Basic Math Questions and Answers

Suppose a closed economy has an aggregate savings equal to 300 and intended investment equal to 450 By how much must the government be in surplus round your answer to the nearest whole value Your Answer

Which of the following number s rounds to 0 19 Select all that apply A 0 19559 B 0 19198 C 0 18786 D 0 18186

nd the accumulated present value of an investment over a 10 year period if there is a continuous money flow of 2800 per year and the current interest rate is 8 compounded continuously ote Do not use commas in your answer

Lett be the number of years since 1984 What does t 13 mean in this situation t 13 represents the year

Perform the exponentiation Leave ans 3 5 3 64 3 5 125 Simplify your answer

76 inches to centimeters 1 pound 0 454 kilograms 1 inch 2 54 centimeters 1 mile 1 61 kilometers 1 pint 0 473 liters 1 fluid ounce 0 0296 liters 76 in cm Round to two decimal places as needed

45 m to centimeters Kilo 1000 basic units Hecto 100 basic units Deka 10 basic units Deci 0 1 basic units Centi 0 01 basic units Mili 0 001 basic units 5m

A couple deposits 25 000 into an account earning 4 annual interest for 15 years Calculate the future value of the investment if the interest is compounded monthly Round your answer to the nearest cent Itranscript Formulas

The least common denominator LCD of 3 10 1 3 and 71 3 is

Suppose a closed economy has an aggregate consumption function given by C 300 0 50Yd and generates 3000 output and income in equilibrium Suppose also that the government collects a lump sum tax of 200 How much will the private sector be saving total in equilibrium round your answer to the nearest whole value Your Answer

Pro m 2 A horizontal force of 100 N is required to start a 40 kg block sliding along a horizontal sur face What is the coefficient of static friction Solution

A 100 foot vertical tower is to be erected on the side of a hill that makes a 6 angle with the horizontal Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower see figure Note that x 100 in the figure Round your answers to one decimal place shorter wire ft ft longer wire x ft 75 ft 75 ft

suppose you are a researcher in a hospital You are experimenting with a new tranquilizer You collect data from a random sample of 9 patients The period of effectiveness of the tranquilizer for each patient in hours is as follows 2 5 2 5 2 8 3 2 8 2 4 2 1 2 3 What is a point estimate for the population mean length of time Round answer to 4 decimal places 2 points Which distribution should you use for this problem 1 point O normal distribution Ot distribution What must be true in order to construct a confidence interval in this situation 1 point O The population mean must be known O The population standard deviation must be known O The sample size must be greater than 30 O The population must be approximately normal Construct a 99 confidence interval for the population mean length of time Enter your answer as an open interval i e parentheses Round upper and lower bounds to two decimal places 4 points What does it mean to be 99 confident in this problem 2 points O 99 of all simple random samples of size 9 from this population will result in confidence intervals that contain the population mean O The confidence interval contains 99 of all samples O There is a 99 chance that the confidence interval contains the population mean Suppose that the company releases a statement that the mean time for all patients is 2 hours Is this possible 1 point

Which of the following graphs have Hamiltonian circuits H U U X OA S R H X Oc T Y Q S P K T M S U OB OD I N R V H 0 G

Indicate below which graphs are forests and which are trees If the graph is neither don t check any boxes 0 H K OA Is a forest OA Is a tree G P Q I J OC Is a forest OC Is a tree R I G F H E I OB Is a forest OB Is a tree E F F NA E G J H D J D OD Is a forest OD Is a tree I C

K I L H M G Consider the graph given above Add an edge so the resulting graph has an Euler circuit without repeating an existing edge SI Now give an Euler circuit through the graph with this new edge by listing the vertices in the order visited

F G E D Consider the graph given above Give an Euler circuit through the graph by listing the vertices in the order visited

Construct a simple graph with vertices J K L M whose degrees are 3 3 2 2 What is the edge set

Given a triangle with angle A 94 degrees and sides a 29 and b 18 Find side c C

a b d What is the area of this figure area Figure is not to scale Find the area of the quadrilateral shown The lengths are a 4 9 b 5 3 c 7 9 d 8 8 and e 8 3 all measured in yards C vd

Given the triangle Area 16 42 t find the area of the triangle Round your final answer to 4 decimal places 13 Q units

Which of the following graphs have Euler circuits R S T 0 U 0 R V N S M P 0 OA Has Euler circuit OB Has Euler circuit 0 LK R Q S J R I T OC Has Euler circuit OD Has Euler circuit

