Mathematics Questions and Answers October 30, 2019

A tumor is injected with 0.92 grams of Iodine-125. After 1 day, the amount of Iodine-125 has decreased by 1.15%- Write an exponential decay model with A (t) representing the amount of Iodine-125 remaining in the tumor after t days. Enclose arguments of the function in parentheses and include a multiplication sign between terms. For example, c * In

f (x) = 5x g (x) = x -2 h(x) = -2x2+ x+ Perform the oneration h d. ( x ) C

Calculators are allowed on the problems below. (Note that phone calculators and calculator-sharin not allowed.) 1. (6 pts) Create a rational function whose graph has the following characteristics. Give the algebraic equation for the graph rather than drawing a picture of the graph. Touches the x-axis at x = 7 even Crosses the x-axis at x = -3 odd

x 8 , where is f not differentiable

I just need the syntax only In r coding for statistics( use R Code to solve this, first identifies which test you want to use) These data are modeled on the results of the National Educational Assessment tests of 4th and 8th graders in the United States, which, due to COVID, was only recently given again (2022) after a 3-year gap (last given in

. Question 3 v 80/1 pt '0 3 Z 19 (9 Details Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues. 7 10 13 16 19 2' 4' 8' 16' 32"\" Assume the first term is 0,1 an

Example differential equation \fEcuacian Diferencial Sel. Exd, Derivacion 3x dry = 5 xy+ by 2 y = 5 x 3 ( 6*2 ) (2) 1 = 5x(6X3) y' = 30 X5 = X = 5( 30) +5-1 y= 150 x 4 9 y" = 150-4-1 4 (150) =600 SUST (2) on ( 1 3 x ( 600 x 3 ) = 5X( 30X5 ) +6X 1800 x 6 = 150 *6 + 6x = > 1800x6- 150 x6-6x=d 1 1650X - 6x / EC. Differencial

Find a table of summary measures for these variables that includes (at least) the means, medians, standard deviations, first and third quartiles, and 5th and 95th percentiles. Use these to compare the arrival process at the different times of day. Round your answers to one decimal place, if necessary.

A box without a lid is required to have volume, V = 32000 cm 3 . Minimize the amount of cardboard required to form this box. Do NOT use Lagrange Multipliers. I am unsure how to do this problem without using La granges Multipliers

Differentiate the following function. 9 In (8x) y= VX d 9 In (8x) dx VX

Differentiate the following function.

Solve the given initial-value problem. X' = 1 - 1 X + X(0) = 1 3 t+1 X(t) =

Solve the given initialvalue problem.

PLEASE SOLVE THIS WORKSHEET AND PLEASE ONLY DO IT HAND WTITTEN WITH BLUE OR BLACK INK PEN PLEASE, REMEMBER I ONLY WANT IT DONE HAND WRITTEN AND WITH BLUE OR BLACK IN PEN, PLEASE WRITE VERY CLEARLY, THANK YOU. 3) The graph of the derivative of the function h is given in red a) List all the domain values of h at which a local maximum occurs. b) List

Suppose f(x, y, z) = xy23 + e(4-x?) (a) At the point (-1,1,2), find the direction in which the maximum rate of change of f(x,y,z) occurs. (b) What is the maximum rate of change of the function at the point (-1,1,2)? Enter your answer in the blank below. Round your answer to two decimal places. Your

Question 15 2 6 Evaluate 13xl 9x24 1 10 Points clx.

Assignment 4.1: Exponential Functions Score: 8.55/12 10/12 answered 0 Question 9 v A car was valued at $39,000 in the year 1990. The value depreciated to $13,000 by the year 2004. A) What was the annual rate of change between 1990 and 2004? r- = S Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in

HI can you help me solve the problem below with step by step and notes please? Instructions: Determine if the following converges or diverges and state the test used. n = 2 l n ( n ) ( 1 ) n n

A random 8 kindergarten children were recruited to participate pre and post instruction assessments. They were assessed before and after instruction and their grades were recorded to investigate whether there is a difference between pre and post grades: ID 1 2 3 4 5 6 7 8 Pre 80 60 73 90 100 70 94 98 Post 85 63 77 92 100 85 96 100 Post-Pre 1.

