Hello,
I note (a,b,c) the result of a quarters, b dimes and c pennies:
2 solutions:
106=( 3, 3, 1)=( 1, 8, 1)
106=( 0, 0, 106) but : 100= 0*25+ 0*10+ 100
106=( 0, 1, 96) but : 100= 0*25+ 1*10+ 90
106=( 0, 2, 86) but : 100= 0*25+ 2*10+ 80
106=( 0, 3, 76) but : 100= 0*25+ 3*10+ 70
106=( 0, 4, 66) but : 100= 0*25+ 4*10+ 60
106=( 0, 5, 56) but : 100= 0*25+ 5*10+ 50
106=( 0, 6, 46) but : 100= 0*25+ 6*10+ 40
106=( 0, 7, 36) but : 100= 0*25+ 7*10+ 30
106=( 0, 8, 26) but : 100= 0*25+ 8*10+ 20
106=( 0, 9, 16) but : 100= 0*25+ 9*10+ 10
106=( 0, 10, 6) but : 100= 0*25+ 10*10+ 0
106=( 1, 0, 81) but : 100= 1*25+ 0*10+ 75
106=( 1, 1, 71) but : 100= 1*25+ 1*10+ 65
106=( 1, 2, 61) but : 100= 1*25+ 2*10+ 55
106=( 1, 3, 51) but : 100= 1*25+ 3*10+ 45
106=( 1, 4, 41) but : 100= 1*25+ 4*10+ 35
106=( 1, 5, 31) but : 100= 1*25+ 5*10+ 25
106=( 1, 6, 21) but : 100= 1*25+ 6*10+ 15
106=( 1, 7, 11) but : 100= 1*25+ 7*10+ 5
106=( 1, 8, 1) is good
106=( 2, 0, 56) but : 100= 2*25+ 0*10+ 50
106=( 2, 1, 46) but : 100= 2*25+ 1*10+ 40
106=( 2, 2, 36) but : 100= 2*25+ 2*10+ 30
106=( 2, 3, 26) but : 100= 2*25+ 3*10+ 20
106=( 2, 4, 16) but : 100= 2*25+ 4*10+ 10
106=( 2, 5, 6) but : 100= 2*25+ 5*10+ 0
106=( 3, 0, 31) but : 100= 3*25+ 0*10+ 25
106=( 3, 1, 21) but : 100= 3*25+ 1*10+ 15
106=( 3, 2, 11) but : 100= 3*25+ 2*10+ 5
106=( 3, 3, 1) is good
106=( 4, 0, 6) but : 100= 4*25+ 0*10+ 0
Answer:
The total length of all 8 movies is 740 minutes
Step-by-step explanation:
* Lets revise the arithmetic series
- In the arithmetic series there is a constant difference between
each two consecutive numbers
- Ex:
# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)
# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)
# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)
* General term (nth term) of an Arithmetic series:
- If the first term is a and the common diffidence is d, then
U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
So the nth term is Un = a + (n – 1)d, where n is the position of the
number in the series
- The formula to find the sum of n terms is
Sn = n/2 [a + l] , where l is the last term in the series
* Lets solve the problem
- A new movie is released each year for 8 years to go along with a
popular book series
∴ n = 8
- Each movie is 5 minutes longer than the last
∴ d = 5
- The first movie is 75 minutes long
∴ a = 75
- To find the total length of all 8 movies find the sum of the 8 terms
∵ Un = a + (n - 1)d
∵ The last term l is u8
∵ a = 75 , d = 5 , n = 8
∴ l = 75 + (8 - 1)(5) = 75 + 7(5) = 75 + 35 = 110
∴ l = 110
∵ Sn = n/2 [a + l]
∴ S8 = 8/2 [75 + 110] = 4 [185] = 740 minutes
* The total length of all 8 movies is 740 minutes
Answer:
Mean = $123.8
Range= $72
Variance= $607.344
Standard deviation=$ 24.64
Step by step explanation:
The list of the data of electricity bill on ascending order
$88,$90,$90,$95,$110,$115,$120,$126,$144,$150
Mean = (summation of($88,$90,$90,$95,$110,$115,$120,$126,$144,$150))/10
Mean = 1238/10
Mean = $123.8
Range= highest value- Lowest VA
Range= 150-88
Range= $72
Variance=( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)/10
Variance= (1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)/10
Variance= 6073.44/10
Variance=$ 607.344
Standard deviation= √variance
Standard deviation= √ 607.344
Standard deviation=$ 24.64
