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Task 1-Normal DistributionScores 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 EquationsCreate 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 FunctionsCreate 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 EquationsUsing 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/xPart 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 TheoremCreate 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 functionTask 6-Polynomial IdentitiesPick 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.
The table below is based on surveys of double-income families and the percent of men and women in these families who said they had the greater responsibility for various areas of the housework.
Describe the span of the given vectors in terms of the coefficients x, y, z of a general vector b= (x,y,z) in the span. Write b as a linear combination of the given vectors. Question. a1=(3, -6, 3), a2=(-3, 5, 6), a3=(3, -7, 12)
Simplifying the equation
a computer store helps models of a computer m1m2m3m4. each model can be fitted with 3 sizes of hard drive ab and cwhat
Graph the equation.
Solving equation by using arithmetic operations.
grandmas bakery sells single-crust apple pies for 6.99 and double-crusts pies for 10.99. the total number of pies sold
Prove that in the equation x^2 - 3xy +2y^2 - 2x - 3y - 35 = 0, for every real value of y there is a real value of x, and for every real value of x there is a real value of y.
Some people say that the Difference of Two Squares formula helps to multiply large numbers without using a calculator. How would you use this formula to multiply 201 by 199? Find at least on more of numbers that can be multiplied this way.
Find the ordered pairs
explain what it means for a rational equation to have more than one solution. provide an example of a rational
Venn diagrams
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