Math - Others Questions

Use estimation to select the best response Do not calculate If you purchase an item for 1 290 at an interest rate of 9 8 and you finance it for 1 year about how much is the amount of add on interest O 13 O 130 O 500

If I Prt and P 49 233 45 r 10 5 and t 2 years estimate I O 600 O 10 000 O 50 000 O 120 000 K

Growth Company s current share price is 19 95 and it is expected to pay a 1 30 dividend per share next year After that the firm s dividends are expected to grow at a rate of 4 3 per year a What is an estimate of Growth Company s cost of equity The required return cost of capital of levered equity is Round to two decimal places

ppose that you are given the task of learning 100 of a block of knowledge Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it The Ebbinghaus learning model asserts that P is given by P t Q 100 Q where Q is a percentage that we would never forget and k is a constant that depends on the knowledge learned Suppose that Q 40 and k 0 6 Complete parts a through e below Find the percentage retained after 0 weeks 1 week 2 weeks 6 weeks and 10 weeks Complete the table to the right 4 Time Passed Percentage 0 weeks 1 week 2 weeks 6 weeks 10 weeks

Consider the strategy we introduced about adaptive error control which uses two different methods of different order with the same step size Assume we use Euler s method to get w and midpoint rule to get u to approximate y that solves y y t 1 with y 0 0 5 and h 1 simultaneously a Compute w and by the two methods b Assuming the desired local truncation error is 0 1 compute the largest q so that qh for Euler s method can approximately ensure that the local truncation error is smaller than 0 1 Point out whether the current step size is acceptable or not You do not need to consider the case that there is an extra factor 2 in the definition of q hint recall the expression for q in Lec 7 and choose n 1

The equation A t 50000 06t a Find a formula for b Find and interpret A 9 Include appropriate units C Compare the approximation of 515 to the actual change Report your answer to two decimal places dA C gives the balance after t years of an initial investment of 5000 dollars which pays 6 00 compounded continuously

Farmers wishing to avoid the use of purchased seeds are increasingly concerned about inadvertently growing hybrid plants as a result of pollen drifting from nearby farms Assuming that these farmers raise their own seeds the fractional portion of their crop that remains fr hybrid plants t years later can be approximated by P t 0 98 a Using this model predict the fractional portion of the crop that will be free of hybrid plants 5 yr after a neighboring farm begins to use purchased seeds b Find P 5 and explain its meaning c When will half of the crop be hybrid plants a After 5 yr 90 of the crop will be free of hybrid plants Round to the nearest integer as needed b P 5 Round to one decimal place as needed

Differentiate g x x 2 1

Find an equation of the line tangent to the graph of G x 7e 6x at the point 0 7 The equation of the line is y

Find the derivative of the following function A 870 1 620 Type an exact answer

9 5 x 9 0 dx

2012 34 1 of all glass containers were recycled A beverage company used 450 000 lb of glass containers per year After recycling the amount of glass in pounds still in use after t years is given by N t 450 000 0 39 3 Find N 5 and explain its meaning b Find N 5 and explain its meaning c When will 7 of the original amount of glass still be in use a N 5 lb Round to two decimal places as needed CITE

Differentiate y 11 7

Differentiate g x 3 7x 2

An office machine is purchased for 7900 Assume that its salvage value V in dollars depreciates according to a method called double declining balance by 20 each year and is given by V t 7900 0 80 where t is the time in years after purchase a Find V 7 and explain its meaning b Find V 7 and explain its meaning c When will the salvage value of the office machine be half of the purchase price a V 7 Round to the nearest cent as needed

Farmers wishing to avoid the use of purchased seeds are increasingly concerned about inadvertently growing hybrid plants as a result of pollen drifting from nearby farms Assuming that these farmers raise their own seeds the fractional portion of their crop that remains free on hybrid plants t years later can be approximated by P t 0 98 a Using this model predict the fractional portion of the crop that will be free of hybrid plants 5 yr after a neighboring farm begins to use purchased seeds b Find P 5 and explain its meaning d When will half of the crop be hybrid plants a After 5 yr of the crop will be free of hybrid plants Round to the nearest integer as needed

x bir sayma say s d r a x b 2 c 14 x oldu una g re a b c arp m en ok ka t r A 80 B 90 C 100 D 120 E 150

1 Give the definition of velocity 7 of a mass point with mass m at position and time t in direction x zonal direction in cartesian coordinate system and zonal direction in geographic coordinate system

