Math - Others Questions

Deborah has two pairs of slacks three shirts and six sweaters From how many combinations can she choose if she chooses a pair of slacks a shirt and a sweater each day She can choose from possible combinations

In a fraternity with 34 members 18 take mathematics 5 take both mathematics and literature and 8 take neithe mathematics nor literature How many take literature but not mathematics members take literature but not mathematics

Of the eighth graders at the Paxton School 9 played basketball 9 played volleyball 10 played soccer 1 playe basketball and soccer only 2 played volleyball and soccer only 1 played basketball and volleyball only and 2 played volleyball basketball and soccer How many played one or more of the three sports How many eighth graders played one or more of the three sports

Let A o p q r s a How many subsets does A have b How many proper subsets does A have c How many subsets does A have that include the elements o and p a A has subsets Type a whole number b A has proper subsets Type a whole number c A has subsets that include the elements o and p Type a whole number

Fill in the Venn diagram with the appropriate numbers based on the following information n A 26 n B 39 n C 23 n AB 13 n B n C 15 n An C 9 n An BnC 5 n U 66 A Venn diagram is a graphical representation of sets Remember that n A is the number of elements in set A Region I contains Region II contains Region III contains containe elements elements elements elements I A II VI VII V IV VIII CI B

Suppose B is a proper subset of C a If n C 9 what is the maximum number of elements in B b If n B 9 what is the maximum number of elements in C a What is the maximum number of elements that B could have O A There is no limit on how many elements B could have OB The maximum number of elements in B is b What is the maximum number of elements in C A The maximum number of elements C could have is OB There is no limit on how many elements set C could have

Complete the truth table for the given statement by filling in the required columns q p Complete the truth table P T FL T F T P qA P

In a survey of 1090 investors it was determined that 650 invested in stocks 675 in bonds and 360 in both stocks and bonds a How many invested in only stocks b How many invested in stocks or bonds c How many did not invest in either stocks or bonds a How many invested in only stocks b How many invested in stocks or bonds c How many did not invest in either stocks or bonds D U IV A I II III B

If a statement and its converse are both true which of the other forms inverse and contrapositive are also true if any Choose the correct answer OA Both the inverse and the contrapositive are true OB Only the contrapositive is true OC Neither the inverse nor the contrapositive are true OD Only the inverse is true

Answer parts a and b a n A U B 16 n A n B 6 and n B 10 find n A b If n A 6 n B 16 and n A n B 3 find n A UB a n A b n A U B

A student asks if ACB and BCC do we know ACC How do Choose the correst response www you answer OA The expression ACB means every element of A is contained in B The expression BCC means that every element in B is contained in C Therefore every element of A is contained in C and so ACC must be true OB There could be an element in A that is in B but not in C Therefore if ACB and BCC it is not necessarily tr that ACC

1 Suppose during our 25 year mortgage from the previous Investigation exercises that a lump sum payment of 13 800 was made at the end of the 1st 5 year term and a lump sum payment of 18 000 was made at the end of the next 10 year term The final term would then consist of the remaining 10 years a Complete the following table the payment amount for Term 1 can be obtained from Investigation 1 exercise 1 a Term 1 5 years Term 2 10 years Term 3 10 years b Outstanding Number principal at beginning of term 300 000 payments in term Lump sum payment at beginning of term 13 800 18 000 Outstanding Payment principal after Lump sum payment 300 000 Total amount paid during the term including lump sum payment Number payments remaining in mortgage at end of term Calculate the total amount paid during the lifetime of the mortgage by adding

blem 6 The U S consumption of natural gas from 1965 to 1980 can be modeled by C x 0 00012342 0 00568923 0 08792 0 5145z 1 514 where 6 corresponds to 1966 and a 20 to 1980 Consumption is measured in trillion cubic feet Source Department of Energy a Determine symbolically if the consumption function C x is odd even or neither b Evaluate C 12 and interpret the result c Evaluate the average rate of change of the consumption function on the interval 12 13 and interpret your result Be sure to include appropriate units d Graph the function on the domain 6 20 and label the axis Use the graph to describe the energy usage e Determine and interpret the meaning of the local and absolute extrema if any

Question 4 4 Translate the sentence into an algebraic equation Use x for the variable 22 less than twice a number results in 6 Question Help Message instructor

Translate the phrase into an algebraic expression Use x for the variable 21 less than a number

The function g is the inverse of f Also f 17 19 and f 22 17 Calculate g f g 17 Give an exact answer Use symbolic notation and fractions where needed gofog 17

2 x 1 Label the appropriate functions as g and h et f x 0 Oy x 1 2 x 1 2 1 Write f as a composition g h of two functions g and h in two different ways g h and g2 0 O O y y x 2 X N x 81 h Answer Bank 82 h

Find the domain of given the following 8 The domain of f is 4 16 The domain of g is 5 21 Also g 5 0 and g x 0 for all other x in the domain of g Give your answer as an interval in the form Use the symbol co for infinity U for combining intervals and an approp type of parenthesis depending on whether the interval is open or closed Enter if the interval is empty

The fixed costs for a certain small business are the costs such as rent or mortgage payments that the company must pay each month no matter how much business is conducted The variable cost is the hourly wage paid to employees When employees work E hours in a month the total cost is given by C 30E 1300 dollars Identify the fixed costs and the variable cost in the formula for the total cost function Give an exact answer for each Use symbolic notation and fractions where needed fixed costs variable cost dollars per month dollars per hour

Macmillan Learning 4 3 2 2 1 0 1 2 3 4 5 f x 2 3 4 Find the domain of the function f 8 LO 5 g x 6 7 8 9 X Give your answer as an interval in the form Use the symbol co for infinity U for combining intervals and an appropri type of parenthesis depending on whether the interval is open or closed Enter if the interval is empty Expres numbers in exact form Use symbolic notation and fractions where needed

