Answer:
Step-by-step explanation:
17/60 = 0.2833333333..... 3 repeating
25/60 = .025 terminating
31/44 = 0.7045454545..... 45 repeating
54/72 = 0.75 terminating
The absolute change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.
The answer was 1,150.0 but as a whole number its 1,150.
Short Answer: 18 minutes
Remark
The answer to this problem is less than the smallest time of the two people working together. that fact lets out C and D (38 minutes and 75 minutes). Now you have to choose 15 minutes and 18 minutes. There's a method. No guessing needed.
Givens
Let the time for Sophie = S
Let the time for Simon = M
Let the job to completion = 1
S = 45 minutes
M = 30 minutes
Step One
Convert minutes to hours.
45 minutes = 45 / 60 = 3/4 hour = 0.75 hour
30 minutes = 30 / 60 = 1/2 hour = 0.50 hour
Step Two
Set up the Equation
The formula is a form of job / hour.
Let the time = t that they both have to work
job = 1 in these problems.
1/S + 1/M = 1/t
1/0.75 + 1/0.5 = 1/t
Solve
1 ÷ 0.75 = 1.33333
1 ÷ 0.5 = 2
1.3333 + 2 = 3.33333
3.3333 = 1 / t Multlply both sides by t
3.3333*t = 1
t = 1 / 3.333333333
t = 0.3 of an hour
1 hour = 60 minutes
0.3 hours = x Cross Multiply
x = 60 * 0.3
x = 18 minutes
Answer working together it took them 18 minutes <<<<<
1)
Break up the irregular shape into two rectangles
12 * 4.5 = 54
2 * 5 = 10
54 + 10 = 64 cm^2
2)
Break up the irregular shape into a triangle and rectangle
24 * 8 = 192
To get the base of the triangle:
24 - 6 - 6 = 12
To get the height of the triangle:
16 - 8 = 8
1/2(12 * 8) = 48
192 + 48 = 240 yd^2
3)
Separate into triangle and semi circle
To get the base: 8 * 2 = 16
1/2(15 * 16) = 120
(pi (8)^2)/2 = 100.5
120 + 100.5 = 220.5 cm^2
4)
Separate half circle from rectangle
(pi (7.5)^2)/2 = 88.4
7 * 15 = 105
88.4 + 105 = 193.4 m^2
5)
Separate triangle from trapezoid
2.8 * 7 = 19.6
(7+9/2)(3.6) = 28.8
19.6 + 28.8 = 48.4 ft^2
6)
Separate semi circle from trapezoid
(pi(3)^2)/2 = 6.3
(6+10/2)(8) = 64
6.3 + 64 = 70.3 yd^2
