Assume:
Size of sides = x m
Depth of the pool = y m
Therefore, surface area = x^2+4xy =10 m^2
Then, y = (10-x^2)/(4x)
Now,
Volume (V) = x^2*y = x^2*y =x^2(10-x^2)/4x = (10x-x^3)/4 = 1/4(10x-x^3)
For maximum volume, first derivative of volume function is equal to zero.
That is,
dV/dx =0 = 1/4(10-3x^2)
Then,
1/4(10-3x^2) = 0
10-3x^2 = 0
3x^2=10
x= sqrt (10/3) = 1.826 m
And
y= (10-1.826^2)/(4*1.826) = 0.913 m
Therefore,
V= 1.826^2*0.913 = 3.044 m^3
Answer:
c
Step-by-step explanation:
Because of speed, acceleration and movement.
Answer:
a) 68%; b) 99.5%
Step-by-step explanation:
The empirical rule states that 68% of data falls within 1 standard deviation of the mean; 95% of data falls within 2 standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.
For part a,
We are asked the approximate percentage of women whose platelet counts are within 1 standard deviation of the mean. According to the empirical rule, this is 68%.
For part b,
We are given the endpoints of the interval. The lower endpoint is 181.5; this is 250.8-181.5 = 138.6 away from the mean. Dividing by the standard deviation, 69.3, we have
138.6/69.3 = 2
This is 2 standard deviations away from the mean.
The higher endpoint is 320.1; this is 320.1-181.5 = 138.6 away from the mean. Dividing by the standard deviation, 69.3, we have
138.6/69.3 = 2
This is standard deviations away from the mean.
This means this interval includes about 95% of women.
