For cosФ×sinФ =0, then either cosФ or sin Ф must be zero.
cos 90 = cos 270 = 0
sin 0 = sin 180 = sin 360 = 0.
So, the values that would give you 0 are:
1. cos 90 sin Ф
2. cos 270sin Ф
3. cos Ф sin 0
4. cos Ф sin 180 and
5 cos Ф sin 360.
Answer:
a
The distribution of X is normal
b
c
Step-by-step explanation:
From the question we are told that
The population mean is 
The standard deviation is 
Generally given from the question that the amount of time spent alone by the population size is normally distributed then then the distribution of X (i.e the amount of time spent by the sample size (the one Mercurian)) will be normally distributed
Generally the probability that the child spend less than one hour in a day is mathematically represented as
Here 
So
From the z-table the value of
So
Generally the percentage of children that spends over 3.5 hours unsupervised is mathematically represented as
From the z-table the value of
So
9x - 8y = -11
-9x + 3y = 21
Add the second equation
9x - 8y = -11
+ (-9x) + 3y = 21
-5y = 10
divide both sides by -5
y = -2
substitute y into one of the two equations in the beginning
9x - 8(-2) = -11
9x + 16 = -11
subtract 16 on both sides
9x = -27
divide both sides by 9
x = -3
The answer is (-3, -2)
x = -3
y = -2
Answer:
A
Step-by-step explanation:
Khan Academy
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
