Math - Others Questions

A radioactive material decays according to the function A t Age 0 0244t where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist has a sample of 400 g of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 30 years d When will only 300 grams of the radioactive material be left e What is the half life of the radioactive material a The decay rate of the radioactive material is 2 44 Type an integer or a decimal b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 A Q B O c There will be about gram s of the radioactive material left after 30 years Do not round until the final answer Then round to the nearest tenth as needed O C 20 Q OD Sa Q

A sample of bacteria is decaying according to a half life model If the sample begins with 900 bacteria and after 10 minutes there are 360 bacteria after how many minutes will there be 40 bacteria remaining When solving this problem round the value of k to four decimal places and round your final answer to the nearest whole number

After the 25 years have passed I plan on retiring and will now use the money that has built up as my retirement pay I will make monthly withdrawals every month for 20 years 5 How much money can I withdraw each month from this same account 3 5 compounded monthly for the next 20 years Show all work

A plane has an airspeed of 127 km h It is flying on a bearing of 85 while there is a 27 km h wind out of the northeast bearing 225 What are the ground speed and the bearing of the plane The ground speed is km h Round to the nearest tenth as needed

Let A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply A 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 OD 3 3 6 6 8 8

Find the adjacency matrix for the relation r 3 9 6 5 8 5 6 9 from the set A 3 6 8 to the set B 3 5 9

Which of the following relations on P are symmetric Select all that apply Be able to explain your answers DA i e the relation of divides OB OC OD DE 2

Let A 3 4 8 Which of the following relations on A are symmetric Select all that appl DA 3 8 4 8 8 3 8 4 8 8 B 3 3 3 4 4 3 4 8 8 8 OC 3 3 4 4 OD 3 4 3 8 4 3 4 8 8 3

The link below gives the Hasse diagram for a poset with partial ordering Click this link to view the Hasse diagram Which of the statements below are true Select all that apply DA bza OB a a OC c f OD d b DE b d OEde e a b C

4 1 4 relation r relation 3 2 3 4 relation relation r 3 2 3 4 attempts remaining The link below gives the digraphs for four different relations r1 12 13 14 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are antisymmetric Select all that apply Be able to explain your answers OA TA OB rs DC n OD 12

Problem 07 021 Heat transferred between two reservoirs Heat is transferred at a rate of 2 kW from a hot reservoir at 900 K to a cold reservoir at 300 K Calculate the rate at which the entropy of the two reservoirs changes Round the final answer to three decimal places The rate at which the entropy of the two reservoirs changes is Is the second law satisfied Click to select Click to select Yes No kW K

11 az a 160 B 7 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where nee

Macmillan Learning Solve the given triangle Use degree measure B A 55 A 5 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where n C A

Macmillan Learning Find the area of the triangle in the figure 5 area 3 Macmillan Learning Crauder et al Preparation for Calculus le 2022 Give an exact answer Use symbolic notation and fractions where needed

4 1 relation r 4 relation N 3 2 3 4 1 4 relation r relation r 2 2 3 4 attempts remaining The link below gives the digraphs for four different relations r 72 73 74 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are reflexive Select all that apply Be able to explain your answ nswers A Ti B 73 OC T2 OD T4 Submit answer

oblem 1 Use the Law of Sines of the Law of Cosines when it applies Solve each triangle and assume standard labeling a b 3 4 c 2 8 A 82 b A 30 a 20 B 45 c A 30 a 5 b 5 2 d a 19 b 2 c 3 e a 40 2 A 135 B 30 f A 63 C 55 a 8 3

ne opens an account at the local bank by depositing 50 of his birthday money He continues to deposit 50 each month for 5 years If the account 3 25 interest compounded monthly how much is in the account after 5 years 0 10000 Word Limit

Let A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply OA 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 P 3 3 6 6 88

Let A 3 4 8 Which of the following relations on A are symmetric Select all that apply OA 3 8 4 8 8 3 8 4 8 8 B 3 3 3 4 4 3 4 8 8 8 OC 3 3 4 4 OD 3 4 3 8 4 3 4 8 8 3