2.2.18 please explain how to get the solution step by step. v \\ 1 f(x) _ k 18. If the quotient of f and g is a constant (8% _ for all x) then how are g - f' and f - g' related

(10 points) If two resistors with resistances R1 and R2 are connected in parallel, as in the figure, then the total resistance R, measured in Ohms (Q), is given by: 1 1 1 _ = _ + R R1 R; If R1 and R2 are increasing at rates of .3 9/8 and .2 9/3, respectively, how fast is R increasing when R1 = 80 Q and R2 = 100 9? 9/5 (10 points) Suppose that a

The radius of a right circular cylinder is increasing at the rate of 4 in/s, while the height is decreasing at the rate of 6 in/s. At what rate is the volume of the cylinder changing when the radius is 14 inches and the height is 20 inches? O A. - 56 in3/s O B. - 56x in /s O C. 1,064x in3 /s OD. - 76 in' /s

> Next question Get a similar question You can retry this question below Consider the function f(x) = 6, /x + 9 on the interval [4, 8]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4, 8) such that f' (c) is equal to this mean slope. For this problem,

Chrome File Edit View History Bookmarks Profiles Tab Window Help X Q 8 Fri Mar 10 5:55 PM . . . E M6 Skills Practice 6 P Review Homework X P M9 Final Skills Review X + C mylab.pearson.com/Student/PlayerTest.aspx?canvas_enrollment_state=active&canvas_user_id=421253&canvas_module_item... ( * = D () : c stuff Business MATH 112 Applied Calculus for

I Question 4 v Suppose that a density function is given by the formula Ea: if 0 g a: S 6 f(- The life (in months) of a certain computer component has a probability density function defined by 1 it?) = Ee'f for x in [0, 00). Find the probability that a component randomly selected will last between 14 and 21 months? 0 Question 6 v E 0/2 pts '0 1

Please show your answers to at least 4 decimal places. Find the directional derivative of the function f(a:,y) : ln(:c5 + 3/4) at the point (2, 2) in the direction of the vector (3, 3). l

(1 point) Convert from polar to rectangular coordinates: (a) (8, 3x) 2 = ( x , y ) (b) (3, 1) 7 (x, y ) (c) (3, 0) 7 ( x, y )

Please help me answer this questions in statistics hypothesis testing with complete steps and explanation Determine whether there's a significant difference between the performance of males and females in Math. Follow steps in testing hypothesis. No Male Female 1 34 32 2 45 48 3 38 40 4 34 30 5 43 41

Use the graph of f (x) = x2 below to find a number o such that x2 - 1

Use the graph of f (c) a below to find a number 5 such that 07 2 11 0.3 whenever O 1 11 5. Round your answer to four decimal places.

1. How much better is the return on a 9% yearly interest rate investment that is compounded daily as opposed to compounded yearly? Show all of your reasoning to justify your answer. W Q 2. Which of the following equations has the same solution as O ~ 4X = 9 O 3 * O 4( x - 3) = NIX O * - 2 WIN W Q 3. What value of x satisfies the following

Please solve The Acme Widget Company has found that if widgets are priced at $ 373, then 47000 will be sold. They have also found that for every increase of $ 14, there will be 800 fewer widgets sold. The marginal cost of widgets is $ 186.5. The fixed costs for the Acme Widget Company are $ 36000. If I represents the price of a widget find the

3. (10 points) Let f : B - R be a uniformly continuous function. Let A be a nonempty subset of B. Prove that the restriction of f to A is a uniformly continuous function. Note: This function is denoted by fA : A - R. It is simply defined by flA(x) = f(x) for r E A

