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
Phythagoras theorem:
hypotenuse²=leg₁²+leg₂²
Data:
leg₂=7.2
hypotenuse=11.1
Therefore:
(11.1)₂=leg₁² +(7.2)²
123.21=leg₁²+51.84
leg₁²=123.21 - 51.84
leg₁²=71.37
leg¹=√(71.37)
leg₁=8.4
Answer: b=8.4
Answer:
C. 30
Step-by-step explanation:
15 men do work in 16 days
This means that 7.5 men (15/2) would do that same work in 32 days (16x2).
If the number of men increase, the amount of days decrease.
8 men would do that work in 30 days
8 men > 7.5 men
30 days < 32 days
The total number of leaves that was collected by Lisa is the product of the number of days in a week and the number of leaves she collected per tree. This is shown below,
(7 trees / week) x (7 leaves / 1 tree) = 49 leaves / week
Thus, Lisa collected 49 leaves in a week.
<h3>
Answer: 14400</h3>
Chances are your teacher doesn't want you to enter any commas. You won't type in the dollar sign either.
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Explanation:
Nice work on selecting the correct equation to set up.
We'll cross multiply to help solve for x.
The idea of cross multiplication is that 
turns into 
So,
That means the person would pay $14,400 on a property worth $800,000.
