Basic Math Questions and Answers

Sometimes probability statements are expressed in terms of odds The odds in favor of an event A are the following ratio P A P A P not A P AC For instance if P A 0 60 then P AC 0 40 and the odds in favor of A are 0 60 6 3 0 40 4 2 a Show that if we are given the odds in favor of event A as n m the probability of event A is given by the following P A n m n 1 P A n Hint Solve the following equation for P A P A 1 P A n nP A n n m n written as 3 to 2 or 3 2 n DAY P A P A P A 1 nP A P A

Directions Complete the following providing all work You may use a graphi the IB SL formula booklet Round to 3 s f if not otherwise specified 2 Srinivasa places the nine labelled balls shown below into a box 0 33 Srinivasa then chooses two balls at random one at a time from the box The first ball is not replaced before he chooses the second a l b R c A DOO U M Find the probability that the first ball chosen is labelled A a li Find the probability that the first ball chosen is labelled A or labelled N 2 PCAUN N 9 Find the probability that the second ball chosen is labelled A given that the first ball chosen was labelled N Find the probability that both balls chosen are labelled N

4 On a school excursion 100 students visited an amusement park The amusement park s main water slides W and virtual reality rides V The students were asked which main attractions they visited The results are shown in the Venn diagram a l Find the value of a a ii b c U 6 Find the value of b A total of 74 students visited the rollercoasters or the water slides R 32 Write down the value of 1 RnW 12 9 5 18 10 V a 16 W 8 J Find the number of students who visited at least two types of main attraction 68 b

A school caf sells three flavours of smoothies mango M kiwi fruit K and banana B 85 students were surveyed about which of these three flavours they like B 35 students liked mango 37liked banana and 26 liked kiwi fruit 2 liked all three flavours 20 liked both mango and banana 14 liked mango and kiwi fruit 3 liked banana and kiwi fruit Using the given information complete the following Venn diagram B Find the number of surveyed students who did not like any of the three flavours A student is chosen at random from the surveyed students Find the probability that this student likes kiwi fruit smoothies given that they like mange smooth

The diagram shows a circular horizontal board divided into six equal sectors The sectors are labelled white W yellow Y and blue B a First spin 6 A pointer is pinned to the centre of the board The pointer is to be spun and when it stops the colour of the sector on which the pointer stops is recorded The pointer is equally likely to stop on any of the six sectors Eva will spin the pointer twice The following tree diagram shows all the possible outcomes Eva will spin the pointer twice The following tree diagram shows all the possible outcomes Second spin 1 3 W 3 Blue W Yellow B Find the probability that both spins are yellow White W 6 O 6 1 3 Blue Yellow White Blue Yellow White Blue Yellow White

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers a y b 16u v uv7

Which model would best represent the scatter plot shown at the right a Cubic b Logistics Curve c Exponential d Sinusoidal

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers a b x8

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers b 4 x 6 x

Simplify the expression a x 27x b 4 18rt3 5 32r 5

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbe a x16 4 1 4 16 4 3 b 9s54 1 2 49 2

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers a 54x 4 2x y

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers a 27s 13 2 3 st 12 1 4 32xSy 3 2 2 5 5 3 2 3 3 5

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers al 66 3 a x 26 1 a3 2 1 3 9st 3 2 3s 27st 4 2 3 41 3

Evaluate each expression Simplify your answers completely a 811 4 b 641 3 c 9 1 2

Simplify the expression a b 50 18 48 75

Simplify the expression a 9x 9 b 36x 36y2

Simplify each expression and eliminate any negative exponents 2 a b b u v 2 u v 2 3 362 c3

Simplify each expression and eliminate any negative exponents a 9a9b 6 3a 465 b y 3x 5 2

Simplify the expression Assume that a and b denote any positive real numbers a 16a4b5 b Va b8a b

Simplify each expression and eliminate any negative exponents a y 22 7 y 1 b 2 2 x y 2 x 3y

a If you roll a single die and count the number of dots on top what is the sample space of all possible outcomes Enter you answers as a comma separated list of numbers Are the outcomes equally likely The events are not all equally likely The events are all equally likely b Assign probabilities to the outcomes of the sample space of part a Enter your answers as fractions Outcome Probability 1 2 3 4 5 6 Do the probabilities add up to 1 Should they add up to 1 Explain Yes but they should not because these values do not cover the entire sample space Yes because these values cover the entire sample space No because these values do not cover the entire sample space No but they should because these values cover the entire sample space c What is the probability of getting a number less than 6 on a single throw Enter your answer as a fraction d What is the probability of getting 4 or 5 on a single throw Enter your answer as a fraction

Write the radical expression using exponents 1 3

Evaluate each expression Simplify your answers completely 132 3 a b 3 243 c 125 125

Simplify each expression and eliminate any negative exponents a a 5 a a b a a4 3 c 3 2 5x6

