A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded regioni Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. yd Y\" YET \fIn a linguistics course, the professor asked the students to list all the languages they speak besides English. The table lists the answers of eight students. Using the table, complete the following. (@) Choose a set that is equal to the set of languages spoken by Boris. Student Set of spoken languages Manuel {Arabic, Urdu, Tagalog} (Choose one) Isabel {German, Welsh, Tagalog, Czech} Heather {Greek, Latin} (b) Choose a set that is equivalent, but not equal, to the set of languages spoken by Diane. Mai {German, Greek, Welsh, Latin} Boris {Tagalog, Arabic, Urdu} (Choose one) Kira {welsh, Spanish, Oromo, French, Russian} (9) Find two students whose sets of spoken languages are neither equal Diane {German, Zulu, Korean, Norwegian, Danish} nor equivalent. Maya {Bengali, Arabic, Urdu} (Choose one) 7 and (Choose one) X 5Sets / and F are defined as follows. J = {-1, 1, 5, 8) F = {-1, 0, 1, 2, 3, 5) Answer each part below. Write your answer in roster form or as . (a) Find the union of J and F. O.0.... JU (b) Find the intersection of J and F. X 5 JOF=Complete the following truth table. Use T for true and F for false. You may add more columns, but those added columns will not be graded. P (9 - p) vp p q T T O DAD OVO T F 0-0 0+0 F T X 5 F F(a) Use one of DeMorgan's Laws to choose a statement equivalent to the following. Tuesday isn't the name of a month and March isn't a day of the week. Equivalent: |(Choose one) (b) Use one of DeMorgan's Laws to choose a negation of the following statement. We get out of school early today and there are students in the office. Negation: |(Choose one) Consider this conditional statement. If an animal species is no longer in existence. then the animal species is extinct. (a) Give the contrapositive of the statement. X If I (Choose one} VI then (Choose one) V (b) Give the converse of the statement. If (Choose one) V then (Choose one) V (c) Give the inverse of the statement. If (Choose one) V then (Choose one) V A twelyeSided die with Sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 4? Write your answer as a fraction. When ordering the Kids' Lunch at Burger Universe, the customer must choose a size, whether or not to have cheese, a type of bun, a side order, and a type of fruit drink. Here are the DOSSIDIIItIeS for each ch0ice. Size Small, Large Cheese? With cheese, Without cheese Type of bun Plain bun, Sesame seed bun, Wheat bun Side order Fries, Onion rings Fruit drink Orange, Grape How many Kids' Lunches are possmle? X 53 An 8-sided die with faces labeled 1 to 8 will be rolled once. The 8 possible outcomes are listed below. Note that each outcome has the same probability. Complete parts (a) through (@). Write the probabilities as fractions. (a) Check the outcomes for each event below. Then, enter the probability of the event. Outcomes 00 Probability 3 4 5 F 7 8 X 5 Event A: Rolling a number greater than 6 0 O 0 O 0 Event B: Rolling an even number O 0 Event A and B: Rolling a number greater than 6 and rolling an even number 0 0 0 0 0 0 O O 0 Event A or B: Rolling a number greater than 6 or rolling an even number O 0 0 0 0 0 (b) Compute the following. P(A) + P(B) - P(A and B) = 0 X 5 (c) Select the answer that makes the equation true. P(A) + P(B) - P(A and B) = (Choose one) XSuppose each license plate in a certain state has one digit, followed by four letters, followed by one digit. The letters F, O, S, and X and the digit 0 are not used. So, there are 22 letters and 9 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format? license plates X 5A certain train has 8 cars that are being lined up on a track. One of the cars is the engine, and another is the caboose. The engine will be the first car in line. The caboose will be the last car in line. In how many ways can the cars be lined up? X 5Suppose we want to choose 2 objects, without replacement, from the $ objects pencil, eraser, desk, chair, and lamp. (@) How many ways can this be done, if the order of the choices is relevant? X 5 (b) How many ways can this be done, if the order of the choices is not relevant?Suppose we want to choose 4 letters, without replacement, from 18 distinct letters. (a) How many ways can this be done if the order of the choices is taken into consideration? D (in) How many ways can this be done; if the order of the choices is nottaken into consideration? D E31\" (@) A bank analyst wants to ask customers who have