Consider the following graph a b A a B b g C c OD d O E e OF f C f Which vertices are in the connected component of this graph that contains the vertex c Select all that apply d

Which of the following graphs are connected N U 0 T L P A C H RH I K I B D H L F J G E

L K M N H Consider the graph given above a How many vertices does the graph have b What is the degree of vertex M c What is the degree of vertex K d How many connected components does the graph have

Integrated Directions Please show work on the fest Diagrams are not drawn to scale 1 In the following problems find the value of n M 659 75 30 S 18 80 n 12 b 110 130 b 120 2 Calculate the area of each regular polygon below Round answers to the nearest tenth a 16

Acceleration is the rate at which velocity changes The formula is a a is acceleration vo is initial velocity speed v is final velocity to is initial time t is final time Solve this formula for v Units must be consistent If the units for vand vo are feet per second and the units for t and to are seconds what must the units for a be feet second 2 Ov a t to v Ov a t to vo Ova t to Ov a V V0 t to t to Vo where A car was stopped at a red light When the light turns green the car reaches a speed of 31 miles per hour

PERFORM THE FOLLOWING CALCULATIONS AND ROUND YOUR ANSWER TO THE CORRECT SIGNIFICANT FIGURES REMINDER When adding or subtracting round to the least number of decimal places When multiplying or dividing round to the least number of significant figures Multiplication and Division 1 13 7 x 2 5 2 200 x 3 58 3 0 00003 x 727 4 5003 3 781 5 89 9 0 6 5000 55 7 0 00005 x 538 Addition subtraction 4 60 3 1 2 0 008 0 05 3 22 4420 56 981 4 201 87 3 5 67 5 0 009 6 71 86 13 1 7 357 89 0 002

A 76 912 State Population a Apportion the seats using Hamilton s method b Suppose that a fourth state with the population shown in the table is added with five additional seats Does the new states paradox occur using Hamilton s method State C D Population 744 096 95 680 A 76 912 B 282 992 a Apportion the seats State Population Number of Congressional Seats Type whole numbers B 282 992 A 76 912 population of each state is shown in the table Total Q C 744 096 1 104 000 B 282 992 0 C 744 096 Total 1 199 680

x 19 5 pts The machine that produces patties for Hardee s Myocardial Infarction Burger is set to produce patties with a mean of 8 1 ounces of beef like stuff with a standard deviation of s 0 5 ounces Assume that the weights of the patties are distributed normally What percentage of the patties chosen at random from the line will have less than 7 8 ounces of beef like stuff in them

K A country with three states has 30 seats in the legislature The population of each state is shown in the table below a Apportion the seats using Hamilton s method b Does the Alabama paradox occur using Hamilton s method if the number of seats is increased from 30 to 31 State Population A 163 B 251 A 163 a Complete the table with the apportionment of the seats using Hamilton s method State Population Hamilton s apportionment B 251 C 486 U Total 900 C 486 Total 900 30 HILS

K A company has 30 000 employees in three cities as shown in the table below It wishes to give promotions to 200 employees Cities B A 9140 Original Number of Employees 6050 a Apportion the promotions using Hamilton s method b Suppose that in 10 years the cities have the following number of employees and the company wishes to again give promotions to 200 employees Does the population paradox occur Hamilton s method Cities Number of Employees 10 years later A 9170 A 9140 C 14 810 B C Total C 6050 14 905 30 125 a Complete the table with Hamilton s apportionment for the original number of employees Cities Original Number of Employees Hamilton s Apportionment B 6050 Total 30 000 C 14 810 Total 30 000 200

31 75 N attached as the last p rk in detail for The principal P is borrowed and the loan s future value A to the nearest tenth of a percent 4 P 170 A 238 00 1 4 years Interest 288 00 17

18 10 pts Find the percent of the total area under the standard normal curve which is a between z 38 and 2 1 71 b to the left of z 0 94

K A company has employees in country A and country B The number of employees in each group is shown in the table below There are 44 managers to be apportioned between the two groups Country A B 857 3543 Total C 4400 Employees a Apportion the managers using Hamilton s method b Suppose that additional employees in country C with the number of employees shown in the table below are added with 7 new managers Does the new states paradox occur using Hamilton s method Country Employees A 857 B 3543 C 733 A 857 a Complete the table with Hamilton s apportionment of the 44 managers to countries A and B Country Employees Hamilton s Total 4400 apportionment Total 5133 B 3543 44 www

