Sequences & Series Questions and Answers

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1 Solve each rational equation Check your solutions 15 7 8 x 1 x 1 25 10 b 24 7m C d x 5 32 12 P 2p 6 P 8 P

ng is a rectangular right prism with dimensions 7 in by 5 in by 11 in For the purpose of this activity let s assume these measurements are exact a What is the surface area of the bottom of the prism b How many cubes 1 inch on each side would fit on the bottom of the prism c Next is a picture of the prism with a layer of cubes on the bottom How many layers of cubes will it take to fill up the entire prism d The next picture shows the prism entirely filled with cubes How many cubes are there 7 in 7 in 11 in 5 in 11 in 5 in 11 in

Which expression is equivalent to a 3 2 a2 A OB 2 9 2 92 3 2 a1 3 al 3 2 92 3 Oc a a 2

Find the equation of the line that contains the point 6 8 and is parallel to the line y 2x 3 Write the line slope intercept form Graph the lines

Find the equation of the line that contains the point 3 8 and is parallel to the line y 4x 2 Write the line in slope intercept form Graph the lines The equation of the parallel line is Simplify your answer Type your answer in slope intercept form Use integers or fractions for any numbers in the equation Use the graphing tool to graph the lines Click to enlarge graph C 10 8 6 2 4 6 Ay 8 10

Find an equation of the line through the points 1 1 and 2 4 O A x y 1 1 t 3 3 B x y 1 1 t 1 3 O C x y 2 4 t 1 1 D x y 1 1 t 2 4 E x y 2 4 t 1 5

H E G FECH ic F Complete the proof showing that quadrilateral EFGH is a parall Statement CITT

A twelve sided die with sides labeled I through 12 will be rolled once Each number is equally likely to be rolled What is the probability of rolling a number greater than 9 Write your answer as a fraction

Dylan is swimming laps to practice for a swim meet One Dylan completes 40 strokes each minute Part A Which proportion could be solved to determine the nu O A 1 85 100 4

What is the equation OUT IN 1 0 1 2 n 2 3 8 13 n Enter

Completely factor the following expressions if possible HINT LOOK FOR GCF FIRST 9 4k 14k 12 11 2x y 8x y 6xy

Find the value of x or y so that the line passing through the two points has the given slope 16 3 y 9 2 m 1 17 x 7 1 2 m 3 18 9 y 3 2 m 1 2 25 4 2 3 me table shows the numberof days you keep a rented movie before returning it and t Ovie Find the rate of change in cost with repect to time and interpret its meaning days ollars 6 00 5 8 25 6 7 10 50 19 7 5 x 2 m 3 4 ty theater performed a play each Saturday evening for 10 consecutive shows the attendanco for

and P5 from a P1 P3 to approximate sin 1 What is the maximum possible error in your approximation of using f x sinx a 0 sin 1 P5 Find the taylor series of sin x then find the maximum possible error

Given the following relations find the following compositions x 21 3 1 3 5 4 0 y 0 2 2 1 x 6 4 21 5 11 h y 29 1 3 9 19 1 3 11 6 5 4 3 2 1 24 1 0 2 3 4 4 6 y 5 1 1 8 0 f x a x 4 5 6 g x 2 2 5 10 26 k y 10 NU 2 5 8 17 29 5 6 7 8 9 10 11 Find f g 2 Find g f 0 Find hk 0 Find k h 0 Find f g 1 Find g f 3 Find g f 0

The function is defined for all x except for one value of x If possible define f x at the exceptional point in a way that makes f x continuous for all x f x x 2 9x 8 x 1 X 1

What value is 2 5 standard deviations above the mean

Consider the parent function x How would the original graph be transformed if it were to be changed to x 1 The graph would be translated right 4 and up 1 The graph would be translated left 4 and down 1 The graph would be translated right 1 and up 4 The graph would be translated left 1 and down 4

Given f x is graphed below What is the RANGE of f x y 5 4 32 x 2 5 Oxz s 4 32 2 4 1 to tois 2 2 f x 2 2 f x

Determine S11 for the following partial geometric series 3 6 12 24 48 3069 3072 6141 16896

What is the common difference of the sequence shown below 32 27 22 17 12 5 O 44 0 5 44

Find the inverse of the following y 6 7 0 y log x 7 y log x 7 y log x 7 y log x 7 0 Question 14 2 points Simplify each expression write your answer with positive

Which shows the graph of the function x 2in x 2 1 O N 3 44

What is the y intercept of the function f x 2 3 Oy 2 Oy 3 Oy 4 Oy 5

Directions Drag each number into its correct group Growth Factor or Decay Factor DRAG DROP THE ANSWER 2 01 2 1 12 98 99 99 1 01 Growth Factor Decay Factor

Given f x is an exponential function shown in the graph what is most likely the asymptote of the function Ox 0 Oy o 0x X 3 Question 4 2 points The function f x 2x 3 is graphed at the right What is the range of the function f x shown f x 34334 77 4 33 Y 2

