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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.
Company reports the following operating results for the month of August: Sales $350,000 (units 5,000); variable costs $210,000; and fixed costs $90,000. Management is considering the following independent courses of action to increase net income.
find the exponential function fxcax whose graph goes through the points 02 and
Polynomial long division and multiplication-Use polynomial long division to divide
Linear equation on three variables
Solve the triangle by using law of cosines.
Determine a quadratic regression function that represents the distance the ball will travel in terms of its speed when it is hit at a 40 degree angle.
what are the steps for solving an equation? show an example. what and how are inverse operations used? are equations
If you have an arbitrary polynomial P(x) of the nth degree in x, and you graph the equation y = P(x), describe the overall shape of this graph.
The fourth degree Taylor Polynomial for f(x) about x = 3 is: Show that the function has a local maximum at x = 1.
which equation represents a line that intersects y-23x2 at exactly one point at 90
Make a graph for the quadratic function
A wall is to be constructed around 3 sides of a rectangle of area 220 square yards, with a fence running the length of one side. The construction cost for the wall is $15 per linear yard
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