F(x)=x^2-x at (-2,2) Find an equation for the line ranger to the graph of the given function at the indicated point

Given (4) = 13. f (4) = 19. g(4) = 7, and g' (4) = - 10. find the value of A'(4) based on the function below. h(x) - (x) + 5x - 9 8 (x)

Given f(x) = 5x2 - 5x + 9 A) Find f(x + n) and SIMPLIFY. f(x+h)=|:| B) Find f(x + n) f(x) and SIMPLIFY. f(x+ n) - f(x) = D f(x + n) f(x) C) Find f and SIMPLIFY. f(x+h)-f(x) T = D . . f(X+h)f(X) . . D) Find Itm and SIMPLIFY. This IS f'(x). h>O h f(x + n) f(x) h =D E) Evaluate f'(5) f\"(5) = D h>0

EIG'iV'E' the function s 2 s 2 for) = 1,2; with For) = and f\"(x) = 3:31 a. Using limits, how that the lines with the equation x = 1 and y = x + 4 are asyinptotes of the graph of f . h. Identify the critical number, and the possible points of inection of the graph of f . c. Construct a table of signs for f \"andf\". Specify the following: I. The

For which values of c do the following series converge? Show all work. DO (a) 2 ck k=1 DO (b) S 12c k=1

Two discrete random variables X and Y have the following support sets: 26' = {0.1} and y = {1,0, 1}. The joint probability mass function (pmf) describing the two random variables is given by the following table: b) Compute the probability that X and Y are nonnegative, i.e., Pr(X 2 0, Y 2 0). [5 marks] c) Give the expectation of X + Y. i.e., E(X +

. Question 2 v 80/1 pt '0 3 819 G) Details Find a formula for the general term on of the sequence assuming the pattern of the first few terms continues. 9 9 9 9 9 4'16'64'256' 1024' Assume the first term is 01

10/ 4 152/ 46. ret What is the domain and range of the function in the graph? t (time) 6 7 8 d (depth) D:

PT 1. Make up a data set by yourself and use SPSS to find the mean, median, mode, standard deviation, variance, and range. Next make a histogram. Data Set: Make up a data set that contains 50 numbers representing the hypothetical answers the 50 students gave when asked to provide an estimate of the number of hours each they spend studying per

The linear trend model with seasonality y = Bo + B1 dj + Bad2 + Bad3 + B4t + & can be modified to reflect an exponential trend by using the model In(y) = Bo + B1 d1 + Bad2 + Bad3 + Bat + E. True O FalseIn a regression model with two dummy variables and an interaction variable d1d2:y= BO + B1o'1 + 520'2 + [33d1d2 + a, the interaction variables are

Explain why the solution to the problem x' - 2(cost)x = cost, x (0) = NI- must oscillate, i.e. it must have arbitrarily large zeros

The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit) and the demand x (units per week) was given approximately by the following equation. p=2352 - 0.16x 0

Question 7 evaluate Question 8 evaluate Question 9 evaluate 3 x yxy Dy 3 x yxy D2f DyDx ( 3 x yxy D2f if if if if if if x, y (0,0 x, y (0,0

Based on the information in the table below, calculate (round to 2 decimal places) the rates for questions 24-27 Community Hospital Annual Statistics 20XX Discharges: Adult and children Newborn 1,784 123 Deaths: Adults and children Newborn 12 1 Nosocomial infections: Adults and children Newborn 13 3

3.3.6 homework problem 3 statistics using technology textbook Which of the following best describes the child described in 3.3.6 Homework Problem 3. relatively tall and heavy relatively tall and light relatively short and heavy relatively short and light relatively average height (either light or heavy) relatively average weight (either tall or

1. The population of the world was 5.28 billion in 1990 and 6.07 billion in 2000. Find an exponential model for these data and use the model to predict the world population in the year 2022. (1.5 marks) O 7.25 billion O 7.90 billion O 8.25 billion. O 8.90 billion O None of above2. The population of the world was 5.28 billion in 1990 and 6.07

