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Mathematics Questions and Answers October 07, 2021

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The distance calculated from Virac, Catanduanes to San Diego, California by great circle sailing method was 6307.76 miles. M/V Maynila had a maximum speed of 11.25 knots. Approximately, (a) how many days and hours will the vessel cover the distance? (b) If the vessel leave Virac at 2300H on December 30, 2020, what time and date would she arrive in

The local Piggly Wiggly grocery store uses self-serve check-out counters which allows customers to check out on average in 5 minutes. The store is willing to add more self-serve check-out counters if the actual time to check-out is less than 5 minutes. The store takes a sample of 56 self-serve check-out customers and determines that average check

(7) Your employer offers a 401(k) plan with a 23% match, and you set a goal of retiring in 29 years with $888,208 in your account. If the account earns an annual interest rate of 5%, how much should youcontribute each month? This is a future value annuity problem. To solve it we will use the future value annuity equations FV = (PMT)(sn|i) and sn|i

((3) Consider the following system of linear equations1 where o: is a constant :1:+(o:5]y=0 (or5):I:+y20 Find the 1values of o: for which the system will have a non-trivial solution (i.e., in- nitely many solutions)? [2]
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Questions- 1)Clearly state your estimated conditional expectation function (sample regression line).Note that you do not need to estimate your equation manually, but rather you should simply write down your sample regression line using the estimated intercept and coefficient of X given in your summary regression output from Excel.2)With reference
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TB MC Qu. 13-39 (Static) A researcher with the Ministry of... A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each

Find a power series for the function, centered at c. g(x) 4X x 2 + 2X - 3 C =0 n =0 Determine the interval of convergence. (Enter your answer using Interval notation.) (-1, 1 ) Need Help? Read Watch I" Talk to a Tuter
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Question 2 2 pts Iron (III) oxide forms according to the following reaction: 4Fe + 302 - 2Fez03- What mass of FezOg is produced from 7.0g of Oz? O 0.15g O 6BE O 0.023g
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Formulated for the demands of professionals, Diamond Vogel Architectural Coatings offers a full range of architectural and heavy-duty protective coatings that are right for your project. Suppose that a paint supply general dealer wanted to estimate the correct amount of paint contained in five-litre cans purchased from Diamond Vogel Architectural
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Questions shows in pictures B Assignments - Mathematics 20-1 x 3 Microsoft Word - Week 12 Assign X Microsoft Word - Week 12 Assign X * Homework Help - Q&LA from Onl X + X - C File | C:/Users/z2427/Desktop/Week%2012%20Assignment%20(1).pdf ii Apps Reading list Microsoft Word - Week 12 Assignment 1 / 3 - 100% + Math 20-1 HUB - Week 12 Assignment 1.
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Fill in the blank with the correct conjugation of the word in the parentheses next to the blank Esta tarde, Juan va a mi casa. Primero, nosotros vamos a estudiar (to study) para el examen de espaol. Mi mam _________ (to cook) pasta para todos, ella cocina muy bien. Mis hermanos no _________ (to eat) con nosotros porque ellos tienen la prctica de

Three young trees are planted one by one randomly and independently along the same street of length 10m. (a) (4 points) Find the expected distance from the left end of the street to the tree which is closest to that end. (b) (4 points) Find the expected distance from the left end of the street to the first planted tree given that that tree is

In an ANOVA to examine a main effect, one: Select one: O a. Examines one interaction at a time. O b. Temporarily ignores one way that the participants were classified while examining the results of the other way they were classified. O c. Looks at all effects simultaneously. O d. Examines both ways participants were classified at the same time in

Find the following product. left parenthesis negative 10 right parenthesis left parenthesis negative 1 right parenthesis

MATH 140 EXAM 1 NAME________________________ Professor: Dr. J. Beyers INSTRUCTIONS The exam is worth 100 points. There are 20 problems (each worth 5 points). This quiz is open book and open notes, unlimited time. This means that you may refer to your textbook, notes, and online classroom materials. You may take as much time as you wish, provided

The following tasks are all done under 95% confidence or a 5% P -value requirement. Use theTornadoesData and your statistical expertise to answer the questions: Is it reasonable to claim that there are more tornadoes in April than in August? 1. What test/procedure did you perform? a. One-sided t-test b. Two-sided t-test c. Regression d. Confidence

