Math128 Exam 2 April 13 th, 2017 Name Signature Student ID Number (all 8 digits) Please shut off all electronics Please put everything away except a #2 pencil and a calculator that is not attached to a cell phone You will have 90 minutes to complete the twentyfive multiple choice questions on this exam It is very important that you fill in your answers (the bubbles ) on the answer sheet correctly so that the grading machine reads your answers correctly Please be conscientious in filling out the bubble sheet 1 Please fill in the information at the top of this page 2 On the bubble sheet where it says Name, please print your last name, leave a space, and then print your first name in the rectangles Then fill in the bubbles underneath 3 On the bubble sheet, where it says Identification Number, please CAREFULLY write your entire Student ID number in the rectangles and fill in the bubbles underneath Please double check to make sure you bubbled in your ID # correctly 4 On the bubble sheet, where it says Special Code please write the number 130417 in the rectangles and fill in the bubbles underneath 5 On the bubble sheet, where it says Grade or Educ bubble in your section number Section 1 Calden Tues/Thurs 830AM Section 2 Calden Tues/Thurs 10 AM Section 3 Hayes MWF 1220 6 Lastly do not write anything in the sections labeled Sex or Birth date Please double check that you bubbled your answers correctly on the bubble sheet and circle your answers on your test booklet before you hand it in When you are finished, quietly gather your belongings and come to the front of the room Have your student ID card ready to show us Grades will be posted on your MOODLE page just as soon as they are done Please do not call or email asking for your grade We cannot give grades out by phone or email GOOD LUCK!!
1 The following graph is of a population density function The function equals 0 for x < 0 and x > b Based on the graph, which of the following is false? a p(x) b (A) The area under the curve must be 1 (B) The total population is a times b (C) This is a uniform distribution PDF (D) The product of a and b must be 1 2 Any exponential distribution PDF can be written in the form p(x) ae bx If b 1, 5 what must the value of a be? (A) 5 (B) 5 0 (C) 1 5 (D) 1 5 exponential distribution :P 'HKe* 3 Which of the following is false about the population density function, p(x) and cumulative distribution function, P(x) if they are for the same set of data? (A) The area under the curve of p(x) from to t equals P(t) (B) The area under the curve from a to b of p(x) equals P(b) minus P(a) (C) p(x) is the derivative of P(x) (D) The limit as x goes to infinity of p(x) is the same as the limit as x goes to infinity : of P(x) while lim pix X & mih)1 n CDF )o PDF * on
' ( pls 4 The distribution of heights of tomato plants is given in the PDF below What fraction of the tomatoes have a height more than 6 feet? try 181 (61*35) is linear p(x) P x (feet) 6 8 **WX#H aus Plxldx sreentriamkwhat of area is pls )? Area must be I so ti6' To (A) 1 1+28 ) 4178 ) PHKYY 4 (B) 7 16 anenaof triangle @(C) 9 16 through 10,0 ) " and ( 8 4) (D) 3 So pm passes 4 giving 5 Let p(x) be the PDF and P(t) be the CDF for some set of data For the PDF below, find the value of t to the nearest thousandth if P(t) 04 (A) 0002 (B) 1026 (C) 2210 (D) 10800 0 04 taflotat pix )3tzX check! find the eqnof the line ) 0 if x < 0 1 p(x) { 9 x2 if 0 x 3 0 if x > 3 041?H ftpadi/!+fx2dx or, t3 (041127) or 1+303) t 2 10427 )" 322104
6 A study in public transportation is done looking at the amount of time students wait at bus stop 1 and bus stop 2 The graph below was made of the CDFs for each stop Which of the following can be concluded based on the graph? P(t) 1 2 p 1 5 10 t (minutes) (A) More students wait less than 5 minutes at stop 2 than at stop 1 (B) Students at stop 1 are generally more satisfied with the bus service than at stop 2 (C) All students at stop 2 wait longer than students at stop 1 (D) More students wait less than a minute at stop 2 than at stop 1 Ibusz (1) > I,zu,,e#) 7 Which of the following is false about the median and mean of a set of data? (A) The median is the t value such that P(t) 5 (B) The mean is the area under the curve from to of p(x) (C) The median is the t value where area under the curve of p(x) from to t is 5 (D) The mean and median of a uniform distribution are equal to each other 8 The height of corn in a field can be modeled with a normal distribution where the mean is 75 inches and the standard deviation is 3 inches What percent of the corn would you expect to be over 76 inches? Give answer to the nearest percent (A) 5% (B) 10% (C) @ 37% (D) 42% µ mean 75 6 standard deviation 3 3, Fei " d 036944
