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Mathematics Questions and Answers May 13, 2023

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(a) Let the finite group G act on a set S; and let H be a subgroup of G. Show for any x S, |G : stabG(x)| |H : stabH(x)|. Under what conditions is the inequality an equality? Here stabG(x) denotes the stabilizer of x in G and |G : K| denotes the index of the subgroup K in the group G. (b) Show that stabH(x) is a subgroup of stabG(x). (c) Show that

Thank you! A chemist has three different acid solutions. The first acid solution contains 20 % acid, the second contains 35 % and the third contains 65 % . He wants to use all three solutions to obtain a mixture of 42 liters containing 50 % acid, using 2 times as much of the 65 % solution as the 35 % solution. How many liters of each solution
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1.Consider a population that grows according to the recursive rulePn=Pn1+95 Pn = Pn -1+95, with initial populationP0=40 P0 = 40 . Then: P1 P1 = P2 P2 = Find an explicit formula for the population. Your formula should involvenn(use lowercase n) Pn= Pn = Use your explicit formula to findP100 P100 P100 P100 = 2.A population of beetles are growing

On the figure above, sketch the image of quadrilateral DEFG after translating 3 units to the left and up 5 units. Label appropriately. Write the domain and range

Explain how you construct one of the following figures: congruent segments, segment bisectors, angles, angle bisectors, parallel lines, or perpendicular lines using a compass and straightedge or technology? Provide an example of how to draw transformed figures that are translated, reflected, and rotated. What type of information do you need to

Questions 2023. Atmospheric pressure decreases by about 12% for even}:r kilometer you climb. The pressure at sea level is about 1313 atmospheres. 2i]. Construct a model to represent the atmospheric pressure at a given altitude in kilometers. 21. How man'}r atmospheres of pressure will vou feel at 5.335 km? {Top ofMt. Kilimanjaro} [round to the
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students are required to submit all three assignment sets. ASSIGNMENT DETAILS MARKS Assignment A Five Subjective Questions 10 Assignment B Three Subjective Questions + Case Study 10 Assignment C Objective or one line Questions 10
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Part III: How much did Maya pay for her points? Part IV: What were Maya's total nonrecurring closing fees? Part V: Who had a larger amount of nonrecurring closing fees, Sebastian or Maya? 8. Charlotte is purchasing a $90,000 house with a 30-year fixed-rate mortgage that has an interest rate of 8.9%, and she will be making a down payment of $9000,
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Solve the equation by factoring or the quadratic formula. 4n2= -12n - 2

Part 1ii'l: What is the actual interest rate for Joel's EDIEU mortgage? 5. Angelina is purchasing a $181.0-U house with a ayear xed-rate mortgage that has an interest rate of 5.3%. She will make a down payment of $35.2oo, so her mortgage will be for $144,800. Angelina plans on buying 1 point. and she wants to know her breakeven point. Provide
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Calculate the mean, median and mode of the following data set. Round values to the nearest tenth if the answer is not an integer.22, 24, 16, 15, 24, 21

help please A rancher has 480 feet of fencing to construct six corrals, as shown in the figure. Find the dimensions that maximize the enclosed area. What is the maximum area? The larger dimension x is feet . The smaller dimension y is feet. The maximum area is square feet
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Round your answer to the nearest whole number. The physician orders 500 mL of NS to infuse at 175 mL/h for a patient with vomiting. Tubing drop factor is 15 gtt/mL. Calculate the flow rate in drops per minute
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Week 4: Discrete Data Probability Distributions - Discussion Discrete Probability Variables ( graded ] Provide an example that follows Either the binomial or Poisson distribution , and explain why that example follows that particular distribution . In Your responsE's to other students , make UP numbers for the example provided by' that other
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Transforming Graph (a) The graph of y=f (x) is shown. Draw the graph of y = f (-x). X (b) The graph of y = g (x) is shown. Draw the graph of y = - g (x). X
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What kind of comparison group was Used In this Study ! HOW WERE they selected It what broader population is this group intended to be representative ?"
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4. The feasible region is determined by the in the linear programming problem. 5. When the slack is zero, this indicate the constraint is 6. In a graphical solution to a linear programming problem, the optimal solution is located at a of the diagram. 7. The over satisfaction of a constraint is known as in linear programming. 8. In the linear
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eight people come to a party and shake hands with each other. If each person shakes the hand of every other person. How many handshakes occur?