1. Para qu les dio la carta Nuria a Selena y a sus amigos? para que eligieran sus platos para que se sienten para que paguen la cuenta 2. Qu pidi Selena? ensalada con tomate y atn ensalada con tomate y pollo asado hamburguesa con papas fritas 3. Qu les trajo Nuria muy rpido a los amigos? los refrescos los platos la cuenta 4. Cul fue el mejor plato

Kim is carrying five pages of math homework and five pages of English homework. A gust of wind blows the pages out of her hands and she is only able to recover seven random pages. What is the probability that she recovers at least four pages of her math homework? Use combination and/or permutation formulas: nCr/nPr

i am having issues with this Do not write solutions on this page. Section B Answer all questions in the answer booklet provided. Please start each question on a new page. 5 [Maximum mark: 13] Let f(x) = 25in(3x) + 4 for xeR. (a) The range of f is ksx) Sm. Find k and m. [3] Let g(x) = 5f(2x). (b) Find the range of g. [2] The function g can be
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Find the x-coordinate of the point on curve y=ln(3x 2 -4x) where the tangent line is horizontal. Just enter the number rounded to 4 places.

QT: Let A be 3. 511:] by 500 matrix, where :11,- = 255 and HLUHJ = adj for i Z:- I and any 3'. Determine the value of {313,39 and (113,14. 3.) 313.30 = 2 and Guns = 13 13:] [113131] = ED and 1110,15 = 30 '3) 513.31] = '30 and 310.15 = 29 {21:} [11313:] = 13 and (2513,15 = 15
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4. B Given that AACB-AWZY, which of the following could be used to solve for x? A 7 X 17.5 20 1 15 7 20 17.5 20 b 20 17.5 15 15 7 17.5 20 17.5 5. C Which pair of triangles below are congruent? E (c) D A A C D
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Problem 6.6 Show that f is a convex function- 3For easier notation, we use (3,50 instead of (31,12). 10 Next, we impose two constraints
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(1 point) For the differential equation dy dx = Vy2 - 1 does the existence/uniqueness theorem guarantee that there is a solution to this equation through the point ? v 1. (-4, 7)? ? v 2. (-8, 3)? ? v 3. (-3, -1)? ? v 4. (-7, 1)
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Name: Math 95 MTWR 8am Quiz 5 Due: 4/6/2023 by 11:59pm Directions: Show all work for credit an answer without work will be a zero. Record final answers on the blank provided. Homework Problem #23 from 11.3 p.692 (5 points): 23. Simplify. Assume that all variables represent positive real numbers. 354 Homework Problem #83 from 11.3 p.693 (5 points):
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Macmill X B Chapter X B Chapter X Macmill: X Manzan X G Give me X M Sent Ma X My Driv X Manzan X Manzan X Edready X Course X C cpcc.edready.org/assessment/retakeTopic?assessmentld=76016&groupld=93218&studyPlanTopicld=61269648&continue=false G M Apps i CP Links Descriptive Essay... Reading List 15 CENTRAL PIEDMONT EdReady Manzanza Lutuangu
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A researcher wishes to determine whether there is a difference in the average age of middle school, high school, and college teachers. Teachers are randomly selected. Their ages are recorded below. Find the test statistic F to test the hypothesis that there is no difference in the average age of each group. Use a = 0.01. Middle School Teachers
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A E D F B G H V
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My lucky numbers has always been 6,14,20,16,28,3, how did you land on those numbers, and did you believe that those numbers were more likely, less likely, or as likely as all other numbers to occur

- 11 3 Consider the differential equation. "+ 17x ) dx + (In(x) - 16) dy = 0, x>0 (a) Determine whether the given equation is exact. The differential equation is Choose one (b) If it is exact, solve the differential equation. NOTE: Write the solution in implicit form as y(ry)=C There is General solution: = C no solution (c) Use technology to draw
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6. (a) Suppose : RR is a differentiable function defined implicitly: where c E R. Carefully state the implicit function theorem as it applies to (x) . (b) Consider the special case where(T) is defined by: and C = 4 Use the implicit function theorem to determine whether 2 can be expressed as a function of 1 around the point " = (0 1). What is the
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Please solve. 8. Generate a counterexample (graph or formula) and use it to explain why the statement below is false. Suppose f is defined on a closed interval [a, b). If u is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c) = u
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A geometric sequence, has a common ratio of 2 and first term of 1/3? a. Write the first 4 terms of the sequence. b. Write an explicit rule for the sequence. (Identify the key data before you write the rule) c. Write the recursive rule for the sequence.

