Basic Math Questions and Answers

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

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

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

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

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

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

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

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

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

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

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

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 58 ints eBook Print References Navajo Company s year end financial statements show the following The company recently discovered that in making physical counts of inventory it had made the following errors Year 1 ending inventory is understated by 65 000 and Year 2 ending inventory is overstated by 35 000 For Year Ended December 31 a Cost of goods sold b Net income c Total current assets d Total equity Year 1 740 000 283 000 1 262 000 1 402 000 1 595 000 Year 2 970 000 290 000 1 375 000 Year 3 805 000 265 000 1 245 000 1 260 000 Required 1 For each key financial statement figure a b c and d above prepare a table to show the adjustments necessary to correct the reported amounts 2 What is the total error in combined net income for the three year period resulting from the inventory errors Complete this question by entering your answers in the tabs below Required 1 Required 2 What is the total error in combined net income for the three year period resulting from the inventory errors

ok ht ences 4 Compute gross profit earned by the company for each of the four costing methods Note Round your average cost per unit to 2 decimal places Sales Less Cost of goods sold Gross profit O Specific Identification O Weighted Average FIFO OFIFO Quro LIFO Weighted Average 5 The company s manager earns a bonus based on a percent of gross profit Which method of inventory costing produces the highest bonus for the manager Specific Identification

Consider the region S of space inscribed with in the sphere x 2 2 y 2 1 z 2 and satisfying x y y Use cylindrical coordinates to compute 2 2 SS y x y dx dy dz S

A Plot the function f x over the interval 1 10 Go to the wrench at the top right of your screen and change the x axis to be 0 11 with 1 0 step and y scale to be 0 2 with 0 5 step Uncheck the box for minor gridlines B Without using calculus just by looking at the graph try to find a rough estimate of the area between the graph of f x and the x axis from x 1 to x 2 Hint what is the area of each rectangle Repeat this for x going from 1 to 5 Although tedious and inaccurate the process you just followed could be repeated to get an estimate of the area from x 1 to x a for any a 1 For any value of a we input the output is a number i e a function F a the area between f x and the x axis from x 1 to x a C In Desmos define F a to be the integral from 1 to a of 1 x dx To get an integral in desmos type int and the integral sign will appear a Evaluate F 2 b Evaluate F 5 c Do your estimates match your answers from question 2

18 According to the study unit the commutative property means O A the order in which you add the numbers does affect the sum O B the order in which you add the numbers doesn t affect the sum O C the way the numbers are grouped doesn t affect the sum O D the way the numbers are grouped does affect the sum

11 Of the following numbers which one is prime 32 42 29 15 O A 15 O B 32 O C 42 O D 29

13 Solve 567 1000 OA 5670 OB 56 700 O C 5 670 000 O D 567 000

14 What s one way to check the answer to 5 6 30 O A 30 x 6 5 OB 30 x 5 6 OC 5 6 30 O D 30 6 5

7 If 31 2 pounds of bananas cost 1 96 how much would one pound cost OA 18 B 56 O C 1 76 OD 66

16 How could you check the answer to 27 15 12 using addition O A 12 15 27 O B 27 15 12 O C 27 12 15 OD 15 12 27

15 Write 850 as the product of its prime factors OA 5 10 17 OB 10 x 85 OC 2 5 5 17 OD 17 x 50

19 The solution to 5 1 will be what kind of number O A Even OB A multiple of 2 O C Perfect square O D Prime

cos L sin 0 sin cos sin 0 cos 0 Hint Evaluate the determinant and use Pythagorean trig identity Proof Attach File Browse Local Files QUESTION 5 sin 0 cos 0 Browse Content Collection 5 Prove that for every 2 x 2 matrix A LIPHAY 0

Select the best answer for the quest 8 A real estate broker sold your house for 72 000 The broker s commission was 6 of the selling price How much would you get for the house after the commission is paid O A 76 320 B 70 800 C 67 680 O D 73 200

12 Select the proper placement for parentheses to speed up the addition for the expression 4 6 5 O A 5 4 6 O B 5 6 4 O C 4 6 5 O D 4 6 5

9 The least common multiple of 2 5 6 and 9 is O A 45 OB 60 O C 180 OD 90

10 Which is another way to check the sum of 52 23 10 78 O A 163 52 23 10 78 O B 78 52 10 23 O C 78 52 10 23 O D 78 10 23 52

5 Over a four week period Gail earned the following commissions Week 1 250 00 310 00 275 00 195 00 Week 2 Week 3 Week 4 What was her average weekly commission for the period O A 257 50 O B 240 00 O C 207 50 O D 205 00

This question is based on the circle graph below which shows how an electrical contracting company divides its monthly income 47 Personal salary 25 Helper s salary O A 47 O B 76 C 72 8 DEN Parts supplies Gas 2 Advertising 2 Insurance Investments 1 What percent of the contractor s income is spent on salaries Taxes Miscellaneous

6 To change 3 to a fraction you must put 3 over what denominator O A 1 OB 100 O C 10 O D 1

3 A strip of wood 66 inches long is to be cut into 51 2 inch pieces How many pieces can be cut O A 12 B 33 O C 30 D 14