Questions

Use a Riemann sum to approximate the area under the graph of f x 4ex on the interval 1 x 2 using n 5 subintervals with the selected points as the right end points The area is approximately units Round to six decimal places as needed

Find the area under the given curve y x 1 from x 0 to x 16 Set up the integral needed to compute the area dx

Evaluate the given integral In 2 S 0 ex e ex 3 dx HO In 2 ex ex 3 dx Type an integer or a simplified fracti

1 1 15 X 4 x 8 8x 16

Use a Riemann sum to approximate the area under the graph of f x shown below on the interval 1 x 5 using n 4 subintervals with the selected points as the left end points Draw the approximating rectangles In which graph below are the selected points the left end points of the 4 approximating rectangles O A O B 8 6 4 2 0 2 9 6 8 8 6 6 4 4 2 2 0 0 024 68 E 02468 C D 66 2 024 68 x 86 8 6 4 2 0 0 2 4 6 8 N

6 Given a 6 and 12 S Given f x dx 6 and f x dx 11 find 1 1 12 f x dx Simplify your answer 6 12 f x dx 6

Use Theorem I to compute the shaded area shown to the right The shaded region has an area of Type an exact answer tx Ay y 2 2 3 Q 4 5 6 X

What is the measure of XY N 55 Y

Use a Riemann sum to approximate the area under the graph of f x x3 on the interval 0 x 2 using n 5 subinterv with the selected points as the left end points The area is approximately Type an integer or a decimal

Define a quadratic function y f x that satisfies the given conditions Vertex 4 1 and passes through 0 33 f x

4 4 4 Given f x dx 9 and g x dx 5 find 2f x 5g x dx 2 2 2 4 S12f x 2f x 5g x dx Simplify your answer

a Compute the area of the shaded region using simple geometric formulas b Compute the area of the shaded region by applying the theorem for the area under a graph 6 f x 5 5 4 3 2 1 0 0 3 2 a Let b be the base s and let h be the height What is a formula to find the area of the shaded region OA A b b2 h OB A b h 1 OC Ab h X

Draw the region whose area is given by the definite integral So x 5 dx Choose the correct graph below O A B C D 100 08 60 10 5 0 5 10 X 10 5 0 5 10 Ly 10 5 0 5 10 X Ly 100 80 60 10 5 0 5 1

Set up the definite integral that gives the area of the shaded region Do not evaluate the integral The definite integral is 7 3 y 2 2x 0 0 1 2 3 4 5 6 7 8

Find the area under the given curve over the indicated interval y 2x x 2 to x 5 The area under the curve is Simplify your answer

Which description compares the domains of Function A and Function B correctly Function A f x x Function B 10 8 10 B g x 9 2 2 8 10 40 10 B The domain of both functions is the set of real numbers less than or equal to 0 The domain of Function A is the set of real numbers greater than 0 The domain of Function B is the set of real numbers greater than or equal to 0 The domain of Function A is the set of real numbers greater than 0 The domain of Function B is the set of real numbers less than or equal to 0 The domain of both functions is the set of real numbers greater than or equal to 0

F THE EM afferent arterioles renal corpuscle Capsular space 10 B A Renal cortex Renal colymn Major calyx Lab Exercis 24 Post Efferent arteriole Endothelium 7 Re pe Un Renal

Which of the following represents a weakness in using GDP to gauge America s economic health

21 x cos 2

Eliminate the parameter t in each of the following 15 x sect y tan t 17 x3 sec t y 3 tan t 19 x 2 3 tan t y 4 3 sec t 16 x tant y sect 18 x 3 cott y 3 csc t 20 x 3 5 tan t y 2 5 sect

Which graph represents the function f x x x 6 7 6 5 4 1 2 3 4 5 6 7 7 6 5 4 3 2 1 2 3 4 5 6 7 7 6 5 8 3 2 8 7 1234567 7 6 5 4 3 234567

Which graph represents g x x 3 2 5 4 3 2 9 x 0 8 9 10 10 8 6 4 2 g x 32 N 5 6 0 0 7 6 5 4 3 2 g x 9 x 2 3 8910

2 Suppose 1000 raffle tickets are sold at a price of 5 each Two first place tickets will be drawn with a prize worth 200 Five second place tickets will be drawn at a prize valued at 100 and ten third place tickets will be drawn at prize valued at 50 Find the expected value of the net gain to the consumer Note In this example X represents the net gain You have to be careful because this is a game you pay to play In other words if you win first prize you do not gain 200 you gain 195 because you paid for a ticket

A diet is to contain at least 969 units of carbohydrates 1348 units of proteins and 1222 calories Two foods are available F which costs 0 06 per unit and F which costs 0 08 per unit A unit of food F contains 1 units of carbohydrates 2 units of proteins and 8 calories A unit of food F contains 9 units of carbohydrates 8 units of proteins and 2 calories Find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimal nutrition requirements Corner points of the feasible region If there is more than one corner point type the points separated by a comma i e 1 2 3 4 Minimum cost is when F and F units units

What is the average rate of change from 0 to 2 of the function represented by the graph 3 y 2 1 Enter your answer in the box 2 3

4 Probability Given the following frequency table answer the following questions Left hand 71 Male Female 7 Total 18 Right hand 3 Total 14 19 26 22 40 a How many variables does the table have b Are the variables categorical or quantitative c What percent of all students are females d What percent of students are males with right hand

