Sequences & Series Questions and Answers

Convert the measurement to the indicated unit of measurement 200 minutes hours 60 minutes 1 hour 200 minutes hours Simplify your answer Type an integer proper fraction or mixed number

25 1 point Simplify the radical expression completely 5 28 2 45 10 7 6 5 2 7 3 5 4 7 4 2

Calculate the area of the triangle below 1 Area base base height x x 4 ft 8 ft 12 ft ft

Graph the solution to the inequality on the number line u 6 24 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11

The number of crimes that occurred in a certain city per 1000 people had decreased from 46 7 in 1920 to 46 1 in 1940 Find the average rate of change in the number crimes per 1000 people that occurred from 1920 to 1940 The average rate of change was Round to the nearest hundredth as n crimes per 1000 people cities years per crimes per 1000 people cities per year crimes per 1000 people per year years years per thousands of people years per city Clear all Check answ

5 3 2 1 7 A cup of boiling water is placed outside at 1 00 pm One minute later the temperature of the water is 152 F After another minute its temperature is 112 F What is the outside temperature

4 1 point Simplify the radical expression 121 25 O 11 5 not possible 121 5 11

2 1 point The legs of a right triangle are 3 in and 4 in Use the Pythagorean theorem to find the length of the hypotenuse 6 in 12 in 7 in 5 in

7 1 point Multiply 5x y 3x y 15x5 y5 8x5y5 8x6y 15x6

Using Green s Theorem calculate the area of the indicated region 4 The area bounded above by y 3x and below by y 4x3

nd the solution of each inequality in the interval 0 27 Enter your answers using interval notation a sin x 0 5 7 6 6 b cos x 0 5 2 4 3 3 c 2 tan x 2 sin x 5 4 4 X 3 4 4 X d 3 cos x 3 sin x

Consider a spiral curve C in the zy plane with parametrization r t cost sin t i cost sint j 0 1 7 2 a Use MATLAB to plot the curve b Find the work done by the force field F x y x y 1 i in moving a particle alon

When Hakeem runs the 400 meter dash his finishing times are normally distributed with a mean of 70 seconds and a standard deviation of 2 seconds Using the empirical rule determine the interval of times that represents the middle 68 of his finishing times in the 400 meter race

Given 3 unique non zero vectors in 2 space a b c what does the calculation a X b Xc determine O a Coplanar O b None of the other answers are correct Oc Parallel O d Orthogonal O e Area of a parallelpiped

write each statement using the appropriate mathematical language 8 Even numbers are in the set of integers

Write the rational number in lowest terms 33 99

Find the following quotient 1 41 4 18 49 18 49 1 44 14 Type an integer or a simplified

Subtract 81 58 81 58 Simplify your answer

Evaluate the expression 18 9 18 9

For any real number a other than 0 there is a real number a called the such that a a a a Use integers or fractions for any numbers in the expression inverse or

Find the exact value of the expression cos tan cos tan 4 1 1 3 4 3 COS 7 25 Simplify your answer including any radicals expression COS 1 1 7 25

7 cm 16 cm 6 cm

Houghton Mifflin Harcourt Publishing Company A relation is a set of ordered pairs x y where x is the input value and y is the output value The domain is all possible inputs of a relation and the range is all possible outputs of a relation For example the given relation represents the number of whole wheat cracker boxes sold and the money earned 1 4 2 8 3 12 4 16 Domain 1 2 3 4 Reflect Range 2 12 16 For the following relation the input x is the ages of boys and the output y is their corresponding height in inches 1 41 8 45 9 49 10 52 10 53 11 55 12 59 B Fill the values in the table Plot the points on the graph Complete the mapping diagram E State the dornain of the relation State the range of the relation Height in 60 50 40 30 20 10 0 8 9 10 11 12 X 10 Age yr ID 2 4 6 Age yr Height in 41 45 49 52 53 55 59 45 419 52 Fr 8 10 12 nhrr 19 appears twice in the x column of the table How many times is it written in

Replace the with the correct symbol 63 7 63 9

Determine whether the statement is true or false 7 7 Is the statement true or false O False O True

For males in a certain town the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 5 Using the empirical rule determine the interval of systolic blood pressures that represent the middle 99 7 of males

You take a 60 day single payment loan with an interest rate of 14 on 815 What is the amount of the maturity value 833 76 836 67 O 842 33

26 A plumber and two helpers together earned 360 a day How much did each earn in a day if the plumber earned 4 times as much as each helper

Find the least common multiple LCM of the following number 20 50 and 30 The LCM of 20 50 and 30 is

A formula that is used when designing AC alternating current circuits is 1 10 12 2 0 fo 2 LC Rationalize the right hand side and restate the formula