In a study at a large hospital the researcher wants to assure that male nurses are adequately represented. At this hospital 5% of the nurses are male. The researcher separates the nurses into female and male hats. He draws 95 female names and 5 male names. This is an example of: Select one: O a. Simple random sampling. O b. Stratified random

For better interpretability you would like to have some additional graphics with your results. What PCA function would you select

Question 1 You have been engaged as a consultant to your organisation's/Catanza executive to consider the information presented. You are asked to apply decision analysis techniques to the decision problem facing your organisation/Catanza Technologies and advise the company on their outcome options and recommended course/s of action. Clearly state

Please solve on paper and then upload and explain and be clear everything thanks! 1 Let u = 2 and v = 2| . Show that among all the scalar multiples cy of the 4 vector v, the projection of u onto v is the vector closest to u, that is, show that d(u, pro u) is a minimum
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Only to be done in R studio, and not in excel. Problem 1. Download the data set salary-class.csv URL http://safetekllc.com/wp-content/uploads/2020/09/Salary-Class.csv . This data set (drawn from census data) will be used to predict whether a person has income more or less than $50K (this is 1990 data). The fields are as follows: AGE: Age of person

An art dealer uses the following probability model to predict the selling price of a famous painting at the next auction. \f
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Hello, can someone solve and explain this problem to me? Let X1, X2, X3 be i.i.d. Binomial random variables with parameters n = 2 and p = 1/2. Define two new random variables Y1 = X1 - X3, Y2 = X2 - X3- We further introduce indicator random variables Z; E {0, 1} with Z; = 1 if and only if Y; = 0 for i = 1, 2. Calculate the covariance of Y1 and Y2.
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Can you show me how they get this answer? A forest management service wanted to determine the volume of a certain Which of the following is the predicted volume of a tree with a 40-inch species of pine tree from only its circumference. A scatterplot of the relationship circumference? between circumference in inches, x, and volume in cubic feet, y,
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4. Give the definition of duration and convexity of a bond and write the relationship between the change in yield and the bond price
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Create a class diagram that shows the structure of the classes with the appropriate relations. The goal is to end up at a design level class diagram, but it is a good idea to create an analysis level diagram first. Feel free to add this analysis level diagram to your submission. Classes should of course be named, have relevant attributes (fields)
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Please figure this out. I need it quickly. Let S be a subset of IR" that contains n + 1 vectors. Can S be a basis for IR"? Please justify your reasoning
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Please help on this homework 7. Let :9 = (61, . . . , 6p) ' denote the random parameters, the likelihood function is p(:1:|6), and the prior is MB). (a) (3pts) Why do we use MCMC to summarize the posterior distribution for SIX? For instance, what other options are available for summarizing the posterior and what, if any, are the relative benets of
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write note on these topic. i- What do you understand by estimation? ii- What do you understand by a population in statistical sense? iii- What is the need of sampling as compared to complete enumeration? iv- Define the term statistic. v- Is the systematic sampling superior to simple random sampling and stratified sampling?

