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An experiment is pulling a ball from an urn that contains 3 blue balls and 5 red balls. a.) Find the probability of getting a red ball. b.) Find the probability of getting a blue ball. c.) Find the odds for getting a red ball. d.) Find the odds for getting a blue ball.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The urn contains 3blue balls 5 red balls

a) probability of getting a red ball

P=no of favourable of outcomes /total no outcomes

P(red ball) = 5/8

b) Probability of blue ball

P(blue ball) = 3/8

c) Odds getting a red ball

odds in favour of any object = m/n

m : event to occur

n : event will not occur

Odds(red ball) = 5/3

Odds(blue) = 3/5

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Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedurex1+4x2 =11
2x1+7x2=18
Find the solution to the system of equations.

Answers

Answer:

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:

Step(i):-

Given equations are x₁+4 x₂ = 11 ...(i)

2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

A X = B

$\left[\begin{array}{ccc}1&4\n2&7\n\end{array}\right] \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n8\n\end{array}\right]$

Step(ii):-

$\left[\begin{array}{ccc}1&4\n2&7\n\end{array}\right] \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n8\n\end{array}\right]$

The Augmented Matrix form is

$[AB] = \left[\begin{array}{ccc}1&4&11\n2&7&18\n\end{array}\right]$

Apply Row operations, R₂ → R₂-2 R₁

$[AB] = \left[\begin{array}{ccc}1&4&11\n0&-1&-4\n\end{array}\right]$

The matrix form

$\left[\begin{array}{ccc}1&4\n0&-1\n\end{array}\right] \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n-4\n\end{array}\right]$

The equations are

x₁ + 4 x₂ = 11 ...(a)

- x ₂ = - 4

x ₂ = 4

Substitute x ₂ = 4 in equation (a)

x₁ + 4 x₂ = 11

x₁ = 11 - 16

x₁ = -5

Final answer:-

The solution of the Given matrix

( x₁ , x ₂ ) = ( - 5 , 4 )

Solve graphically, 2x^2+2x-4=0

Answers

The answer is in the picture below !

Consider the following model:E(y) = βo + β1x1 + β2x2 + β3x3 + β4x1x2

where y represents exam score (0 to 100 points), x1 represents the amount paid to a tutor (in dollars) in the week before the exam, x2 represents the number of hours of sleep in the week before the exam, and as represents number of study hours in the week before the exam. How many independent variables are included in this model?

a. 3
b. 2
c. 1
d. 4

Answers

Answer:

a. 3

Step-by-step explanation:

An independent variable is the variable that is changed in an experiment to test its effects on the dependent variable. i.e. inputs

A dependent variable is the variable being tested, measured or predicted in an experiment. I.e a outcome

In this case, the the effects of the amount tutors are paid a week before exam, the amount of sleep before exam and the number of study hours are input variables to determine or predict a students score in exam

The independent variables are;

x1 =represents the amount paid to a tutor (in dollars) in the week before the exam

x2 = represents the number of hours of sleep in the week before the exam

x3 = number of study hours in the week before the exam

The dependent variable is the exam score

B0, B1, B2,B3, B4 are coefficients

8. Willow earns $10 per hour working part-time at a diner. Write and solve an inequality to determinethe number of hours, h, Willow must work in a week in order to earn more than $200. Then interpret
the solution.
Willow must work
hours this week.