A carpet is to be installed in one room and a hallway as shown in the diagram below At a cost of 14 50 per square meter how much will it cost to carpet the area Assume a 4 7 m b 6 5 m and c 10 7 m Round your answer to the nearest cent 1173 38 X

llar course shown in the figure below C 433 mi 300 mi 200 mi B A a Use the Law of Cosines to find the angle located at vertex B Round to the nearest degree as needed b Use the Law of Sines to find the angle a located at vertex A Round to the nearest degree as needed

The extreme temperatures for each continent for a given year are listed in the da a table Usir dicted a cubic model a location with a maximum temperature of 95 degrees Fahrenheit is have a minimum temperature of 86 degrees How reliable is this prediction Give a reasons to defend your answer ast two Continent Maximum F Minimum F Africa Antarctica Asia Australia Europe Oceania North America South America 136 59 129 128 122 108 134 120 11 129 90 9 67 14 81 27

Problem 3 A pole tilts towards the sun at an 8 angle from the vertical and it casts a 22 foot shadow The angle of elevation from the tip of the shadow to the top of the pole is 43 How tall is the pole Include a diagram

The triangle in the figure may require the law of sines or the law of cosines Choose the appropriate method and solve the triangle A 11 Use decimal notation Give your answers to two decimal places Include the degree symbol in your answers where needed If two solutions exist just pick one and either will be counted as a correct one Enter DNE if the triangle has no solution B 15

8 of 13 The triangle in the figure may require the law of sines or the law of cosines Choose the appropriate method and solve the triangle A 45 b b A 5 C Use decimal notation Give your answers to two decimal places where needed Include the degree symbol in your answers where needed If two solutions exist enter one solution and either will be counted as correct Enter DNE if the triangle has no solution 30

The triangle in the figure may require the law of sines or the law of cosines Choose the appropriate method and solve the triangle A 5 B B b 8 Use decimal notation Give your answers to two decimal places Include the degree symbol in your answers where needed If two solutions exist just pick one and either will be counted as a correct one Enter DNE if the triangle has no solution 14

A service ramp is 20 feet long and makes an angle of 10 with the horizontal See the figure It is found to be out of compliance with regulations of the Americans with Disabilities Act ADA and must be replaced with a new ramp that makes an angle of 5 with the horizontal New ramp length 20 50 10 How long is the new ramp Give your answer to the nearest whole number feet

Macmillan Learning Solve the triangle which is a case of SSA A B B 45 10 Use decimal notation Give your answers to two decimal places Include the degree symbol in your answers where needed If two solutions exist enter one solution and either will be counted as correct Enter DNE if the triangle has no solution 116

on Macmillan Learning Solve the triangle which is a case of SAA 60 C 60 b C 9 Give exact answers Use symbolic notation and fractions where needed Include the degree symbol in y where needed

n 1 of 13 Macmillan Learning Solve the triangle which is a case of ASA B 40 a 11 70 C Use decimal notation Give your answers to two decimal places if needed Include the degree symbol in your answer where needed B

Letr be the following relation on the set Z cry if and only if y x 2 Which of the following are elements of r Select all that apply OA 10 4 OB 2 4 OC 5 9 OD 5 1

The definition of transitive may be restated as follows Definition Let r be a relation on A Then r is transitive if and only if whenever a b er and b c Er it must be true that a c Er Let A 2 3 6 10 14 Let r be the following relation on the set A r 2 2 2 6 3 14 6 2 6 6 14 10 a Find all the elements in r2 Enter your answer below as a list of ordered pairs separated by commas Answer 4 b List all ordered pairs that are in r2 but not in r Answer c The relation r is not transitive Explain why not by filling in the following blanks with the appropriate ordered pairs Answer r is not transitive because is in r and is in r but is not in r

4 4 attempts remaining The link below gives the diagraph for a relation r on t set A 1 2 3 4 Click this link to view the graph Find all the elements in r Enter your answer below a list of ordered pairs separated by commas Answer r

Let A 2 4 6 Define r to be the relation on the set A defined by the following xry if and only x y 2 Enter each answer below as a list of ordered pairs separated by commas a Find all the elements in r Answer r b Find all the elements in r

