Matrices & Determinants Questions and Answers

Levi want so make a square patio in his yard He has enough concrete to pave an area of 140 square feet If A represents the area of the patio and s represents the side length of the patio use the formula s A to find the length of each side of his patio Round your answer to the nearest tenth of a foot Answer

Q25 Solve applications exponential functions Homework Answered 11EA DU

liguel s gerbil jumped out of his closet It ran 21 meters turned and ran 16 meters and then turned 105 to face his closet How far away from his closet is Miguel erbil Round to the nearest hundredth

The Honda dealership is having a sale SUVs that were regularly priced at 48 550 are on sale for 43 750 What is the percentage of change in the price of the vehicle

Solve the following system of equations using matrices row 3 x 4y 3z 2x 6y 6z 6 5x 6y 15z 15

2 3z 10z Solve 3x2 10x 8 Use a comma to separate multiple solutions

Find the volume of the solid shown r 6 cos 0 z 2 y

26 If y 5 is an equation representing a line on a graph what is the slope m m

Which of the following correlations represents the strongest correlation Or 18 O r 76 Or 81 Or 20

Fey Company s organization chart includes the president the vice president of production three assembly plants Dallas Atlanta and Tucson and two departments within each plant Machining and Finishing Budget and actual manufacturing cost data for July 2020 are as follows Finishing Department Dallas direct materials 42 830 actual 47 450 budget direct labor 83 050 actual 83 730 budget manufacturing overhead 52 150 actual 49 780 budget Machining Department Dallas total manufacturing costs 224 290 actual 216 490 budget Atlanta Plant total manufacturing costs 424 830 actual 423 750 budget Tucson Plant total manufacturing costs 495 160 actual 497 650 budget The Dallas plant manager s office costs were 96 120 actual and 92 040 budget The vice president of production s office costs were 135 930 actual and 131 210 budget Office costs are not allocated to departments and plants a Prepare the reports in a responsibility system for The Finishing Department Dallas S In Your answer is partially correct Budget 47450 2330 49780 S Actual 42830 83050 60150 12 Neither Favorable nor Unfavorable 4620 Favorable Unfavorable 2250 Favorable Favorable

Determine if w 1 2 is in Nul A where A 1 1 3 6 st 4 1 4 3 2 2 5 s w in Nul A Select the correct choice below and fill in the answer box to complete your choice Simplify your answer A No because Aw B Yes because Aw

The number of trips from country A to country B has declined approximately linearly from 43 0 million in 2002 to 21 7 million in 2007 Find the average rate of change of the number of trips per year The average rate of change of the number of trips per year was Type an integer or decimal rounded to two decimal places as needed million

a find the orthogonal complement Stand cb find the direct sum sest S span

Change the following into drops per minute using a micro drip 60gtts cc 50cc hour gtts min o nearest whole number

Let p represent any number in the interval 3 21 Rewrite the possible values for p in inequality notation 3 21 p Tuno inter 3 21

Write each vector as a linear combination of the vectors in S If not possible enter IMPOSSIBLE S 2 1 3 5 0 4 a z 5 5 11 Z b V c W d U V 23 1 75 W 8 9 19 u 5 1 1 S1 5 H 2 152 N

Evaluate the formula z x O S n when u 118 n 22 x 123 and 12 Round to three decimal places as needed

esting J S are t investment 13 Paul Durant invested 100 000 at 6 compounded daily for 4 years and 100 000 at 6 compounded monthly for 1 year a What is the interest earned for 1 year on each investment b What is the annual percentage yield for each investment daily in a credit

9 Jacob Hernandez invests 25 000 in a CD for 5 years The CD earns interest at an annual rate of 5 5 compounded quarterly What is the annual percentage yield to the nearest hundredth of a percent

1 Multiply the polynomials a 3x4 2x 2 b 4x 6 x 3 c 7x 1 5x 2 10x 2 3x 4 d

Use Descartes s Rule of Signs to determine the possible numbers of positive and negativ f x 3x 7x 7x 6x 4 What is the possible number of positive real zeros Use a comma to separate answers as needed

4 Write an equation for the quadratic relatio 3 a The graph of y x is translated 6 unit b The graph of y x2 is translated 7 unit c The graph of y x is stretched by a fa 5 Write an equation for the parabola with v vertical stretch of 3 3

If z x 3x 4y3 find the following a Zxx b Zxy c Zyx

Question 1 12 5 points Given the following graphs of the two function which statement must be true f x 7 44 1 2 1 3 8 x Rx 3 x 3 200 Question 2 12 5 points The parent function is shown in the graph below f x

What should we multiply the 2nd equation by in order to eliminate the y using the first two equations i e what multiplier should be written where the hand is shown below so that the y s will be eliminated 23x y 4z 8 1 5x 2y 7z 12 6x 2 82 16 5x 2x 72 12 0 2 1 5 Z 4 2x 5y 3z 10 3x y 4z 8 5x 2y 7z 12 1 2

Find the exact value of each expression if 0 0 90 If tan 9 4 find sec 8 O 17 O 17 O 15 O 5

KENNEL The manager of a kennel records the weights for a sample of dogs currently being housed Weight pounds 31 67 8 37 12 87 14 34 105 57 42 8 16 54 17 20 72 23 27 63 24 52 14 44 27 5 28 22 33 15 6 36 41 21 46 Use a graphing calculator to create a histogram and describe the shape of the distribution Then describe th center and spread of the data using either the mean and standard deviation or the five number summary Justify your choice O Positively skewed the distribution is skewed so use the five number summary The range is 5 to 105 pounds The median weight is 28 pounds and half of the dogs weights are between 16 and 46 pounds O Negatively skewed the distribution is skewed so use the five number summary The range is 5 to 105 pounds The median weight is 28 pounds and half of the dogs weights are between 16 and 46 pounds O Symmetric the distribution is symmetric so use the mean and standard deviation The mean is 28 and the standard deviation is 15

