Math - Others Questions

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximatin rectangle 12 10 8 6 4 1 1 2 4 y 2 2 4 Find the area of the region x 7 4 6 6 8 8 X X 2 4 6 8 10 12 y 3 6 6 8 8 X

5 Calculate the next two negative coterminal angles a 53 b 138

The scores on a psychology exam were normally distributed with a mean of 63 and a standard deviation of 5 A failing grade on the exam was anything 2 or more standard deviations below the mean What was the cutoff for a failing score Approximately what percentage of the students failed The cutoff for a failing score was Simplify your answer

The scores on a psychology exam were normally distributed with a mean of 70 and a standard deviation of 4 What is the standard score for an exam score of 75 The standard score is Round to the nearest hundredth as needed

Y NOTES ASK YOUR TEACHER Sketch the region enclosed by the given curves 1 y x y x 8 y 8 6 4 5 5 10 10 Find the area of the region X X 25 15 15 20 PRACTICE ANOTHER 20 25 25 X 8 6 y 8 6 4 5 5 10 10 15 15 20 20 25 25 X X

The scores on a psychology exam were normally distributed with a mean of 51 and a standard deviation of 5 About what percentage of scores were less than 41 The percentage of scores that were less than 41 was Type an integer or a decimal

V speed of a space shuttle that orbited Earth at an altitude of 682 km 5 646 X107 4

I can relate to many teenagers today by admitting the fact that I am a heavy social media user Over the past few weeks I have read many articles that have been headlining how influential social media is towards affecting people s personality and confidence From this I did not just become concerned about how I might be affected but also how it may affect other teenagers or even adults According to Whatls com social media is the collective of online communications channels dedicated to community based input interaction content sharing and collaboration Whatls 2016 All sounds very social however according to articles from USA Today Science Daily and Readers Digest have all made comments about how we humans are becoming narcissists Science Daily expressed individuals with narcissist syndrome to think of themselves as being exceptionally talented remarkable and successful Meaning they love to present themselves to other people and seek approval from them Gnambs 2017 Reading this article was shocking because I asked myself the question am I really that desperate This lead me to compose an investigation on whether social media was affecting two key expressive traits that being personality and confidence Even though we may be living in generation me where we could easily assume from that we are highly confident and mixed in personality types I believe that world only exists on social media because we have a screen to protect us from either the good or bad expression made by others This protection must have some deliberate affect towards our real confidence or personality traits The observation made above has allowed this investigation to find out whether the amount C Ca ex pe

The inspiration of this mathematical investigation comes from an essential aid that helps me and my friend to get through the IB ice cream Whenever my friends and I are stressed about the workload from the IB we would work together with some ice cream by our side to cheer us up However it would always frustrate us when we concentrate on work for a long while only to find that the ice cream has melted Therefore when I had to come up with a topic for the Maths IA I thought it would interesting to connect calculus maths differentiation and integration an abstract concept to something that I not only love but also something that is real something that I can touch and see or even to eat Eventually I chose to do it on ice cream which is something I cannot live without I have always been a curious learner So when I came up with the idea I was very excited by it and started to think how ice cream melts In my observation I found out that ice cream melts faster when it is more exposed in the air In other words the rate at which the ice cream melts is actually proportional to its surface area I find that quite interesting and decided to look more into the 3D shapes of ice cream The aim of this investigation is to compare the melting rates of different solids of the ice cream It will be looking at basic solids of ice cream such as sphere hemisphere cubes and cuboids as stored in containers as well as some more interesting shapes i e platonic solids tetrahedron and dodecahedron The rate can be calculated by using calculus differentiation and integration I hope that through this exploration I can find the solid with the slowest and fastest melting rate and from that see if the abstract mathematics coincides with real life practicality

Find the slope of the line passing through the two given points 5 10 and 6 1 The slope is Type an integer or a simplified fraction

point s possible According to a census there were 65 people per square mile this is called the population density in a certain country in 1980 By 2000 the number of people per square mile had grown to 80 Use this information to develop a linear equation in slope intercept form In developing the equation think of 1980 as year zero ELE Let x be the time in years and let y be the population density Write a linear equation in slope intercept form to model the given information The equation is Simplify your answer Use integers or fractions for any numbers in the equation

Which of the lines on the given graph have a negative slope d a b C Select all lines with a negative slope 0 000 e f d b C This question 1 point s possible a None of the lines have a negative slope

K In the given graph call the x intercept of each line p 0 and the y intercept of each line 0 q Identify the line s where pxq is negative Choose the correct answer below C c and d d This question 1 point s possible

