Basic Math Questions and Answers

Suppose that you were given a prepaid coffee card The graph shows how much is remaining on the card after buying cups of coffee What is the domain and range of the function in the graph 8 7 6 5 4 m 24 P D R d dollars to to c cups 4 5 6 7 8

Find the domain of the function f x O 1 1 8 O T 1 8 O 1 2 8 Quortio 8 x 8

Question 22 Find the domain of the given function Enter the solution using set builder and interval notation 1 12r 10 2 g x Using set builder notation the domain is x 1 Using interval notation the domain is Question Help Video 1 Video 2

The following table gives the sales of CD Rom drives and compact disk players for selected years and can be found in Glassma Sales are in millions Year 1988 1990 1992 1993 Sales 0 075 0 24 1 5 4 8 A On the basis of this data find the best fitting exponential regression Let x 0 correspond to 1988 State the square of the correlation coefficient Use 4 decimal places in you answers S x B Use this model the estimate the sales in 1997 Round to the nearest player In 1997 there were about million CD ROM and compact disk players sold

The following table gives the calories fat and carbohydrates per ounce for three brands of cereal How many ounces of each brand should be combined to get 659 calories 5 9 g of fat and 164 8 g of carbohydrates Cereal All Fiber Frosted Puffs Natural Mixed Grain All Fiber Frosted Puffs Natural Mixed Grain OZ OZ OZ Calories 50 108 127 Fat g 0 0 1 5 5 Carbohydrates g 22 0 25 7 18 0

The function f x y xy has an absolute maximum value and absolute minimum value subject to the constraint 2x 2y 3xy 49 Use Lagrange multipliers to find these values Find the gradient of f x y xy Vf x y

ng to another question w ed to classical conditionin

What is the domain of the following function f x 0x8 0 8 00 O 5 00 O 5 8 U 8 00 O All real numbers x 5 I 8

Express the interval in set builder notation 0 2 The interval in set builder notation x Graph the inequality 10 9 8 7 6 5 4 3 2 1 0 1 2 3 Clear All Draw 4 5 6 7 8 9 10

Find the the domain of the function f x O x x 10 and x 5 O x x 50 x x 4 O x1 x 50 O xl x 50 and x 4 2 4 T 5 50

Domain and Range The function f x is defined as a set or ordered pairs Using that set of data identify the Domain and Range of f x Write your answer as an ordered list enclosed in curly brackets f x 6 0 5 38 19 94 33 55 38 72 45 73 Domain Range

Determine the domain and range of the function using the graph below 15 14 13 Question 14 13 2 12 11 10 09 8 6 4 3 2 2 Ce 9

swer the questions below a The perimeter of a rect If the length of the gard Width of the garden

Determine the Domain and Range for the graph below Write your answer in Interval Notation and in Set Builder Notation Note To type in the sign type For example to enter the Domain 10 10 you would type 10 x 10 5 4 3 2 O Domain written in Interval Notation Range written in Interval Notation By 5 4 3 2 1 1 2 3 4 5 y 70 2 3 x Git 4 5 Domain written in Set Builder Notation x1 Range written in Set Builder Notation

In the past two years both product A and product B have had similar sales and the production investment is also the same for both of them This year the manufacturer feels that Product A may have more sales as compared to Product B Determine the null and alternate hypotheses as well as what each potential error represents in terms of reality and researcher conclusion Which potential error do you think is more severe OA Type I error has more severe effects in this scenario OA Type Il error has more severe effects in this scenario OA Type I error and a Type Il error have equally severe consequences in this scenario OIt is impossible to tell which error type has more severe consequences in this scenario

Domain and Range The function f x is defined in the table below Using the table identify the Domain and Range of f x Write your answer as an ordered list enclosed in curly brackets Domain Range X 25 19 18 6 14 50 f x 91 32 31 67 63 85

Use the following roster notations to write in set builder notation use as the variable 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 is an Select an

3 4 The Rational Zero Theorer K Find all zeros of the polynom obtaining the first zero or the f x x 7x 18x 1 Find the zeros of the poly