Find the absolute maximum value on (0, 00) for f(x) = x4 - 4x3. (E Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. (:3. A. The absolute maximum is at x = B. There is no absolute maximum. Describe the graph of f at the given point relative to the existence of a local maximum or minimum. Assume that

Write an expression in factored form for the polynomial of least possible degree graphed below. 6+ 5 NN WA -5 -4 -1 2 uit 4 -1 y( X) =

Contents 3 Derivatives Section 3.9 Exercises Introduction For the following exercises, find f' (x) for each function. ighlights 3.1 Defining the Derivative 3.2 The Derivative as a Function 3.3 Differentiation Rules 332. f (x) = 3.4 Derivatives as Rates of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Derivatives of

V Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. P(CSZSO.6)=O.7118 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. [l x 63

14. (15%) Given the polynomial function p(x) = 3(r + 2)(x - 5)1 a. List each real zero and its multiplicity. b. Determine whether the graph crosses of touches the x-axis at each x-intercept. c. Determine the maximum number of turning points

Determine if the vectors are linearly independent. 16 4 V 440 V2 4 Question 2, 1.7.4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The vectors are not linearly independent because if c and C 1, both not zero, then C CV 0. B. The vectors are linearly independent because the vector equation

After about 1,000 charges, smartphone batteries lose about one-fifth of their charging capacity. A brand new phone is currently at 78%. What would this phone's battery percentage show after 1,000 charging cycles? (round to the nearest whole number

2. Find the area of the region bounded above by the graph of 54(1) = 1 and below by the graph ofx) = x2 + 2x 2

4. [-/2 Points] DETAILS LARCALCET7 7.1.015.MI. Consider the following equations. 9 y = -x+5 X = X = 2 Sketch and shade the region bounded by the graphs of the functions. (Use solid lines for the bou Graph Layers After you add can use Grap O properties. Fill U No Solution Help WebAssign. Graphing Tool Find the area of the region

Find the critical numbers of f, if any Find the open intervals on which the function is increasing or decreasing Apply the first Derivate test to identify all relative extrema 2 f(x X X 2

The region bounded by f(x) = - 3sinc, x = 1, x = 2x, and y = 0 is rotated about the y-axis. Find the volume of the solid of revolution. Find the exact value; write answer without decimals

Show the steps on how we got this In a standard normal distribution, 84.80% of the data lies between z = -1.72 and z = k. The percentage of the data with a z-score greater than k is a. 7.60% b. 10.93% c. 13.17% d. 16.28%

Model the data using an exponential function f(x) f(x) 400 120 zii 39

Which of the following represents vector w 2120) in trigonometric form O O O O w 29(cos 46.6030i sin 46.6030j) w 29(cos 223.6030i sin 223.6030j) w 29(sin 46.6030i cos 46.6030j) w 29(sin 223.6030i cos 223.6030j)

10 Homework Question 1, 7.1.5 x Points: 0 of 1 Multiply and simplify. K (1 - tan o)2 (1 - tan a)2 = (Simplify your answer.) lew an example Get more help Clear

True or False: l) If a sequence is monotonic, then it must be bounded. )) If a sequence is bounded, then it must be convergent. ) A bounded monotonic sequence is convergent. ) A pseries with p = 1/2 converges. ) If 2a,, and 21),, both converge, then 241an converges. I An innite geometric series diverges if | r | 2 1, where r is the common ratio. .