A Simplify 2x 3x 5 x

4 Determine whether or not the following 2 step methods satisfy the root condition If yes classify them as either strongly or weakly stable a The Leapfrog method W 1 W 1 h 1 2f t w

Company Schubert Inc Chapman Inc Rust Inc Murphy Co Pickman Inc 12 58 11 65 10 15 Coupon Maturity Last Price 8 13 01 01 2026 9 63 01 01 2046 4 50 5 38 01 01 2021 7 75 01 01 2026 12 05 01 01 2021 Which bond is trading at a premium Murphy Co 82 25 80 48 95 18 101 02 93 11 Last Yield If Chapman Inc wants to issue new 30 year bonds today what coupon rate would the bonds have to pay to be issued at par 11 11 12 05 5 62 5 14 EST Spread UST Years 6 20 7 15 1 37 0 89 3 89 10 30 5 5 10 EST Volume 1000s 72 070 65 275 59 277 57 465 56 305

Espa ol The data points show the distance y in meters required to stop a train traveling at a speed x in kilometers p Each figure has the same data points However each figure has a different curve fitting the data The equation for each curve is also shown Answer the questions that follow 2500 2000 1500 1000 500 y 1 5x Figure 1 100 125 3x 2675 a Which curve fits the data best O Figure 1 O Figure 2 2500 2000 1500 1000 500 Figure 2 y 0 29x 1 48x 100 2500 2000 1500 P 1000 500 Figure 3 y 0 12x O Figure 3 b Use the equation of the best fitting curve from part a to predict the distance required to stop the train when it is travelling 20 kilometers per hour Give an exact answer not a rounded approximation meters 100 25 1x 52 1 0 K

Water cannot be streamed outside of the fountain area When you have your final design you will need to create a google folder that has the following 1 A sheet that has the pattern in which your fountain will go along with the equation to get it there Example Step 1 J to B 20 32x 16x Step 2 B to A 2 Labeled screenshots of every equation with graph you use to get from one spot to the next The best tool to use is Desmos for this You will lose points if they are not labeled in some way for me to know which step the graph is associated with 3 An image of your pool that shows your path and shows where you placed your fountain

Step 4 Average rate of Change 4 pts Compute the average rate of change per year of the cost over each time period Just fill in the result don t show the calculation Time Line Price dollars 1970 1980 2003 2009 2013 2015 0 20 0 50 2 00 2 25 2 50 2 75 Average rate of change XXXXXXXXXXXXX Do these values suggest a linear trend Explain

15 Suppose a company is able to determine functions that predict its revenue and costs as R x x 30 x and C x 6x 44 A Find the marginal profit function B Find the range of x values for which the profit is positive

Some angles and the length of a side of a triangle are given in the figure The altitude of the triangle is included C 46 13 perimeter A HA B Find the area and perimeter of the triangle Note that you may wish first to find some of the unlabeled sides Express numbers in exact form Use symbolic notation and fractions where needed units area square units

3 of 13 When there is moisture on the ground microorganisms are found in the thin layer of water on leaves A monolayer containing these organisms is formed on the top and because of the spreading pressure of this monolayer the floating organisms spread upward when the surface is tilted This is a dispersal method onto newly fallen leaves In the provided figure the horizontal segment represents the ground and the angle t measures the amount by which the surface is tilted Assumed that t is less than 90 The length d is the distance the organisms move and the length u is the change in the elevation d Find a formula giving u in terms of d and t Express numbers in exact form Use symbolic notation and fractions where needed V Assume that the distance the organisms move is 34 centimeters Find the change in elevation if the angle t is 15 and if the angle 1 is 30 Give your answers to the nearest whole number cm

The value expressed in terms of x of one of the trigonometric functions of an acute angle t is given Find the values of the other five trigonometric functions of t in terms of x Use 1 as the hypotenuse cos t 13x 1 Express numbers in exact form Use symbolic notation and fractions where needed sin t cot t csc 1 tan t sec t

Macmillan Learn In a certain right triangle the side opposite one of the acute angles t is five times as long as the adjacent side Find the sine cosine and tangent of t Express numbers in exact form Use symbolic notation and fractions where needed sin t cos t ton

A drone is flying due north at a constant speed An observer uses a laser to locate the drone due east at a distance of 120 feet One minute later the observer rotates the laser by 40 to locate the drone See the figure 40 speed Observer How fast is the drone traveling Give your answer to the nearest whole number I 120 Path of drone Enter numeric value feet per minute

