Mathematics problem solving

1) Prove: If 3x+5 is irrational then x is irrational. [3] 2) Prove: If a|c and b

1) Prove: If 3x+5 is irrational then x is irrational. [3] 2) Prove: If a|c and b|c then ab|c^2 [3] 3) List 6 numbers congruent to 8mod5 [2] 4) Given: n,m,a,b are all integers and …

1) Purpose Statement “The dependent variable _______ is determined by independen

1) Purpose Statement “The dependent variable _______ is determined by independent variables ________, _________, ________, and ________.” In one paragraph, state the correlation a…

1) Random samples of size 1,600 are drawn from a population in which the proport

1) Random samples of size 1,600 are drawn from a population in which the proportion with the characteristic of interest is 0.05.   The sample size is large enough toassume that th…

1) Random samples were selected from two independent populations - 160 observati

1) Random samples were selected from two independent populations - 160 observations from population 1 (dual degree students) and 140 from population 2 (management only degree). It…

1) Recall that we discussed one of the tallest men who ever lived, Robert Wadlow

1) Recall that we discussed one of the tallest men who ever lived, Robert Wadlow. The equation that approximates the relationship between Wadlow's age and height is h 2.6a+51, whe…

1) Recently, a group of students was interested in the different factors that in

1) Recently, a group of students was interested in the different factors that influence people to pet walked dogs. They compiled a list of all possible time slots between classes …

1) Record the following for your histograms for length and width. (For each numb

1) Record the following for your histograms for length and width. (For each number of measurements, enter an integer.) a) number of measurements within 1 standard deviation from t…

1) Reduce ((n + 1)!)/((n - 2)!) 2) Evaluate the sequence 1(1!)+...+2(2!)+...+n(n

1) Reduce ((n + 1)!)/((n - 2)!) 2) Evaluate the sequence 1(1!)+...+2(2!)+...+n(n!) for n=5 3) If you are given a sequence function f(n) = 4n-1, find the recursive sequence that wi…

1) Regarding the ImPACT example, how many athletes studied were not in fact conc

1)Regarding the ImPACT example, how many athletes studied were not in fact concussed? 2)Regarding the ImPACT example, how many athletes studied did the screening test fin to be co…

1) Researchers claim that the mean body temperture of healthy adults is differen

1) Researchers claim that the mean body temperture of healthy adults is different from 98.6 F. In order to test this claim researchers collected sample data from 100 individuals. …

1) Researchers recorded the temperatures at Castleton Square Mall in Indianapoli

1) Researchers recorded the temperatures at Castleton Square Mall in Indianapolis in November and December 2014, then again in April and May 2015. For these same days, they record…

1) Respond to question of probability. Write only a number as your answer. Round

1) Respond to question of probability. Write only a number as your answer. Round your answers to 4 decimal places. Do not write as a percentage. A) The weights of bowling balls ar…

1) Respond to question of probability. Write only a number as your answer. Round

1) Respond to question of probability. Write only a number as your answer. Round your answers to 4 decimal places. Do not write as a percentage. A) The weights of bowling balls ar…

1) Rewrite the given function in the form acos(4x) + bsin(4x). Enter the missing

1) Rewrite the given function in the form acos(4x) + bsin(4x). Enter the missing coefficients as decimals accurate to within 0.001. 4sin(4x + 1.77) =       ______cos(4x) + ______s…

1) Rick’s Toy Store faces the following probability distribution of fire losses

1) Rick’s Toy Store faces the following probability distribution of fire losses in its store over the next year: Probability Loss a. Calculate the expected value and standard devi…

1) Run a multiple regression (in Excel) with body fat as the dependent variable

1)     Run a multiple regression (in Excel) with body fat as the dependent variable and skinfold, midarm and thigh as independent variables using the table below. Show the results…

1) Salaries in the NBA are very complicated, with some caps in place.However, ev

1) Salaries in the NBA are very complicated, with some caps in place.However, even with limits being placed on salaries some players still receive significant salaries. Andrew Wig…

1) Select two variables that interest you and are ratio/interval level of data.

1) Select two variables that interest you and are ratio/interval level of data. Choose variables that you believe might be related to one another, you will use these variables for…

1) Show that a positive integer m is divisible by 11 if and only if the al- tern

1) Show that a positive integer m is divisible by 11 if and only if the al- ternating sum of its digits is divisible by 11. Hint: notice that 10-1 (mod 1) 2) Is 212121212121212121…

1) Show that each of the following sets is countable: a) set of negative integer

1) Show that each of the following sets is countable: a) set of negative integers; b) set of integers that are multiples of 5; For a) and b) write the one to one correspondence be…

1) Show that if G has two edge-disjoint spanning trees, then it has a spanning E

1) Show that if G has two edge-disjoint spanning trees, then it has a spanning Eulerian subgraph. 2) Show that if G is 2k-regular for some k  1, then it has a spanning 2-regular …

1) Simpson‘s paradox—heart disease patients Today we are going to look at common

1) Simpson‘s paradox—heart disease patients Today we are going to look at common numerical arguments often used in newspapers and in television. Often when newspapers and other me…

1) So the inequality below. Write the solution set using interval notation and g

1) So the inequality below. Write the solution set using interval notation and go out the solution set on a number line. 7) Given the linear equation, -5x + 10y = -8 find the slop…

1) State College is evaluating a new English composition course for freshmen. A

1) State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and the students are placed in the course during their…

1) Student Sam has access to two types of internet connection: a 4G phone connec

1) Student Sam has access to two types of internet connection: a 4G phone connection, and a WiFi connection. The WiFi has unlimited data but is very unstable. The 4G connection is…