9. Here are two expressions with a missing number: Expression 1: ______Expression 2: ______ + 4 Choose the same number to put in both blanks, so that both expressions would result in an irrational answer. You can choose your number from the following list: 3.2, , , and 0.232323... Explain your reasoning. (4 points: 2 points for the answer and 2

3. Write a function forward_eval that evaluates the interpolating polynomial using New- ton's Forward Difference table. The function prototype and descriptive comments have been provided: function y = forward_eval (X, T, x) FORWARD_EVAL Evaluate Newton's forward difference form of the interpolating polynomial % y = FORWARD_EVAL (X, T, x) returns y
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If Bill was traveling v mi/h, how would you represent Daemon's speed in mi/h if he was traveling30mi/h faster? ------------- Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has3more than4times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is123? Don:

Solve for x. 15m2 (the two is over the m) - 6m = 0 a. 0,*2/5 (negative fraction) b. 0 c. 0, 2/5 (positive fraction) d. 2/5 , -2/5(negative fraction)

The opening value of a stock index on the rst day of trading from 1994 to 2010, can be modeled using the following polynomial: N(t) = 11.8690t3 + 20.3119t2 + 22.0273t + 757.2156 where t is time in years since 1994. Graph this function in an appropriate window, label and scale the axes showing an appropriate window based on context
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9. Determine the number of routes there are to get from Point A to Point B, if you can only travel in the stated direction. (3 marks) a. North and East b. South and East C. North and East B A B A A B
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13. A class of 22 students consists of 12 girls and 10 boys. A committee of five students is being chosen from this class to plan a school event. Determine the number of 5 student committees that can be formed if: a. the five students are chosen at random (1 mark) b. the committee must consist of 3 girls and 2 boys (1 mark) c. the committee must
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2) Two bookstores are competing for customers. Both bookstores can decide to offer discounts to attract more customers. BookstoreA has a 30 probability of offering a discount. The probability that BookstoreB will offer a discount is unknown, and is represented by P. The payoffs for the bookstores depending on whether discounts are offered are
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1.what is the domain of log(x+2)=2-log(1-x)? 2.the equation y=2^5x can also be written as; a)log2x/5 b)log2y/5 c)log5x/2 d)log5y/2 3.the exponential form of log(x)+log(y)=-2 is a)x-y=10^-2 b)xy=10^-2 c)10^xy=-2 d)x+y=-10^-2 4.the expression 5log^3(27)equals a)27 b)25 c)125 d)17 5.given that log3(x)=y,find the value of log3(27x) a)1/2(27+y)

the questions about the following function. f(x) = 3x ^ 2 - x - 2 (a) is the point (2, 8) on the graph of f? (b) If x = - 1 what is f(x) ? What point is on the graph of f? (c) If f(x) = - 2 what is x? What point(s) are on the graph off (d) What is the domain off e) List the x-intercepts), if any, of the graph of f. () List the y-intercept, if

Question 9 0 out of 1 points An HR manager was looking at the effects of an employee involvement scheme on commitment levels of the organization's staff. Three groups were used: no scheme applied, experiencing the scheme and post scheme (a group who had been subjected to the scheme 6 months before). The change in commitment over the time that the
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BLUE's Bistro BLUE'S Bistro 2010 2011 Current Ratio 1.74 2.11 Quick Rello Inventory Turnover IASSUME inventures Hurt``CO lar 20 0^ Property and Equipment Turnover TITTIES Interest Earned! Debt to ASSETS Profit Margin Return On ASSETS Return on Equity*
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Redo the circuit but with 7408 instead, and fill in the following truth table. Note you may need to rewire for this. sw1 SW2 LED Instructor check OFF OFF OFF ON ON OFF ON ON Turn on the power and check the LED according to the switch settings. When you are done. ask the instructor to check
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Birth weights of babies born to fullterm pregnancies follow rougbl},F a Normal distribution. At one hospital. the mean weight of babies born to fullterm pregnancies is 7\" lbs with a standard deviation of 14 oz (1 lb : 16 oz). Dr. Anastos {who works at this hospital) has one delivery for fullterm pregnancies coming up during the night. Assume that
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Dr. Rob has developed a new drug that he believes can cure Zombieism and stop the Zombie apocalypse. To test his new drug he captures 30 Zombies and randomly separates them into two groups. One group receives his new drug the other a placebo. a. What type of ttest would you use to see if the new drug had a significant effect? b. What are the
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in this lab, we will compare 3 different loan options. Suppose that you are buying a house for $205,000. The loan is at a fixed APR of 3.5% for 30 years. Option 1: Making a down payment 1. If a 10% down payment is required, calculate this amount: ______________ 2. What amount remains to be financed (this will be your loan amount)? _____________ 3.

