Sequences & Series Questions and Answers

16 How much water should be added to 105 oz of 60 acid solution to dilute it to a 40 acid solution O 52 5 oz O45 65 oz O 5 25 oz O impossible to do 17 Given two circles X and Y with radii 1 in and 12 in respectively the ratio of the areas is Write your answer as a fraction

27 If there are 11 girls in a class of 16 what is the ratio of girls to boys in the class O Of O O 28 The perimeters of two similar figures are 42 in and 48 in What is the ratio of lengths of corresponding sides State your answer as a fraction x

A school playground is in the shape of a rectangle 700 feet long and 500 feet wide If fencing costs 20 per yard what will it cost to place fencing around the playground

Find the perimeter of the rectangle Express the perimeter using the same unit of measure that appears on the given sides The perimeter of the rectangle is Points 0 of 1 3 yd 5 yd

Multiply the monomials 3x y 4xy4 5x y 3 3x y 4xy4 5x y Simplify your answer

Evaluate the expression when a 5 b 6 and c 1 b 4ac S

Use the Quotient Rule to simplify All variables are nonzero 12zx7 2z5x 12zx 5 3 11

Evaluate the algebraic expression for the given value x 4x 2 for x 7 When x 7 x 4x 2

Multiply the monomials 2x5y 6x y 2x5y 6x y

Use the quotient rule to simplify All variables are nonzero 32x 4x 32x

Simplify the expression 3 25 5 3

Add the polynomials 3x 1 8x 3 3x 1 8x 3

d u dt2 u sin t a linear b third order c second order d nonlinear e first order Of fourth order

Suppose U x x 3x x E IR and W x x 3x x E IR a Prove or disprove that U and W are subspaces of IR3 b Describe U W using symbols c Describe U W without symbols

200 pounds lbs kilograms kg Please round to the nearest tenth

to a poster that is 3 ft by 1 ft 5 How many milliliters of pure acid should be added to 25 ml of 50 acid to make 80 acid solution Round your answer to the nearest hundredth if necessary x ml 6 17 9 of 43 is O 769 7 O 7 697 O 76 97 O2 402

Explain how to solve the following 5 8 10 x 100 X Choose the correct answer below OA Apply the cross products principle then isolate x on one side of the equation X OB Subtract from both sides 8 Oc Multiply each side by the reciprocal of the other side OD Divide the numerators by their respective denominators

10 HW Write the English phrase as an algebraic expression Let x represent the number Twelve more than a number The phrase written as a algebraic expression is

Perform the indicated operation 35 36x 72x 6x 5 35 36x 72x 6x 5 x 7 x 7 the

Perform the indicated operation 5xy2 3x y 3x y 8xy 5xy 3x y 3x y 8xy Simplify your answ

Perform the indicated operation 6ab b a b 7ab a Cab 1 2 2 b 7b Simplify your answe

A cyclist is riding a bicycle whose wheels have a radius of 12 inches Suppose the wheels turn at a rate of 230 revolutions per minute a Find the angular speed of the wheels in radians per minute b Find the speed of the cyclist in miles per hour Use the fact that I mi 5280 ft Do not round any intermediate computations and round your answer to the nearest whole number a Angular speed radians per minute b Speed of the cyclist miles per hour X

a Draw CD parallel to AB 5 Draw EF perpendicular to AB

Use the law of exponents to simplify Write the answer with positive exponents All variables are nonzero 7x y 3 2 C 7x y 3 2 Simplify your answer Type exponential notation with positive exponents Use integers or fractions for any numbers in

Use the negative exponent rules to simplify 1 1 3 11 4 Simplify your answer

se the negative exponent rule to simplify Write the answer with only positive exponents All variables are nonzero

Use the Quotient Rule to simplify All variables are nonzero 6y7x9 4 3 3y x 6y7x 4 3

Use the quotient to a power rule to simplify 5ad LA 5a d II 2

implify the following expression All variables are nonzero 2wz 7w 2wz 2 2 2 2 7w II 2

Simplify the following expression 10b4 6b 10b4

Simplify the expression Write the answer with only positive exponents All variables are nonzero 4a 9a 4a 9 9a

Simplify Step by Step Solution Step 1 Rearrange factors Part 1 of 4 Write the answer with only positive integer exponents All variable O Points 0 of 1 4 D D

Simplify each expression a 50 b 5 c 5 a 5 Simplify your onewor Tyno

Simplify each expression so that all exponents are positive All variables are nonzer a y 9 b y 9 c y 9

