Math - Others Questions

Evaluate each of the following expressions a 80 000 1 0 04 11 b 980 1 02 1 0 02 Round to two decimal places Round to two decimal places

Select the greater fraction from the following 27 6 Question 8 of 8 30 7

Find I in the circuit in Fig P2 2 13 given that lo 12 mA 6 mA M 6 mA 21 FIGURE P2 2 13

An automobile uses two halogen headlights connected as shown in Fig P2 6 Determine the power supplied by the battery if each headlight draws 3A of current Use V 15 V for voltage V Figure P2 6 Notes on entering solution Enter your solution in Watts W Enter your solution to 2 decimal places Do not include units in your answer ex 5 W is entered as 5 00 Give the answer for the power supplied and not the current

Find in the network in Fig P2 10 given 12 5 mA and 13 2 mA 1 m www Figure P2 10 www 12 mA W Notes on entering solution Enter your solution in milliAmperes mA Enter your solution to 2 decimal places 13 mA mA Do not include units in your answer ex 5 mA is entered as 5 00

Find Vfb in the circuit in Fig P2 20 Given the voltage reading on the resistors of V1 10 V V2 6 V and V3 5 V V1 a 12 V ww 8 2V Figure P2 20 ww V2 C ex 5 V is entered as 5 00 3 V V4 e Notes on entering solution Enter your solution in Volts V Enter your solution to 2 decimal places Do not include units in your answer V3 Reminder Vfb means that f is the high side and b is the low side

Find Vec in the circuit in Fig P2 20 Given the voltage reading on the resistors of V1 6 V V2 6 V and V3 4 V V1 a 12 V ww 8 2V Figure P2 20 b ww V2 f C ex 5 V is entered as 5 00 3 V V4 d V3 Notes on entering solution Enter your solution in Volts V Enter your solution to 2 decimal places Do not include units in your answer Reminder Vec means that e is the high side and c is the low side

A model for a standard two D cell flashlight is shown in Fig P2 5 Find the power dissipated in the lamp Given V1 5 V V2 16 V and R 80 V1 V2 R lamp Figure P2 5 Notes on entering solution Enter your solution in Watts W Enter your solution to 2 decimal points Do not include units in your answer ex 5 W is entered as 5 00 Give the answer for the power supplied and not the current

Determine the power dissipated in the resistor in Fig P2 1 Given V 6 V and R 40 V v Figure P2 1 R Notes on entering solution Enter your solution in Watts Enter your solution to 2 decimal points Do not include units in your answer ex 5W is entered as 5 00

Four different linear functions are represented below 10 6 3 Function 1 10 Function 3 y x 4 Answer the following questions 6 8 10 Function 2 X 2 1 0 1 2 y 4 st 1 2 5 8 Function 4 The slope is 5 and the y intercept is 1 a Which function has the graph with a y intercept closest to 0 O Function 1 Function 2 Function 3 Function 4 b Which functions have graphs with y intercepts greater than 2 Check all that apply Function 1 Function 2 Function 3 Function 4 c Which function has the graph with the greatest slope Function 1 Function 2 Function 3 Function 4

Four different linear functions are represented below 10 8 Function 1 10 11 aft Function 3 y x 2 answer the following questions 6 8 10 Function 2 a Which function s graph is the least steep X 2 1 0 1 2 y 11 6 1 4 9 Function 4 The slope is 2 and the y intercept is 4 Function 1 O Function 2 Function 3 Function 4 b Which functions have graphs with slopes less than 4 Check all that apply Function 1 Function 2 Function 3 Function 4 c Which function has the graph with the greatest y intercept O Function 1 Function 2 Function 3 Function 4

The monthly cost in dollars of water use is a linear function of the amount of water used in hundreds of cubic feet HCF The cost for using 14 HCF of water is 33 53 and the cost for using 25 HCF is 51 68 What is the cost for using 16 HCF of water Monthly cost in dollars Water usage in HCF