5. Let's explore the process of random assignment to determine whether it does \"work.\" First, let's focus on the sex (male vs. female) variable. Suppose we put each person's name on a slip, put those slips in a hat and mix them up thoroughly, and then randomly draw out 12 slips for names of people to assign to the elevating strategy. What
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Suppose the horses in a large stable have a mean weight of 992 lbs, and a standard deviation of 141. What is the probabilitj:r that the mean weight of the sample horses would be greater than 9.7"? lbs if 3? horses are sampled at random from the stable? [Round your answer to 4 decimal places}
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by the factor theorem, what can be said about the polynomial function f(x) if f(-1)=0? By the Factor Theorem, what can be said about the polynomial function f(2) if f (-1) = 0? O f (x) has 1 real zeros O z | 1 is a factor of f () O f (x) has no real zeros O - 1 is a factor of f (z) Ne
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Please help, thank you! Graph the parabola. function button. Plot five points on the graph of the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a- 12- 10- X 5 ? 12 -10 8 -6 -2- 10 12 8- 12
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In this exercise we use the Distance Formula and the Midpoint Formula. If M (2,5) is the midpoint of the line segment AB and if A has coordinates(4,2), find the coordinates of B . ( x , y ) =

How do i do question 1 the a is what confuses me because shouldnt i multiply k with a but then that isnt what they are asking for, so what do i do when i have ay+k also how would i turn an eqatuino such as 2y+2=f((1/5)(x-1)) Workbook 3. 1 Lesson 3. Explore Your Understanding Assignment 3.1 This assignment includes 17 marks. You are expected to
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QUESTION 22 Forecasted room revenue calculations are based on the number of rooms available, the number of operating days, the average room rate and the forecasted occupancy. Calculate the room revenue (to the nearest dollar) using the data in the table below. Number of rooms Forecast Average Room available Rate Operating Days Forecasted room
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Count the number of measurements in the intervals x I s, x 1 2s, and x 1 35. Express each count as a percentage of the total number of measurements
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"Loudness" is measured in decibels. The formula for the loudness of a sound is given by "Db = 10log[ I / I 0 ]" where I 0 is the intensity of "threshold sound", or sound that can barely be perceived. How many decibels is a noise with an intensity of I = (9 * 10 10 )I 0 ?

7. Here is this week's Mathbucks problem, where we use the $ notation as if we were talking about real dollars. A certain game involves ipping 3 fair coins. The payoffs, from the player's point of View, are as follows ---n Each ticket to play the game once, is free! But you do have to decide, before the game is played, how many tickets you are
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12. 13. 14. The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $10. Find the probability that a random selected utility bill is between $85 and $125. (a) 0.0668 (b) 0.9938 (c) 0.5000 (d) 0.9500 (e) 0.9270 If 300 utility bills are randomly selected from this city, approximately how many of
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Problem 4. Some Audio Effects Apply each of the following MATLAB functions to both the sine wave and speech segments that you digitized in the previous section. Store your new signal to a .wav file using writewav and then play back the signal. Observe the effect of these digital manipulations on the audio properties of the signal. 1. The MATLAB
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15 the Stock Market independent? "the standard and Poor bUU (S&P 500) is a weighted average of the stocks for 500 large companies in the United States. It is commonly used as a measure of the overall performance of the US stock market. Between January 1, 2009 and January 1, 2012, the S&P 500 increased for 423 of the 756 days that the stock market
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Find the real and imaginary parts of the complex number. 4+7 i / 2

