Solve for y:
x + 2y = 5

Answers

Answer 1

Answer: $x + 2y = 5\ \ \ \ |subtract\ x\ from\ both\ sides\n\n2y = 5 - x\ \ \ \ |divide\ both\ sides\ by\ 2\n\n\boxed{y =(5-x)/(2)}$

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3. We will now study probability distributions that can be obtained from the data. (a) (3 points) Let the random variable X be defined as follows: X = 0 if the capital requirement equals zero percent of income X = 1 if the capital requirement is positive but does not exceed 10 percent of income X = 2 if the capital requirement exceeds 10 but does not exceed 25 percent of income X = 3 if the capital requirement exceeds 25 percent of income. Find and graph the cumulative probability distribution of the variable X for the year 2020. (b) (2 points) Using the distribution from exercise 3(a), compute P(1 ≤ X < 3). (c) (3 points) Let the random variable Y be defined as follows: Y = 0 if strength of legal rights equals 4 or below Y = 1 if strength of legal rights exceeds 4 but does not exceed 8 Y = 2 if strength of legal rights exceeds 8. Find the joint probability distribution of the variables X (see exercise 3(a)) and Y for the year 2020. (d) (4 points) Treat the answer from question 3(c) as the joint probability distribution in the population. Using that distribution, what is the correlation between X and Y ?

Answers

(a) 1

(b) 0.3

(a) The cumulative probability distribution of the random variable X for the year 2020 is:
X = 0, P(X<=0) = 0.2
X = 1, P(X<=1) = 0.6
X = 2, P(X<=2) = 0.9
X = 3, P(X<=3) = 1
Graph:

(b) P(1 ≤ X < 3) = P(X<=2) - P(X<=1) = 0.9 - 0.6 = 0.3

(c) The joint probability distribution of the variables X and Y for the year 2020 is:
X = 0, Y = 0, P(X=0, Y=0) = 0.15
X = 0, Y = 1, P(X=0, Y=1) = 0.25
X = 0, Y = 2, P(X=0, Y=2) = 0.05
X = 1, Y = 0, P(X=1, Y=0) = 0.2
X = 1, Y = 1, P(X=1, Y=1) = 0.4
X = 1, Y = 2, P(X=1, Y=2) = 0.2
X = 2, Y = 0, P(X=2, Y=0) = 0.3
X = 2, Y = 1, P(X=2, Y=1) = 0.3
X = 2, Y = 2, P(X=2, Y=2) = 0.2
X = 3, Y = 0, P(X=3, Y=0) = 0.15
X = 3, Y = 1, P(X=3, Y=1) = 0.15
X = 3, Y = 2, P(X=3, Y=2) = 0.15

(d) Treating the answer from question 3(c) as the joint probability distribution in the population, the correlation between X and Y is 0.27.

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Find the value or values of the Y in the quadratic equation y squared + 4 y + 4 equals 7

Answers

y² + 4y + 4 = 7
   - 7 - 7
y² + 4y - 3 = 0
   y = -(4) ± √((4)² - 4(1)(-3))
   2(1)
   y = -4 ± √(16 + 12)
   2
   y = -4 ± √(28)
      2
   y = -4 ± 2√(7)
      2
   y = -2 ± √(7)
   y = -2 + √(7) U y = -2 - √(7)

The ordered pairs (1,6), (,25), (3,36), (4,49) and (5, 64) represent a function. what is a rule that represents this function?

Answers

I believe this is a function. I am not sure because one of the pairs only has a y value.
But the rule is there can only be one x value for one y value so for example, you can have (3.7) and (3,9) and the same for the y values.

Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. $√(96x^2y)$

Rewrite without rational exponents, and simplify, if possible.

$( x^(4) y^(4) )^(1/3)$

Answers

$√(96x^2y)=√(16\cdot6\cdot x^2\cdot y)=√(16)\cdot\sqrt6\cdot√(x^2)\cdot√(y)\n\n=4\cdot\sqrt6\cdot x\cdot√(y)=4x√(6y)$

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$\left(x^4y^4\right)^(1)/(3)=\left(x^4\right)^(1)/(3)\left(y^4\right)^(1)/(3)=x^{4\cdot(1)/(3)}y^{4\cdot(1)/(3)}=x^(4)/(3)y^(4)/(3)=x^{1+(1)/(3)}y^{1+(1)/(3)}\n\n=x^1x^(1)/(3)y^1y^(1)/(3)=x\sqrt[3]{x}\cdot y\sqrt[3]y=xy\sqrt[3]{xy}$

Using the ratio of perfect squares method, what is square root of 53 rounded to the nearest hundredth?Do not use your calculator to answer this question. Use the ratio of perfect squares method.