Answer: ![P(A\cap B)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cfrac%7B1%7D%7B3%7D)
![P(A)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B1%7D%7B3%7D)
![P(B)=1](https://tex.z-dn.net/?f=P%28B%29%3D1)
![P(A|B)=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7B1%7D%7B3%7D)
Step-by-step explanation:
From the given figure it can be seen that
Total number on cube= n(S)=6
Intersection of A and B = n(A ∩ B)= 2
Therefore,
![P(A\cap B)=\frac{n(A\cap B)}{n(s)}=\frac{2}{6}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cfrac%7Bn%28A%5Ccap%20B%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Also, The number of elements in A = 2
Therefore,
![P(A)=\frac{n(A)}{n(s)}=\frac{2}{6}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7Bn%28A%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B2%7D%7B6%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Similarly, The number of elements in B= 6
Therefore,
![P(B)=\frac{n(B)}{n(s)}=\frac{6}{6}=1](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7Bn%28B%29%7D%7Bn%28s%29%7D%3D%5Cfrac%7B6%7D%7B6%7D%3D1)
The formula to find the conditional probability is given by :-
![P(A|B)=\frac{P(A\cap B)}{P(B)}\\\\\Rightarrow P(A|B)=\frac{\frac{1}{3}}{1}=\frac{1}{3}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D%5C%5C%5C%5C%5CRightarrow%20P%28A%7CB%29%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B1%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Need the choices cant really answer your question
Answer:
Y = 28.31
Z = 13.29
Angle A = 28
Step-by-step explanation:
For Angle A:
Remember a triangle has a total of 180 degree angles. So set up your formula as
180 - 62 -90 = Angle A
For Y:
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
sin (B) = opp/hyp or b/c or (y)
sinB = 62
b = 25
Rewrite as c=b/2SinB -> c=25/sin62 -> Y = 28.31
For Z:
Use the Pythagorean theorem to find the unknown side.
![z^{2} = 28.31^{2} - 25^{2}](https://tex.z-dn.net/?f=z%5E%7B2%7D%20%20%3D%2028.31%5E%7B2%7D%20%20-%2025%5E%7B2%7D)
z = 13.29
Answer:
![x\geq3](https://tex.z-dn.net/?f=x%5Cgeq3)
![12x+7y\leq63](https://tex.z-dn.net/?f=12x%2B7y%5Cleq63)
![y\geq0](https://tex.z-dn.net/?f=y%5Cgeq0)
Step-by-step explanation:
If we let x be the amount of live bait and y be the amount of natural bait, Then we can come up with the following inequalities;
We are told that John would like to get at least 3 pounds of live bait. At least 3 means 3 or more. Since x represents the amount of live bait, we have;
![x\geq3](https://tex.z-dn.net/?f=x%5Cgeq3)
Moreover,we are informed that;
The store sells live bait for $12 a pound and natural bait for $7 a pound. x pounds of live bait would cost 12x while y pounds of natural bait would cost 7y. The total cost would thus be;
12x + 7y
but John only has a budget of $63. This implies that he can spend $63 at most, thus;
![12x+7y\leq63](https://tex.z-dn.net/?f=12x%2B7y%5Cleq63)
Finally we can have our last inequality as;
![y\geq0](https://tex.z-dn.net/?f=y%5Cgeq0)