For the linear programming problem Maximize f 6x1 7x2 subject to 50 60 6x19x2 3x1 2x2 X1 0 X2 0 A Fill in the initial tableau feel free to just draw on paper x1 x2 S t

Comment on who appears to be the market share leader and how the market shares are changing over time In Year 1 and Year 2 Hertz was the clear market share leader In Year 3 and Year 4 Hertz and Avis have approximately the same market share The market share for Dollar appears to be declining In Year 1 and Year 2 Dollar was the clear market share leader In Year 3 and Year 4 Dollar and Hertz have approximately the same market share The market share for Avis appears to be declining In Year 1 and Year 2 Avis was the clear market share leader In Year 3 and Year 4 Avis and Hertz have approximately the same market share The market share for Dollar appears to be declining In Year 1 and Year 2 Avis was the clear market share leader In Year 3 and Year 4 Dollar and Avis have approximately the same market share The market share for Hertz appears to be declining In Year 1 and Year 2 Hertz was the clear market share leader In Year 3 and Year 4 Hertz and Dollar have approximately the same market share The market share for Avis appears to be declining Construct a bar chart showing rental cars in service for Year 3 Cars in Service 1000s 350 300 250 200 150 100 50 0 Hertz Dollar Company Avis Is this chart based on cross sectional or time series data O cross sectional time series Cars in Service 1000s 350 300 250 200 150 100 50 0 Hertz Dollar Company Avis Cars in Service 1000s 350 300 250 200 150 100 50 0 Hertz Dollar Company Avis Ox Cars in Service 1000s 350 300 250 200 150 100 50 0 Hertz X Dollar Company Avis

A lighthouse sits at the edge of a cliff as shown A ship at sea level is 1100 meters from the base of the cliff The angle elevation from sea level to the base of the lighthouse is 48 1 The angle of elevation from sea level to the top of the lighthouse is 50 5 Find the height of the lighthouse from the top of the cliff Do not round any intermediate computations Round your answer to the nearest tenth Note that the figure below is not drawn to scale A 50 5 48 1 1100 meters

or each of the polynomial descriptions below draw a sketch that may represent that function Degree 3 4 Lead Coefficient ve ve Number Number of of T P Zeroes 2 3 3 1 Sketch

Looking up Ivanna sees two hot air balloons in the sky as shown She determines that the lower hot air balloon is 365 meters away at an angle of 23 from the vertical The higher hot air balloon is 1035 meters away at an angle of 41 from the vertical How much higher is the balloon on the right than the balloon on the left Do not round any intermediate computations Round your answer to the nearest tenth Note that the figure below is not drawn to scale 365 meters 23 41 1035 meters meters 5

Your company wants to set aside a fixed amount every year to a sinking fund to replace a piece of industrial equip costing 248 000 at the end of three years from now The sinking fund is expected to earn 4 interest How much your company deposit each year to meet this goal Click the icon to view the interest factors for discrete compounding when i 4 per year Your company nust deposit each year to meet this goal Round to the nearest dollar

Joe s starting salary as a mechanical engineer is around 80 000 Joe is planning to place a total of 8 of his salary each year in mutual funds Joe expects a 4 salary increase each year for the next 25 years of employment If mutu funds will average 6 annual return over the course of his career what can Joe expect at retirement Click the icon to view the interest factors for discrete compounding when i 6 per year The amount Joe can expect at retirement is Round to the nearest dollar

What is the equal payment series for 12 years that is equivalent to a payment series of 15 000 at the end of t first year decreasing by 1 000 each year over 12 years Interest is 8 compounded annually Click the icon to view the interest and annuity table for discrete compounding when 8 per year The equal payment series equivalent is Round to the nearest dollar

ompute the value of P in the accompanying cash flow diagram assuming that i 9 250 250 100 100 P 1 150 150 2 3 200 200 4 Years 5 6 7

You have borrowed 50 000 at an interest rate of 12 Equal payments will be made over a three year period The fi payment will be made at the end of the first year What will the annual payment be and what will the interest paymen be for the second year Click the icon to view the interest factors for discrete compounding when i 12 per year