17. Look more closely at the simulated null distribution for the difference in proportions of yawners between the two groups. a. Is this null distribution centered around 0? Explain why this makes sense. (Hint: Think about the choice of statistic and about the null hypothesis, which was the basis of the simulation analysis.)
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Given this information , held Ting calculate the following investor rating : a. Earnings QET SHERE `. Price per Earnings C. Dividend Payout Ratio 4 . Dividend Yield Ratio
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2} An article was published concerning the incidence of cardiac death attributable to the earthquake in Los Angeles 0011th on January 17, 1994. In the week before the earthquake there were an average of 15.6 cardiac deaths per day in Los Angeles County. On the day of the earthquake, there were 51 cardiac deaths. a} What is the exact probability of
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Find the x - and y -intercepts of the graph of the equation. (If an answer does not exist, enter DNE.) y = x 2 3

Im so confused of this. Clear explain to me Let ((x) =3x2 -5x and g(x) = x2 - x + 2. Find (f + g)(x). (f -g)(x). (fg)(x), and (x). Give the domain of each. (1 +g)(x) =(Simplify your answer.) (1 -g)(x) =(Simplify your answer.) (fg)(x) =(Simplify your answer.) ()(x)=(Simplify your answer.) The domain of (f + g)(x) is (Type your answer in interval
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The equation V (volume [mL]) T (time [min]) x C (drop factor [gtts/mL]) = R (rate [gtts/min]) yields the IV flow rate for manually regulated IVs. Using this formula, calculate the IV flow rate (gtts/min) for the following provider order: D 5 LR 500 mL to be infused in 2 hours; drop factor = 10 gtts/min.

3. Predict and analyze sales for the next four weeks. a. Using your preferred linear model, predict sales for the next four weeks. Show your calculations. 13. Using these predicted values, compute the percent rate of increase (y2 y1)f y] for the next four weeks
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Overview To date we have learned about the primary pricing techniques covered in the FAR and the CPRG. What techniques can you use to accomplish this group assignment? Your task is to review the price proposals received in response to a solicitation for Medical Physical Examinations. To accomplish this we are providing you with the following
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Ifacy has a cell phone plan that provides 250 free minutes each month for a flat n of $29. For any minutes over 250, Tracy is charged $0.35 per minute. Which of the following piecewise functions represents charges based on Tracy's cell phone plan 29,$250 | 29 +0.35x, >
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Initial Investment outlay of $30 million, consisting of 325 million for equipment and 35 million for net working capital (NVC ) (plastic substrate and Ink Inventory ), NV recoverable in terminal year Project and equipment life: 5 years Sales: $25 million per year for five years Assume gross margin of 60% (exclusive of depreciation) Depreciation:
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Solve for x. 7(x + 4) = 9(x - 2) Group of answer choices infinite number of solution 3 11/8 23

31 . Selection of an inventory cost formula by management should be influenced most by the A. fiscal year end . B. physical flow of goods . C. goal of reporting inventory at its lowest cost . D. income tax effects
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Fall 2111 3 Quantitative Methods For Business [ms'r 50-100] Assig nmen I'.-2 1} A gardener can use one of me three brands of Fertilizers during the next growing season. The following decision table shows the expected gross income per acre for each fertilizer brand and weather condition for the growing season. The chance of a drjir season is shown
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UseDescartes' rule of signsto help list the possibilities for the nature of the solutions for the equation. Do not solve the equation. (Select all that apply.) 3 x 3 5 x 2 +5 x +4= 0 1 negative and 2 nonreal complex solutions 1 positive and 2 nonreal complex solutions 1 negative and 2 positive solutions 1 positive and 2 negative solutions 3

Simon runs on a 5 mile path several times a week.Since he is just beginning this exercise program, he runs part of the way and walks the rest of the way.Simon's running speed is 7mi/hr. and his walking speed is 5 mi/hr.Write an equation to represent Simon's exercise program. The equation should be inslope-intercept form

# A. Mr. Smith , an avid reader , must decide on which books to take with him during a long flight . Mr. Smith will use his carry - on bag , which can hold a maximum of 20 pounds . Mr. Smith has attached a satisfaction index for each book , based on a 5 - point scale ( 1 = low satisfaction , 5 = high satisfaction ) , as shown below . Book
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2. How did shifting product market conditions affect Corning's restructuring and its success ? Th rotoo
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Find the 100th and the nth term for each of the following sequences. a. 1, 7, 13, 19,..... b. 70, 120, 170.... c. 1, 4, 16,..... d. 9, 9 3 , 9 7 .... e. 127+52 31 , 127+62 31 , 127+72 31

