Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
Hi!
Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
Answer:
Option C
Step-by-step explanation:
Given that u-ai + bj and v-ci + dj are vectors
We have dot product
hence inner product of u and v. So option a is true
The dot product of u and v is a scalar is true because dot product is always a scalar
The dot product of u and v is a vector. is false because dot product is only a scalar and has no direction and hence cannot be a vector
The dot product of u and v is given by the expression ac+bd
True because we multiply corresponding i components and j components and add.
So only C is not true.
The answer is B. Since the right angles is 90 degrees then the equation is 5x + 30 + 5x = 90. Please mark me Brainiest
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Answer:
y = 8√3
Step-by-step explanation:
In the 30°-60°-90° "special" triangle, the ratio of sides lengths is ...
1 : √3 : 2 = 8 : y : hypotenuse
In order for these ratios to be equal, we must have ...
y = 8√3
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If you want to solve this using your trig skills, you recognize that ...
Tan = Opposite/Adjacent
tan(30°) = 8/y
y = 8/tan(30°) . . . . where tan(30°) = 1/√3
y = 8√3
Answer
I believe the variable is a but I'm not 100% positive sorry