The following data give the family size x and number of pets per family y for a random sample of 13 families 54 Create a scatterplot for the data 11 10 9 8 7 6 5 4 3 2 1 y I Y 1 6 4 9 10 Clear All Draw 4 2 2 1 2 H 4 1 2 3 4 5 6 7 8 9 10 11 23 33 3 3 8 5 3 1 2 8 58 5 5 6 Determine the least squares regression line for the data Round values to four decimal places if necessary Determine the correlation coefficent Round the solution to four decimal places if necessary Use the model to predict the number of pets owned by a family with 2 members Round the solution to the nearest whole number

warranty for 952 on all new cars of a certain model The terms of the warranty would be that MotoWin would replace the car free of charge under certain specified conditions Replacing the car in this way would cost MotoWin 13 600 Suppose that under the warranty there is a 7 chance that MotoWin would have to replace the car one time and a 93 chance they wouldn t have to replace the car If necessary consult a list of formulas If MotoWin knows that it will sell many of these warranties should it expect to make or lose money from offering them How much To answer take into account the price of the warranty and the expected value of the cost from replacing the car O MotoWin can expect to make money from offering these warranties In the long run they should expect to make dollars on each warranty sold O MotoWin can expect to lose money from offering these warranties In the long run they should expect to lose dollars on each warranty sold O MotoWin should expect to neither make nor lose money from offering these warranties

Let a and b be real numbers with ab Match each set builder expression with the correct interval by selecting a letter from each drop down selector a a L b b b b a x a x b b ra x b c x x b d x a x e r ER f x x b g xa x b h ra r 1 x a r b

Match each interval with the correct set builder expression by selecting a letter from each dro selector a b V b a E a a b b V a b V a b x a x b x a x b c x a x d x a x b e x x b f x xER g x x b h x a x b

Applying the ratio test to the series you would compute lim k ak 1 ak lim k 00 Hence the series diverges 5k 1 km1 k 1 4k 5 4 Note that you will have to simplify your answer for the limit or you will get an error message

5 The population of a small town P t is modelled by the function P t 6t 110t 3000 where t is time in years NOTE t 0 represents the year 2000 a When will the population reach 6000 4

4 a Determine the equation of the quadratic in factored form that has zeros 3 and 5 and passes though the point 0 75 3

Match each factored form with the correct standard form Connect the correct pair with a line 4 a f x x 3 2x 7 i f x 2x 15x 7 b f x x 7 2x 1 ii f x 2x 8x 42 c f x 2 x 7 x 3 iii f x x 4x 21 d f x x 3 x 7 iv f x 2x x 21

2 Sketch the graph of y x 4x 5 by factoring to find the x intercepts zeros and then find the coordinates of the vertex 5

3 Determine the zeros and the maximum and minimum value for each function 8 a f x x 2x 15 b f x x 8x 7

00 Use the limit comparison test to determine whether an an n 8 n 8 a Choose a series b with terms of the form b n 8 answer as a fully simplified fraction For n 8 an lim lim n o bn 1 8 an lim n 0 bn 9n5n 8 4 4n4 converges or diverges b Evaluate the limit in the previous part Enter co as infinity and o as infinity If the limit does not exist enter DNE 1 and apply the limit comparison test Write your nP c By the limit comparison test does the series converge diverge or is the test inconclusive Diverges

Let g t be the function g 8 g 2 9 100 P t t 1 1 Find the following

Based on the table below evaluate f 6 f 6 x 0 1 f x 6 48 2 29 3 21 4 22 5 10 6 7 57 8

A 12 sided die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 7 8 9 10 11 12 Find the probability of rolling a 1 The probability of rolling a 1 is

Spring 2023 Sp23 MAT Points DETAILS etch a graph of the polar equation 3r 2 0 1 5 Assignment 9 Polar Expressions Tri 1 0 0 5 R 2 1 5 1 0 0 5 0 5 1 0 0 5 1 0 1 5 0 Homepage N ical College Homepage Northl

t View History g 2023 Sp23 MAT ts DETAILS 10 Bookmarks Window Help a graph of the polar equation r 6 5 Assignment 9 Polar Expressions Tri R 2 10 5 5 10 0 webass Homepage N ical College Homepage Northlar 10 5

flips 6 1 Suppose that we flip a coin with P H p and P T 1 p Let X be the number of until the first head Find the probability distribution function fx k P X k k 1 and its expectation E X

4 The number of typos per page of a certain book has a Poisson distribution of rate 5 What is the probability that there is no typo on the page

Walt Whitman has been describ once described Americans as having the fullest poetical nature In the 1855 preface to Leaves of Grass Walt Whitman outlines his vision of the American poet and describes what he or she should write about With a partner read the preface and use what you learn to answer these questions QUESTION In the paragraph starting with The American poets are to enclose how would you paraphrase some of the istics Whitman lists ANSWER

2 Suppose that two people Jane and Tom toss coins First Jane tosses a coin 10 times then Tom tosses the same coin 15 times The probability that the coin lands on the head is p 0 1 a Let X and Y are the number of total heads for Jane and Tom What are the distributions of X and Y b Suppose that Z is the sum of total heads for Jane and Tom combined What should be the distribution of Z