If the temperature is held constant the pressure of a gas in a container varies inversely as the volume of the container Assume that the gas pressure in a piston cylinder the container is 6 pounds per square inch when the volume of the cylinder is 130 cubic inches If the volume of the cylinder is reduced to 125 cubic inches what is the pressure of the gas pounds per square inch Round to two decimal places as needed GILB

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length A beam that is 4 inches wide 8 inches deep and 8 feet long can support a weight of 1920 pounds If the same type of beam that is 7 inches wide and 4 inches deep can support 480 pounds how long is the beam The beam is feet long Type a whole number

While in a foreign country Ben rented a car whose speedometer is calibrated in both miles and kilometers per hour The marking on the speedometer shows that 30 miles per hour corresponds to 48 kilometers per hour While driving from the airport to the coast he sees a road sign that says Ocean 40 kilometers How many miles does he still have to drive He still has to drive miles www

There are 449 seats in a nation s House of Representatives The number of representatives per state is calculated using a statistical formula determined by law but allocation is roughly proportionate to population In 2010 the nation s population was estimated to be 308 6 million The state s population was estimated at 24 9 million How many representatives would you expect to be assigned to the state Suppose the state actually has 39 representatives Compare this with the expected number of representatives from the state The expected number of representatives in the state is Round to the nearest integer as needed

The braking distance of a car varies directly as the square of the speed of that car Assume that a car traveling 40 miles per hour can stop 44 feet after the brakes are applied How long is the braking distance for that same car traveling at 55 www feet Round the final answer to the nearest integer as needed Round all intermediate values to four decimal places as needed

Assume that the amount of water that Mario uses for irrigation at his vineyard is inversely proportional to the amount of rainfall If he uses 80 000 gallons during a month in which there is 3 inches of rain how much water would he use in a month that has 6 inches of rain gallons Round to the nearest integer as needed

If the speed limit is 50 miles per hour and a person s trip takes 2 5 hours at that speed how much time does the person save by traveling 60 miles per hour www The person saves minutes Round the final answer to two decimal places as needed Round all intermediate values to four decimal places as needed

To determine the number of trout in a lake a conservationist catches 131 trout tags them and throws them back into the lake Later 56 trout are caught 14 of them are tagged How many trout would the conservationist expect to be in the lake The conservationist would expect that there are trout in the lake

Many tax preparation organizations will prepay customers tax refunds if they pay a one time finance charge In essence the customer is borrowing the money the refund minus the finance charge from the tax preparer prepaying the interest as in a discount note and then repaying the loan with the tax refund This procedure allow customers access to their tax refund money without having to wait Joy had a tax refund of 742 77 due She was able to get her tax refund immediately by paying a finance charge of 40 36 What annual simple interest rate is paying for this loan assuming the following are true Assume 360 days in a year a The tax refund check would be available in 5 days b The tax refund check would be available in 10 days c The tax refund check would be available in 20 days a The annual simple interest rate is about Type an integer or decimal rounded to the nearest hundredth as needed

Assume that r varies jointly as s and b2 If r 525 when s 6 and b 5 what is the value of b when s 4 and r 1134 Points 0 of

Solve the following variation problem by first writing the variation as an equation and finding the constant of variation Then answer the question Assume that r varies inversely as s If r 8 when s 1 2 find r when s 1 Which of the following is the appropriate problem solving method OA Try a simpler version of the problem B The splitting hairs principle C Choose good names for unknowns OD Draw pictures C

K 3 If D varies inversely as C and D when C5 find D when C 24 D Type an integer or a simplified fraction

Assume that y varies jointly as x and w and inversely as z If y 15 when x 2 5 w 8 and z 20 what is the value of y when x 7 w 7 and z 14 y Type an integer or a simplified fraction TEE

K Find the missing number in the proportion 12 3 x w 8 x

K Solve for x in the following proportion 2 x 6 21

A country s population in millions in 2002 and 2010 are given below Use this information and the exponential model A P 1 r to find the growth rater for the country over this period population in 2002 137 million population in 2010 134 million The country s growth rate over this period was Round to the nearest hundredth as needed