Answer:
<em><u>According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.</u></em>
<em><u>She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z</u></em>
Step-by-step explanation:
Given the equation solved by Wayra expressed as;
Step 1: 13(z+6) = 4(z-3)-5z
She is find the value of z from the equation;
Step 2: Open the parenthesis using the distributive property;
13(z+6) = 4(z-3)-5z
13z + 13(6) = 4z - 4(3) - 5z
13z + 78 = 4z - 12 - 5z
Step 3: Simplify
13z + 78 = 4z - 5z - 12
13z + 78 = -z -12
Step 4: Collect the like terms;
13z + z = -12 - 78
Step 5: Simplify the result
14z = -90
Step 6: Divide both sides by 14
14z/14 = -90/14
z = 6.428
<em><u>According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.</u></em>
<em><u>She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z</u></em>
(a) This is the same as computing 4⁵⁵ (mod 11). We have
4² ≡ 16 ≡ 5 (mod 11)
4³ ≡ 4 • 5 ≡ 20 ≡ 9 (mod 11)
4⁴ ≡ 4 • 9 ≡ 36 ≡ 3 (mod 11)
4⁵ ≡ 4 • 3 ≡ 12 ≡ 1 (mod 11)
Then from here,
4⁵⁵ ≡ (4⁵)¹⁰ • 4⁵ ≡ 1¹⁰ • 1⁵ ≡ 1 (mod 11)
(b) Each term in the sum
4ⁿ + 4ⁿ⁺¹ + 4ⁿ⁺² + 4ⁿ⁺³ + 4ⁿ⁺⁴
has a common factor of 4ⁿ, so this sum is the same as
4ⁿ (1 + 4 + 16 + 64 + 256) = 4ⁿ • 341 = 4ⁿ • 11 • 31
So the sum is indeed divisible by 11 for all integers <em>n</em>.
(c) Since 4ⁿ = (2ⁿ)², we know the sum is also divisible by 11 when <em>a</em> = 2.
Answer:
Tammy has sold 40 boxes so far
Step-by-step explanation:
Answer:
Step-by-step explanation:
We begin with the fact that P + Q + R = 25300. Now we need to state all of those variables in terms of just one, since we can't have more than one unknown in an equation.
If Q is half as much as P, then
Q = 1/2 P
If R has twice as much as Q, then
R = 2Q, but since Q = 1/2P then
R = 2(1/2P) which is just P. So
R = P and the equation then becomes
P + 1/2P + P = 25300 and
R also is 10120.
Since Q is half of that,
Q = 5060
cross multiply to find your answer
x/250 = 20/100
250 X 20= 5000
5000=100x
x = 50
250 - 50 = 200
hope this helps :)
