3 x 2 = 6 years to get Rs. 1324
This is a mathematical relationship that transcends currencies. In other words, it also applies to Dollars, Pounds and Yen.
“Annual compound interest” is a phrase of dubious meaning. The process is a “compound interest problem”, but the item I think you are looking for is simply the amount of interest.
Month 0: interest: 0 balance: 4,000
Month 6: interest; 200 balance: 4,200
Month 12: interest 210 balance: 4,410 12-month total interest: 410
Month 18: interest: 220.5 balance: 4,630.5 12-month total interest: 430.5
Month 24: interest: 231.525 balance: 4,862.025 12-month total interest: 452.025
Month 30: int: 243.10125 bal: 5,105.12625 12-month total int: 474.35125
Keep expanding this progression until the 12-month total interest meets or exceeds 1324, the answer will be the number of months in the last line.
E[W] = $25 (assuming the currency is in dollars)
Var(W) = 1041.67
Probability of winning first starts with the coin toss.
For a win, the coin needs to land on heads.
Probability of that = 1/2 = 0.5
Then probability of winning any amount = 1/100 = 0.01
Total probability of winning any amount = 0.5 × 0.01 = 0.005
But expected value is given by
E(X) = Σ xᵢpᵢ
where xᵢ is each amount that could be won
pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005
E(W) = Σ 0.005 xᵢ
Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign
E(W) = ∫ 0.005 x dx
Integrating from 0 to 100
E(W) = [0.005 x²/2]¹⁰⁰₀
E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25
Variance is given by
Variance = Var(X) = Σxᵢ²pᵢ − μ²
μ = expected value
We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100
Σxᵢ²pᵢ = Σ 0.005xᵢ²
Σ 0.005 xᵢ² = ∫ 0.005 x² dx
∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67
Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.
<u>2/3 i</u><u>s the</u><u> slope </u><u>of a line that is perpendicular to the line whose equation is 3x 2y=6.</u>
What is slope?
we can find the slope from the equation that is given buy solving the equation for y
3x+2y = 6
2y = 6-3x
y = 3-3/2x
y = -3/2x+3
now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2
perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have
-3/2 → 3/2 → 2/3
Therefore, the slope of the perpendicular line is 2/3.
Learn more about slope
For a system to have an infinite number of solutions, both expressions must be equal. We can go through each system and determine this:
x + 2 = y
4 = 2y - x
If we rearrange so that both are in the same format, we get:
x + 4 = 2y
These cannot be equal, so they do not have infinite solutions.
2y + 6 = 4x
-3 = y - 2x
-y - 3 = -2x
We can try to make the bottom equation look like the top equation by multiplying all terms by -2. We get:
2y + 6 = 4x. This is the same as the top, so G has infinite solutions.
Just to be sure, we can go through the others:
y + 3 = 2x
4x = 2y - 3
2y - 3 = 4x. Cannot be equal to the other equation.
y = 2x - 5
y = 2x - 2. Not equal.
The correct answer is G.
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