Answer:
84 is the highest possible course average
Step-by-step explanation:
Total number of examinations = 5
Average = sum of scores in each examination/total number of examinations
Let the score for the last examination be x.
Average = (66+78+94+83+x)/5 = y
5y = 321+x
x = 5y -321
If y = 6, x = 5×6 -321 =-291.the student cannot score -291
If y = 80, x = 5×80 -321 =79.he can still score higher
If If y = 84, x = 5×84 -321 =99.This would be the highest possible course average after the last examination.
If y= 100
The average cannot be 100 as student cannot score 179(maximum score is 100)
10+4x+6y because 25-15 3+1 and 16-10
Answer:
Children: $13
Adults: $18
Step-by-step explanation:
Well for both sets we can set up the following system of equations,
So first we need to solve for a in the first equation.
3a + 4c = 106
-4c to both sides
3a = -4c + 106
Divide 3 by both sides
<u>a = -4/3c + 35 1/3</u>
Now we plug in that a for a in 2a + 3c = 75.
2(-4/3c + 35 1/3) + 3c = 75
-8/3c + 70 2/3 + 3c = 75
Combine like terms
1/3c + 70 2/3 = 75
-70 2/3 to both sides
1/3c = 4 1/3
Divide 1/3 to both sides
c = 13
Now we can plug in 13 for c in 3a + 4c = 106,
3a + 4(13) = 106
3a + 52 = 106
-52 to both sides
3a = 54
Divide 3 by both sides.
a = 18
<em>Thus,</em>
<em>an adult ticket is $18 and a children's ticket is $13.</em>
<em />
<em>Hope this helps :)</em>
Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
