Task 1 normal distribution | Mathematics homework help

Task 1—Normal Distribution
Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.
Task 2—Non-Linear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
Part 1. Show all work to solving your system of equations algebraically.
Part 2. Graph your system of equations, and show the solution graphically to verify your solution.
Task 3—Graphing Rational Functions
Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.
Task 4—Solving Rational Equations
Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.
x+a/ax = b/x
Part 1. Show all work to solve for x in the equation and check the solution.
Part 2. Explain how to identify the extraneous solution and what it means.
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function
Task 6—Polynomial Identities
Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)^2 = x^2 − 2xy + y^2 to square your number without using a calculator.