Use (a) The Midpoint Rule (b) Simpsons Rule to approximate the given integral with the specified value of n. Compare your results to the actual value to determine the error in each approximation. 0...
Evaluate the integral. e2x 1+ e** ,4x
Evaluate the integral. 1 + x?
Find the exact area of the surface obtained by rotating the curve about the x-axis. y 2 = x + 1, 0 x 3
Find the exact length of the curve. y = (x + 4) 3/2 , 0 x 4
Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x 3 , 0 x 2
Hungry Howies is opening a new restaurant. The company estimates that there is a 85% chance the restaurant will have a profit of $200,000, a 5% chance the restaurant will break even, and a 10% chance...
If 5 cards are dealt from a standard 52-card deck, how many different ways can 4 aces and 1 other card that is not an ace be dealt?
If 5 cards are dealt from a standard 52-card deck, how many different ways can 3 kings and 2 queens be dealt?
Consider the five figures shown. In how many different ways can the figures be arranged a) From left to right? b) From top to bottom if placed one under the other? c) From left to right if the...
A person randomly selects one of the four envelopes shown above and to the right. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or...
Fajar has six different meals from a meal delivery service. Three meals include chicken, two meals include beef, and one meal is vegetarian. Fajar will eat one of these meals per day for the next six...
Use the following results of a coffee taste test given at a local grocery store. If one of these individuals is randomly selected, determine the probability the individual selected a) Prefers...
Determine the mean, median, mode, and midrange of the set of data. Where appropriate, round your answer to the nearest tenth. 11, 12, 12, 14, 16, 16, 16, 27, 29
A mean average of 70 or greater on six exams is needed to get a C in a course. On his first 5 exams, Quincy received grades of 74, 82, 76, 70, and 54. a) What grade must he receive on his last exam...
The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid using (a) x as the variable of integration (b) y as the variable of integration. y =...
(a) Set up an integral for the area of the shaded region. (b) Evaluate the integral to find the area. yA (1, e) y= e, (1, 1) y =x?
Identify the curve by finding a Cartesian equation for the curve. r = 5 cos
Evaluate the iterated integral. cos(s') dt ds
Suppose that f sx, y, zd t(sx2 1 y2 1 z 2 ), where t is a function of one variable such that ts2d 25. Evaluate yyS f sx, y, zd dS, where S is the sphere x2 1 y2 1 z2 4.
(a) Set up an iterated integral in polar coordinates for the volume of the solid under the graph of the given function and above the region D. (b) Evaluate the iterated integral to find the volume of...
Calculate the iterated integral. dy dx y
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Table 1.2.3, and then applying the appropriate transformations. y = sin 4x
A metal plate is situated in the xy-plane and occupies the rectangle 0 x 10, 0 y 8, where x and y are measured in meters. The temperature at the point (x, y) in the plate is T(x, y), where T is...
(a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change of f at P in the direction of the vector u. f(x, y) = x'e', P(3, 0), u =(3i 4j)
Find the sum of the series. 3" 5"n!
Determine whether the sequence converges or diverges. If it converges, find the limit. (-1)"*'n an n+1 n + yn
The mean weight gain for women during a full-term pregnancy is 30.2 pounds. The standard deviation of weight gain for this group is 9.9 pounds, and the shape of the distribution of weight gains is...
Find the frequency, proportion, and percentage of women in Table 1A on page 31. College Units Acquired Commute Height (inches) Number Living Female Distance (Miles) Hair Color Ring Size of Aunts...
Find the frequency, proportion, and percentage of brown-haired people in Table 1A on page 31. College Units Acquired Commute Height (inches) Number Living Female Distance (Miles) Hair Color Ring Size...
According to a 2015 University of Michigan poll, 71.5% of high school seniors in the United States had a drivers license. A sociologist thinks this rate has declined. The sociologist surveys 500...
Each of workers is independently qualified to do an incoming job with probability p. If none of them is qualified then the job is rejected; otherwise the job is assigned to a randomly chosen one of...
Nine values are 7, 13, 28, 36, 13, 29, 31,13 and x. a. Write down the name and the value of the measure of central tendency that can be found without knowing the value of x. b. If it is known that x...
One student is randomly selected from a school that has 837 boys. The probability that a girl is selected is 4/7. Find the probability that a particular boy is selected.
When they are switched on, certain small devices independently produce outputs of 1, 2 or 3 volts with respective probabilities of 0.3, 0.6 and 0.1. Find the probability that three of these devices...