Which equation is equivalent to log 36 22 O2 36 O x 36 36 2 O O x 36

system ere is no solution or if there are infinitely many solutions and the system s equations are dependent so state 5x 10y 3z 3 x 5y z 0 y z 15 10x Select the correct choice below and fill in any answer boxes within your choice A There is one solution The solution set is 0 Simplify your answers B There are infinitely many solutions OC There is no solution

1 3 O Linear 2 6 Exponential 3 12 4 24 5 48 f x A geometric sequence such as the one in the table could be defined explicitly as which type of function

Subtract and simplify the rational expression OFF 0 20 10 9x O O O 10

Test 5 1 5 2 Directions Use properties of exponents to answer all parts of each question You must show your work to receive credit The use of cellphones or other electronic devices is strictly prohibited If you are caught using cellphone or electronic device your test score will result in an automatic zero No exceptions 1 Rationalize the denominator Write your answer in simplest form 1 2 2 Write the expression in simplest form 256x 2 3 Perform each indicated operation Write your answer in simplest form

Condition improved 1 No change N Condition worse W c P MU W Total Check Clear b E A participant saw their condition get worse P E Check Clear Used medication M Used placebo L 100 500 100 300 3800 4000 Let M be the event that a participant used the medication L the event that a participant used the placebo I the event a the participant s condi improved and so on as shown by the letters in the headings Find the relative frequency in each case a P I Check Clear d F A participant used the placebo or saw no change in their condition P F Check Clear 200 e GA participant whose condition improved used the placebo 1000 Total 600 400 4000 5000

Find the area of the parallelogram whose vertices are listed 1 2 2 6 6 6 9 2 of the morallelogram is square units

Solve the system of equations 6x 7y 13 and x 3y 7 by combining the equations try 6x 7y 13 x 3y 7 6x 7y 13 x 3y 7 x y

O Which of the following graphs represelll the inverse of the function A 3x 8 x

Find the inverse of the following y log x 6 O y 2x 6 O y 6 Oy 2x 6 Oy 2 6

Question 7 Factor the polynomial func The zeros are

rite the complete solution as a plus any multiple of s in the nullspace x 3y 3z 1 2x 6y 9z 5 x 3y 3z 5

b In this question write the given sum in Sigma notation as the Riemann sum for cb function and express the limit as a definite integral f x dx a 2 2 4 6 2n lim m 272 1 n n Then evaluate the integral

9 Consider the following basis B of P B 1 x r x 1 2x 4x of P Notation E 1 2 z2 is the standard basis of P 3 a Directly from the definition of coordinates if p z B 5 find p z b Directly from the definition of coordinates if g x 3 4x 5x find g x B c Find the change of basis matrix PE B Use this matrix to solve problem 9 a d Find the change of basis matrix PB E Use this matrix to solve problem 9 b

6 Let E be the standard basis of R3 and another basis given by B 2 3 5 B a First show that B actually is a basis of R 2 b If ve R and v n find v c if we R and w 3 find w n

Exercise 10 0 12 B level Prove that 6 o6 0 implies that im 60 C ker 8 Our Goal is to find bases Bim a C Bim 0 which will be helpful in some data analysis later on To start I will finally show you how to compute the kernel more efficiently We will unfortunately be working on a silly example but I ll have you practice this method after you see it So we re going to take 5 augment it vertically with the identity and then column reduce it to an upper triangular matrix 1 1 1 00 1 0 000 0 1 000 0 0 100 O 01 0 001 0 0 0 E colycola col E cols cola cola Bker 81 2 The key is now that the vectors of Q under the zero columns of 6 Q will actually form a basis for ker 6 So if we call v through vs the five columns of 6 Q the four vectors in our case that form a basis for the kernel are 0 0 y 10 0 0 0 11 1 00 01 0 00 00 1 00 0 0 0 0 1 0 04 0 0 1 00 Q I E E 10 01 U 0

Exercise 10 0 13 C Level Check that U2 U3 U4 U5 ker 8 by the definition of kernel Exercise 10 0 14 B Level Check that Bker 61 forms a basis for ker 6 by first showing these four vectors are linearly independent and then using the Rank Nullity theorem and an analysis of the pivot s of 6 above to conclude it must be a basis for dimension reasons

point x has the coordinates point b has the coordinates ab as a column vector 3 5 and 7 2 write

Question 10 of 25 Step 1 of 1 A student bought a calculator and calculator cost 25 more than twi the textbook The corresponding r

Find the value of x in the next 3 diagrams to nearest tenth 10 2 11 2 31 2 26 24 13 X Note In question 12 x is the angle 12 X 14

k HW 3 2 Polynomial Functions ist B 9 10 K For the polynomial function f x x x 5 x a Use the Leading Coefficient Test to deter Which of the following is the correct stateme A The graph rises to the left and to the OB The graph falls to the left and rises t C The graph falls to the left and to the D The graph rises to the left and falls t

2 For the following system of homogenous linear equations 4 marks 2x y 8z y 14z 0 Use elementary row operations to solve the above system Identify the free variable s if an

258 3ft What is the area of the figure 129 15 ft O 123 ft 18 4 ft O 110 4 ft 20 5 ft 6 ft 2 1 ft