5x - 4 5. lim x-5 x - 2

5, lim

a3ij c2i2j2k (a) Find the equation of the plane that passes through all three points a, b, and c. (b) Compute lc (a x where x is the cross product, is the inner product, and I is the absolute value. (c) Find the absolute value of the determinant of the matrix P e IR33 where its first row is c, second row a, and its third row is b. (d) Draw the

A piecewise function g(x) is defined by g (x) = - log4 (x - 2) + 2 Part A: Graph the logarithmic function g(x) and determine the domain. (5 points) Part B: Determine the vertical and horizontal asymptotes of g(x). Show all necessary calculations. (5 points) Part C: Describe the interval(s) in which the graph of g(x) is positive and determine the

I'm having trouble solving this question. Please guide me thank you. Use a table of integrals to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) In(x) dx x(4 + 5 In(x)) 10(5 In(x) - 4In|4 +5In(x) |) + c X Need Help? Read It Watch It

5. What is the largest possible domain of the function f(x) = sin (sin (x)) ? 6. Find the general solution of 2 sinx = -1. 7. Find the general solution of cosx - V3 sinx = 2 by writing the left-hand side of the equation in the form of A cos(x + a), where A > 0 and 0

Problem 5. (1 point) Consider the plane which passes through the three points: (3, 6, 7) , (6, 7, 4), and (6, 8, 6). Find the vector normal to this plane which has the form: (-5, Note: You can earn partial credit on this

A random variable X has a PDF 1 fx (x) = - [u(x + 2) - u(x - 2)] where u(x) is the unit step function. Suppose the random variable Y = X2 a) Find the mean value of Y. b) Compute the mean-square value of Y. c) Determine the variance of Y. Answer (a) 4/3; (b) 16/5; (c) 64/45

6. Use the divergence theorem to find the outward flux F . ndS, for: S a). F = xi + yj + zk, where S is the surface of the region bounded by a' +?' = 1, z = 0, z = 1

x=8t^(2)-5 y=t^3 t=1 Find d^2y/dx^2 value at the point defined by value of t

Newtons method to approximate the zeros of the function. Continue the iterations until two successive approximation differ by less than 0.001

Let the demand function for a product be given by the function D(q) - -1.4q + 280, where q is the quantity of items in demand and (q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $5, 000 and variable costs are $2 per item produced. If 188 items are produced and

18. [-/5.26 Points] DETAILS 0/30 Submissions Used Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate. f ( x ) = x + _; x= 2 X' Submit Answer 19. [-/5.32 Points] DETAILS 0/30 Submissions Used Find the equation of the tangent line to the graph of the given function at the point with

Part 2. Post a reason (try to make it one that hasn't already been posted) for taking, or not taking, the AP Exam. This posting doesn't need to address the results you found in step 1. Below are some "pro and con" points to consider as you write your posting. While there may be a good reason for you not to take the Exam, we hope you will because

Consider the following hypotheses. Ho: P = 0.60 H1: p # 0.60 Given that p = 0.54, n = 400, and

3. Evaluate. (2 marks each) a) S[3xz + 2 Vx -] dx b) J x+2 dx Vx2+4x Page 2 of 4 c) Stan x In(cosx) dx 73 d) S 1+x4 x

Determine if the improper integral converges or diverges. Justify your answer. If it converges, nd the value. 00 3 3 (a)/ 4 :1: dsc. 2 3 + 10 00 2:8 I 23) | 1 (b) \\[a With}? where b > '0'. 00 332 ((3) 1005844434, where b> 0

question (d) and (e) 6. Letf be a function defined on the closed interval -3 5x 5 4 with f(0) =3 and f(-1) = 2. The graph of f', the derivative of of a line segment and a semi-circle, as shown to the right. on a. On what interval(s), if any, is f decreasing. (50 point) ( E3, - 2] , if is decreasing, because y-value is negative at that part of

In a game of chance, you have 1/20 probability of winning $100 and a 19/20 probability of losing $10. What is theexpected value of your gain? ( Hint : In the case of loss, a gain is negative.)