1) Student Sam has access to two types of internet connection: a 4G phone connec

1) Student Sam has access to two types of internet connection: a 4G phone connection, and a WiFi connection. The WiFi has unlimited data but is very unstable. The 4G connection is…

1) Suppose P(C) =0 .048, P(M and C) = 0.044, and P(M or C) = 0.524. Find the ind

1) Suppose P(C) =0 .048, P(M and C) = 0.044, and P(M or C) = 0.524. Find the indicated probability. 1) P(M'or C') 2) P(C') 2) if 3 balls are drawn from a bag containing 3 red and …

1) Suppose Y 1 , . . . , Y n is random sample from N(3, 2 ). Then, b 2 = Pn i=1(

1) Suppose Y1, . . . , Yn is random sample from N(3, 2 ). Then, b 2 = Pn i=1(Yi3)2 /n is a sufficient and unbiased estimator of 2 . Yes / No. 2) Suppose Y1, . . . , Yn is a random…

1) Suppose Y 1 , . . . , Y n is random sample from N(3, 2 ). Then, b 2 = Pn i=1(

1) Suppose Y1, . . . , Yn is random sample from N(3, 2 ). Then, b 2 = Pn i=1(Yi3)2 /n is a sufficient and unbiased estimator of 2 . Yes / No. 2) Suppose Y1, . . . , Yn is a random…

1) Suppose a 95% confidence interval is computed for resulting in the interval (

1) Suppose a 95% confidence interval is computed for resulting in the interval (112.4, 121.6). Then there is a 95% chance that falls within the interval (112.4, 121.6). 95% of all…

1) Suppose a die is rolled 3 time and the outcome is recorded for teach roll. a)

1) Suppose a die is rolled 3 time and the outcome is recorded for teach roll. a) How many different results can be recorded from this set of 3 rolls? b) How many results will have…

1) Suppose a particle has a position function given by x(t) = t 3 + 2, where x i

1) Suppose a particle has a position function given by x(t) = t 3 + 2, where x is distance in meters and t is time in seconds. Find the average speed of the particle between t = 0…

1) Suppose a person is chosen at random. Use your knowledge about the world to d

1) Suppose a person is chosen at random. Use your knowledge about the world to decide whether the event that the person has brownbrown eyes and the event that the person is female…

1) Suppose a plasma bubble with a radius of r (mm) and mas of m (mg) is predicte

1) Suppose a plasma bubble  with a radius of r (mm) and mas of m (mg) is predicted to have a temperature of T degrees according to the formula : root (T)=m^(5/4)r^(3/2)   note: a …

1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer ch

1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer choices. If a student takes the quiz and randomly guesses on every question.... A) Find the probabili…

1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer ch

1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer choices. If a student takes the quiz and randomly guesses on every question.... A) Find the probabili…

1) Suppose a simple random sample of size n=1000 is obtained from a population w

1) Suppose a simple random sample of size n=1000 is obtained from a population whose size is N=1,500,000 and whose population proportion with a specified characteristic is p=0.72.…

1) Suppose n objects are permuted at random among themselves, what is the probab

1) Suppose n objects are permuted at random among themselves, what is the probability that k specified objects occupy k specified objects? (Each of k specified objects occupies a …

1) Suppose that 1.68 percent of the products manufactured at by a company are de

1) Suppose that 1.68 percent of the products manufactured at by a company are defective. If a product from this company is defective, it will break within the first year with prob…

1) Suppose that 25% of students at a particular college have SATscores over 1200

1) Suppose that 25% of students at a particular college have SATscores over 1200. If I pick 5 students at random from this student body, what is the probabilitythat at least one o…

1) Suppose that 25% of students at a particular college have SATscores over 1200

1) Suppose that 25% of students at a particular college have SATscores over 1200. If I pick 5 students at random from this student body, what is the probabilitythat at least one o…

1) Suppose that a coin is flipped and a die is rolled. Let E1 denote the event “

1) Suppose that a coin is flipped and a die is rolled. Let E1 denote the event “the coin shows a tail”, let E2 denote the event “the die shows a 3”, let E3 denote the event “the c…

1) Suppose that a health expert has claimed that 21 % of college students smoke

1) Suppose that a health expert has claimed that 21 % of college students smoke cigarettes. To investigate this claim, researchers survey a random sample of college students. Usin…

1) Suppose that a single card is selected from a standard 52-card deck. What is

1) Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a queen? Now suppose that a single card is drawn from a stan…

1) Suppose that a student pilot passes a written test for a private pilot\'s lic

1) Suppose that a student pilot passes a written test for a private pilot's license is .07.Find the probability that the student will pass the test a) on the third try b) before t…

1) Suppose that among 10,000 men with HIV-negative, 200 will develop a disease w

1) Suppose that among 10,000 men with HIV-negative, 200 will develop a disease within 2 months; and among 500 men with HIV-positive, 35 will develop a disease within 2 months. A r…

1) Suppose that b is the least squares coecient vector of the regression of y on

1) Suppose that b is the least squares coecient vector of the regression of y on X and that c is any other K 1 vector. Prove that the dierence between the two sums of squared resi…

1) Suppose that f(x)=x 4 +12x 3 a) Increasing: 2) Suppose that f(x)=3x?2/(x+4) a

1) Suppose that f(x)=x4+12x3 a) Increasing: 2) Suppose that f(x)=3x?2/(x+4) a) Increasing:   b) Decreasing:   c) Local maxima at x =   d) Local minima at x =   e) Concave up:   f)…

1) Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normall

1) Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 39.6 and 3.8 mpg, respectivel…

1) Suppose that you are climbing a hill whose shape is given by z = 321 ? 0.03 x

1) Suppose that you are climbing a hill whose shape is given by z=321?0.03x2?0.01y2 , and that you are at the point (20, 30, 300). In which direction (unit vector) should you proc…