Math - Others Questions

Sammy Aww thank you so much That means a lot to me and yes I got all my grades except for one of my classes I have three A and one A I miss you so much Ms Christmas Yes I miss you as well Even if I don t see you during your break I will definitely come and see you at Harvard

An adjustable brace is placed against a tree to support a beam perpendicular to the tree The brace and beam are 12 feet long The brace can slide up the tree and can transverse left and right along the beam tree B A beam brace Question 2 1 Part A 25 points Write a function that expresses the distance the brace is from the tree A as a function of the distance from where the

3h 1 2h 7 Evaluate L 4 for L h Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Write your answer as a simplified fraction Give exact simplified answers

Let A the event someone tested positive for a virus and B the event someone has the virus What is the contextual difference between P A B and P A and B OP A B represents the number of individuals who have the virus among those who test positive P A and B represents the number of individuals who have the virus and test positive OP A B represents the population of individuals who test positive among those who have the virus P A and B represents the population of individuals who have the virus and test positive O P A B represents the probability that an individual who has the virus tests positive P A and B represents the probability that an individual has the virus and tests positive P A B represents the population of individuals who have the virus among those who test positive P A and B represents the population of individuals who have the virus and test positive OP A B represents the probability that an individual who tests positive has the virus P A and B represents the probability that an individual has the virus and tests positive

5 1 5 The following Vern diagram shows the events A and B where P 4 0 3 The values shown are probab b in Find the value of p Find the value of q Find d ULR U 0 1 B 0 4

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

2 5 Pablo drives to work The probability that he leaves home before 07 00 is 4 If he leaves home before 07 00 the probability he will be late for work is If he leaves home at 07 00 or later the probability he will be late for work is Copy and complete the following tree diagram b before 07 00 07 00 or later 8 S late not late late not late Find the probability that Pablo leaves home before 07 00 and is late for work thot be leu home before

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

15 A plane needs to travel to a location 1550 km away at a direction N30 E The plane flies at a velocity of 625 km hr and there is a wind of 80 km hr at a direction N10 W a What heading should the pilot take to arrive at the destination A 3 b How long will it take T 2

A person created a large pond in their backyard and they wanted to stock it with fish The first year they started with 8 fish and then watched the growth of the population of the fish over the years They found the population could be modeled by 67 1 19 19 341 Where y is the population size of fish and x is the number of years after they began What do you think will be the best estimate for the maximum number of fish the pond will sustain based on their model a 86 b 8 c 19

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

Personality types are broadly defined according to four main preferences Do married couples choose similar or different personality types in their mates Suppose the following data were collected to attempt to answer this question Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four Three Two One None 1 2 25 3 132 115 Suppose that a married couple is selected at random a Use the data to estimate the probability that they will have 0 1 2 3 or 4 personality preferences in common Round your answers to 2 decimal places 64 39 4

John runs a computer software store Yesterday he counted 131 people who walked by the store 66 of whom came into the store Of the 66 only 27 bought something in the store Round your answers to two decimal places a Estimate the probability that a person who walks by the store will enter the store b Estimate the probability that a person who walks into the store will buy something c Estimate the probability that a person who walks by the store will come in and buy something d Estimate the probability that a person who comes into the store will buy nothing

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 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 e n M n 1 P A P A Hint Solve the following equation for P A P A 1 P A n n m n nP A 77 n m n n written as 3 to 2 or 3 2 2 P A P A P A 1 P A P A P A nP A b A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 2 to 19 What is the probability of a successful call Round your answer to two decimal places A sports announcer says that the odds a basketball player will make a free throw shot 5 to 3 What is the probability the

A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants However there is some concern about the germination of seeds from the new plant To estimate the probability that a seed from the new plant will germinate a random sample of 3 000 seeds was planted in warm moist soil Of these seeds 2 570 germinated a Use relative frequencies to estimate the probability that a seed will germinate What is your estimate Round your answer to 3 decimal places b Use relative frequencies to estimate the probability that a seed will not germinate What is your estimate Round your answer to 3 decimal places c Either a seed germinates or it does not What is the sample space in this problem O germinate germinate or not germinate not germinate Do the probabilities add up to 1 Yes No Does this make sense The above result Select make sense since we see that the table Select sample space the sum Select d Are the outcomes in the sample space of part c equally likely probabilities for all outcomes in the

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

Consider a family with 4 children Assume the probability that one child is a boy is 0 5 and the probability that one child is a girl is also 0 5 and that the events boy and girl are independent a List the equally likely events for the gender of the 4 children from oldest to youngest Let M represent a boy male and F represent a girl female Select all that apply FMFF MMMF FFFM MMFM MMFF MFMM FFFF MFFF MMMM MFMF FFMM FMMF FMFM FFMF MFFM FMMM b What is the probability that all 4 children are male Enter your answer as a fraction X Notice that the complement of the event all four children are male is at least one of the children is female Use this information to compute the probability that at least one child is female Enter your answer as a fraction

Write the radical expression using exponents 1 3

Simplify each expression and eliminate any negative exponents a x 7 x5 b w 2w 6w7 c x20 x14

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

Jane Roznowski wants to invest some money now to buy a new tractor in the future If she wants to hav 350 000 available in 3 years how much does she need to invest now in a CD paying 4 85 interest compounded monthly Jane needs to invest now Round to the nearest cent as needed

Let A and B be two events defined on the same sample space with p A 0 6 P B 0 3 and p AUB 0 7 then p AUB O a 0 6 O b 0 8 O c 0 7 d 0 4 0 2 O e

Let A and B denote two events defined on the same sample space If P A 0 7 P B 0 3 then If the events A and B are mutually exclusive disjoint the value of P AU B equals to O a 0 68 O b 1 0 O C O d 0 7 O e 0 79 P Flag question 0 21