Sequences & Series Questions and Answers

By recognizing each series below as a Taylor series evaluated at a particular value of x find the sum of each convergent series A 1 3 31 31 3 7 B 3 1 72 272 1 1 ng2n 1 2n 1 M

As age increases so does the likelihood of a particular disease The fraction of people x years old with the disease is modeled by 0 8 f x 1 271e 0 122x a Evaluate f 25 and f 65 Interpret the results b At what age does this likelihood equal 60 CELEB a Select the correct choice below and fill in the answer boxes within your choice OA 25 Round to three decimal places as needed and f 65 This means that among people age 25 have the disease while among people age 65 have the disease B 25 0 058 and f 65 0 729 Round to three decimal places as needed This means that among people age 25 5 8 have the disease while among people age 65 72 9 have the disease b At about yr this likelihood equals 60 Do not round until the final answer Then round to the nearest integer as needed

5 2 x 3 8

Find the function f t such that f t f t 40 t and f 1 7

plity each expression 1 5 8r 8 3 I 3 8 6p 8 2 5 3 1 8n 8 7 3 8 y 7 9 7 3x 2 7x C B 2 8 7 7x 1 4 6n 6 4n 2 6 7 8b 1 1 8 7 7 n 6 10 7 5 x 7 6

Solve the equation log 4256 2x 2 Change the given logarithmic equation to exponential form 256 42x 2 Type an equation Do not simplify The solution set is Type integers or simplified fractions Use a comma to separate answers a

se the given function f to answer parts a through f below X 4 f x 4 5 Choose the correct graph of f below OA B 10 y 10 40 10 X 10

How does an SAT score of 1120 compare to an ACT score of 23

Use the given function f to answer parts a through f below X 4 f x 4 5 112 LU 40 c From the graph determine the range and any asymptotes of f The range of fis IU N

What are the solutions for the given equations belo 15 0 5

Change the exponential statement to an equivalent statement involving a logarithm ex 2

5 5 32x x 30 x 18x x 6 A x 5x 2x 5 B x 5x 4x 3 C x 5x 2x 6 6 D x 5x 4x 3 B 41m n 2 1 71 n 54 C 41m 5 x 6 6 X 6 7 41n 2214n 71 54 76 A 41m n 1 54 70 54 D 41m 1 71 54 X 6 x 6 8 6 6 36 3 b 3 A b b B b b 2 C b b 3 3 D b b 3 b 3 2 b 3 7 b 3 8 66x 2912x x 3036 96 x 41 A x 30x 29 B x 30x 35 C x 30x 33 D x 30x 32 96 X 39 96 x 37 ZOO 96 X 36 96 x

Use the parent function f x b and transformation techniques to graph h z 5 1 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of h Select all transformations that apply Reflect the graph of f about the y axis Shift the graph of f1 unit to the right Reflect the graph of f about the x axis Shift the graph of f 1 unit down Horizontally compress the graph of f by a factor of 1 Vertically stretch the graph of f by a factor of 1 Vertically compress the graph of f by a factor of 1 Shift the graph of f 1 unit to the left Shift the graph of f 1 unit up Horizontally stretch the graph of f by a factor of 1

Teo has x wooden beads at 0 50 each and 6 glass beads at 1 25 each The average cost of the beads is 0 75 Which equation models the situation

5x 5 2 6 16

Let p and q represent the following statements p 8 4 12 q 10 7 70 Determine the truth value for the statement paq Choose the correct truth value below Op q is false O p q is true

Construct a truth table for the given statement PA P Fill in the truth table P T F p PA P

7 Which of the following expressions is equivalent to 3 x 4x 4 4 x 3x 2 a x 4 b 1x4 12x 20 c x 24x 4 d 1x 24x 20

The table gives the values of a function obtained from an experiment Use them to estimate 3 4 5 6 7 8 9 f x 3 5 2 1 0 6 0 3 0 9 1 4 1 8 fro f x dx using three equal subintervals with right endpoints X a Estimate R3 If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than greater than one cannot say S F X f x dx using three equal subintervals with left endpoints b Estimate L3 If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than Ogreater than one cannot say 1 x f x dx using three equal subintervals with right endpoints left endpoints and midpoints c Estimate M3 x f x dx using three equal subintervals with midpoints If the function is known to be an increasing function can you say whether your estimate is less than or greater than the exact value of the integral less than greater than