Complete the sentence If a is a nonzero real number and n is a positive integer then a If a is a nonzero real number and n is a positive integer then a 1 C

Simplify the following expression All variables are nonzero 18x8 21x7 18x8 21x7 11

Which of the following scenarios have a reasonable solution Read each one carefully and select all that apply Scenario A student takes out two loans totaling 5000 at 4 and 6 annual interest The total interest after 1 year is 254 Find the amount of each loan Solution The loan at 4 interest is 2300 and the loan at 6 is 2700 Scenario An athlete ran for part of an hour at 6 miles per hour and for the rest of the hour at 8 miles per hour The total distance traveled is 7 miles How long did the athlete run at each speed Solution The athlete ran for half an hour at 6 miles per hour and one and a half hours at 8 miles per hour Scenario The perimeter of a rectangle is 40 feet The rectangle s length is 3 times as long as it s width Find the dimensions of the rectangle Solution The width of the rectangle is 5 feet The length of the rectangle is 15 feet Scenario If 2 bags of popcorn and 3 soft drinks cost 7 and 3 bags of popcorn and 2 soft drinks cost 8 find the price of a bag of popcorn and the price of a soft drink Solution A bag of popcorn costs 3 and a soft drink costs 2

Brandon has a jar of quarters and dimes with a total value of 6 05 The number of quarters is 7 les twice the number of dimes How many quarters and how many dimes does Brandon have Number of quarters Number of dimes

Marty is 3 years younger than 6 times his friend Warren s age The sum of their ages is greater than 11 What is the youngest age Warren can be Enter your answer as a whole number in the box years

Plot the inequality on the number line a 1 ora 8 Choose the proper tools with the correct endpoints then click and drag the endpoints to the correct location Notice the trash can is available if an error is made 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

What is the interval notation for the compound inequality I 3 or 1 7 O 3 7 O 0 3 or 7 O 0 3 or 7 O 3 7

he slope and a point on a line are given Use this information to locate three additional points on Slope 3 point 2 4 etermine three points on the line with slope 3 and passing through 2 4 OA 1 1 3 7 4 10 O B 1 1 7 3 10 4 OC 5 5 3 1 2 4 O D 5 5 1 3 4 2

Calculate the change of enthalpy for the reaction CH4 g NH3 g HCN g 3H2 g from the following reactions Reaction 1 N g 3H2 g 2NH3 g Change in enthalpy 91 8 kJ mol Reaction 2 C s graphite 2H2 g CH4 g Change in enthalply 74 9 kJ mol Reaction 3 H g 2C s graphite N g 2HCN g Change in enthalpy 270 3 kJ mol To earn FULL POINTS you need to include ALL YOUR WORK used to complete the calculation the correct calculated value AND the correct units

14 15 16 17 18 19 20 21 Temperature C 22 Warm Up The dot plot shows a town s daily low temperature in degrees Celsius for 24 days Briefly describe the data distribution and relate the measure of center to the shape of the dot plot shown

Use the Quotient Rule to simplify All variables are nonzero 4z7w5 2z4w 4z7w5 2 4 3 11

Find the product 4x 4x 4 4x 6 Type an expression using x as the variable Simplify your a

Example Grace is making a model of a building that is shaped like a parallelogram The dimensions of the parallelogram in her model are shown What is the area of the parallelogram in Grace s model The segment labeled 4 in is perpendicular to the side labeled 18 in So the base of the parallelogram is 18 in and the height is 4 in You can use the formula for the area of a parallelogram A b h A 18 4 72 10 7 in The area of the parallelogram in Grace s model is 72 in 4 in 18 in Look at the parallelogram in the Example Describe a way to decompose the octangle

Use the graph of f x to find the x intercepts of the graph and the zeros of the function The x intercepts are Type ordered pairs Use a comma to separate answers 10 8 8 Ay 20 16 12 B R

Letitia Brianne and Jake met at the mall on December 31 Letitia said that she intends to come to the mall every fourth day throughout the next year Brianne said that she inten be there every third day and Jake said that he would be there every fifth day Letitia said that she knew she would be at the mall a total of 91 days since 365 4 is 91 with a rem of 1 Brianne said that she d be at the mall 121 days since 365 3 is 121 with a remainder of 2 Moreover Brianne said that of those 121 days she would expect to see Letitia 3 times since they will both be coming every 12 days and 365 12 is 30 with a remainder of 5 Complete parts a through d below

Use the laws of exponents to simplify 3 3 3 1 10 3 1 35 3 10 Simplify your answer Type exponential notation with positive