Suppose you have the alternative of receiving either 24 000 at the end of seven years or P dollars today Currently have no need for money so you could deposit the P dollars in a bank that pays 3 interest What value of P would make you indifferent in your choice between P dollars today and the promise of 24 000 at the end of seven years Click the icon to view the interest factors for discrete compounding when i 3 per year The value of P that would make you indifferent in your choice is Round to the nearest dollar

Suppose that you are obtaining a personal loan from your uncle in the amount of 39 000 now to be repaid in four years to cover some of your college expenses If your uncle usually earns 11 interest annually on his money which nvested in various sources what minimum lump sum payment four years from now would make your uncle happy Click the icon to view the interest factors for discrete compounding when i 11 per year The minimum lump sum payment four years from now should be Round to the nearest dollar

Consider the following sequence of deposits and withdrawals over a period of four years If you earn 15 interest on your deposits how much will you able to withdraw at the end of four years 800 830 1 030 At the end of four years you will be able to withdraw 2 1 330 B Click the icon to the interent factor for dinarata campaunding when in 15 marun Round to the nearest dollar

ou are considering purchasing a machine that is expected to produce the following cash flows 63 000 in year 1 72 000 in year 2 68 000 in year 3 54 000 in year 4 and 41 000 in year 5 If your interest rate is 11 what wou e your maximum offer purchase price on this machine Click the icon to view the interest factors for discrete compounding when i 11 per year

What is the present worth of these future payments a 25 500 eight years from now at 12 compounded annually b 58 000 twelve years from now at 4 compounded annually c 25 000 nine years from now at 6 compounded annually d 35 000 four years from now at 9 compounded annually Click the icon to view the interest factors for discrete compounding when i 4 per year Click the icon to view the interest factors for discrete compounding when i 6 per year Click the icon to view the interest factors for discrete compounding when i 9 per year Click the icon to view the interest factors for discrete compounding when i 12 per year a The present worth is Round to the nearest dollar

You are paying into a mutual fund that earns 8 compound interest If you are making an annual contribution 13 000 how much will be in the funds in 12 years Click the icon to view the interest factors for discrete compounding when i 8 per year will be in the funds in 12 years Round to the nearest dollar

ou are interested in buying a piece of real property that could be worth 300 000 in 10 years Assuming that your oney is worth 8 how much would you be willing to pay for the property Click the icon to view the interest factors for discrete compounding when i 8 per year he maximum amount you would be willing to pay for the property is thousand Round to the nearest hole number

You are about to borrow 15 000 from a bank at an interest rate of 8 compounded annually You are required to make three equal annual repayments in the amount of 5 820 50 per year with the first repayment occurring at the end of ye 1 Show the interest payment and principal payment in each year Fill in the table below Round to the nearest cent End of Year 0 Principal Repayment Interest payment Remaining Balance

1000 900 800 a range 700 600 Amount 500 of flour grams 400 300 100 Time minutes Write your answers as inequalities using x or y as appropriate Or you may instead click on Empty set or All reals as the answ h demain 0 0 0 0 Oso 8 08 20 Empty set a reals

Complete the description of the piecewise function graphed below Use interval notation to indicate he intervals 7 4 4 4 4 4 3 0 s 4 2 2 to t f x 4 if x 4 fe 0 2 2 3 2

John and Susan just opened savings accounts at two different banks Each deposited 1 900 John s bank pays simple interest at an annual rate of 11 whereas Susan s bank pays compound interest at an annual rate of 10 5 No principal or interest will be taken out of the accounts for a period of five years At the end of five years whose balance will be higher and by how much John s interest earned by 1 900 for five years at 11 simple interest is Round to the nearest dollar

Find the domain and range of the function graphed below Domain Range m 27 2 3 FANT CENTRE CURRENT 4

