Answer:
For each player:
Headbands = 11.67 inches of fabric
Wristbands = 9.31 inches of fabric
Step-by-step explanation:
Shauna is making accessories for the soccer team
For Headbands
She uses 513.48 inches of fabric on headbands for 40 player and 4 coaches
The total number of persons = 40 players + 4 coaches
= 44 persons
Hence:
44 persons = 513.48 inches
1 person = x
Cross Multiply
44x = 513.48 inches × 1
x = 513.48 inches/44
x = 11.67 inches per person
For Wristbands
She uses 372.40 inches of fabric on wristbands for just the players how much fabric was used on a headband and wristband for each player?
Number of players = 40
Hence
40 players = 372.40 inches
1 players = x inches
Cross Multiply
40x = 372.40 inches
x = 372.40 inches/40
x = 9.31 inches
Hence, 9.31 inches per player.
Therefore
For each player:
Headbands = 11.67 inches of fabric
Wristbands = 9.31 inches of fabric
Problem: find 0 ≤ x ≤ 28 such that x^85 ≡ 6 modulo 35.
By Fermat-Euler theorem:
If a and n are coprime, i.e. (a,n)=1, then
a^phi(n) ≡ 1 mod n
where phi(n)=totient function, the number of positive integers less than n that is coprime with n.
for n=35, phi(35)=24 calculated as follows:
There are 10 positive integers from 1 to 34 which are NOT coprime with 35, namely {5,7,10,14,15,20,21,25,28,30}.Therefore phi(35)=34-10=24
From Fermat-Euler theorem,
x^(phi(35) = x^24 ≡ 1 modulo 35 since (24,35)=1, i.e. 24 and 35 are coprime.
=>
x^12 ≡ ± 1 modulo 35. ...........(1)
and
x^85 ≡ x^(85-3*24) ≡ x^(85-72) ≡ x^(13) ≡ 6 mod 35 ............(2)
Substituting (1) in (2)
x^(12)*x ≡ 6 mod 35
=>
(+1)*x = 6 mod 35 or (-1)*x ≡ 6 mod 35
x ≡ 6 mod 35 x ≡ -6 mod 35 (rejected)
=> x=6
So
6^85 ≡ 6 mod 35
If any clarifications are needed or if you find any errors, please post.
4 3/8 is in simplest form.
Answer:
12.5
Step-by-step explanation:
4.5 - 3 = 1.5, so 11 + 1.5 = 12.5
Answer:
The graph so C
Step-by-step explanation:
Cause u can’t get two or more x values for different for one y value( if u plug in 3 and u get 5, u can’t plug in 3 again and get 10)