State the y intercept and slope of the graph of the equation y 8x 6 The y intercept is 0 The slope is

This question 1 point s possible Solve the equation by using the rules for rewriting equations An approach that makes solving equations with fractions or decimals easier is to multiply each side of the equation by a suitable constant to make the coefficients easier to work with 0 6y 5 1 4y 3 Submit quiz The solution is y Type an integer or a decimal

K Identify the sequence as either arithmetic or geometric List the next two terms of the sequence 5 2 9 16 Is the sequence arithmetic or geometric OA Geometric OB Arithmetic List the next two terms in the sequence 5 2 9 16 Type integers or simplified fractions

A change equation together with a function value that is not the initial value are given Solve the equation dy dx In 2 y y 1 22 Express numbers in exact form Use symbolic notation and fractions where needed Give the equation in terms of y and x solution

Problem 3 a and y are angles in quadrants 1 2 and 3 respectively such that tan a tan B COS Y This time we also that 27 a y 47 Evaluate the following a b c d b COS c tan sin sec 2 sqrt 2 4 sin 9 COS tan 2 0 2 Problem 4 0 is an angle in quadrant 3 such that 0 and such that cos 0 a sqrt 7 sqrt 5 14 5 02 0 3 2 Calculate the following

10 10 IRR calculations Given the following free cash flows determine the the three independent projects A B and C Initial outlay Cash inflows Year 1 Year 2 Year 3 Year 4 Year 5 PROJECT A 50 000 10 000 15 000 20 000 25 000 30 000 PROJECT B 100 000 125 000 25 000 25 000 25 000 25 000 PROJECT C 450 000 200 000 200 000 200 000

10 6 Payback period NPV PI and IRR calculations You are considering a proj ect with an initial cash outlay of 80 000 and expected free cash flows of 20 000 at the end of each year for 6 years The required rate of return for this project is 10 percent a What is the project s payback period b What is the project s NPV c What is the project s PI d What is the project s IRR

10 6 Payback period NPV PI and IRR calculations You are considering a proj ect with an initial cash outlay of 80 000 and expected free cash flows of 20 000 at the end of each year for 6 years The required rate of return for this project is 10 percent a What is the project s payback period b What is the project s NPV c What is the project s PI d What is the project s IRR

Assume the nominal interest rate for an account is 9 per year Find the effective annual interest rate corresponding to each compounding period below Round your answers to four decimal places after writing each rate as a percentage a monthly b weekly c dally x x d continuously x

Megan bought a bag containing 50 Beads for 9 95 She received a 10 discount What was the discounted price of the beads 10 10 10 995 10 Discount Amount

Let G be a group with G e a b c where e is the identity Construct the multiplication table for G under the following conditions 36 a e and b e 37 a b and b e

2 or ever for It turns positive on 4 ion and eir own the field O a b C d a a d a C b a d b C C a b C d d b b d d The multiplication table above is defined on the set S a b c d 5 Is S closed under o misilgalam bue no 12 do dodamago vamaid ame 6 Compute a ob 7 Is o commutative in S Why or why not 11 gas chur 8 Is o associative in S Why or why not 9 Does S have an identity with respect to o If so what is it 2 aindes

The three sides of a right angle triangle are shown below What is the area of the right angle triangle A D A A A A 15 6 2 12 2 2 14 6 3 17 3 2 5 3 X 3 5

Question 3 Simplify the following expression 2x 1 2x y 1 A B C D 2y x 2y x 2y 2y 2y 2x 2x 2x y y

Perform the indicated operations and express the result in simplest radical form with rationalized denominators 2 C 15 2 15 4 25 2 15 6 15 4 15 15 3 15 15

Perform the indicated operation and express the answer in simplest form with rationalized denominator 2 6 5 3 6 4 5 A B 16 5 30 26 26 5 30 16 16 5 20 22 20 5 34 26 G

Evaluate the given expression 4 1 5 12 51 2 36 1 2 A B C D 13 10 26 5 10 26 36 10 Shey

Question 4 Simplify the given expression a 2 a 2 4 2 A B C D a 1 a a a 2 a 4 2a a 2 Story

Perform the indicated operation and express the result in simplest radical form with rational denominator 3x 2 3x A B y 6x 3xy 12x y 6x 3xy 12x y 6x 3 xy 12x y I 6x 3x y 12x y

The three sides of a right angle triangle are shown in the image below What is the perimeter of the triangle A 6 2 2 6 B 4 2 2 6 6 2 2 3 C I X 2 2 2 6

Perform the indicated operation and express the result in simplest radical 1 6 3 2 3 2 1 6 B 1 6 1 3 3 2 A Jy