Previous Page Next Page Page 22 of 23 Question 22 (2 points) Below is a scatterplot of two quantitative variables: amount of particulate in rainfall and daily rainfall amounts. Amount of Particulate vs Daily Rainfall Amounts 160 140 120 Amount of Particulate 100 y = -6.324x + 147.91 R= = 0.9578 80 60 40 20 0 5 Amount of Daily Rainfall Calculate
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Question 2 I PLS What does the term "extrapolation" mean for regression problems? O switching the dependent and independent variables O making predictions outside of the range of the data that has already been collected O making extra guesses O making predictions within the range of the data that has already been collected
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[(1) Determine the reactions atA and E if P = 1000 N. The reactions are positive if to the right or up, negative if to the left or down. [bl What is the maximum value which P may have for static equilibrium? Neglect the weight of the structure compared with the applied load 5. Answers: [a] lfP= 1000 N, n l~ \"mummmm. "
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I HAVE ONLY 10 minutes to answer this question, please help me Question 11 15 points Save Answer Janie is buying a used car for $7950. She has two options for financing. Option A is a 4.5% annual simple interest for two years. Option B is 3.20% annual simple interest for eighteen months. (15 pts.) a. Using the simple interest formula, calculate
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29,30,36,37,38 (-3, - 1)7 -2 proposed water pipe 28. MODELING WITH MATHEMATICS A parks and a. Did one of the students pay a greater registration recreation department is constructing a new bike path. fee? Explain. Mathem The path will be parallel to the railroad tracks shown and pass through the parking area at the point (4, 5). b. Did one of the
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A Two functions are shown. y = f (x) is the function on the left and y = aflb(x -c)] +d where a =1, b,c,d >0, a transformed version of y = f (x), on the right. The values of b, c, and d in that order are
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You deposit $ 274 each month into an IRA earning 6.4 % interest compounded monthly.How much will you have in the account in 17 years? $__________(Round to 2 decimal places if necessary)

How would you summarize this article? Then add your own thoughts under the summary? Mackus et al. hangover cure. Using the same test. these variables were also compared between those who state they would consume more alcohol when an effective hangover treatment was available. those who do not know. and those who state that they would not consume
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A clothing company determines that its marginalcost, in dollars perdress, is given by the function below. The total cost of producing the first 200 dresses is $8600. Find the cost of producing the 201st through the 280th dress. C'(x)= 2/25x+51, x <630

(Please show your work for full credit.) 1. Parabolic cylindrical coordinates are defined in terms of the variables (u, v, z), where x = 1 2 (u2 v2), y = uv and z = z. Let f (u, v, z) be a scalar field in terms of the new variables and F = F1 uu + F2 uv + F3 uz be a vector field in terms of the new variables and unit vectors. (a) Find the scale

If r = .9, sY = 10, and sX = 5, what is the slope b of the regression line?

The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a Normal distribution. This distribution has a mean of 62 and a standard deviation of 5. Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 47 and 72? Do not enter the percent symbol. ans

Please provide with full answers and explanations, thanks! Prove that if a transformation has a range space isomorphic to its null space, then the dimension of its domain is even.

The earth's modern atmosphere evolved approximately: Question 2 options: 540,000 years ago, in the middle of the Pleistocene Epoch 5,400,000 years ago, at the end of the Miocene Epoch 540,000,000 years ago, at the end of the Precambrian Eon

4. Let ? be the sample space of a two coin toss experiment. Suppose our o-algebra is given by F = 10, 0, {HH, TT} {HT, TH} }. Let the functions X : 0 - R and Y : 0 - R be defined by 1 if we {HT} 1 if we {TH}, X(w) = 0 if we {HH, TT, TH} Y(w) = 0 if we {HH, TT, HT} a. Is X a random variable? why or why not? b. Is Y a random variable? why or why
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Find the domain and range of the relation. Use interval notation where appropriate. Express numbers as decimals. Part 1 01'2
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Which of the following graphs are bipartite? T A. P U H B. R N S U T F E C. G H I U D. R H Y
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The sampling distribution of the sample mean is the probability distribution of all Multiple Choice the sample statistics and their probability of occurrence the possible sample means of a given sample size the possible sample means for all sample sizes the sample means Incorrect Next

Fomentar la elaboracin de normas en todo el mundo para facilitar el intercambio intencional de bienes y servicios, y para desarrollar un entendimiento mutuo en las esferas intelectual, cientfica, tcnica y econmica es: Pregunta 1Respuesta a. El propsito de la DGN b. El objetivo de ISO c. La funcin de la SECOFI d. El objetivo de OSI

Scientist have repeatedly stated that the earth's temperature has changed since industrialization. Throughout history the earth's mean temperature has been 50 degrees. For the last 40 years the mean temperature has been 51 degrees with a standard deviation of 2 degrees. Using a .05 significance, test the hypothesis that the earth's temperature has

solve the following Let I be the set of all ordered pairs of real numbers. Check whether I is a vector space over R with respect to the indicated operations. If not, state the axioms which fail to hold. (i) (a, b) + (c, d) = (a+ c,b+d) and k(a, b) = (ka, b) (ii) (a, b) + (c, d) = (a, b) and k(a, b) = (ka, kb) (iii) (a, b) + (c, d) = (a+ c, b+d)
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A probability experiment is conducted in which the sample space of the experiment is S equals= {8,9,10,11,12,13,14,15,16,17,18,19} , event F equals F={8,9,10,11,12} , and event G equals G={12,13,14,15} . Assume that each outcome is equally likely. List the outcomes in F or G. Find Upper P left parenthesis Upper F or Upper G right

