Basic Math Questions and Answers

he sales decay for a product is given by S 20 000e 0 3x where S is the monthly sales and x is the number of months that have passed since the end of a promotional campaign a What will be the sales 6 months after the end of the campaign Round your answer to two decimal places b How many months after the end of the campaign will sales drop below 1 000 if no new campaign is initiated Round up to the nearest whole number months

A company sells sets of kitchen knives A Basic Set consists of 2 utility knives and 1 chef s knife A Regular Set consists of 2 utility knives 1 chef s knife and 1 slicer A Deluxe Set consists of 3 utility knives 1 chef s knife and 1 slicer The profit is 20 on a Basic Set 60 on a Regular Set and 80 on a Deluxe Set The factory has on hand 800 utility knives 400 chef s knives and 200 slicers a If all sets will be sold how many of each type should be made up in order to maximize profit What is the maximum profit b A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set yet the result from part a recommends making up more Basic Sets than Regular Sets She is puzzled how this can be the best solution How would you respond a Find the objective function to be used to maximize profit Let x be the number of Basic Sets let x be the number of Regular Sets and let x3 be the number of Deluxe Sets What is the objective function Z x x x3 Do not include the symbol in your answers To maximize profit the company should make up Simplify your answers Basic Sets Regular Sets and Deluxe Sets

Set up the following for solution by the simplex method First express the linear constraints and objective function then add slack variables to convert each constraint into a linear equation and then set up the initial simplex tableau A manufacturer of bicycles builds racing touring and mountain models The bicycles are made of both aluminum and steel The company has available 92 600 units of steel and 45 000 units of aluminum The racing touring and mountain models need 11 22 and 39 units of steel and 18 26 and 16 units of aluminum respectively How many of each type of bicycle should be made in order to maximize profit if the company makes 9 per racing bike 18 per touring bike and 22 per mountain bike What is the maximum possible profit constraints and objective function subject to with Z X1 92 600 45 000 X2

For the given maximization problem a determine the number of slack variables needed b name them and c use slack variables to convert each constraint into a linear equation a How many slack variables are needed b Which slack variables should be used OA X X2 OB S S2 S3 OC S S2 OD X X2 X3 c What is the equation using a slack variable that correennnde to the first constraint Maximize subject to with z 10x 3x x3 5x 8x2 10x3 140 3x 5x2 14x3 206 x 20 X 20 X3 20 E

A coffee company has found that the marginal cost in dollars per pound of the coffee it roasts is represented by the function below where x is the number of pounds of coffee roasted Find the total cost of roasting 120 lb of coffee disregarding any fixed costs C x 0 022x 6 25 for xs 200 The total cost is

Elena began to solve this equation 12x 6 4x 3 3 12x 6 4x 3 3 2 6x 4 2 12x 6 4x 3 6 6x 4 6 12x 24x 18 36x 24 6 2 6x 4 2 When she got to the last line she stopped and said the equation is true for all values o How could Elena tell

What are possible equations for these 2 lines y y x Why X How many solutions does this system of equations have

What is the future value if 8200 is invested for 11 years at 8 compounded semiannually Round your answer to the nearest cent

16 pts In the following circuit the resistors have values R your abc123 multiplied by 202 R your abc123 multiplied by 4 52 R your abc123 multiplied by 4 92 R your abc123 multiplied by 4 2 a If the source voltage is your abc123 divided by 10 V what is the voltage V 8 points b What value for R would make V 0 8 points RI A Vo G C Rx B

8 What is the surface area to one decimal place a an ice cream cone top open Trst b a gas storage tank top closed oy bib elinu ferW to 16 6 cm 6 yd 9 4 cm m1111 7 1 2yd

al Thinking Skille indeed 3 4 5 Inference Drawing conclusions based on relevant data information and personal knowledge and experience Communication Sharing and receiving information with others verbally nonverbally and in writing Problem solving The process of gathering analyzing and communicating information to identify and troubleshoot solutions

Suppose you have been offered two identical jobs Consider the salaries of the jobs Job 1 starting salary of 45 000 with yearly raises of 2 000 Job 2 starting salary of 41 000 with yearly raises of 2 400 How much will each job pay for your tenth year on the job Job 1 Job 2 Which job will pay you more for your tenth year on the job O job 1 starting salary of 45 000 O job 2 starting salary of 41 000

For the investment situation below identify the annual interest rate the length of the investment in years the periodic interest rate and the number of periods of the investme 12 compounded quarterly for 6 years a the annual interest rate b the length of the investment in years yr c the periodic interest rate d the number of periods of the investment

If you make 34 800 and get 1200 raises each year in how many years will your salary double Assume you do not receive a raise the year you are hired yr

How long in years would 700 have to be invested at 11 3 compounded continuously to earn 300 Interest Round your answer to the nearest whole number yr

A couple needs 45 000 as a down payment for a home If they invest the 30 000 they have at 4 compounded quarterly how long will it take for the money to grow to 45 000 Round your answer to the nearest whole number yr

What is the compound interest if 43 000 is invested for 15 years at 6 compounded continuously Round your answer to the nearest cent