Question 18 Measure the slope angle at point Y on the topographic profile in with your protractor. The slope angle at Y is a. just under 1 degree. b. just under 5 degrees. c. just under 30 degrees. d. just under 45 degrees. e. just under 60 degrees. Question 19 Based upon the slope angles just measured and the provided scale in the figure above,
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a) You put $300 per month in a savingsplan that pays an APR of 3.5%. How much money will you have after 18 years? b)How much of that is interest? Round to nearest tenth

What happens if we graph both f and f -1 andon the same set of axes, using the x-axis for the input to both f and f -1 ? Suppose f : R > R is a function from the set of real numbers to the same set with f(x) = x+1 . We write f 2 to represent f f and f n+1 = f n f . Is it true that f 2 f = f f 2 ? Why? Is the set {g: R > R I g f = f g} infinite?

Weight Weight Small Stock and Bond Portfolio Large Stock and Bond Portfolio Stock Bond SD (Ret) Expected Ret. SD (Ret) Expected Ret. 0.9 0.1 0.8 0.2 0.7 0.3 0.6 0.4 0.5 0.5 0.4 0.6 0.3 0.7 0.2 0.8 0.1 0.9 0
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28. Find the rejection region at 0: = 0.05. (a) Rejection region: 2 > 1.96 (b) Rejection region: z 1.645 (d) Rejection region: 2 1.645 29. Find the pvalue of this test. (a) 0.0011 (b) 0.025 (c) 0.10 (d) 0.05 (e) 0.9989
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1. Problem 3.12 (page 158, tsa4): In the context of equation (3.63), show that, if y(0) > 0 and y(h) -+ 0 as h - co, as h - 0, then I'n is positive definite (for every n). Proof: Without loss of generality, we assume EXt = 0. Suppose I'n is singular for some n. Then there exists an integer 1 k, Xn can be represented by a linear combination of the
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Summarize the strategic hints for problemsolving, and give an example of the meaning of each one. Which of the following best summarizes the strategic hint"There may be more than oneanswer" and provides an example of themeaning? A. Every problem in mathematics has more than one answer. Forexample, both x equals 2 x=2 andx equals negative 2 x=2 are

Use the following problems to answer questions 6 8 Of 2,000 students surveyed, 85% indicated that they commute to school each day. Of those that commute to school each day. 88% spend more than $25 a week on gasoline. Of those that do not commute to school each day, 95% indicated that they do not spend more than $25 a week on gasoline. A student
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The city of Plainview is building a new sports complex. The complex includes eight baseball fields, four soccer fields, and three buildings that have concessions and restrooms. Arrange the structures in the sports complex using translations, reflections, and rotations so that the final arrangement satisfies each of these criteria: . All the fields
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Draw the EER diagrams for the following problems using JAIL notation , Crow's Foot notation and Chen notation ." 1 . A bank has three types of accounts : checking , savings and loan . Following are the attributes* for Each type of account . CHECKING . Acct KO, Date Opened , Balance . Service Charge SAVINGS : Acct NO, Date Opened, Balance ,
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What is the equation of the line that passes through the point (-5,2) and has an undefined slope?

1. Use algebra tiles to multiply (x-1)(3x-2). 2. Can every expression be factored? Build and sketch each expression below as a rectangle if possible. Then write an equation showing that the area is is equal to the product of its side length factors. Check by multiplying the factors to get the original expression. if the expression cannot be built
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Compute the probability of drawing a King or a heart from a deck of cards.