A parabola can be drawn given a focus of 8 9 and a directrix of y 11 Write the equation of the parabola in any form T T 1 I I directrix 12 11 10 12 11 10 9 8 7 6 5 4 3 2 1 1 2 I T 9 8 7 6 5 4 3 2 1 i c 4 5 T 7 Y 6 7 8 o 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 1 I I I I I I 1 F 8 9 1 I X

A parabola can be drawn given a focus of 6 8 and a directrix of 4 Write the equation of the parabola in any form 1 F 6 8 directrix I I I 1 I I 28765 I 12 11 10 9 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 4 3 2 1 7 8 9 y 1 2 3 4 5 6 7 8 9 10 11 12 X

for v 3 v 5 7 2v 10 4 here is more than one solution separate here is no solution click on No solution

A ceiling fan with 28 in blades rotates at 55 rpm a Find the angular speed of the fan in rad min rad min b Find the linear speed of the tips of the blades in in min in min

1234505078 6 9 GERE 66 10 11 12 13 14 15 26 26 35 30 21 35 21 35 27 30 29 21 28 26 Show Transcribed Text Researchers conducting a study of 15 children with a diagnosis of ADHD wish to assess whether the BMI of the children is correlated with degrees of hyperactivity in the child The BMI of the children is shown in the image What is the Q1 value for BMI in the study

A particle moves along the curve x t 2 y t 2 t z 3t 5 where t is the time Find the curvature of the trajectory at time t Find the components acceleration direction of of its velocity and at time t 1 in the 3 200

Let c the number of cookies left O c 5 O c 5 O c25 Oc 5 Oc 5 QUESTION 13 Choose the correct translation of the following into symbolic algebra The amount of snow that fell was more than eight inches Let s the amount of snow that fell inches Os 8 Os 8 S28 8

Choose the correct translation of the following into sy the square of the opposite of a number Where t a number A t B t C 1

and the x intercept s and the coordinates of the vertex for the parabola y x 2x 35 If there is more than one x intercept separate them with commas X intercept s vertext CD X DO S

A 3 Reasoning and Proof Write the converse inverse and contrapositive of the statement below D counterexample If I am in New Jersey then I am in the East OD If I am not in the East then I am not in New Jersey Part 3 o Determine the truth value of the converse Choose the correct answer A The converse is true inion can be in Delaware and still be in the E

The percentage of a country s population 25 years and older with at least a high school diploma is shown in the table for selected years Let x 0 represent 1950 x 10 represent 1960 and so on a Use the data for 1950 and 2000 to find a linear function f that models the data b Use the function from part a to approximate the percentage of the country s population 25 years and older who were at least high school graduates in 1995 High School Graduates Year 1950 1960 1970 1980 1990 2000 2005 Percent 34 5 40 7 52 8 66 1 77 1 87 5 88 3

3 C x is the 10 10 1 by 10 10 1 by graph 123 15 Part 1 Evaluate C 2 Part 2 Evaluate C 1 Part 3 Determine c 2 c 1

Solving a word problem using a quadratic equation with rationa The area of a rectangle is 28 m and the length of the rectangle is 1 m more than twice the width Find the dimensions of the rectangle Length Width

5 E x 4x 33 Part 1 Evaluate E 22 Part 2 Evaluate E 82 Part 3 Determine E 82 22

Red Cross tested 119 people and showed these ults If A and B antigens are missing blood type is O if antigen is missing the blood type is negative How y people were classified O negative samples were classified O negative SCLE of Samples Antigen in Blood 50 18 82 5 31 11 4 A B Rh A and B A and Rh B and Rh A B and Rh

In American roulette the wheel has the 38 numbers 00 0 1 2 34 35 and 36 marked on equally spaced slots If a player bets 5 on a number and wins thi the player keeps 5 and receives an additional 175 Otherwise the player is awarded nothing and the casino takes the player s 5 Find the expected value E x the player for one play of the game If x is the gain to a player in a game of chance then E x is usually negative This value gives the average amount per game th player can expect to lose The expected value is Sl

4 points Consider a clock with an hour hand and a minute hand What is the measure of the angle the minute hand traces in 46 minutes Your answer should be in radiars Ihelp numbers

EXPONENTS AND POLYNOMIALS sing the Pythagorean Theo gth of the longer leg of a rig of the shorter leg Find the

O EXPONENTS AND I Using the Pythag The hypotenuse of a rig

A personal chef charges 125 per meal her monthly expenses are 3400 If she sells 50 meals how much profit does she make Let x the number of meals sold Write an inequality that represents the problem of selling enough meals to make a profit of at least 2200

A student s grade is based on the average of three exams where an average of 60 is a passing grade If the student s grade on the first two exams is 27 and 37 the student must get at least O points on third exam to have an average of 60 in the course

II Evaluating a piecewise defined function Suppose that the function is defined on the interval 2 5 1 5 as follows 2 if 2 5 x 15 1 if 1 5 x 0 5 0 if 0 5 x 0 5 1 if 0 5 x 1 5 Find h 1 5 h 0 3 and h 0 5 h x h 1 5 1 h 0 3 0 h 0 5 0 X

Decide whether the lines are parallel perpendicular or neither 2x 5y 4 5x 2y 12 O perpendicular Oneither O parallel

The pitch of a roof is its slope Find the pitch of the roof shown Simplify your onewer 8A