Algebra Questions

Part 2 Using Unit Rate to Make Comparisons 1 Jean sells M Ms to friends at 4 for 5 cents The machine at the store sells 9 for 25 cents Which is the better deal 2 The hardware store sells 4th of July sparklers for 19 cents each The fireworks stand charges 85 cents for four Where would you purchase sparklers The 3 Frosted Flakes has 11 grams sugar per ounce and Raisin Bran 13 grams per 1 4 ounces Which cereal has more sugar per ounce

Fill in the blanks so the resulting statement is true A measure that is used to describe the strength and direction of a relationship between variables whose data points lie on or near a line is called the r COL A measure that is used to describe the strength and direction of a relationship between variables whose data points lie on or near a line is called the to r ranging from r ranging from r causation coefficient regression line correlation coefficient regression coefficient to

7B HW The scatterplot provided shows a set of data Choose the best description for the trend of the data Choose the correct answer below O A increasing linear OB U shaped OC decreasing linear O D exponential Ay 24 20 16 12 8 4 0 0 N 2 A 4 6 8 X 10 Q

Fill in the blank so the resulting statement is true The line that best fits a set of points is called a an The line that best fits a set of points is called a an scatter line distribution line regression line

The scatterplot provided shows a set of data Choose the best description for the trend of the data Choose the correct answer below OA U shap OB decreasing linear OC increasing linear OD exponential 12 10 2 10 5

The atterplot provided shows a set of data Choose the best description for the trend of the data Choose the correct answer below OA U shaped OB exponential OC decreasing linear OD increasing linear 15 10 5 0 5 10 15 20 25 30 O 4 8 10

7B HW Decide whether the given ordered pair is a solution of the given system 1 4 3x 5y 23 4x 2y 12 Question 8 4 1 15 Is the ordered pair a solution to the equation Yes O No

Determine whether the given number is a solution of the equation 5z 3 18 z 3 Is z 3 a solution of the equation 5z 3 18 O No OYes

Solve the equation and check the proposed solution 497 20 z The solution set is Simplify your answer

Decide whether the given ordered pair is a solution of the given system 3 4 x y 1 5x 3y 13 Is the ordered pair a solution to the system of equations OYes O No

7B HW Determine whether 18 is a solution of the equation x 12 30 Is 18 a solution O No OYes

Use the distributive property to help you solve the equation 3 t 6 0 11

VB HW Solve using the multiplication property 9x 45 Question 3 R The solution set is

Correct The volume of a gas in a container varies inversely as the pressure on the gas If a gas has a volume of 340 cubic inches under a pressure of 10 pounds per square inch what will be its volume if the pressure is decreased to 5 pounds per square inch Round your answer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

a b c x KEZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 B x b which is given by x t lim x 1 1E1 b t b Thus x 1 lim xo f f s X s ds x 1 EB xo b for each 1 to b t b MKk k 1 x 1 x 1 1 2 Finally the validity of this integral equation has the following two implications X x f s x s ds x 0 x 1 to b t b k20 x lim ff s x s ds x lim f s x s ds x f f s lim x s ds x f f s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f f s x s ds for all r te b t b dx dt 0 df f s x s ds f t X t This now proves that the curve X 1 8 4 89 thus obtained is a solution of the initial value problem

About the sequence keZ we have the following a x 1 B x b for each te to b t b MKk k 1 1 x 1 te t b t b k20 c x keZ is uniformly Cauchy on t b to b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8B x b which is given by XI lim x 1 11 b to b b Thus x t lim x 1 2 x lim ff s x s ds x f S Finally the validity of this integral equation has the following two implications X 1 x f s x s ds x 0 xo dx dt f s x s ds x f f s lim x s ds x f s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f s x s ds for all t 16 b 1 b aff 0 lim f s x s ds ff s x s ds f 1 X 1 This now proves that the curve X 10 8 1 82 thus obtained is a solution of the initial value problem

dealership wants to try out a new leasing arrangement which will allow a buyer to trade a car back to the dealership for a certain amount of credit at any ti throughout the first four years of ownership For a car in good condition the arrangement will value the car at depreciate the value of the car linearly over the course of the four years What is the value of a car with initial purchase price P at the end of the third year Write the original price at the end of four years and 4 answer as an expression in terms of P Write the exact answer Do not round swer BEER Keyboard

2 f x tek fonksiyon g x ift fonksiyon olmak zere f 2 g 2 11 f 2 g 2 3 oldu una g re f 2 ka t r A 3 B 4 C 5 D 6 E 7

1 point Solve the system by finding the reduced row echelon form of the augmented matrix reduced row echelon form How many solutions are there to this system OA None B Exactly 1 OC Exactly 2 D Exactly 3 E Infinitely many F None of the above z y 3z x y z x 2y 4 6 a ww 3 3 If there is one solution give its coordinates in the answer spaces below If there are infinitely many solutions enter z in the answer blank for z enter a formula for y in terms of in the answer blank for y and enter a formula for a in terms of in the answer blank for z If there are no solutions leave the answer blanks for z y and empty