Qo quantizing distortion decreases with the number of quantizing levels available. There is usually a price to be paid for such an option. What would this be ? Was that apparent in the present experiment ? Explain
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Part II : How much in total would Jaden pay per month for the first two years of the mortgage ?" Part II1 : What is Jaden's monthly salary ? Part IV: What is a quarter of Jaden's monthly salary? Part V. Can Jaden afford the house he is considering buying ? Why or why not ?"
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A MildlyTALLLITTLE CILILL'S`` WILLL LLLL`LATILL THIHILL ~ HILLLILES PHILAGLIETTIEATS IN THE DATA. What percentage of production does not meet the acceptance limits ! None of the other answers are correct 0. 46% 0. 67 9/6 0. 14%6\\ 0. 8196
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An investor wants to save money to purchase real estate. He deposits $ 1500 at the end of each year in an ordinary annuity that pays 9% interest, compounded annually. Answer each part. Do not round any intermediate computations nor answers. If necessary, refer to the list of financial formulas. (a) Find the total value of the annuity at the end of
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I L" 12} '11} 1.3! ii} I '' '12 1 1 1} R1! | 2D. "What is the smallest number of times you would need to toss a fair coin in order to he sure of having probability at least .9 of ton-ting at least one head
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You have seen that there are two states for each of the inputs and outputs in a digital logic, either on or off, logic high or logic low, and 1 or D. Obviously, if we want to add two \"digital numbers\" together, each of them could only he either 1 or t}. This leads to 4 input combinations, i.e., [II and t}, t] and 1, 1 and t}, or 1 and 1. The
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Set up the equation but do not solve. For $7.52 you purchased 8 pens and highlighters from a local bookstore. Each highlighter cost $1.09 and each pen cost $0.69. how many pens did you buy?

Fart Ill : If wyatt refinances. the balloon payment with another 30 -year fixed- rate mortgage with an interEs! rate of 5 . 4{` , what will be his new monthly payment ?" Fart MY _ If watt refinances the balloon payment with another 30- year fixed - rate mortgage with an interest rate of 5. 4{` , how much will he have paid in total for his house
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Gonzalez Manufacturing borrowed $42000. Part of the money was borrowed at 10%, part at 12%, and part at 14%. The annual interest was $5080, and the total amount borrowed at 10% and 12% was twice the amount borrowed at 14%. Use Gaussian elimination or Gauss-Jordan elimination to find the amount borrowed at each rate.

A nutritionist 1n the EDA wants to compare the caloric content or medium rrencn tries sold by Wendonald (Population 1) and McKing (Population 2) fastfood chains, to see if there is any difference between them. To test this, random samples from each chain is taken and the caloric contents of french fries are measured. Their nding is summarized in
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3. A basketball player makes each free throw with a probability of 0.75. What is the probability that he makes no fewer than 65 of 75 shots
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55. Write a query to display the book number , title , subject , author last name , and number of book's written by that author . Limit the results to book's in the " [LOL SUBJECT . Sort the results by book title and then author last name . BOOK HUM\\BOOK TITLE BOOK SUBJECT ALL LNAME HUM BOOKS by Author 5246 Capture the CLOUD CLOUD 524 4 Cloud -
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3. In a crosssectional study, 9,000 people were identified as the source population, and 6,000 agreed to participate. The distribution by exposure and disease status is shown below for both groups. Source population Study population a} What is the most appropriate relative measure of association to use in this study? b} Comparing the study
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(b) State a linear function g(x) that represents Company B's total charge for an order o
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The greatest integer function, shown below, is defined so that it produces the greatest integer or equal to x. f(x) =[x] 1.02 Quiz: Graphing Functions Pool 6 Question 6 (2 points) Given the piecewise function shown below, select all of the statements that are true. 2x , X 1 (21=4 1751 -1 TA-21=4
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Question 6 . 6 . You have just graduated from college and have been offered your first job . The following table gives the salary schedule for the first few years of employment . Bonuses are* not included . Let v represent your salary after * years of employment . Year of Employment , x Salary , Y ( $ ) O 29, 125 31 , 100 2 33, 075 Write the
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8. Can you use polynomial tting to find the formula for the nth term of the sequence 4, T, 11, '18, 29, 47, . . . ? Explain why or why not
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Related topics: Tutte's theorem, Optimal and pessimal stable matchings, type-O graphs. Lemma's that can be used- 1. Let G be a graph satisfying Tutte's condition. Suppose Gis a subgraph of Hwhere V(H)=V(G). Then Hsatisfies Tutte's condition. 2. If G is Type-O and satisfies Tutte's condition, then G has a perfect matching. Let k be a positive
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Year 1 Year 2 Sales $320,450 $542,052 Equipment and leasehold improvements $16,000 $16,000 Opening inventory (ice cream) $100,000 $0 Training and other administrative costs $25,000 $0 Variable costs $232,006 $392,446 % of sales 54% for ice cream and 68% for retail 54% for ice cream and 68% for retail sales sales
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