Evaluate each expression Simplify your answers completely a 416 b c 27 81 27 V 49

Evaluate each expression Simplify your answers completely a 7 2 b c 4 3 30 2

Evaluate each expression Simplify your answers completely a 26 b 2 6 c 3

Write the radical expression using exponents 1 3 X

Write the radical expression using exponents X5

a Using exponential notation we can write 17 as b Using radicals we can write 171 2 as 17 c Is there a difference between 172 and 17 Yes No X

Determine the monthly principal and interest payment for a 20 year mortgage when the amount financed is 275 000 and the annual percentage rate APR is 4 5 The monthly principal and interest payment is Round to the nearest cent as needed 2 Monthly Principal and Interest Payment per 1000 of Mortgag Rate 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 Click here for table of Monthly Payments 8 0 8 5 9 0 9 5 25 30 Number of Years 10 15 20 10 12451 7 39688 6 05980 10 36384 7 64993 6 32649 5 27837 4 77415 5 55832 5 06685 5 36822 10 60555 7 90794 6 59956 5 84590 10 85263 8 17083 6 87887 6 14087 5 67789 11 10205 8 43857 7 16431 6 44301 5 99551 11 35480 8 71107 7 45573 6 75207 6 32068 7 75299 7 06779 6 65302 8 05593 7 38991 6 99215 8 36440 7 71816 7 33765 8 67823 8 05227 7 68913 8 99726 8 39196 8 04623 8 40854 8 73697 9 32131 11 61085 8 98828 12 13276 11 87018 9 27012 9 55652 9 84740 12 39857 12 66758 10 14267 12 93976 10 44225

The limit represents the derivative of some function f at some number a State such an f and a 3 81 lim X 4 X 4 x a

One of the following number doesn t denote to negative correlation coefficient O a 0 3 O b 0 9 O c 1 1 O d 0 8

If an estimated regression line has a y intercept of 10 and a slope of 4 then when x 2 the estimated value of y is Oa 15 O b 18 O c 14 d unknown

What is the slope of the line y 3 4x 2 5 O a insufficient information to determine Ob 3 4 O C 2 5 O d 3 4 O e 2 5

A regression analysis between sales in 1000 and price in dollars resulted in the following equation y 50 000 8X The equation implies that an O a increase of 1 in price is associated with a decrease of 8000 in sales O b increase of 8 in price is associated with an increase of 8 000 in sales O c increase of 1 in price is associated with a decrease of 8 in sales O d increase of 1 in price is associated with a decrease of 42 000 in sales

If P A P B and P AUB then P A B 11 O a 1 O b 2 3 O C Od Oe 350 556 no correct answer

Not yet answered Marked out of 1 00 If P A B P A and P BA P B then A and B are O a no correct answer b Mutually exclusive O c Dependent O d independent Oe Equally likely

List the elements of the given set that are natural numbers integers rational numbers and irrational numbers Select all that apply 5 5 0 2 3 2 71 7 3 14 100 4 a natural numbers 5 5 0 3 2 71 T 3 14 100 4 X b integers 5 5 10 3 2 71 T 3 14

Find the distance between the given numbers Simplify your answer completely 10 8 WebAssign NumberLine 2 0 6 8 10

Complete the tables Simplify your answers completely 1 x X 1 2 10 100 1000 X 1 0 0 5 0 1 0 01 0 001 What happens to the size of the fraction 1 x as x gets large As x gets large 1 x stays the same As x gets large 1 x gets smaller As x gets large so does 1 x What happens to the size of the fraction 1 x as x gets small As x gets small 1 x stays the same As x gets small so does 1 x As x gets small 1 x gets larger 1 x

List the elements of the given set that are natural numbers integers rational numbers and irrational numbers Select all that apply 1 3 1 3333 3 5 34 300 12 V9 245 20 579 a natural numbers 1 3 1 3333 3 5 34 300 9 246 579 20 5 b integers 1 3 1 3333 3 5 34 D 300 013

Express the interval in terms of inequalities 7 10 7 x 10 10 x 0 07 x 10 07 x 10 07 x 10 Graph the interval Use the tools to enter your answer 10 00

1 x y ve z say lar s ras yla 2 3 ve 5 say lar ile ters orant l d r 6x 3y 10z 8 oldu una g re x ka t r A 6 B 5 C 4 D 3 E 2

The distance between a and b on the real line is d a b X So the distance between 1 and 8 is 9

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Tulips O Roses Pink Yellow White Pink Yellow White Determine how many ways a respondent could answer all of the questions

Combine the Multiplication Principle and combinations to answer the question A certain multistate lottery game has a player pick 5 balls numbered from 1 to 69 then another ball that is a number from 1 28 How many different ways can these lottery numbers be picked ways

Write the expression without using exponents See Example 2 Objective 1 4t3