Boyu 4 metre iken dikilen han meli i e i her ay 0 5 metre b y mektedir Han meli i e inin x ay sonra boyu g x fonksi yonu ile ifade edilmektedir Buna g re Yusuf Bey in dikti i han meli i e inin boyu 6 ay sonra ka metre olur A 4 B 5 C 6 D 7 E 8

To say that 5 4 is the same as saying z is in the closed interval A B where A is and where B is

ite sec 14 in terms of its cofunction 14 0 e an exact answer Simplify your answer Type any angle measures in degrees Do not include the de answer

Suppose ABC is a right triangle with sides a b and c and right angle at C Use the Pythagorean theorem to find the unknown side length Then find the values of the six trigonometric functions for angle B Rationalize the denominators when applicable a 7 b 24 What is the length of side c A c 25 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression sin B 24 25 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression cos B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression b

Solution To get the sampling distribution of probability value we should first determine whether the Sample is sufficient using the following two conditions npz 10 n 1 P 10 mp 150x 0 25 37 5210 The two conditions are fulfilled We understand from the central limit theorem that the as being is roughly normally distributed with the mean up p and the standard deviation PFP along with of 7 npzlo and n 1 P 10 Therfore the 2 conditions which satisfy the proportion of sample that were normally distributed by the mean up P and the Standard deviation PCHPJJ o p Sample proportion mean is up P 0 25 The sample proportion of the sitem and deviation of op 3 0 25 0 25 150 0025 0 0625 P 1 P n J 10 1875 0 00125 150 0 035 pproximately normer MP 0 25 op 0 035 Hence is correct option

To help with the startup costs of his new comic book store Jose is taking out a 56 000 amortized loan for 10 years at 8 5 annual interest His month payment for this loan is 694 32 Fill in all the blanks in the amortization schedule for the loan Assume that each month is 1 12 of a year Round your answers to the nearest cent Payment number 1 2 60 61 Interest payment 242 91 Principal payment 0 0 451 41 New loan balance 55 402 59 33 841 96 0 X S

To go on a summer trip Henry borrows 700 He makes no payments until the end of 5 years when he pays off the entire loan The lender charges simple interest at an annual rate of 3 Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Henry have to pay b What will the total repayment amount be including interest X S

16 yd 4 yd 9 yd 8 yd 7 yd

1 point Write each of the summations in expanded form a 2 k 1 n 1 b k 4 0 2 O 4 1 8 1 2 2 n

About the sequence x kEZ we have the following a x 1 Bxo b for each t 10 b t b MKk b x 0 x 1 k 1 11 b t b k20 c x k Z is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 B x b n which is given by x t lim x 1 tet b t b Thus x 1 lim x 1 Finally the validity of this integral equation has the following two implications X t x f s x s ds x 0 x x lim ff s x s ds x lim f s x s ds x f f s lim x s ds x ff s x s ds Thus the function rx 7 satisfying the integral equation x 1 x f f s x s ds for all 1 t b t b 2 f s x s ds ff s x s ds f 1 X 1 This now proves that the curve X 10 8 4 82 thus obtained is a solution of the initial value problem dt 0

About the sequence x keZ we have the following a x 1 EB x b for each te to b t b MKk X 00 017 te to b t bk20 k 1 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 Bx b n which is given by x1 lim x 1 tet b to b b Thus x t lim x ff s x s ds S 8 X 1 de x lim ff s x s ds x flim f s x s ds x f f s lim x s ds x ff s x s ds Thus the function tx t satisfying the integral equation x 1 x f f s x s ds for all t 1 b t b Finally the validity of this integral equation has the following two implications 1 2 x s ds X t xo f s x s ds x 0 x dt 0 s x s ds 1 X 1 dt This now proves that the curve X 1 8 4 82 thus obtained is a solution of the initial value problem

basamakl rakamlar asal ve farkl olan en b y k tek tam say ile iki basamakl rakamlar asal ve farkl olan en k k ift do al say n n toplam ka t r D 681 A 889 B 785 C 730 E 655

7 10 Correct Answer HUNTER FINDLEY The distance that a free falling object falls is directly proportional to the square of the time it falls before it hits the ground If an object fell 53 ft in 10 seconds how far will it have fallen by the end of 6 seconds Round your answer to the nearest integer if necessary Keypad Keyboard Shortcuts

Correct a varies directly as b and inversely as the square of c If a 218 when b 3 and c 6 find a if b 2 and c 7 Round your answer to two decimal places if necessary Answer Keypa

Suppose that y is proportional to the cube root of x and that y 57 when x 3375 What is y when x 1728 Round your answer to two decimal places if necessary Answer y Keyboard

Problem 6 Consider the following matrix A and let B A Find b31 b32 and b33 i e find the entries in the third row of A 1 1 TT 42 1 2

