Answer: a) 
b) 
Step-by-step explanation:
a) To achieve an even total, there are 3 possible combinations:
1) Even, Even, Even, Even 
2) Even, Even, Odd, Odd
3) Odd, Odd, Odd, Odd
Order is irrelevant
Summing these yields your final result: 
b) If one die shows a 2 and another a 3, while the remaining two can show any digits, there’s only one way to get a 2, one way for a 3, and six potential numbers for each of the other two dice.
Answer:
The operation r(180°,0) represents a 180° rotation around the origin.
This rotation shifts our shape to the opposite quadrant (effectively translating it across two quadrants).
Thus, this can be seen as:
A reflection across the x-axis followed by a reflection across the y-axis.
Alternatively.
It can also be depicted as a reflection across the y-axis followed by a reflection across the x-axis.
There exists another reflection method, contingent upon the position of our figure.
When the figure is situated in either the first or third quadrant, reflecting over the line y = -x yields a result equivalent to the rotation.
Conversely, if the figure lies in the second or third quadrant, reflecting over the line y = x corresponds to the rotation.
We can merge these two approaches into a single expression:
A reflection over the line y = (-1)^n*x.
Here, n indicates the number identifying the quadrant containing the figure.
Answer:
Volume of the shaded area = (600 - 36π) units³
Step-by-step explanation:
Volume of the shaded area = Volume of pyramid - Volume of cone
Volume of pyramid = ⅓*l*w*h
Where,
l = length of the base of the pyramid = 15 units
w = width of the base of the pyramid = 10 units
h = height of pyramid = 12 units
Substituting the values helps find the volume of the pyramid
Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³
Volume of Cone = ⅓πr²h,
Where,
r = radius = ½ of diameter = ½ of 9 = 3 units
h = height = 12 units
Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12
= π*3*12 = 36π units³
Volume of shaded area = (600 - 36π) units³
<span>The likelihood of both selected students being sophomores is 6/20, which simplifies to 3/10.
The expression for the probability that both chosen students are sophomores is (6c1) (5c1) /(20c2)
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