8 Oaken left his house and went for a jog After a little while he slowed his jog down He stopped to talk to a friend and then continued on a How fast did he start off jogging b How fast did he jog when he slowed down Distance From Home meters Oaken s Jog 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time seconds

SELECTING TEST SUBJECTS IN A PSYCHOLOGY RESEARCH LABORATORY ONE ROOM CONTAINS EIGHT MEN AND ANOTHER ROOM CONTAINS FIVE WOMEN THREE MEN AND TWO WOMEN ARE TO BE SELECTED AT RANDOM TO BE GIVEN A PSYCHOLOGICAL TEST HOW MANY DIFFERENT COMBINATIONS OF THESE PEOLE ARE POSSIBLE

4 Olaf is driving Make up a story to match the graph nce From Home miles 300 280 260 240 220 200 180 160 140 120 100

Scho fa 32 AABC ASTR where AB 12 RT 9 ST 8 Grid in the scale that maps AABC onto ASTR

O COMPENSATION Ms Math at point M 1 9 wants to walk the shortest distance to the street sale to buy a pie The creet has endpoints A 8 2 and B 6 1 Determine her shortest distance Show all your work for full marks Round your final answer to one decimal place try not to round until the end 6 marks

1 Measure the above line in inches 2 Measure the above line in millimeters 3 Convert 1 above to 4 Convert 2 above to Convert the following values 5 7 7 941 km 0 00247 g 9 20 km 65 L cm mg mi gal C m C cm in mm 6 8 10 12 14 10 C 45 76 cm 16 oz 100 in 16 11 13 98 6 F 15 212 F 4 C 17 A sheet of paper is 8 5 in wide by 11 in long What is its width length in cm in mm mm wide cm wide cm long mm long 5280 ft 18 A jar holds 3000 mL of water How many liters does it hold How many quarts qt 19 A drug bust nets 150 kg of cocaine How many pounds is that km lb kg cm km F F

Part 1 50 Points Watch the videos entitled Embrace the Shake Artist Chuck Close Writes Letter to Younger Self and A Mysterious Story of Frida Kahlo that Reveals Her True Character Use this discussion forum to post two paragraphs in response to the following questions Paragraph 1 How do these artists turn their limitations into artistic possibilities Paragraph 2 In your opinion what is the role of overcoming challenges in the development of an artist s practice Part 2 50 Points Read some of the responses posted by other students Reply to at least two of the posts Each response should be one paragraph Paragraphs are graded according to the criteria listed in the grading rubric for paragraph writing This assignment has multiple parts your initial post and two responses You will receive a grade for this assignment after all these parts have been completed Paragraphs will be graded according to the Paragraph Writing Rubric

Consider the following utility data for some hypothetical consumer QTUApples TUOranges 0 20 0 1 2 3 4 56 7 88NGS99 36 50 62 72 80 86 0 48 88 124 156 180 192 200 A Use this data to assist you in answering the following questions a Derive a linear equation which approximates the income expansion path between M 5 and M 14 Assume PA 1 and Po 2 6 pts b Using the midpoint method compute income elasticity of demand for apples and oranges between M 5 and M 14 Are these goods normal inferior Assume P 1 and Po 2 How do you know Explain 6 pts c Suppose that the price of oranges falls to 1 assume that the price of apples remains unchanged Adjust your budget constraint and point out the new optimal consumption bundle Assume this individual s income 5 6 pts d Using the midpoint method and the aforementioned change in the price of oranges calculate the price elasticity of demand for oranges and the cross price elasticity of demand for apples Are oranges price elastic Are apples and oranges substitutes or complements Show all work and explain 6 pts e Derive a linear approximation of this individual s demand curve for oranges 6 pts

Mixing hot and cold water 5 kg of water at 20 C is poured into a bucket that contains 1 kg of water at 80 C Find the equilibrium temperature neglect the influence of the bucket Write your answer in tenths Only the numerical value will be graded

Answer Answered 2 Points sin si iblo Round to four decimal places if necessary

Find the steady periodic solution Xp t C cos ot a of the given equation mx cx lox F t with periodic forcing function F t of frequency Then graph xap 1 together with for comparis the adjusted function F t F t mo x 4x 43x 11 cos 6t COTTO Xap 1 Use integers or decimals for any numbers in the expression Round to three decimal places as needed

The scale own is not balanced Dgbase ten blocks to the box to show the amount that needs to be to balance the Scale 113 x 49