If you want to earn 2 annual simple interest on an investment how much should you pay for a note that will be worth 18 500 in 10 months Round your answer to two decimal places

a To buy a Treasury bill T bill that matures to 10 000 in 6 months you must pay 9800 What annual simple interest rate does this earn Round your answer to one decimal place b If the bank charges a fee of 60 to buy a T bill what is the actual interest rate you earn Round your answer to one decimal place

Which investment will earn more money a 5000 investment for 5 years at 7 compounded annually or a 5000 investment for 5 years compounded continuously at 6 07 compounded annually 6 compounded continuously

interval notation Also express it as an inequality involving x aph What is the resulting interval

Consider an investment where 42 000 is invested for 10 years at 8 compounded continuously How much will this investment be worth after 10 years Round your answer to the nearest cent What is the total amount earned in compound interest Round your answer to the nearest cent

What are the future value and the interest earned if 3600 is invested for 6 years at 8 compounded quarterly Round your answers to the nearest cent future value interest earned

If 5000 is invested at 5 annual simple interest how long does it take to be worth 6250 yr

1 point What are the remaining zeros for the P x 5x 4 2x 3 21x 2 8x 4 polynomial that has zeros of 2

g x cos 2x 3 sin 2x a Express the function in terms of sine only g x 1 b Graph the function 20 2 A wwwww 2 2 y 2 2n

assign net SITI ZX Read It y son x DISZ

36 1 Points DETAILS Find the exact value of the expression 3 cot 3 3 2 cos sin 1 Need Help Read It

Use a triple integral to find the volume of the given solid The solid enclosed by the cylinder x2 y2 9 and the planes y z 20 and z 2

While skiing you make a 4 inch diameter snowball and roll it down the mountain After a sho while the snowball picks up an additional 0 25 inches all the way around a Use differentials to approximate the increase in volume of the snowball b Is your approximation a good approximation

1 Peixotto Media s charter authorizes the sale of 35 000 000 shares of stock but it will begin by offering 20 000 of them at a par value of 4 per share John William currently has 500 that he would like to invest in this company s stocks a How much stock will John William be able to purchase 2 points 1a John William will be able to purchase 2000 shares of stock I b What privileges will John William have as a shareholder in Peixotto Media 3 points 1b The privileges that John Williams will have as a shareholder in Peixotto Media are that

Portability Sound projection Warranty Brand A Brand B Brand C Tammy related the brands as follows 0 5 Brand A Brand B Brand C 0 3 10 5 Sound Portability Projection Warranty 7 8 8 7 9 10 7 Using the consumer buying matrix compute the quantitative product evaluation rating for each brand Do not round your intermediate calculations Round your answers t decimal place 11

Given the distribution from the previous example Table 6 1 Joint pdf for X Y for balls in box X of Red 0 0 0 0

Use the pieces at the right to construct 26 26 A Given BAL AC CDL DB AB DC Prove AABC ADCB T 1 2 1 3 4 5 6 7 Statements BALAC CD 1 DB AB DC CB CB AABC and ADCB are right triangles LA and LD are right angles AABC ADCB D 1 2 3 1 4 5 ent Triangles and Proofs Original 6 7 B Reasons Given Given Given Reflexive Property HL Clever C D Vida 35 o LA and LD are right angles Definition of a Right Triangle AB DC BALAC Given Definition of Perpendicular Lines Reflexive Property Given HL Definition of Perpendicular Lines AABC and ADCB are right triangles Given AABC ADCB CB CB

Given the joint distribution from the previous example Employee 96 1 0 1 0 W

Calculate the following problem and round the answer correctly m s 3 13 m 6 8 s X 6 92 s

ketch the vector indicated The vectors u and v are shown in the figure v 2u 10 5 y 10 8 6 4 2 A 10 X

Write the complex number in polar form with argument between 0 and 2 5 5i

Graph the complex number 4 3i 5

Sketch the given vector with initial point 5 3 6 2 U

xpress the vector v with initial point P and terminal point Q in component form Assume that each point lies on the gridlines 10 8 6 6 8 O 10 x

Find 2u 4v u v and 4u 5v for the given vectors u and v Simplify your answers completely u i j v i j 2u 4y u v 4u 5v

Write the given vector in terms of i and u 1 2

Write the given vector in terms of i and j u 6 4 H 11

Use the given points to graph the line and find the slope 24 23 Point 1 9 10 Point 2 3 1 Point 1 0 Point 2 2

The area of the bigrectangle is 45x 9 and the area of the small rectangle is 12x 42 5x 1 2x 7 Find the expression that represents the shaded area

A farmer finds that if she plants 80 trees per acre each tree will yield 50 bushels of fruit She estimates that for each additional tree planted per acre the yield of each tree will decrease by 4 bushels How many trees should she plant per acre to maximize her harvest trees Give your answer rounded to the nearest whole number

Use the Divergence Theorem to calculate the surface integral s F ds that is calculate the flux of F across S F 3xy xe 2 S is the solid bounded by the cylinder y z 1 and the planes x 3 x 3

At noon the person had 375 ml emesis 2 large bowl movements and 1500 ml of urine What their total output

Washing his dad s car alone Randall takes 6 hours If his dad helps him then it takes 1 5 hours How long does it take Randall s dad to wash the car by himself hours