Solve the quadratic equation of 2x^2-5x+1=0

Using the substitution method, the solution to the system of linear equations is: x = -7 and y = 5.

The substitution method used in solving a system of linear equations involves substituting a variable for an expression into the other equation given.

Given the system:

2x − 3y = −29 - eqn. 1

x + 4y = 13 - eqn. 2

Rewrite eqn. 2

x = 13 - 4y

Substitute x = 13 - 4y into eqn. 1

2(13 - 4y) − 3y = −29

26 - 8y - 3y = -29

-11y = -29 - 26

-11y = -55

y = 5

Plug in the value of y into x = 13 - 4y:

x = 13 - 4(5)

x = -7

The solution is: x = -7 and y = 5

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a. The unconditional mean of X = 1.75 cars.

b. Conditional Mean of X Given Y=1 is 1.38 cars.

c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3 is 1.07.

d. The covariance COV (X,Y) is 0.23. COV(X,Y) ≠ 0, X,Y not independent.

e. The correlation coefficient is 0.52, The strength is (0.3-0.5) and the direction is positive correlation.

f. The expectation and variance of Z are 10.25 cars and 6.66 cars².

Step-by-Step Joint Probability Distribution of Cars Sold:

a. Unconditional Mean of X:

1. Calculate marginal probabilities of X:

P(X=1) = 0.57, P(X=2) = 0.29, P(X=3) = 0.14

Calculate expected value of X:

E(X) = Σ(xi × P(xi)) = (1 × 0.57) + (2 × 0.29) + (3 × 0.14) = 1.75 cars

b. Conditional Mean of X Given Y=1:

1. Calculate conditional probability:

P(X=1|Y=1) = 0.40 / 0.52

2.Calculate conditional mean:

E(X|Y=1) = (1 × 0.806) + (2 × 0.194) = 1.38 cars

c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3:

1. Calculate conditional probability:

P(Y=1|X=3) = 0.15 / 0.14 = 1.07 (impossible, probabilities must be between 0 and 1)

d. Covariance and Independence:

1. Calculate joint expected values:

[tex]E(XY) = \sum (x_i \times y_i \times P(x_i,y_i)) = 2.74[/tex]

2. Calculate individual variances:

Var(X) = 0.74, Var(Y) = 0.24

3. Calculate covariance:

COV(X,Y) = E(XY) - E(X)E(Y) = 2.74 - (1.75 × 0.88) = 0.23

Since COV(X,Y) ≠ 0, X and Y are not independent.

e. Correlation Coefficient:

1. Calculate correlation coefficient:

ρ(X,Y) = COV(X,Y) / (σ(X) × σ(Y)) = 0.23 / (√0.74 × √0.24) ≈ 0.52

2. Strength: weak positive correlation (0.3-0.5)

3. Direction: positive correlation (positive coefficient)

f. Expectation and Variance of Z:

1. Use properties of mean:

E(Z) = E(3X+5) = 3E(X) + 5 = 3 × 1.75 + 5 = 10.25 cars

2. Use properties of variance:

Var(Z) = 9Var(X) = 9 × 0.74 = 6.66 cars²

Complete and correct question:

The joint probability distribution of variables X and Y is shown in the table below. Rebecca and Rachel are car salespeople. Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month.

          x=1       x=2      x=3

Y=1    0.40     0.18      0.15

Y=2   0.12      0.11      0.04

a. Find the unconditional mean of X.

b. Find the conditional mean number of cars that Rebecca will sell in a month given Rachel sells 1 car in a month.

C. What is the probability that Rachel will sell 1 car in a month given that Rebecca sold 3?

d. Find covariance COV (X, Y). Are X and Y independent? Explain why.
e. Find the correlation coefficient between X and Y. Discuss the strength and the direction of its relationship.
f. Chris, another salesperson, sells a car better than Rebecca. Let Z denote the number of cars that Rebecca will sell in a month, where Z = 3X +5. Get the expectation and variance of Z using the properties of the mean and the variance.

Hi there!

This set you have given is not a definitive set, therefore there is not definitive answer that can be given. It is a indefinite set, which means that any set of integers can be put in as a solution to this set. Unless there are defining quantifiers then the set and solution are both infinite.

Your friend, ASIAX

The value of (2a - 2b)/(5a + 5b) can be simplified to c.

To find the value of (2a - 2b)/(5a + 5b) when the equation (a + b)/(a - b) = c is given, we can substitute the value of (a + b)/(a - b) with c. Rearranging the equation, we get:

(2a - 2b)/(5a + 5b) = c

Simplifying the expression, we have:

(2(a - b))/(5(a + b)) = c

So, the value of (2a - 2b)/(5a + 5b) is c.

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There are 211 quarters and 216 dimes in Steve's piggy bank.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Let Steve has x quarters,

Therefore, Steve will have x + 5 dimes,

Given that,

Steve has total $74.35.

To solve, use equation format,

0.1(x+5)+0.25x=74.35

0.35x+0.5=74.35

0.35x=73.85

x=211

So the number of quarters x= 211

And number of dimes (x+5) =216

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The fraction that is greater than 1/2 and less than 3/4 is 2/3. This is demonstrated by placing these fractions on a number line, where 2/3 falls between 1/2 and 3/4.

The question is asking for a fraction that is both greater than 1/2 (or 0.5) and less than 3/4 (or 0.75). To find such fraction, we can consider fractions between these two numbers. A possible solution is 2/3 (or approximately 0.67) which is truly greater than 1/2 and less than 3/4.

Now, let's explain this visually. If you translate these fractions on a number line, 1/2 would be at the middle of the line, 3/4 would be three quarters way forward and 2/3 would be somewhere in the middle of these two fractions.

Consider the representation on a number line, 0 -> 1/2 -> 2/3 -> 3/4 -> 1. We see that 2/3 does fall in between 1/2 and 3/4.

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Answer:

Option (3) is correct.

The value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

Step-by-step explanation:

Consider the given expression in the image given,

[tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]

First solve for square term in the denominator,

[tex]3^2=3 \times 3 = 9[/tex]

Expression becomes,

[tex]\frac{-3(7+5)}{9}+9(2)[/tex]

Now solve for numerator,

7 +5 = 12 and -3(12) = -36

Expression becomes,

[tex]\Rightarrow \frac{-36}{9}+9(2)[/tex]

[tex]\Rightarrow -4+9(2)[/tex]

[tex]\Rightarrow -4+18[/tex]

[tex]\Rightarrow 14[/tex]

Thus the value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

he ended with 16

he earned 6 for mowing the lawn, so before mowing the lawn he had 16-6 =10

he spent half on pizza and had 10 left so allowance = 10*2 = 20

 he gets $20 a week for allowance

Answer:

Perimeter: 2(3x+6)+ 2(2x-4)

X=9

Step-by-step explanation:

In order to create the expression you just have to remember that the perimeter of a rectangle equals 2 bases plus 2 sides, so the expression would be:

Perimeter: 2(heights)+ 2(bases)

Perimeter: 2(3x+6)+ 2(2x-4)

IN order to solve for X we just have to insert the value of perimeter, which is 94:

Perimeter: 2(3x+6)+ 2(2x-4)

94=2(3x+6)+ 2(2x-4)

94= 6x+12+4x-8

94=10x+4

94-4=10x

x=90/10

x=9

So the value of x would be 9.