6 yyl5y2 Pei ( 10M ft 013533 9 Find the mean and median of the following exponential distribution: p(x) 3e 3x (A) The Mean is 033 and the Median is 062 (B) The Mean is 333 and the Median is 062 (C) The Mean is 333 and the Median is 231 (D) The Mean is 033 and the Median is 231 Kc KX mean k median hl" @ Ind k 3 K o z 3333 23104 10 The total revenue, R(l, t, d), in dollars of Jack s lemonade stand is a function of the number of lemonades he sells, l, the number of iced teas he sells, t, and the number of hot dogs, d, he sells Interpret the statement R(15, 26, 35) 91 (A) If Jack sells 15 lemonades, 26 iced teas, and 35 hot dogs his revenue is $91 (B) If Jack sells 26 lemonades, 15 iced teas, and 35 hot dogs his revenue is $91 (C) If Jack sells 35 lemonades, 26 iced teas, and 15 hot dogs his revenue is $91 (D) If Jack sells 26 lemonades, 35 iced teas, and 15 hot dogs his revenue is $91 :# 11 Suppose z f(x, y) 5xy 3 3x 2 y, which of the following statements is TRUE? (A) z is an increasing function of x and a decreasing function of y for x > 0 & y > 0 (B) z is an increasing function of y and a decreasing function of x for x > 0 & y > 0 (C) z is an increasing function of x and an increasing function of y for x > 0 & y > 0 (D) z is a decreasing function of x and a decreasing function of y for x > 0 & y > 0 5y3 Gx ) 2,115*123 23 154 12 The concentration, C, of bacteria in the blood (in millions of bacteria/ml) following the injection of an antibiotic is a function of the dose x(in gm) injected and the time (in hours) since the injection Suppose we are told that C f(x, t) te xt Calculate f x (2,1) to the nearest hundredths place (A) 114 t ext ) ) F (B) 054, (C) 132 text (D) 014 @ fx ( 2, ), ' l eta )
13 If z f(x, y) is given in the contour diagram below then find z f(2,0) o 0 ; (A) z f(2,0) 2 (B) z f(2,0) 4 (C) z f(2,0) 6 (D) z f(2,0) 8 14 Find a possible linear equation for the function with the contour diagram below: (A) H(x, y) 4 + x + y (B) H(x, y) 4 + 2x 2y (C) H(x, y) 4 + x y (D) H(x, y) 4 + 2x y
Axtfybqbo 15 Consider the function given in the graph below which represents the temperature, H(x, t), of a bowl of milk placed x, feet from a fire, measured after t, minutes Estimate H x YoF (5,8) (A) 0 H x (5,8) 1 (B) H x (5,8) 1 5 (C) H x (5,8) 1 14 (D) H x (5,8) 1 5 16 For a function z f(x, y) we are given that f(60,130) 504 and f x (60,130) 02 and f y I (60,130) 039 Use this to estimate f(63,134) (A) 348 (B) 72 (C) 564 F ( 63,134 )~~f 160,130) + 160,130) @(D) 408 408 17 Given z g(x, y) ln(xy) sin(x) + cos(y) e xy then g x (A) 1 cos(x) sin(y) exy x 9 yiy e Yy cosnnto (B) 0 1 cos (x) yexy x I cosh ye* sin(y) xyexy (C) 1 xy (D) 1 cos(x) sin (y) xexy xy H l5,s)~~hl@ tk ) ) Ay + 2) f (6360)+(0391434130)504+06 156
18 Z f(w, s) has data represented below with w, weight, in pounds and s, speed, in miles per hour Which statement about this function is FALSE? (A) f w is positive (B) f s is negative (C) f w (160,10) 005 (D) f s (160,10) 16 @ 19 Suppose z f(x, y) 3x 3 y 2 find f xy (A) 0 18x 2 y (B) 18xy f 9 4/2 Fx)y(9x2y2)y18 2 (C) 27xy (D) 9x 2 20 Which of the following is false? fs > 0 : Past here (A) If there is a critical point at (x 0, y 0 ), both f x (x 0,y 0 ) and f y (x 0, y 0 ) are either 0 or undefined (B) The second derivative test will tell you if it is a maximum or minimum (C) A critical point is always a maximum or minimum (D) You can test xvalues around a critical point to see if it is a maximum or minimum 21 Which of the following is true for f(x, y) x 3 27x y 3 + 12y? as s increases we (A) There are 2 critical points both are local maximums (B) There are 2 critical points one is a local maximum and one is a local minimum (C) There are 4 critical points one is a local maximum, one is a local minimum, and two are neither (D) There are 4 critical points two are local maximums and two are local minimums is see F increases value of W In material NI, on EXAM 2 Spring 2018 for
22 Find A, B, and C such that f(x, y) x 2 + Ax + y 2 + By + C and f(2,3) is a local minimum with a value of 25 What is A + B + C? (A) 0 (B) 3 (C) 13 (D) 28 23 Which of the following is a critical point of z f(x, y) x 2 2x + y 2 4y + 5? (A) (1,2) (B) (2,1) (C) (0,1) (D) (2,0) 24 Use Lagrange Multipliers to find the maximum for the following f(x,y) subject to the constraint f(x, y) xy, 4x + 6y 40 (A) 333 (B) 533 (C) 1667 (D) 4267 25 It is determined that with a constraint of $65,000 in production costs, the maximum amount of production is given by f(125, 200) 500 The Lagrange Multiplier is 0002 If the constraint is lowered to $60,000 estimate the new maximum production (A) 300 (B) 400 (C) 450 (D) 490