Simplify the given expression A B C D 4x2 2y2 x2 4x 2 v 2x y2 Jay

Let f 4 5 7 7 11 13 be a bijection Which of the following statements must be true Select all that apply DA fof 13 13 OB fo f is the identity function on the set 7 11 13 OC f of is the identity function on the set 4 5 7 OD f f 7 7 DE f of is the identity function on the set 7 11 13 OF fo f is the identity function on the set 4 5 7

Which of the following functions are surjective Select all that apply OA f 2 3 7 12 2 11 17 defined by f 2 11 f 3 11 f 7 2 f 12 17 OB f 6 8 9 13 2 3 7 12 defined by f 6 12 f 8 3 f 9 7 f 13 3 OC f 2 3 7 6 8 9 13 defined by f 2 13 f 3 8 f 7 9 OD f 6 8 9 13 2 3 7 12 defined by f 6 12 f 8 3 f 9 7 f 13 2

Let S 1 5 11 17 and T 4 2 8 14 Which of the following are functions from S into T Select all that apply DA 5 8 11 14 17 4 1 2 OB 1 14 5 4 11 8 1 2 OC 1 14 5 14 11 2 17 2 OD 1 4 5 2 11 8

Use Lagrange multipliers to find the maximum and minimum values of f x y x 5y subject to the constraint if such values exist Round your answers to three decimal places If there is no global maximum or global minimum enter NA in the appropriate answer area Maximum x y 64 Minimum

Use Lagrange multipliers to find the maximum and minimum values of f x y x 3y subject to the constraint if such values exist Enter the exact answers If there is no global maximum or global minimum enter NA in the appropriate answer area Maximum x y 3 Minimum

nich digits replace A B and 25 31 21 2 A C 94 47 B 2

2 If the sum of five positive distinct even two digi numbers with different digits is 140 what is the maximum of the greatest one

Given the above information in Q1 Shannon s wants to increase its sales to retailers by 20 in the next year Management estimates that the incremental promotion program required to generate sufficient demand to boost sales by 20 will be 60 000 exclusive of commission 59 882 43 244 Personal Selling Costs Consumer Advertising Trade Promotion Sales Promotion 25 000 Shannon s will need to hire an additional salesperson paid a salary and commission and provide some added administrative support The salesperson s salary plus administrative support will cost about 60 000 per year The salesperson s commission will be the equivalent of 0 05 per six pack sold Unit variable costs exclusive of the salesperson s commission are the same as in Q1 The incremental costs of consumer advertising trade promotion and sales promotion necessary to support sales in the new market will be substantial as indicated in the table above How many six packs must be sold to break even on the incremental costs that are anticipated

Write 1 242 102 in standard notation

blem 4 Cesium 137 is an isotope of cesium that is a common product of fission in a nuclear reactor The rate of change in the amount of any radioactive substance is proportional to the amount present Let C denote the amount of cesium 137 remaining in spent nuclear fuel rods after t years a Using r for the proportionality constant write an equation of change for C b Solve the equation from part a Use Co for the initial value c The half life of cesium 137 is 30 14 years Use this information to find the value of the proportion ality constant r from parts a and b Give the exact value and then round it to three decimal places d How long does it take for the amount of cesium 137 to decay to one tenth of the initial amount Round your answer to the nearest year

oblem 2 A model rocket is shot upward from a height of 10 feet Its height H in feet above the ground after t seconds is given by H t 10 159 16t a Determine the time at which the rocket strikes the ground b Sketch the graph of the height function labels all axes and include units dH c Sketch the graph of the upward velocity dt of the rocket labels all axes and include units

Fill in the missing cells in the following table Quantity of Output Q Units 0 1 23 45 67009 8 10 Total Fixed Cost TFC Dollars 200 200 200 200 200 200 200 200 200 200 200 Average Fixed Cost AFC Dollars Total Variable Cost TVC Dollars 0 30 50 60 65 75 95 125 165 215 275 Average Variable Cost AVC Dollars Total Cost Dollars Marginal Cost MC Dollars Average Total Cost ATC Dollars

5 Determine if each logarithm is defined If not explain why not If it is defined determine if the value is whole number or not a log312 b log3 9 c log255 5 x 109 x y 109 x y

14 14 Use the Divergence Theorem to evaluate the surface integral SS F F ds where F x y z x siny i cos y j z sin y k and S is the boundary of the region bounded by th planes x 1 y 0 y z 0 and z x with outward normal vector You must use this method to receive full credit

12 10 Give a parametric representation for the surface consisting of the cap of the sphere x y z 16 for 2 2 z 4 Remember to include parameter domains