Answer:
Step-by-step explanation:
Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:
3a +5c = 52
2a +4c = 38
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We can solve this system of equations using "elimination" as follows:
Dividing the first equation by 2 we get
a +2c = 19
Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:
3(a +2c) -(3a +4c) = 3(19) -(52)
c = 5 . . . . . . collect terms
a +2·5 = 19 . . substitute for c in the 3rd equation above
a = 9 . . . . . . subtract 10
One adult ticket costs $9; one child ticket costs $5.
Answer:
(a): Marginal pmf of x
(b): Marginal pmf of y
(c): Mean and Variance of x
(d): Mean and Variance of y
(e): The covariance and the coefficient of correlation
Step-by-step explanation:
Given
<em>x = bottles</em>
<em>y = carton</em>
<em>See attachment for complete question</em>
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Solving (a): Marginal pmf of x
This is calculated as:
So:
Solving (b): Marginal pmf of y
This is calculated as:
So:
Solving (c): Mean and Variance of x
Mean is calculated as:
So, we have:
Variance is calculated as:
Calculate
So:
Solving (d): Mean and Variance of y
Mean is calculated as:
So, we have:
Variance is calculated as:
Calculate
So:
Solving (e): The covariance and the coefficient of correlation
Covariance is calculated as:
Calculate E(xy)
This gives:
So:
The coefficient of correlation is then calculated as:
--- approximated
Answer:
Hemisphere radius = 3 inch
Sphere volume = 4/3 • π • radius^3
Sphere volume = 4/3 • π • 27
Sphere volume = 113.0973355292 cubic inches
Cylinder Volume = π • radius^2 • height
Cylinder Volume = π • 9 * 10
Cylinder Volume = 282.7433388231 cubic inches
TOTAL VOLUME = 113.10 + 282.74 cubic inches
TOTAL VOLUME = 395.84 cubic inches
Step-by-step explanation:
Group and factor
group y's with y's and z's with z's
(y²-10y)+(10z-yz)
factor
y(y-10)+z(10-y)
force undistribute -1
-y(10-y)+z(10-y)
factor
(10-y)(-y+z)
(z-y)(10-y) or
(y-z)(y-10)
a. The component tells you the particle's height:
b. The particle's velocity is obtained by differentiating its position function:
so that its velocity at time is
c. The tangent to at is