Evaluate the integral Consider the following plot of a function y = f(x). 2 y =f(I) 2 -2 ) (15 points) Let F(x) = / f(t) at, where f(x) is the function depicted above. -1 Evaluate F(x) F(x) f(x) dx

Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(a) = 4.5x + 90000x + 36000 models their total inventory costs (in dollars) as a function of a the lot size for each of their orders from the supplier. The inventory costs include such things as

14. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 7.5.010. Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 350 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 40 centimeters to 70 centimeters? 10500 X N-cm

Chapter 8 Confidence Intervals (Mean) Score: 02'14 W14 answered Progress saved Done '3 E1 ' 5 0 Question 8 v 80/1 pt '0 3 Z 99 CD Details A researcher is interested in finding a 90% confidence interval for the mean number of times per day that college students text. The study included 130I students who averaged 39.4 texts per day. The standard

Given the force field F, find the work required to move an object on the given orientated curve. F= (y,x) on the parabola y = 6x from (0,0) to (2,24)Given the force field F, find the work required to move an object on the given oriented curve r(t). F = (4z,4x,4y) , r(t) = (sin t, cost,t) , for Osts 2x . . . The amount of work done is (Type an

(a) Align the input data to the number of years x after 17. Find an exponential function that models the MySpaca female user data. (Round all numerical values to three decimal places.) fo =| 10.420(0.88%) (h) According to the model in part (a), what is the percentage change in the percentage In your model? Y (c) What percentage of female MySpace

9 1 point A 55kg cyclist on a 10kg bicycle starts coasting on level ground at 25m/s. Use v = voe m, where k is about 3.9kg/s. 1. About how far will the cyclist coast before reaching a complete stop? Ans: type your answer... m (Round to the nearest tenth if necessary.) ? 2. How long will it take the cyclist's speed to drop to 1m/s? Ans: type your

Please answer the questions below fully and completely. Be sure to show your steps, use correct notation, and make your work clear. It is expected that you attempt each problem and if you get stuck, explain your uncertainty. Remember that fixes cannot be made on problems that have no attempt and/or explanation of the sticking point for you. 1.

a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. 2 f ( x ) a X . . . a. f (a) =

For the function f (x) = -4vx -1, find the inverse function. (1 point) of(x)=- (x+1)3 ,x5-1 16 of(x) = (x+1) x2-1 16 of(x) = (x+1)2 16 of ( x ) = x+1Y x5-1 16

1 Let a = 52 + 47 and b = - 42 + 67. Find a - bLet a = ( - 2, 1, 2) and b = ( - 5, - 4, - 1). Find the projection of b onto a. proj b <

(1 point) Write the following numbers in the polar form re^(i), 0 <2: (a) 16 r= , >

2. Sketch the region enclosed by the given curves and nd its area. x : y4, y : ,/2 x , y = 0

given the (figure 1.) relation, in spherical coordinates, describe it in cartesian coordinates and draw a picture of it. P = 2 sen useno

4-6 please 4. All stockbrokerage companies provide the same type of services. (T or F) 5. The New York Stock Exchange is located on Wall Street in New York City. (T or F) 6. When investors are optimistic about the overall economy and the stock market, stock prices rise; this is referred to as a bull market. (T or F)

The attached spreadsheet contains data on the year, experience level, and salary in U.S. dollars for random samples of 79 entry-level and 206 mid-level data science jobs from 2020-2022. Suppose that you would like to know if the mean salary for all mid-level data science jobs is greater than the mean salary for all entry-level data science jobs.

3 Compute the interval of convergence For the three series below. Justify your answer. A ) E 3 ( x + 1 1 2 n = 1 b ) g (9 x ) n n = 1 n

An investor is deciding between two investments When the economy has declined, an adviser has given a rosy forecast 50 ofthe time (gloomy forecast 50 ofthe time) When the economy has not changed, the adviser has given a rosy forecast 70 ofthe time When the economy has expanded, the adviser has given a rosy forecast 60 of the time. The adviser

Evaluate the integral x -5/3dx 8 x- 5/3 dx = 1 (Simplify your answer.)

Evaluate the integral 53 53 dx. x (Simplify your answer.)

Determine weather rolles theorem can be applied to f on the closed interval 2 fix - 3 1 1 - 3