Answer: See solution and explanations in the attached documents
Step-by-step explanation:
See explanations in the attached documents
A, FE as a chord is a straight line that goes from one end of the circle to another end. This means both ends of the line should touch the circumference. In FE, only one end of the line is touching the circumference. The other isn't. There FE isn't a chord for circle F
Answer:
3.1623 (sqrt(10))
Step-by-step explanation:
Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.
Mean = Sum of Observations/Total Observations
Mean = (5 + 7 + 9 + 11 + 13)/5 = 45/5 = 9.
Square of the mean = 9^2 = 81.
Now subtracting the mean from each observation and squaring it gives:
(5 - 9)^2 = (-4)^2 = 16
(7 - 9)^2 = (-2)^2 = 4
(9 - 9)^2 = (0)^2 = 0
(11 - 9)^2 = (2)^2 = 4
(13 - 9)^2 = (4)^2 = 16
Sum of squares = 16 + 4 + 0 + 4 + 16 = 40.
Standard deviation = sqrt(40/4) = sqrt(10) = 3.16 (correct to 2 decimal places).
Therefore, answer is 3.16!!!
Answer: 0.78
Step-by-step explanation:
Given : P(bridge and swim) = 0.67
P(bridge)= 0.86
Formula for conditional probability :
So, 
Hence, the probability that the member swims, given that the member plays bridge = 0.78
Answer:
5536 calculators
Step-by-step explanation:
We integrate the function dx/dt to obtain the number of new calculators between beginning of the 3rd week and end of week 4. Note that beginning of 3rd week is the same as end of 2nd week. So, 
= 
Let u = t + 12, then 
= 1. So, du = dt. We also change the limits of our integration. So, when t = 2, u = 2 + 12 = 14 and when t = 4, u = 4 + 12 = 16
Then 
= ∫₁₄¹⁶ ![{5000(1 -\frac{100}{u^{2} } )} \, du = 5000[ u + \frac{100}{u} ]](https://tex.z-dn.net/?f=%7B5000%281%20-%5Cfrac%7B100%7D%7Bu%5E%7B2%7D%20%7D%20%29%7D%20%5C%2C%20du%20%3D%205000%5B%20u%20%2B%20%5Cfrac%7B100%7D%7Bu%7D%20%5D)
₁₄¹⁶ = ![5000[16 + \frac{100}{16} - (14 + \frac{100}{14} )] = 5000 [16 - 14 + \frac{100}{16} - \frac{100}{14} ] = 5000 [2 + \frac{100}{16} - \frac{100}{14} ] = 5535.7](https://tex.z-dn.net/?f=5000%5B16%20%2B%20%5Cfrac%7B100%7D%7B16%7D%20-%20%2814%20%2B%20%5Cfrac%7B100%7D%7B14%7D%20%29%5D%20%3D%205000%20%5B16%20-%2014%20%2B%20%5Cfrac%7B100%7D%7B16%7D%20-%20%5Cfrac%7B100%7D%7B14%7D%20%20%5D%20%3D%205000%20%5B2%20%2B%20%5Cfrac%7B100%7D%7B16%7D%20-%20%5Cfrac%7B100%7D%7B14%7D%20%20%5D%20%3D%205535.7)
≈ 5536 calculators
