Some of the problems in the remainder of this activity require calculations. Feel free to use a calculator or computer, but make sure you write down enough work to explain your results.
There are two ways to calculate the amount spent on coffee in Question 5. First, you can add
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- 2. (a) For each of the following functions, decide whether it is injective, and whether it is surjective. Justify your answers. i. f: Z → 22 Z 3z +1 ii. 9: C→ 22 Re(z) + Im(z)arrow_forwardNot use ai pleasearrow_forward2. Given f(0) = (2 cos 0)² - 3sin²0. 1 a. Show that f(0) = ½ + ½ 7 + - cos cos 20. 2 2 b. Hence, find the exact value of √² 0 ƒ (0) do.arrow_forward
- 2. Given f(0) = (2 cos 0)² - 3sin²0. 1 a. Show that f(0) = ½ + ½ 7 +-cos cos 20. 2 2 b. Hence, find the exact value of √ ƒ (0) d0.arrow_forwardNot use ai pleasearrow_forwardIn a crossover trial comparing a new drug to a standard, π denotes the probabilitythat the new one is judged better. It is desired to estimate π and test H0 : π = 0.5against H1 : π = 0.5. In 20 independent observations, the new drug is better eachtime.(a) Find and plot the likelihood function. Give the ML estimate of π (Hint: youmay use the plot function in R)arrow_forward
- Q9. If A and B are two events, prove that P(ANB) ≥ 1 − P(Ā) – P(B). [Note: This is a simplified version of the Bonferroni inequality.] -arrow_forwardCan you explain what this analysis means in layman's terms? - We calculated that a target sample size of 3626, which was based on anticipated baseline 90-day mortality of 22% and a noninferiority margin of no more than 4 percentage points, would give the trial 80% power, at a one-sided alpha level of 2.5%, accounting for a maximum of 5% loss to follow-up and for early stopping rules for three interim analyses.-arrow_forward(x)=2x-x2 2 a=2, b = 1/2, C=0 b) Vertex v F(x)=ax 2 + bx + c x= Za V=2.0L YEF(- =) = 4 b (글) JANUARY 17, 2025 WORKSHEET 1 Solve the following four problems on a separate sheet. Fully justify your answers to MATH 122 ล T earn full credit. 1. Let f(x) = 2x- 1x2 2 (a) Rewrite this quadratic function in standard form: f(x) = ax² + bx + c and indicate the values of the coefficients: a, b and c. (b) Find the vertex V, focus F, focal width, directrix D, and the axis of symmetry for the graph of y = f(x). (c) Plot a graph of y = f(x) and indicate all quantities found in part (b) on your graph. (d) Specify the domain and range of the function f. OUR 2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1 and u is the unit step function: u(x) = { 0 1 if x ≥0 0 if x<0 y = u(x) 0 (a) Write a piecewise formula for the function g. (b) Sketch a graph of y = g(x). (c) Indicate the domain and range of the function g. X фирм where u is the unit step function defined in problem 2. 3. Let…arrow_forward
- Classwork for Geometry 1st X S Savvas Realize * MARYIA DASHUTSINA-Ba → CA savvasrealize.com/dashboard/classes/49ec9fc00d8f48ec9a4b05b30c9ee0ba A > SIS © = =Wauconda Middle S... 31 WMS 8th Grade Tea... SIS Grades and Attenda.... esc GEOMETRY 1ST < Study Guide T6 K 18 L 63° 9 N M Quadrilateral JKLM is a parallelogram. What is the m ZKJN? mZKJN = Review Progress acerarrow_forwardQ7. A business office orders paper supplies from one of three vendors, V₁, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, (V2, V3) might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day. (a) List the sample points in this experiment of ordering paper on two successive days. (b) Assume the vendors are selected at random each day and assign a probability to each sample point. (c) Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P(A), P(B), P(AUB), and P(An B) by summing the probabilities of the sample points in these events.arrow_forwardQuestion 1arrow_forward
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