Answer:
mean = 160
Variance = 156.8
Standard deviation = 12.52
Step-by-step explanation:
This is solved by the binomial distribution model for approximation.
n = number of random sample in which for this question, n= 8000
p = probability of success = 2% = 0.02
Mean of the sample = Expected value which approximates the average number of cases to expect from the larger sample chosen.
Mean = np = 0.02 × 8000 = 160
Variance = np(1-p) = 160(1-0.02) = 156.8
Standard deviation = √variance = √156.8 =12.52
pretty sure its 0.125 and 0.0625 but let me know!
Answer:
Step-by-step explanation:
Since both the original and transformed graph have the same x value for their vertex, there was no horizontal shift. However the vertex shifted up. Specifically it shifted up 5 units. Therefore:
The plus 5 performs a translation up 5 units. Plugging in for f(x) it can be seen that:
Answer:
4
Step-by-step explanation:
t is replaced by 4 and t = hours
Area of rectangular board = length (inches) x width (inches) = 12" x 16" = 192 in²
Area of the border is given as 128 in²
Adding the area of the board and the border gives (192 + 128)in² = 320 in²
Set this up as the algebraic equation (x + 12)(x + 16) = 320 and solve for x:
Remember to use the FOIL method, which is multiplying the terms in the order of first, outer, inner, last.
x² + 12x + 16x + 192 = 320
x² + 28x + 192 - 320 = 0
x² + 28x - 128 = 0
solve for the two x values:
(x + 32)(x - 4) = 0, and knowing we only need the positive x value
x = 4 or 4 inches is the width of the border