Print Assessment function h given by h x f x using BLUE marker given by g x f x using RED marker YA 8 10 8 00 6 4 y f x 93 2 NU 0 0 4 2 4 1 1 6 4 2 00 NU 2 4 6 8 op 10

10 Parallelogram FTCV Find FT Find CV x x y y Find FC Find TV P y N 6 02

The table shows the values of a function f z What is the average rate of change of f a from 1 to 1 H f x 3 3 2 1 1 3 0 11 1 27 2 59

Let f z z 4 What is the average rate of change of f x from 8 to 14 Round your answer to the nearest hundredth 5 16 O 0 19 0 0 19 05 16

Blink Appliances plans to order microwaves and stoves Each microwave requires 2 hours to unpack and set up in the storeroom and each stove requires 4 hours The storeroom space is limited to 64 items The budget of the store allows only 236 hours of employee time for unpacking and setup Microwaves yields a profit of 137 each and stoves yields a profit of 180 each How many of each should the store order to maximize profit Number of microwaves to order is Number of stoves to order is

P 15 2 m 20 m 8 7 2 cm 18 8 m P A 12 5 cm 6 3 cm

3 SECTION 3 1 a c 3 5 3 2 33 5 e A b 2 B 2 2 7 d d30 d5 x d6 f 5s 2 x 125s3 36

3 3 5 m P 4 m A 5 8 m 4 P A 4 7 in 5 7 in 6 in

A couple wants to invest up to 20000 They can purchase a type A bond yielding 11 return and a type B bond yielding a 12 5 return on the amount invested They also want to invest at least as much in the type A bond as in the type B bond They will also invest at least 10000 in type A and no more than 15000 in type B bond How much should they invest in each type of bond to maximize their return Let a be the amount invested in type A bond and y the amount invested in type B bond a Write the objective function to be maximized P b The feasible region has 3 corner points List the three points Corner points c Determine the amount to be invested in each bond to maximize the return and determine the maximum return Amount to be invested in type A bonds Amount to be invested in type B bonds Maximum return is

Find the Expected Value from the table Outcome Value 400 800 Probability 417 317

Subtract the rational expressions X 10 x 2 x x 6 A x 5 x 3 B x 2x 10 x 2 x 3 C x 3x 10 x 2 x 3 D x 10 x 2

The public university he wants to attend to estimate the cost of attending TUITION FEES 8 000 a What should Darnell estimate the total cost of one year to be ROOM POARD 9 100 DOOKS SUPPLIES TRANSPORTATION ETC 950 650 b Darnell s family can contribute 60 of the total annual expenses before financial aid and Damn estimates that he will qualify for 6 000 in scholarships and grants for his first year How much does that leave for Darnell to cover for his first year of college c If Darnell has 18 months to save how much should he save each month

Find all degree solutions 29 2 sin 30 sin 30 1 0 31 2 cos 20 3 cos 20 1 0

Find all degree solutions for each of the following 13 sin 20 2 15 cos 30 0 3 14 sin 20 2 16 cos 30 1

Find all solutions if 0 x 2 Use exact values only 19 sin 2x cos x cos 2x sin x 2 20 sin 2x cos x cos 2x sin x 5 21 cos 2x cos x sin 2x sin x 2 3 2

Find all solutions in radians using exact values only 23 sin 3x cos 2x cos 3x sin 2x 1 24 sin 2x cos 3x cos 2x sin 3x 1 25 sin 4x 1 27 cos 5x 1 26 cos 4x 1 28 sin 5x 1

Find all solutions if 0 x 2 Use exact values only 7 sin 2x 2 8 cos 2x

All of the following increase genetic variation EXCEPT Multiple Choice O mutation random fertilization mitosis independent assortment crossing over

You are comparing the events of meiosis I in cells from several different organisms You come across one species in which you do hot is Multiple Choice the chromosome pairs will not assort independently chiasmata will form during meiosis I kinetochores of sister chromatids do not fuse there is no crossing over between non sister chromatids

The Rec8 protein holds sister chromatids together during meiosis If an individual has a mutation that prevents degradation of Rec8 this would most likely prevent Multiple Choice normal segregation during meiosis L normal segregation during meiosis L synapsis of homologous chromosomes crossing over during prophase L

At the end of meiosis II each of the four resulting cells contains Multiple Choice two full sets of chromosomes each with 2 molecules of DNA one full set of chromosomes each with 1 molecule of DNA one full set of chromosomes each with 2 molecules of DNA two full sets of chromosomes each with 1 molecule of DNA

Which statement about the reductive division of meiosis is false Multiple Choice During the reductive division sister chromatids migrate to opposite poles of the cell During the reductive division centromeres do not divide At the end of the reductive division each daughter nucleus has one half as many centromeres as the parental nucle During the reductive division homologues migrate to opposite poles of the cell

A geneticist examines a somatic cell from a fly during metaphase of mitosis and determines that 16 chromatids are present If a germ line cell from this the end of meiosis including the first cytokinesis each cell will contain Multiple Choice 4 chromosomes with 8 DNA molecules 8 chromosomes with 16 DNA molecules 8 chromosomes with 8 DNA molecules 4 chromosomes with 4 DNA molecules

The point of connection between two sister chromatids before anaphase II of meiosis separates them is called the Multiple Choice centromere spindle apparatus centrosome kinetochore