Suppose a sample of O rings was obtained and the wall thickness in inches of each was recorded Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed Click here to view the table of critical values for normal probability plots Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table ALLER Using the correlation coefficient of the normal probability plot is it reasonable to conclude that the population is normally distributed Select the correct choice below and fill in the answer boxes within your choice Round to three decimal places as needed Save OC No The correlation between the expected z scores and the observed data critical value Therefore it is reasonableto conclude that the data come from 0 190 0 192 0 192 0 197 0 206 0 221 0 232 0 235 0 254 0 266 0 283 0 291 0 302 0 311 0 307 0 318 OA Yes The correlation between the expected z scores and the observed data Therefore it is reasonableto conclude that the data come from a normal population OB No The correlation between the expected z scores and the observed data critical value Therefore it is not reasonableto conclude that the data come from a normal population does not exceedthe D Yes The correlation between the expected z scores and the observed data Therefore it is not reasonableto conclude that the data como exceedsthe critical value a normal population does not exceedthe exceedsthe critical value

For what value of k will both O A 2 B 0 O C 1 2 O D 1 n 1 n 1 2k and n k n converge

The table shows the number of employed and unemployed workers in the U S In thousands in 2000 Male 67 761 2433 Female 58 655 2285 Total 126416 4718 Employed Unemployed Total 70194 60940 131134 Assume that one person will be randomly selected from the group described in the table Find the probability of selecting a person who is employed given that the person is male 67761 70194 2433 67761 2433 70194

Use the given display to find the median Round to the nearest tenth if necessary Frequency Listen 20 10 5 4 N 21 7 201 10 20 30 40 50 Score

Solve the equation for all exact solutions where appropriate Round approximate answers in degrees to the nearest tenth Write answers using the least poss 3 secx 2 3 0 Choose the correct answer below O A OB O C O D 2nx 2nt where n is any integer 6 76 11x 6 11x 6 6 11x n nt where n is any integer 6 nx where n is any integer 2nt where n is any integer www

A record club has found that the marginal profit P x in cents is given by P x 0 0008x 0 35x 36 7x for x 400 where x is the number of members currently enrolled in the club Approximate the total profit when 240 members are enrolled by computing the sum 6 P x Ax with Ax 40 i 1 The total profit when 240 members are enrolled is approximately Round to the nearest cent as needed Marginal profit in cents 22 000 17 600 13 200 8 800 4 400 0 0 x 0 0008x 0 35x 36 7x IV V VI 100 200 Number of members 300 400 Q G

Describe the population whose properties are analyzed by the given data During 2001 there were 574 crimes in a certain city per 100 000 residents criminals in the country residents of the country O residents of the city criminals in the city

Listen Use the following frequency distribution to determine the class limits of the third class Class 9 11 12 14 15 17 18 20 21 23 Frequency 7 11 8 5 9 lower limit 14 upper limit 18 lower limit 15 upper limit 17 lower limit 14 upper limit 17 Olower limit 15 upper limit 18

15 pts Q6 Find the smallest positive integer s such that s a mod 19 where a 1 1 35 35 Hint Multiply the equation by 351 use modular arithmetic and Wilson s Theorem

Forces of 15 pounds and 7 pounds act on each other with an angle of 105 Round the magnitude to 4 decimal places and the angles to one decimal place The magnitude of the resultant force pounds The resultant force has an angle of force with the 15 pound The resultant force has an angle of with the 7 pound force Be careful on this one One of the angles could be obtuse Also it is best to calculate each angle separately and

ind the equation for the graph of the hyperbola with vertices at 0 3 and 0 3 and one focus 0 6 BANJIC24 ZAHUSANDA TURNG PANG WE SUNDAY AEROPO SETKA ZA Cu 1955