Convert the following expression to exponential notation 11 5 11 11 11 Type exponential notation with positive exponents Type an exact an

Determine a and find the indicated term of the following geometric sequences 3 points for a 1 point for the indicated term 6 3 15 75 375 an as 7 a3 36 as 324 an

ind the domains of the given functions Remember that a domain is a set f x x b f x 21 x x c f x 1 flo flor 3y fl f a x 6 1 x x 1 1 x

Solve 13 22 cosx 8 sin x 0 x 2 3

f sin x 3 5 x 3 2 and sec y 13 12 3 3 2 y 2 3 find the exact value of cos x y

Rewrite the fraction with 36 as the denominator

Given that the sequence is geometric a10 78 732 i e the 10 term is 78 732 and the common ratio is 3 find a i e the 1st term 091 3 9 4 091 78 9 12 Question 5 20 points Consider the first six terms of this sequence 5 7 11 19 35 67 Which equation below explicitly defines the sequence 9 2n 3 9 3 2 9 3 2a 1 3n 2 a

Question 1 20 points Given that the sequence common difference is 5 find a24 i e the 24th term 2 119 24 124 a24 460 24 480 is arithmetic a 4 i e the first term is 4 and th

Q2 Condense the following expression to a single complicated logarithm ONLY 1 2 5 log 3x 1 log 4y m

Ashley manages the team of drivers of a delivery company Each year the 75 drivers need to be allocated to five distribution centers The allocations are done according to each center s projected number of deliveries The numbers of deliveries are shown in the table below Use Webster s method to allocate the drivers to the distribution centers You may use the apportionment tool to help you To do this turn ON the apportionment tool enter a divisor and click on Compute You will then see the quota the lower quota the rounded quota to the nearest whole number and the upper quota for each distribution center You may also click on active cells to fill in the bottom row Apportionment Tool ON Divisor Distribution center Number of deliveries Quota Lower quota Rounded quota Upper quota Pigeon Crest 64 819 Laguna 42 040 Compute Del Mar 69 390 Blackwoods 93 870 C Rio Seco 122 131 Total 392 250 27 U DI E 2

Period 8 14 2023 1 g x 2 x 1 3 State the parent function f x State the transformation of g x

Carrie is finding the set of even numbers within the set of prime numbers Of the sets described which is the universal set all real numbers O all integers Oprime numbers even numbers

Mrs Culland is finding the center of a circle whose equation is x y2 6x 4y 3 0 by completing the square Her work is shown 2 6x 4y 3 0 6x y 4y 3 0 x 6x y 4y 3 x2 6x 9 2 4y 4 3 9 4 Which completes the work correctly O x 3 y 2 2 42 so the center is 3 2 O x 3 2 y 2 2 42 so the center is 3 2 O x 3 y 2 2 42 so the center is 3 2 x 3 y 2 2 42 so the center is 3 2

2 41 2 0 543 2 IN 4 4 4 4 3 X Distance formula x x V V Does the point 1 7 lie on the circle shown Explain O Yes the distance from 2 4 to 1 7 is 4 units O Yes the distance from 2 0 to 1 7 is 4 units O No the distance from 2 0 to 1 7 is not 4 units O No the distance from 2 4 to 1 7 is not 4 units

3 F G In circle G r 3 units Maria draws a circle with do the area of circle G What is the area of Maria s circle 6 units O O 9 units 12 units 18 units

H G 6 cm X 8 cm Point G is the center of the small circle Point X is the center of the large circle Points G H and X are on lin segment GX What would be the area of a new circle that has line segment GX as its diameter O 16 cm O 36 cm 49 cm 98 cm

The measure of central angle YCZ is 80 degrees X 9 W 80 C Z What is the sum of the areas of the two shaded sectors O 18 units 36 units 45 units 817 units

In the diagram below O is measured in radians Which equation represents the relationship between the radius r and arc length s Os r Or 0 s Os 0 r Or 0 s 0 A T B

3 Two cereal companies A and B find that the number of people who will buy one of their products in the first month that it is introduced is linearly related to the amount of money they spend on advertising If company A spends 40 000 on advertising then 100 000 boxes of cereal will be sold and if it spends 60 000 then 200 000 boxes will be sold However if company B spends 40 000 on advertising then 135 000 boxes of cereal will be sold For both companies the number of boxes of cereal sold increases by the same amount for each additional 1 000 they spent on ad vertising How much advertising does each company need to sell 300 000 boxes of cereal 8 marks

C B H For each of the growing patterns A B C and D shown above do the following 2 1 Draw the next pattern 2 2 Complete a table that shows the number of figures for each step 2 3 Describe how each pattern grows in words You must relate the number of figures to the step number 4 4 8 M161