Basic Math Questions and Answers

Use the formula for the surface area of a right circular cone given by A r r n 1 where r is the radius of the base and h is the height The surface area is in square units Suppose an ice cream sugar cone has a radius of 0 934 inches and a height of 4 625 inches What is its surface area in Round the result to three decimal places Assume the sugar cone is a right circular cone in

Simplify the expression which involves exponents Round your answer to two decimal pl 2 33 0 15 0 012

Simplify the expression which involves a square root Round your answer to two decimal pla 0 47 0 53 37

Simplify the expression which involves an exponent Round your answer to two decimal plac 1 645 13 53 12 3 53 2 2 09

Simplify the expression which involves a square root Round your answer to two decimal plac 125 0 04 10 04

Simplify the expression 65 0 04 1 0 04

3 45 u 2 expression equation Identify the variables coefficients and constants Enter your answers as a comma separated list If there is no answer enter NONE Classify variables coefficients as an algebraic expression or an equation

Round 11 400 610 to the hundred thousands place

Translate the difference x minus 29 2 then divided by 2 6 yields 1 85 into an algebraic equation Do not solve the equation

Consider a variable r where r represents the whole numbers from 1 to 15 Stated mathematically the possible values of rare r 1 2 14 15 Determine which values satisfy the given compound inequality Enter your answers as a comma separated list 2 r 6

Consider a variable x where x represents the whole numbers from 0 to 20 Stated mathematically the possible values of x are x 0 1 2 19 20 For the phrase x is more than 17 write an inequality Determine which values satisfy that inequality Enter your answers as a comma separated list

Translate the sum of 22 2 and z multiplied by 5 8 is 63 62 into an algebraic equation Do not solve the equation

q The water heater is not working r We need to wear face mask Translate the following symbolic statement to verbal form 1 pVq r 2 p q r 3 rAp 4 r pVg B Complete the following TRUTH TABLES 1 2 P P 3 PTF p q PT P 9 T T F F P PAP PV q P T T F F P q H F T F P 9 9 VE T F T F T T P p q P PV q P 9 P q

Round 535 795 to the ten thousands place

Round 80 151101 to the next greater whole number

Round 424 to the next greater whole number

Consider the absolute value inequality x4 2 Solve the absolute value inequality and write the answer in interval nota

Consider the set of bivariate data shown in the table Compute X y 0 5 1 18 5 2 20 3 23 4 4 23 2 5 24 1 6 24 8

Consider the absolute value equation x 1 8 Solve the equation Enter your answers as a comma separated list x 9 7 Graph the solution on the real number line Use the tools to enter your answer

Round 339 691 to the thousands place

Determine the currents I I and I for the electrical network shown in the figure Assume V 3 V and V 4 V I A A A 35 1 1 1 R 49 12 ww R 30 13 R 102 V 17

Round 0 00328 to three decimal places

A footwear retailer sold 9 pairs of sneakers for 55 each 18 pairs of leather shoes for 155 each 3 pairs of boots for 240 each and 7 pairs of sandals for 30 each Question 4 of 8 a What is the weighted average price of the footwear sold Round to the nearest cent b What is the simple arithmetic average Round to the nearest cent Which method is the most suitable for determining the average price of the

Find the total weight of three items that weigh 2 4 2 10 kg 3 kg and 7 kg 3 6 4 Question 2 of 8 Total weight Round to two decimal places

Convert the following mixed numbers into improper fractions Simplify your answers and express them in their lowest terms a 5 Question 7 of 8 b 19

Convert the following improper fractions into mixed numbers Simplify and reduce your answer to its lowest terms a b 13 3 29 9 Question 1 of 8 010

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 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

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

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

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

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

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

b 4x 8x 9 0 Answer x and x

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

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

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