26 7 fint Z n 6 m 5 n 1

Suppose that a matrix A satisfies the characteristic polynomial CA A A 2A 3

Let A a Compute A using the formula for the inverse of a 2 x 2 matri A 11 5 b Suppose that C is a matrix so that AC 8 1 3 44 3 Use the inverse from part a to find the matrix C C 94 84

Given the triangle below find the measure of angle x Round to two decimal places Note picture is NOT drawn to scale but x is obtuse 26 26 X

with a truth table 1 Z A B C BC 2 Z A AB A B 3 F XY Z XY Z 4 F X YZ X YZ XZ

Given the lines 1 x 7 4t y 3t z t 4 and 1 x 2 t y 3t Z 6 5t a find equations in general form for the parallel planes containing l and 2 containing 12 T1 2 b determine the geometric relation between the lines they are skew

Find the indicated side x Use either the Law of Sines or the Law of Cosines as appropriate Assume B 22 and C 98 Ros X A C 1000 1 point Simplify the rational expression 2x 1 2x 3

For the triangle shown find the length AD Assume u 19 v 19 2x 10 and y 10 Round your answer to two decimal places AD B The area is V Find the area of the triangle ABC C 131 2 a 45 3 ft and b 35 7 ft square ft D A C

Maximum mark 4 without GDC The second term of an arithmetic sequence is 7 The sum of the first four terms of the arithmetic sequence is 12 Find the first term w and the common difference d

Graph the function f x A 2 if x21 1 x if x 1 19 O B 2 X Q 5 O C G O D

Find the requested value 2x 1 if x 6 f 6 for f x 6x OA 11 OB 36 O C 48 if 6 x 9 6 7x if x 9

Prove that every positive rational number can be expressed uniquely as a finite sum of the form a a2 2 az 3 where an are integers such that An n

What is the accumulated value of periodic deposits of 50 at the beginning of every month for 18 years if the interest rate is 2 58 compounded monthly

8 6x6 9 7x Date x 2 x 7 5 11 8b 6 7b 4 his true true false n has 1 2v 3v 8 ns have infinite solutions or no solutions ed his c Maria solved her got equation and got 8 8 16 16 This equation is ve This equation is ve true false true false This equation has x 6 5x 3x 1 5 3r 7r 7 b Mario solved his equation and got This equation has lutions infite selvtors

iv g x ex 10 9 8 Domain Range x intercept y intercept Horizontal Increasing Degreasing G

1 Select all of the fractions that when converted result in a repeating decimal D O 0 7 6 9 9 3 Add Write in simplest form No calculator 1 0 75 1 0 45 8718 L 0 Subtotal 129 50 Tip 23 27 Subtotal 98 40 6 9 0 3 0 Tip 17 71 Subtotal 142 17 Predicted Actual 5 Subtract Write in simplest form I 9716 11 2 L 20 6 75 10 25 Due 2 Add Write in simplest form 5 3 1 7 For parties of 6 or more people at a certain restaurant a tip of 18 is automatically included on the bill Select yes or no to indicate whether or not each of the following tip amounts is correct for an 18 gratuity on each subtotal Yes No 4 Subtract Write in simplest form 2 45 3 9 6 Julia wants to purchase a pair of headphones that are on sale for 42 79 The sales tax rate in her county is 6 Calculate the amount of sales tax Julia will pay on the purchase Round to the nearest cent if necessary Tip 22 75 8 The table shows the predicted and actual amount of snow for a local city What is the percent of error for the amount of snowfall Round to the nearest tenth of a percent if necessary Similar to Percent of Change Snowfall inches

4k If e 8 what is e k

Let f x 2ln x x 1 find f x

Graph the function Based on the graph state the domain and the range and find any intercepts x 2 if x 2 x 2 if x 2 f x e e Q Q The domain is 0 00 Type your answer in interval notation Q

The graph of an exponential function is given Select the function for each graph from the given options 1 x y 4 1 y 4 y 4 y 1 4 y 4 y 4 y 4 1 Drag each function given above into the area below the appropriate graph depending on which function is represented by which graph 35 Q36 Q37 Q 39 Ox Q 40 y 0 y Q y 4 41 17 Q 38 42 y