a mortgage with the bank about the customers' home-buying experiences. Which of the following best describes a systematic sample of customers? The analyst takes a list of the customers and selects every 3" customer until 78 customers are selected. OO The analyst spends a day calling mortgage customers and selects the first 78 customers who answer because these customers are easily accessible. O The analyst forms groups of 13 customers based on the cities the customers live in. Then, she selects all of the customers in 6 randomly chosen groups. (b) A manager at a bus company wants to survey employees about the new uniforms. Which of the following best describes a random sample of employees? O The manager asks for volunteers and selects every volunteer until 60 employees are selected. She selects the volunteers because these employees are easily accessible. O The manager uses a computer program to draw 60 employees at random and selects these employees. Every set of 60 employees is equally likely to be drawn by the computer program. O The manager takes a list of the employees and selects every 6" employee until 60 employees are selected. (@) A consultant wants to ask workers at a factory about the workers' job satisfaction. Which of the following best describes a cluster sample of workers? O The consultant forms groups of 30 workers based on the lengths of time the workers have worked at the factory. Then, he randomly chooses 3 groups and selects all of the workers in these groups. O The consultant assigns each worker a different number. Using a random number table, he draws 90 of those numbers at random. Then, the consultant selects the workers assigned to the drawn numbers. Every set of 90 workers is equally likely to be drawn using the random number table. O The consultant forms $ groups of workers based on the workers' shifts. Then, he selects 18 workers at random from each group.Here are the hottest recorded temperatures (in 0F) for seven cities throughout North America. Complete the grouped frequency.r distribution for the data. In the distribution, the frequency.r of a class is the number of temperatures in that class. (Note that we are using a class width 0H5.) Temperature Temperature (in -=:=-F) (in -===-F) 5) 114 117r 104 113 101t0106 10? to 112 107 112 104 113 to 113 Below are the times (in days) it takes for a sample of 17 customers from Andrew's computer store to pay their invoices. 19, 15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 30, 26, 26, 21, 21, 21 Send data to calculator Draw the histogram for these data using an initial class boundary of 14.5, an ending class boundary of 49.5, and $ classes of equal width. Note that you can add or remove classes from the figure. Label each class with its endpoints. Frequency X 5 -NWA 0 0 0 Time (in days)Below are the times (in days) it takes for a sample of 20 customers from Jack's computer store to pay their invoices. 19, 15, 43, 39, 35, 31, 27, 22, 18, 14, 42, 38, 34, 30, 13, 13, 13, 41, 41, 37 Send data to calculator Draw the frequency polygon for these data using an initial class boundary of 12.5, an ending class boundary of 47.5 and $ classes of equal width. Note that you can add or remove classes from the figure. Label each class with its midpoint. Frequency + X 5 O O ...... Time (in days)A survey of8 adults employed fulltime was taken. Here are their reported numbers of hours worked per week. 48, 4& 36, iii 37, 58, 46. 60 Send data to calculator (a) What is the mean of this data set?I If your answer is not an integer; round your answer to one decimal place. (b) What is the median of this data set?I If your answer is not an integer; round your answer to one decimal place. (c) How many modes does the data set have, and what are ' zero deBS their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the yaluels) of the :- one mode: [I modets). if applicable. two modes: l] and [l X S Answer the questions below. (9) Here are the prices (in thousands) for 9 houses for sale in a local neighborhood: $289, $290, $293, $303, $305, $306, $308, $309, $310. Which measure should be used to summarize the data? O Mean O Median O Mode (b) At a certain company, the 9 employees have the following weekly salaries: $810, $830, $850, $860, $890, $940, $950, $960, $2090. Which measure should be used to summarize the data? O Mean O Median O Mode (c) The readers of a children's magazine are asked to name their favorite animals. Which measure indicates the animal chosen most often? O Mean O Median O Mode X 5