Answer:
D) 0.51, and do the homework
Step-by-step explanation:
First, we have the event "Probability of give a pop quiz" and event 2 "Probability of not doing homework".
The soccer game, and the pop quiz are not related, which means that the outcome of one or another event, will not affect the fact of the soccer game to be realized, so these 2 previous events are independent events, you can either have the quiz and not doing the homework, or even not have the quiz but still do the homework, the result of one will not affect the outcome of the other, hence:
P(A∩B) = P(A) * P(B)
Replacing the data we have:
P(A∩B) = 0.6 * 0.85
P(A∩B) = 0.51 or 51%
This result is lower than 80%, therefore, you'll do the homework
Answer:
D. RWS and SWT
Step-by-step explanation:
Adjacent angles have a common side and a common vertex but they don't overlaps each other
The two angles that has these requirements are :
RWS and SWT
Without loss of generality, we can assume the semicircle has a radius of 1 and is described by
y = √(1 - x²)
Then the shorter base has length 2x and the longer base has length 2. The area of the trapezoid is
A = (1/2)(2x+2)√(1-x²) = (1+x)√(1-x²)
Differentiating with respect to x, we have
A' = √(1-x²) + (1+x)(-2x)/(2√(1-x²)
Setting this to zero, we get
0 = (1-x²) +(1+x)(-x)
0 = 2x² +x -1
(2x-1)(x+1) = 0
x = {-1, 1/2} . . . . . -1 is an extraneous solution that gives minimum area
So, for x = 1/2, the area is
A = (1 + 1/2)√(1 - (1/2)² = (3/2)√(3/4)
A = (3/4)√3
Of course, if the radius of the semicircle is "r", the maximum area is
A = (r²·3·√3)/4
Answer:
Horizontal ; 4 units right
Vertical ; 5 units down
Step-by-step explanation:
Here, we want to describe a transformation
From what we have, we can see that while 4 was added to the x value, 5 was subtracted from the whole
The 4 added shows a translation to the right of the x-axis while the -5 added is a downward translation on the y axis
So we have our answer as;
horizontal translation of 4 units right and vertical translation of 5 units down
Answer:
D. 2/3 1/6 1/5
Step-by-step explanation:
Answer:
Explanation: