Ross is buying hats for his baseball team. Each package contains 4 hats. Generate the set of ordered pairs for the ratio relatio
1 answer:
You might be interested in
Answer: Anything between 0 and 10, excluding both endpoints.
In terms of symbols we can say 0 < w < 10 where w is the width.
===================================================
Explanation:
You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.
w = width
2w = twice the width
2w-5 = five less than twice the width = length
So,
- width = w
- length = 2w-5
which lead to
area = length*width
area = (2w-5)*w
area = 2w^2-5w
area < 150
2w^2 - 5w < 150
2w^2 - 5w - 150 < 0
To solve this inequality, we will solve the equation 2w^2-5w-150 = 0
Use the quadratic formula. Plug in a = 2, b = -5, c = -150
Ignore the negative solution as it makes no sense to have a negative width.
The only practical root is w = 10.
If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.
----------------------
Based on that root, we need to try a sample value that is to the left of it.
Let's say we try w = 5.
2w^2 - 5w < 150
2*5^2 - 5*5 < 150
25 < 150 ... which is true
This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.
Now try something to the right of 10. I'll pick w = 15
2w^2 - 5w < 150
2*15^2 - 5*15 < 150
375 < 150 ... which is false
It means w > 10 leads to 2w^2-5w < 150 being false.
Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.
Answer:
a) f(x,y) = ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2
b) =
Step-by-step explanation:
joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)
Given Data,
X = The number of blue Pens
Y = The number of red Pens
a)
possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)
Please refer fig. also
total number ways of selecting any 2 pens = =
=28
f(x,y) = ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2
b)
P(X,Y)∈A = P(X + Y ≤ 1)
= P(0,0) + P(1,0) + P(0,1)
= +
+
=