Problem 4 Find the matrix A in terms of B C and D if 5BA C D A B DC B SCDB C CDB D 5BDC E BDC F CDB G 5CDB H 5B Problem 4 Select v

The electric power varies directly as the square of the voltage V and inversely as the electrical resistance R If the voltage is 15 volts and the electrical resistance is 3 ohms then the electric power is 75 watts Express the electric power as a function of voltage and electrical resistance Answer P V R Keypac Keyboard Shortcu

Problem 12 For what value of a do the following matrices commute 8a 1 4 123 23 A 7 0 7

roblem 1 Solve for the matrix A in the following equation A F AT 41 1 2 73 4 35 28 2 10 5 18 Problem 1 Select v 2 B G 39 2 3 C 5 25 6 10 12 H 20 18 2 2 10 4 21 6 D 14 2 4 25 E 10 4 2

roblem 5 If a square matrix A satisfies 46 54 41 0 which of the following is equal to 4 A 51 4 B 51 46 C 41 4 D 51 4 E 51 A6 F 41 A G 51 A H 61 A Problem 5 Select v

Problem 11 a For what values of a b and c is the following matrix symmetric 7a 2b Problem 11 a 3 a a 5b d 7a c 2 a a 5b C b An nxn matrix A is called skew symmetric if AT A What values of a b c and d now make th following matrix skew symmetric a 7a c 0 C 7a 2b 11 3d 0 Enter your answer symbolically as in these examples separate your answers with a comma

oblem 10 Let A and B be nxn matrices Which of the following statements are always true i AB A B ii If the homogeneous system Ax 0 has infinitely many solutions then A is not invertible iii If AB AC then B C A ii and iii only B i and iii only C iii only D all of them E ii only F none of them G i and ii only H i only

Correct Answer 2 The mass varies directly as the kinetic energy K and inversely as the square of the velocity V If the kinetic energy is 40 joules and the velocity is 2 meters per second then the mass is 20 kilograms Express the mass as a function of kinetic energy and velocity Keypad Keyboard Shortcuts

oblem 3 Find the matrix A in terms of B and C if 34T 5CB T 5A 5B A SCTBT 5B B SBTCT 5B C SBTC 5C D SCBT 5C E SCBT F SCTBT 5B G SBCT 5B H SBTCT 5B Problem 3 Select Y

oblem 7 Consider the following two elementary matrices 1 6 E2 0 Problem 7 E1 Suppose that A is a 2 x 2 matrix such that E E A 1 Find the matrix A Enter your matrix by row with entries separated by commas a b would be entered as a k a d e q

Problem 2 For which 2 values of a is the following matrix not invertible a 3 3a 9 2 a 4 Problem 2 Note If there is only one value of a then enter it twice in the answer box e g 8 8 separate your answers with a comma If there is only one value of a then enter it twice in the answer box e g 8 8

A video store manager observes that the number of videos sold seems to vary inversely as the price per video If the store sells 570 videos per week when the price per video is 17 40 how many does he expect to sell if he lowers the price to 13 10 Round your answer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

About the sequence x keZ we have the following a x 1 B x b for each 1 to b to b MK b x 1 x1 1 to b t b k 20 k 1 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 B x b which is given by x t lim x 1 11 b t b Thus X 1 Jim A 506 8 5 de Finally the validity of this integral equation has the following two implications X 1 xo f s x s ds x 0 x 1 x lim ff s x s ds x flim f s x s ds x f f s lim x s ds xo ff s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f s x s ds for all t 16 b 1 b 2 dt 0 ff s x s ds f t X t This now proves that the curve X 1 6 82 thus obtained is a solution of the initial value problem

Find cos A csc B for right triangle ABC if a 3 b 2 O 2 13 b 13 1 13 2 d 2 13 13 3

MATHEMATICS Proposition 3 Let x J y J be two solutions of the initial value problem dx f t x x t x dt then x t y t for all t JOJ Proof Recall that both x and y being solutions of the initial value problem satisfy the integral equations on their domain intervals x 1 x f s x s ds y 1 x ff s y s ds Therefore x 1 y 1 s x s s y s ds which implies x 0 y 0 0 S 5 x s s y s 0 Kx s y s for all t2te Applying Gronwalls result with A 0 we get 0 x 1 y 1 0 for all t t This gives the desired equality x 1 y t for all tj Towards the uniqueness of the solution of the initial value problem 3 we consider all the solutions of the initial value problem 3 Let the totality of them be denoted by x J XEA the solutions x being thus indexed by a suitable indexing set A Above we have verified that any two solutions say x and xx are equal on the overlap of their domains Therefore we patch together all the solutions to get a maximal solution is the solution defined on the largest open interval It is obtained as follows Let J U J A clearly Jis an open sub internal of I with x EJ and all the solutions x patch up to get a solution x J 2 of the initial value problem 3