Answers:
x = 7%
y = 2 slips
Explanation:
The expected value is the result of the sum of each value times its probabilities:
Expeted value = probability 1 × value 1 + probability 2 × value 2 + probability 3 × value 3 + .....
Case 1: at the beginning of the contest:
total number of slips: 30 + 15 + 5 = 50
probability 1 = 30/50
value 1 = 5%
probability 2 = (15/50)
value 2 = x%
probability 3 = (5/50)
value 3 = 15%
⇒ Expected value = 6.6% = (30/50) 5% + (15/50)x% + (5/50)15%
⇒ (15/50)x% = 6.6% - (30/50)5% - (5/50)15%
⇒ (15/50) x% = 2.1%
⇒ x% = (50 / 15) 2.1% = 7%
Answer: 7%
2) Case 2: at one point, ...
Yet, the equation for the expected value is:
Expeted value = probability 1 × value 1 + probability 2 × value 2 + probability 3 × value 3 + .....
Only the probabilities have changed, but the discounts are the same. This is x% is the same value found above: 7%.
The total number of slips now is 4 + y + 2 = 6 + y
And the expected value becomes:
8% = [ 4 / (6+y) ] 5% + [ y / (6 + y) ] 7% + [2 / (6 + y)] 15%
From which you obtain:
Mulitplying by 6+ y: 8% [6 + y] = 4×5% + y×7% + 2×15%
⇒ 8% y + 8%×6 = 4×5% + y 7% + 2×15%
⇒ 8% y - 7%y = 4×5% + 2×15% - 6×8%
⇒ 0.01y = 0.2 + 0.3 - 0.48 = 0.02
⇒ y = 2
120 - 96 = 24
Now we have to find what percent of 120 24 is.
x × 120 = 24
x = 0.2
0.2 means 20%.
The discount is 20% off.
<h3><em>11) x+61 + x+51 + 80 = 180 ( angle sum property )</em></h3><h3><em>2x + 192 = 180 </em></h3><h3><em>2x = 180 - 192 </em></h3><h3><em>2x = -12</em></h3><h3><em>x = -12/2</em></h3><h3><em>x = -6 </em></h3><h3><em>12) x+52 + 67+x + 75 = 180 ( angle sum property )</em></h3><h3><em>2x + 194 = 180 </em></h3><h3><em>2x = 180 - 194 </em></h3><h3><em>2x = -14</em></h3><h3><em>x = -14/2 </em></h3><h3><em>x = -7 </em></h3><h2><em>HOPE IT HELPS !!!</em></h2>
Jerry read 12 hours or 60/5 in those 20 days but I cant tell you how much in September.
