Answer: The original price was $6,400
Step-by-step explanation: To find the original price, divide the sale price by 1 minus the discount rate: 4160 / (1- 0.35) = 4160 / 0.65 = 6400
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For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.
- A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
- The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
- Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
- Mean(μ) = (1+2+3+4+5+6)/6
- Mean(μ) = 21/6
- Mean(μ) = 3.5
- The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
- A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
- σ² = E[X²]−μ²
- σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
- σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
- σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
- σ² = (91/6) - (3.5)²
- σ² = 15.167-12.25
- σ² = 2.917
- σ = √2.917
- Standard deviation (σ) = 1.708
To learn more about variance, visit :
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Answer:
x = -1
Step-by-step explanation:
Step 1: Write equation
-4(-5x + 2) - 3x - 5 = -30
Step 2: Solve for <em>x</em>
<u>Distribute -4:</u> 20x - 8 - 3x - 5 = -30
<u>Combine like terms:</u> 17x - 13 = -30
<u>Add 13 on both sides:</u> 17x = -17
<u>Divide both sides by 17:</u> x = -1
Exactly, Thank you again for these quotes!
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EDIT: THANKS FOR THE POINTS >:3
Answer:
8 seconds
Step-by-step explanation:
Given :
h(t) = -16t2 + initial height
Initial height = 1024 feets
By the time it hits the ground, h(t) = 0
Equation becomes :
0 = - 16t² + 1024
Solve for t
-16t² = 1024
t² = 1024 / -16
t² = 64
t = √64
t = 8
Hence, it will take 8 seconds