The plot below represents the function f x Y 2 ex 2 3 2 72375 3 Evaluate f 1 f 1 MAY bient TAMAN Mari www www wwwww HALK INTEN

3 40 Use nodal analysis to find V in the circuit in Fig P3 40 6 kn V 6 kn Figure P3 40 6 kn 12 V 6 kN 6 kn

3 2 3 2 Find both I and V in the network in Fig P3 2 using nodal analysis 6 kn ww 2 mA Figure P3 2 3 kn Vo 4 mA 12 k

3 100 Use nodal analysis to find V in Fig P3 100 0 3 mA Figure P3 100 10 kn 1 21x 10 k

EXAMPLE 00 ever Have you OO heard the term dark sky park This is a special place where efforts are made to keep the night sky really dark That means the use of light is either completely avoided or kept 31 the absolute minimum People visit dark sky parks to observe stars and planets without artificial lighting and to enjoy the night sky the way it truly should be seen from Earth naturally beautiful contrasting dark and yet shiny The very first dark sky park in Slovakia and the 20th oldest in the world was opened in 2010 in Poloniny Poloniny is a national park 32 in eastern Slovakia near the borders with Poland and Ukraine It is part of the Eastern Carpathians mountain range and is known for 33 pristine nature diverse ecosystems and rich biodiversity Poloniny National Park is an important area for the conservation of natural habitats and species attracting visitors interested in ecotourism and outdoor activities such 34 hiking birdwatching and Stargazing Despite its unique nature Poloniny is the least visited national ark in Slovakia The effects of human activity on the environment re minimal making Poloniny home to an extraordinary number endangered animal and plant species The mountains prevent direct visibility of lights from surrounding towns and villages and the population is very sparse in the area around the park thanks t which there is minimal to 35 artificial lighting Th 36 Poloniny the darkest area in Slovakia with very low light pollution Unfortunately there are no areas with zero li pollution in Slovakia 37 In good conditions objects and phenomena no longer or only rare visible in most of Europe can be observed in the night sky The Milky Way is perfectly visible and nearly 2 000 stars can be seen without a telescope compared to approximately 200 in towns ar 20 in cities Apart from being a great place for outdoor stargazin sessions Poloniny is also home to 38 Observatory on Kolonick sedlo It houses the second largest astronomical telescope in Slovakia with a diameter Vihorlat 39 1 metre and the public can book a night sessie The Poloniny Dark Sko

Josh is exploring the formula for the circumference of a circle He computed the circumferences of several circles wit different radii He then plotted the results and connected them with a line as shown below The graph shows the circumference in mm versus the radius in mm Find the domain and the range of the function shown Circumference mm 150 a domain 135 120 105 90 75 60 45 30 15 36 Radius mm Write your answers as inequalities using x or y as appropriate Or you may instead click on Empty set or All reals as the answer X 030 O OSO 08

5 4 w 2 1 sfx 3 H 13 1 2 a Is g 1 negative Yes No 3 5 b For which value s of x is g x 0 Write your answer using interval notation 0 c For which value s of x is g x 0 If there is more than one value separate them with commas

b 4x 8x 9 0 Answer x and x

Factor fully 11 x 3 y x 3 o 11 y x 3 o 11 y x 3 o y 3 x 11 o y 11 x 3

PHON Solve for x 4x2 28x 48 0 x 11

Factor fully 112x 150x27 8x 3 14x 9 o 8x 9 14x 3 o 8x 9 14x 3 O 9x 8 3x 14

Determine the exponent m when the following expression is simplified m 11 x6 x xm

Choose the simplified form 3x 4 4x 2 3 7 o 12x2 10x 10 O 9x 10x 13 O 9x 10x 13 12r2 70

36y 11x 6y 11x 6y 11x 6y 11x 6y o o 1213 11y 6x 11y 6x 2 11x 6y 3

Determine the coefficients p and q and exponents m and n when the following expression is simplified 2x y 3xy5 3 px qyn

Simplify the following expression and choose the correct answer 4x 4 y 2 x 4y I 4 O 4