I need help. Thanks ANOVA Problem 01 d The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons pere year, expressed as 002 equivalents. Use a.025 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions.
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I could really use some help with completing the problem. the data needs to be input in excel or vssart and then answer the questions provided. the problem- A counselor working with people who are developmentally disabled has read research relating accurate responses to the type of reinforcement they receive. For three weeks, the counselor

After 8:00pm on any Thursday, the amount of time a person spends waiting in line to get into a well-known pub is a random variable represented byX X. Suppose we can model the behavior ofXwith the Exponential probability distribution with a mean of waiting time of 45 minutes. It has been 30 minutes since you entered the lineup to get into the pub,

Question 1 2 pts Ammonia (NHg) is produced by the reaction of nitrogen (N) and hydrogen (H) according to the chemical equation N,+ 3H> > 2NH;. How many moles of nitrogen are needed to react with 4 moles of hydrogen? O 3.0 mol Na 1.3 mol Na O 1.0 mol Nz 0 0.75 mol N2 O 12 mol N2
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The Aggression Escalation Continuum has a number of stages. How many will an individual go through

,,,,,7 7,7, *****5* ,nnuiin, 7,,i, * 7,,ii, iniid, * ,,,,,, Answer ALL Questions. Work must be shown to receive full credit. Question #1: Consider the quadratic function: f (x) = x3 2x +3 . a. Without graphing the function. state whether the function opens upward or opens downward. [3 pts] b. Find all x i and y * intercepts of the function above.
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I. Weekly consumption: Bottles/cans/glasses of imported or domestic beer consumed during the previous week. II. Age: 1. Under 22 2. 21-24 3. 25-29 4. 30-34 5. 35-39 6. 40-45 7. 46 or over 8. Missing values replaced with 4
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l) A sociologist is curious if the poverty level of children in large cities can be predicted with a linear model based on the city's crime rate. Load the data into Stata using the command use http : I 3' people . fast . harvard . eduj~mparzenfstat14fpoverty . cite :1) Using Poverty as the \"Y" variable and Crime as the \"X\" variable, create a
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question in picture IS school portal Browse - Soft Whit.. APA Cita Je Sunday by 11:59pm Points 33 Submitting Test # 8 - Final Exam Score: 2/33 4/33 answered X Question 7 Next question You can retry this question below Express - 9 + -100 as a simplified complex number -9+ -100 Submit Question O
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(b) Suppose 5 people have been selected. How many different batting orders are possible
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Puzzles for Practice Let A, B. and C be subsets of X. Determine if the following are true or false. If false, give a counter example. If true, give a proof. It may help you to draw some Venn diagrams to get an idea of why the statement may be true/false. 1. ACAUB 2. If CCAUB, then AnB C C. 3. If AUCC BUC, then A C B. 4. A C B if and only if Be CAC
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Tried using MATLAB (which I'm not extensive in but the help section helps me manage) & I got an answer different from the online differential calculator, just wondering if I could have some help on this question, thank you! Edit: this problem uses the variation of parameter method, where y = y(homogenous) + y(particular); with initial condions
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Consider this sentence: "To earn an A in the course, it's necessary for Daniel to score 80 on the final exam." Which of the following would be the best SOA (scheme of abbreviation) for the antecedent? O N: It's necessary for Daniel to score 80 on the final exam. O D: Daniel O A: To earn an A in the course. O D: Daniel earns an A in the course. A:

A chef buys frozen French fries in boxes containing 6 bags. Each bag weighs 2.5 pounds. Each box costs the chef $12.64. The chef serves French fries in 3 ounce portions. What is the chef's cost per portion for frozen French fries? Please round your answer to the nearest cent