Some angles and the length of an altitude of a triangle are given in the figure C A perimeter 30 area 31 45 Find the area and perimeter of the triangle Note that you may wish to find some of the unlabeled sides first Express numbers in exact form Use symbolic notation and fractions where needed B un square uni

of 13 The figure shows points on the unit circle In each case one coordinate is given For the trigonometric point P t H find the missing coordinate and then list the six trigonometric function values of t 1 E y cos 1 F cot 1 B A I G H 3 Express numbers in exact form Use symbolic notation and fractions where needed Crauder et al Preparation for Calculus 1e 2022 Macmillan Learning 33 sin t tan t sec t

Question 7 of 9 This question 3 point s possible The amount after 8 years will be Round to the nearest cent as needed Submit quiz Use the formula for computing future value using compound interest to determine the value of an account at the end of 8 years if a principal amount of 11 000 is deposited in an account at an annual interest rate of 6 and the interest is compounded quarterly 2

If a dealer buys a car from the manufacturer for 6 995 and then sells it for 8 387 his markup is 19 9 8 387 6 995 8 387 In doing this problem Angela calculated Select the correct choice below got an incorrect answer of 16 6 What mistake did she make w OA Angela calculated how much lower the manufacturer s price was compared to the dealer s price OB Angela calculated how much she could save on a new car OC Angela used the gross increase and not the net increase OD Angela used the prices measured in thousands of dollars instead of dollars 2

29 6 is what percent of 160 29 6 is of 160 Type an integer or a decimal

The number 44 is 22 of what number The number 44 is 22 of Simplify your answer Type an integer or a decimal

What is 13 25 of 132 is 13 25 of 132 Type an integer or a decimal

In doing this problem Angela calculated make point s possible If a dealer buys a car from the manufacturer for 15 755 and then sells it for 19 158 his markup is 21 6 19 158 15 755 19 158 Select the correct choice below bmit quiz got an incorrect answer of 17 8 What mistake did she OA Angela used the gross increase and not the net increase OB Angela used the prices measured in thousands of dollars instead of dollars OC Angela calculated how much lower the manufacturer s price was compared to the dealer s price OD Angela calculated how much she could save on a new car

point s possible The percent of increase is Round to one decimal place as needed Submit quiz According to a census bureau from 2000 to 2016 the population of a certain region grew from 269 million to 319 million What was the percent of increase

The number 34 is 21 25 of what number The number 34 is 21 25 of Type an integer or a decimal

Use the simple interest formula 1 Prt and elementary algebra to find the missing quantities in the table below 1 1275 1275 P 8500 P 8500 3 r 3 t years point s possible www

Use the formula for computing future value using compound interest to determine the value of an account at the end of 9 years if a principal amount of 2 000 is deposited in an account at an annual interest rate of 5 and the interest is compounded quarterly The amount after 9 years will be Round to the nearest cent as needed E

1 5 pts Graph one continuous function f x such that all of the following hold a f x is increasing on 2 f x is constant on 2 4 C f x is decreasing on 4 6 d f x is increasing on 6 0

12 Consider f x x 4x and g x x 2 a 3 pts Find f g x Simply your answer b 3 pts Find g x f x c 4 pts What is the domain of Use interval notation

11 Consider the function f x 881 x 6265 x 549 x 22196 x 268 a 3 pts The degree of f x is b 3 pts List the zeros of f x MIDDLESEX Fill in the blanks with either co or 00 c 2 pts As x o f x d 2 pts Ax 100 f x EGE

a 2x 3x y 5 Jadratics using the quadratic formula b 5x 80 y

3 Given f x 2x 3 x 5 x 2 answer the following questions a List the zeros of the function b What is the degree of f x c As x o f x d As x o f x IDDLESEX

11 Consider the function f x 881 x 6265 x 549 x 22196 x 268 a 3 pts The degree of f x is b 3 pts List the zeros of f x MIDDLESEX Fill in the blanks with either co or 00 c 2 pts As x o f x d 2 pts Ax 100 f x EGE

Ing functions in vertex form State if the vertex is a minimum or maximum 1 y x 10x 6 2 y 2x 12x 16 520 3 y 3x 6x 5 5 y x 2x 3 7 y 4x 24x 15 4 y x 12x 15 6 y 2x 16x 11 8 y 5x 100x 300

6 A bullet fired vertically and will have its height h in meters after t time in seconds given by h t 80t 5t a At what time did the bullet reach the maximum height b What is the maximum height the bullet will reach c What is the height of the bullet after 5 seconds d After how many seconds will the bullet hit the ground el When is the bullet at a height of 240m