2 y 7 3 0 1 2 f x domain of fg 1 2 3 4 g x LO 5 6 7 X 8 Find the domain of the function f g Give your answer as an interval in the form Use the symbol co for infinity U for combining intervals and an appro type of parenthesis depending on whether the interval is open or closed Enter if the interval is empty Exp numbers in exact form Use symbolic notation and fractions where needed

Find the domain of f g given the following The domain of fis 10 200 and g x Give your answer as an interval in the form Use the symbol co for infinity U for combining intervals and an appropria type of parenthesis depending on whether the interval is open or closed Enter if the interval is empty Use decimals or fractions for endpoints but if you use decimals do not round

8 The gross weight of a package and its contents is 11 pounds 5 ounces If the packaging weighs 1 pound 15 ounces what s the net weight of the contents OA 9 lb 6 oz OB 10 lb 5 oz O C 10 lb 6 oz OD 12 lb 20 oz

10 What s the elapsed time between 3 40 A M and 2 00 PM OA 8 hr 20 min B 11 hr OC 1 hr 40 min OD 10 hr 20 min

19 What s the sum of 5 feet 9 inches and 12 feet 3 inches OA 18 ft 1 in OB 18 ft O C 17 ft 1 in OD 17 ft

17 If military time is 0145 what time is it on a regular clock OA 1 45 P M OB 12 45 P M O C 1 45 A M OD 12 45 A M

6 Solve 6 yd 9 ft 4 in x 2 A 18 yd 12 ft 8 in OB 0 yd 18 ft 8 in OC 12 yd 18 ft 8 in OD 7 yd 0 ft 8 in

18 What would you have to do to change 10 cubic feet into cubic inches OA Multiply by 1 728 OB Multiply by 46 656 OC Divide by 1 728 D Divide by 46 656

20 41 F equals how many degrees Celsius OA 5 C OB 9 C OC 56 C OD 5 C

16 How many 2 inch segments are there in 12 ft A 10 OB 6 C 24 OD 72

15 If a thermometer indicates 40 degrees Celsius what s the temperature in degrees Fahrenheit OA 54 F OB 72 F OC 22 F OD 104 F

14 What s the perimeter of a rectangle with length 12 m and width 5 m OA 17 m B 60 m OC 49 m OD 34 m

13 How many yards are in 5 miles OA 1 760 yd OB 5 280 yd OC 8 800 yd OD 26 400 yd

9 1713 hours is the same as which of the following times OA 7 13 A M OB 7 13 P M OC 5 13 A M OD 5 13 P M

11 Which prefix means 1 10 of a unit in the metric system OA Milli OB Hecto OC Centi OD Deci

7 What s the sum of 6 feet 10 inches and 8 feet 9 inches OA 15 ft 7 in OB 14 ft 7 in O C 15 ft 19 in OD 13 ft 19 in

12 A shoemaker bought 30 pairs of heels How many individual heels did the shoemaker buy OA 15 OB 120 OC 30 D 60

3 Change 75 millimeters to decimeters A 7 500 dm OB 75 dm OC 7 5 dm OD 750 dm

5 A merchant bought 30 dozen pairs of gloves How many individual gloves did the merchant buy A 720 OB 420 OC 300 OD 360

4 If a chicken farm sold 3 000 dozen eggs last week how many individual eggs were sold OA 250 OB 3 600 C 36 000 OD 3 000

1 The English measurement system is primarily used by what country OA United States O B England O C Ireland OD Italy

8 Use the following table to calculate GDP in this economy Corporate Profits R D Government expenditure Proprietors Income Interest Taxes Net Foreign Factor Income Wages Rents Residential Investment Personal Saving Transfer Payment 400 40 400 50 70 300 30 1000 300 200 250 60 9 Why does GDP underestimate the actual amount of output produced in an economy

11 Fill in the blanks in the table below and find a year that has a recession you can use year 2016 as a base year Volume of Goods Services Prices Nominal GDP Real GDP Growth rate of Real GDP 2015 100A 100G 100M 2016 2017 110A 110G 110M 2018 115A 115G 115M 112A 112G 112M A 2 G 3 M 4 A 2 G 5 M 4 A 2 G 8 M 5 A 5 G 10 M 6

9 Why does GDP underestimate the actual amount of output produced in an economy Percent 14 12 10 8 0 4 2 0 2 Year to Year Percentage Change in Nominal and Real GDP 1960 1980 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 Years Change Real GDP Change Nominal GDP

12 Use the following graph to answer the next question Nominal and Real GDP 2000 Time Nominal GDP when export equaled import Real GDP The year 2000 must be a the year b the year when GDP equaled 100 c the base year for real GDP calculation d the year when net foreign factor income equaled zero

10 What is the shortcoming of nominal GDP in measuring output based on the above graph

A sculptor is designing her new triangular masterpiece In her scale drawing the shortest side of the triangular piece to be made measures 4 cm The longest side of the drawing measures 39 cm The longest side of the actual triangular piece to be sculpted must be 11 9 m long How long will the shortest side of this piece be The shortest side of the sculpture measures m Round to the nearest tenth

14 Assume the total real output of a developing country increases from 10 billion to 10 5 billion while its population expands from 15 to 18 million people from one year to the next Over the year how much has real GDP per capita changed What is the growth rate of real GDP

3 A model of a tractor trailer is shaped like a rectangular prism and has a width of 3 in a length of 11 in and a height of 4 in The scale of the model is 1 33 How many times the volume of the model is the volume of the actual tractor trailer

7 Define Gross Domestic Product GDP from the expenditure approach and the income approach In other words what are the components of GDP from each approach