One hundred people are attending a conference. The following Venn diagram shows how many are male (M), have brown eyes (BE) and are right-handed (RH). a. Given that there are 43 males with brown...
Two photographs are randomly selected from a pack of 12 colour and eight black and white photographs. Find the probability that the second photograph selected is colour, given that the first is: a....
Four quality-control officers were asked to test 1214 randomly selected electronic components from a companys production line, and to report the proportions that they found to be defective. The...
Exactly 20 years ago, the mean age of a group of boys was 15.7 years and the sum of the squares of their ages was 16000. If the sum of the squares of their ages has increased by 8224 in this 20-year...
The following table shows the mean and standard deviation of the lengths of 75 adult puff adders (Bitis arietans), which are found in Africa and on the Arabian peninsula. a. Find the mean length of...
The amounts of rainfall, rmm, at a certain location were recorded on 365 consecutive days and are summarised by (r 3) 2 = 9950 and (r 3) = 1795.8. Calculate the mean daily rainfall and the value of...
A girl has 20 plastic squares. There are five identical red squares, seven identical blue squares and eight identical green squares. By placing them in a row, joined edge-to-edge, find how many...
From seven men and eight women, find how many ways there are to select: a. Four men and five women b. Three men and six women c. At least 13 people.
Without using a calculator, find the value of: a. 5!/3! b. 4!/2! 3! c. 7 4! + 21 3! d. 10!/8! + 9!/7! e. 20!/18! 13!/11!
A bakery wishes to display seven of its 14 types of cake in a row in its shop window. There are six types of sponge cake, five types of cheesecake and three types of fruitcake. Find the number of...
A Mathematics teacher has 10 different posters to pin up in their classroom but there is enough space for only five of them. They have three posters on algebra, two on calculus and five on...
A bag contains six red fuses, five blue fuses and four yellow fuses. Find how many ways there are to select: a. Three fuses of different colours b. Three fuses of the same colour c. 10 fuses in...
On average, Diya concedes one penalty in every six hockey matches that she plays. Find the probability that Diya next concedes a penalty: a. In the eighth match that she plays b. After the fourth...
Recently, Ashland MultiComm Services has been criticized for its inadequate customer service in responding to questions and problems about its telephone, cable television, and Internet services....
How will marketers change their organic (unpaid) social media postings in the near future? A survey by Social Media Examiner reported that 65% of B2B marketers (marketers who focus primarily on...
Referring to Problem 14.41 on page 506, you have decided to analyze whether there are differences in fixed acidity, chlorides, and pH between white wines and red wines (0 = white 1 = red). Using the...
The following GSS 2014 frequency distribution presents information about peoples self-evaluations of their lives, based on three categories: (1) exciting, (2) routine, and (3) dull. 1. Find the mode....
For the following exercises, use the given information to find the unknown value. y varies jointly as the square of x and the cube of z and inversely as the square root of w. When x = 2, z = 2, and w...
For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. ln(3ab 5c)
Let f(x, y) = k when 8 x 12 and 0 y 2 and zero elsewhere. Find k. Find P(X 11, 1 Y 1.5) and P(9 X 13, Y 1).
Let X be normal with mean 50 and variance 9. Determine c such that P(X < c) = 5%, P(X > c) = 1%, P(50 - c X < 50 + c) = 50%
For the following exercises, solve the system for x, y, and z. In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag contained the...
Payments of $900 due 30 days from now and $1000 due 210 days from now are to be replaced with a single equivalent payment 90 days from now. If money can be invested at 4%, what single payment made 90...
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (-3)" n=1 n (Jerror | < 0.0005)
Find the radius of convergence and interval of convergence of the power series. 1.3.5 (2n-1) .
If the number of workers in the auto industry in Canada declined by 32% from its peak at the end of 1999 to the beginning of 2011, what was the compound annual rate of attrition in the industry...
Payments of $500 originally scheduled to be paid today and $300 originally scheduled to be paid three months from today are to be replaced with a single payment six months from today. Calculate the...
Refer to Data Set 8 in Appendix B and use the word counts measured for men and women from the couples listed in the first two columns of Data Set 8. Find the best predicted word count of a woman...
Determine whether the sequence converges or diverges. If it converges, find the limit. an 4n - 3n 2n + 1
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 8 n-0 3n+1 (-2)"
Determine whether the sequence converges or diverges. If it converges, find the limit. 4n - 3n 2n + 1
Determine whether the series is convergent or divergent. 00 ke-12 k=1
Find a power series representation for the function and determine the radius of convergence. f(x) = x 2 tan 1 (x 3 )
Use the Integral Test to determine whether the series is convergent or divergent. A=2 1 n(In n)3
List the first five terms of the sequence. an (-1)" 4"
The position (in meters) of a particle at time t seconds is given by the parametric equations (a) Find the speed of the particle at the point (6, 4). (b) What is the average speed of the particle for...
Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. x = 2 t t, y = 2 t + t, 3 t 3
Suppose you know that the series converges for |x| < 2. What can you say about the following series? Why? =o bnx" n=0
Taking a cruise is a costly discretionary expense. In a recent year, the top five cruise lines in the world had this many passengers: Round your answers to the nearest integer. a. The computations...
In each of the equations below, t represents the term of a savings account. Find the value of t to the nearest tenth of a year. a. b. c. d. e. t= log1.03 (1.975) 12
Chris purchases living room furniture for $4,345 from Halloran Gallery. She has a 1-year, no-interest, no-money-down, deferred payment plan. She does have to make a $15 monthly payment for the first...
Suppose Britta only paid the interest during her 2 years in school and the 6-month grace period. What will she pay in interest over the term of her loan? Britta has been accepted into a 2-year...
Arrange the following lending institutions in descending order according to their APRs for a $10,000, 2-year loan. East Meadow Savings 4 1/2% Clinton Park Credit Union 4% Tivoli Trust 4 3/8% First...
Dylan purchased A points, each of which reduced his APR by B%. The cost per point was 1% of the loan amount. His new APR is C%, and his points cost him D dollars. Write an algebraic expression for:...
The Americans with Disabilities Act (ADA) states that ramps for wheelchairs should have a slope of 1/12 or less. The Glen Head Boys Club built a ramp for a local school. The dimensions of the ramp...
Keisha is purchasing an apartment for $180,000. She has been approved for a 4.0% mortgage. She put 10% down and will be closing on April 22. Her first payment is due May 1. How much should she expect...
What is the difference between the days high and low prices for McDonalds Corp?
Van Siclen Farms plants only corn and soybeans on their 4,000-acre fields. The corn yields a profit of $160 per acre, and the soybean profit is $340 per acre. This year the owners have decided to...
A corporation produces mini-widgets. The variable expenses are $1.24 per mini-widget, and the fixed expenses are $142,900. a. What is the total cost to produce one mini-widget? b. What is the total...
Determine and sketch or graph the sets in the complex plane given by < |z - 4 + 2i| < 3
Let a = [1, -3, 5], b = [4, 0, 8], c = [-2, 9, 1]. Find: 5a 13b, 65a b
Find a parametric representation Circle in the plane z = 1 with center (3, 2) and passing through the origin.
Find all the singularities in the finite plane and the corresponding residues. Show the details. cot z
Can we conclude from Example 4 that the integral is also zero over the contour in Prob. 1? Data from Prob. 1 Verify Theorem 1 for the integral of over the boundary of the square with vertices 1 i....
Find all c Z 3 such that Z 3 [x]/(x 3 + cx 2 + 1) is a field.
Show that is a subfield of R by using the ideas of this section, rather than by a formal verification of the field axioms. {a + b(2) + c(2) a, b, c = Q}
Let E be an extension field of F, and let , E. Suppose is transcendental over F but algebraic over F(). Show that is algebraic over F().
Find the degree and a basis for the given field extension. Be prepared to justify your answers. Q(2 + 3) over Q
Let us consider Z[x]. a. Is Z[x] a UFD? Why? b. Show that {a + xf(x)|a 2Z, f(x) Z[x]} is an ideal in Z[x]. c. Is Z[x] a PID? (Consider part (b).) d. Is Z[x] a Euclidean domain? Why?
Let a be algebraic of degree n over F. Show from Corollary 48 .5 that there are at most n different isomorphisms of F() onto a subfield of F and leaving F fixed. Data from Corollary 48.5 Let be...
Calculate the perimeter and area of each of these rectangles of length l and breadth b. Write the units of your answers clearly. a. l = 4cm, b = 7 cm b. l = 8cm, b = 12cm c. l = 4.5 cm, b = 2 cm d. l...
Write an expression for the area of each of the following shapes. a. b. 8 j -j- 3
At a Cambridge college, 65% of the maths students come from England. If there are 240 maths students, how many are not from England?
A circle passes through the points O(0, 0), P(3, 9) and Q(11, 11). Find the equation of the circle.
Find the equation of the circle that passes through the points (7, 3) and (11, 1) and has its centre lying on the line 2x + y = 7.