solving :
- (-2 + 4)² + (3 - 6)² = r²
- r² = 4 + 9
- <u>radius = √13</u>
First pool: 21 liters per min so to get 3100 gone do 3100 divided by 21 which equals 147
Second pool: 33 liters per min and you have 3472 divided 33 = 105