For the rational functionx^2+5x+6/x^2-9answer the following questions: a. Find the horizontal asymptote if any. b. Find all vertical asymptotes. Are there any holes, if yes, explain. c. Write the domain in interval notation. d. Solve the rational inequality and graph on a number line for(x-1)(3-x)/x-2^2 0

You deposit $ 126 each month into an IRA earning 1.1 % interest compounded monthly.How much will you have in the account in 22 years? $__________(Round to 2 decimal places if necessary)

2. A researcher has a collection of 3" pea plants, 4 radish plants and 3 corn plants. She wishes to select a sample of 4 plants In how mam,r ways can this be done if: {a} there are no restrictions
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A function h(x) is defined in terms of a differentiable f(x). Find an expression for h'(x). f(x) h(x) = 3 X +6 h'(x) =
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d) The work done by F = 6\" sin yi + BI cos yj moving an object from through a path from (3, 0) to (U, 3)
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Draw a parallelogram having two of its adjacent sides represented by the vectors v = [5, -2] and w = [4, 1] with their initial points at the origin. Let u be the vector whose initial point is at the origin and that corresponds to one of the diagonals of the parallelogram. What are the coordinates of u? U = L
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(a) Solve the linear system of differential equations d_3: so + dt _ g If dy _ = 4 m+y with initial conditions 33(0) = 1, y(0) = 1. (8 marks) (b) Solve the differential equation with initial conditions y\"8y'+16y=0, 29(0) =b+1, y'(0) =b-1 for y(t), where b is a given real number. (6 marks) (0) Let B = {23225695}. (1) Show that B is linearly
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question shown as follow. 2. Suppose it is relatively easy to sample from the distributions Fi (x), i = 1, ..., n. If n is small, how can we sample from F(x) = Et_, PiF:(x), P: 2 0, Et_ Pi = 1. b. Give a method for sampling from - e-2x + 2x 3 0
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Riverside Bank wants to appear competitive based on loan rates and thus must offer a 7.95% annual percentage rate on its loans. What is the maximum rate the bank can actually charge based on the quoted rate? In other words, if they compounded your interest continuously? Group of answer choices 7.87 percent 8.21 percent 8.27 percent 8.14 percent

9. A phone company offers two options. The first plan is an unlimited calling plan for $34.95 a month. The second plan is a $20.95 monthly fee plus $0.04 a minute for call time. a) When is the unlimited plan a better deal? b) Graph the situation to confirm your answer from part a)
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I need help with this. thanks Perform a Goodness of Fit Using Numerical Data 01a Randomly selected birth records werea
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A new marxist / libertarain Scale has scores between 0 and 30 (0 being very marxist,, 30 being very libertarian). The mean score is 21 and standard deviation of scores is 5. You want to convert the original scale (we will label it "Y") to a new scale (we will label it "Z") that has scores between 0 and 100. What is the standard deviation and mean

Nikolay wants to make annual contributions to his RRSP for the next 25 years. He will increase each annual payment by 4.5%, and the RRSP can earn 9.3% compounded annually. If he wants to accumulate $250,000, what is the amount of his first payment today? 2. If $2,500,000 was invested at 4.8% compounded semi-annually, what payment at the end of

Which of the following has the same solution as this system of equations? 4x + 9y = 10 2x + 3y = 12 A 4x + 9y = 10 B 4x + 9y = 10 4x + 3y = 24 2x + 9y = 36 C 4x + 9y = 10 D 4X + 9y = 10 4x + 6y = 24 2x + 9y = 12
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1 point(s) possible Perform the indicated operation. Leave the result in polar form (20 /2419) (2/850 100 /262 (20 /2410) (2/85 100 /262 (Simplify your answers. Type integers or decimals rounded to two decimal places as needed. Type your answer in degrees Use angle measures greater than or equal to 0 and less than 360.)
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Quiz 5 Started: Jun 10 at 9:21pm Quiz Instructions D Question 1 2 pts Encrypt the following word with a key of 3: travel
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QUESTION 6 Tukey's decision rule, when a p-value =.3 and testing at the .05, means that the hypothesis should be accepted. True False
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what an artists should be looking for as they start to craft a character and performance. Your experiences in creating etudes may support your practical understanding of these principles, but also may have raised questions. In a short reflection, discuss the challenges you see yourself having while developing a character in performance. What

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