Y= 2x-3
the slope of the line is 2, and b, the y-intercept, is -3
Note: you did not provide the answer options, so I am, in general, solving this query to solve your concept, which anyways would clear your concept.
Answer:
Please check the explanation.
Step-by-step explanation:
Given the inequality
![3x-4y>5](https://tex.z-dn.net/?f=3x-4y%3E5)
All we need is to find any random value of 'x' and then solve the inequality.
For example, putting x=3
![3\left(3\right)-4y>5](https://tex.z-dn.net/?f=3%5Cleft%283%5Cright%29-4y%3E5)
![9-4y>5](https://tex.z-dn.net/?f=9-4y%3E5)
![-4y>-4](https://tex.z-dn.net/?f=-4y%3E-4)
![\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A-1%5C%3A%5Cleft%28reverse%5C%3Athe%5C%3Ainequality%5Cright%29%7D)
![\left(-4y\right)\left(-1\right)](https://tex.z-dn.net/?f=%5Cleft%28-4y%5Cright%29%5Cleft%28-1%5Cright%29%3C%5Cleft%28-4%5Cright%29%5Cleft%28-1%5Cright%29)
![4y](https://tex.z-dn.net/?f=4y%3C4)
![\mathrm{Divide\:both\:sides\:by\:}4](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D4)
![\frac{4y}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4y%7D%7B4%7D%3C%5Cfrac%7B4%7D%7B4%7D)
![y](https://tex.z-dn.net/?f=y%3C1)
So, at x = 3, the calculation shows that the value of y must be less
than 1 i.e. y<1 in order to be the solution.
Let us take the random y value that is less than 1.
As y=0.9 < 1
so putting y=0.9 in the inequality
![3\left(3\right)-4\left(0.9\right)](https://tex.z-dn.net/?f=3%5Cleft%283%5Cright%29-4%5Cleft%280.9%5Cright%29)
![=9-3.6](https://tex.z-dn.net/?f=%3D9-3.6)
![=5.4](https://tex.z-dn.net/?f=%3D5.4)
Means at x=3, and y=0.9, the inequality is satisfied.
Thus, (3, 0.9) is one of the many ordered pairs solutions to the inequality 3x-4y>5.
Answer:
A(3) = -6 + (3 - 1) (5)
-6 + (2)(5)
-6 + (10)
4
A(4) = -6 + (4 - 1) (5)
-6 + (3)(5)
-6 + 15
9
A(10) = -6 + (10 - 1) (5)
-6 + (9)(5)
-6 + 45
39
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)
Ok this is really easy if you thinl about it
so every ounce is how many servings?
well all you do is divide 72 by 12
happy solving :)