Consider the apportionment of 40 doctors for a physicians organization The apportionment using Hamilton s method is shown in the table below Does the Alabama paradox occur using Harm method if the number of doctors is increased from 40 to 41 Clinic Patients Standard quota Lower quota Hamilton s apportionment A 246 9 19 9 9 Clinic Patients Hamilton s apportionment B 201 7 51 7 A 246 8 C 195 7 28 7 B 201 7 D 204 7 62 7 C 195 8 E 225 8 40 8 D 204 8 Complete the table below with the new apportionment for clinics A B C D and E using a standard divisor rounded to two decimal places Total 1071 40 00 38 E 225 40 Total 1071 C 41 C www

If a material has a poisson ratio of 0 2 and the strain in the lateral direction is 0 005 what is the axia strain

8 10 pts Consider the random variable z whose probability distribution is given b 4 5 6 22 10 05 a Find P x 2 2 3 11 17 35 I P z 11 b Find the expected value of r

9 15 pts Consider forming a list of three numbers from the numbers in the set 3 4 5 6 7 a How many different lists can be formed if repetitions are allowed b How many different lists can be formed if repetitions are not allowed c How many different lists can be formed if repetitions are not allowed and the lis start with an even number

sec Middle C has a frequency of 264 cycles Which of the following has the same frequency as middle C t time in seconds Enter a b c or d Ort 2 a y 8 sin 1050 b y 7 sin 530ft c y 9 sin 1600 t d y 8 sin 1584 t 3

A small country is comprised of four states A B C and D The population of each state in thousands is given in the following table A D Total State Population in thousands 78 B C 216 294 342 930 According to the country s constitution the congress will have 31 seats divided among the four states according to their respective populations Use Hamilton s method to find each state apportionment of congressional seats State Population Allocated seats AR C 294 78 B 216 7 31 Type an integer in each box One of them has been done for you D 342 Total 930

A hospital has 208 nurses to be apportioned among four shifts Shifts A B C and D The hospital decides to apportion the nurses based on the average number of room calls reported during each shift Room calls are shown in the table below Use the table to determine each shift s apportionment using Jefferson s method Note Divisors do not have to be whole numbers Shift Room calls A 788 Shift Room calls Nurses B C 1040 503 Determine each shift s apportionment using Jefferson s method D Total 165 2496 A 788 B C 1040 503 D 165 Total 2496

A large hotel chain needs to apportion 30 new surfboards for its visitors to rent among three hotels based on the numbers of rooms in each hotel as shown below Use the table to answer parts a and b Hotel Number of rooms A 322 B 236 C 162 a Determine each hotel s modified quota using the divisor 26 Hotel Number of rooms Modified Quota Round to the nearest hundredth as needed A 322 Total 720 O B 236 C 162 Total 720

A small country with a population of 7 000 000 consists of four states A B C and D There are 141 seats in the legislature that need to be apportioned among the four states The population of each state is shown in the table Use the table to answer parts a and b State A 1 229 000 Population a Determine each state s modified quota using the divisor 50 700 State Population Modified Quota Round to the nearest hundredth as needed A 1 229 000 B 2 701 000 B 2 701 000 www C 887 000 C 887 000 D 2 183 000 D 2 183 000 Total 7 000 000 Total 7 000 000

A small city has 32 police officers to be apportioned among 8 precincts based on the population of each precinct The populations are given in the following table Precinct 2 3 4 5 6 1 7 8 Population 2115 3659 3117 1883 4912 4027 2776 3174 Find the standard quota for the Third Precinct Round your answer to two decimals A 4 81 OB 3 26 C 3 89 OD 3 67

Of the trains that recently pulled into Westford Station 16 were full and 4 had room for more passengers What is the experimental probability that the next train to pull in will be full Simplify your answer and write it as a fraction or whole number P full

In an experiment the probability that event A occurs is 2 the probability that event B occur is and the probability that events A and B both occur is 7 What is the probability that A occurs given that B occurs Simplify any fractions

7 4 Find the third degree Taylor polynomial of f x y z xy z at 1 0 1

Irrational Number x Rational Number irrational or rational

9 32 WP Air enters the compressor of an ideal cold air standard Brayton cycle at 100 kPa 300 K with a mass flow rate of 6 kg s The compressor pressure ratio is 10 and the turbine inlet temperature is 1400 K For k 1 4 calculate a the thermal efficiency of the cycle b the back work ratio c the net power developed in kW