Math - Others Questions

Verify the identity algebraically Use the table feature of a graphing utility to check your result numerically 2 sec y 2 cot y 2 Use the Cofunction and Pythagorean Identities and then simplify Simplify your answer completely 2 sec y 2 cot y 2 sec y 2 Need Help Submit Answer Read It ARPRECALCRMRP7 5 2 046 Need Help Read It Watch It 6 1 Points DETAILS Verify the identity algebraically Use a graphing utility to check your result graphically 7 sin x 7 cos x 7 cot x 7 csc x sin x 7 csc x csc x sin x Expand the expression and then use the Reciprocal Identities to simplify Simplify your answers completely 7 csc x csc x sin x 7 sin x 7 cos x 7 cot x 7 csc x sin x sin x LARPRECALCRMRP7 5 2 050 sin x 7 csc 2 x 7 7 7 cot x 7 cot x

The manager at a coffee shop counted the customers once each hour over a few busy weekends The results she obtained are summarized in the bar graph to the right use it to answer parts a through d a What was the largest number of customers in the coffee shop and how often did it occur The largest number of customers was 12 It occurred 2 time s b What was the most frequently occurring nonzero customer count The most frequently occurring nonzero customer count was 6 c For how many hours were the customers counted hours C Frequency 11 11 0 1 2 3 4 5 6 7 8 9 10 Number of Customers

Fill in the missing steps Simplify your answers completely sin x cos x sin x tan x cot x cos x tan x cot x sin x cos x cos x sin x sin x cos x 1 sin x cos x 11 sin x sin x cor x cos x cos

Verify the identity Simplify your answers completely 7 sin t 7 cos t tan t Use a Reciprocal Identity and then simplify 7 sin t 7 sin t tan t cos t 7 sin t cos t

Verify the identity Simplify your answers completely 5 sin z 6 cos z 5 sin z 5 1 cos z

the IB SL formula booklet Round to 3 s f if not otherwise specified The following diagram shows a park bounded by a fence in the shape of a quadrilateral ABCD A straight path crosses through the park from B to D AB 85 m AD 85 m BC 40 m CBD 41 BCD 120 diagram not to scale 85 85 B 1415 40 1 I 120 C VICT PUIGUTTE Calculate the size of angle B D correct to five significant figures 2 The size of angle B D rounds to 77 correct to the nearest degree Use B D 77 for the rest of this question 2

A group of 20 students were asked how many times they visit a certain website per week and the following results were obtained Find the mean median and mode for the distribution 12 8 21 8 9 15 23 19 23 22 5 20 24 23 11 10 2 18 14 8 Find the mean Select the correct choice below and fill in any answer boxes in your choice A The mean is 14 8 Type an integer or decimal rounded to one decimal place as needed B There is no mean for these data C Find the median Select the correct choice below and fill in any answer boxes in your choice OA The median is Type an integer or decimal rounded to one decimal place as needed B There is no median for these data

bike bike walk skateboard car car bike walk car car skateboard bike bus car car car car bike walk bike Transportation walk bike OA 0 5 0 43 0 31 0 2 0 1 car skateboard bus Total Type integers or decimals Construct a bar graph for the data Choose the correct graph below O C 0 5 0 41 0 3 0 2 0 1 0 Walk Walk wym Relative Frequency 0 15 0 30 0 40 0 10 0 05 1 00 Bike Bike Car Skateboard Bus ation to campus of 20 students in a math course Construct a frequency table a relative frequency table and a bar graph for the data Car Skateboard Bus OB Bike 0 6 0 5 4 0 4 0 3 0 23 0 1 O D 0 43 0 3 0 2 0 13 Walk Car Skateboard Bus Walk Bike Car Skateboard Bus

The accompanying table gives the gross domestic receipts for the top 10 movies Find the mean median and mode for each data set Explain which measure best describes a typical value in thi distribution Click the icon to view the data table Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice A The mean is 400 43 Round to two decimal places as needed OB There is no mean for these data Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice Points 0 25 of OA The median is Round to two decimal places as needed OB There is no median for these data

The list contains ages of 60 people who have volunteered to work for a charity Construct a relative frequency table and a histogram for the data given Construct a relative frequency table for the data Age 21 22 23 24 25 26 27 28 29 Total Relative Frequency 1 00 Type integers or decimals Round to the nearest hundredth 23 23 29 24 25 29 24 21 28 24 D 21 22 23 24 25 26 27 28 29 24 28 21 24 29 25 24 29 23 23 29 28 27 26 25 24 23 22 21 24 23 23 29 24 25 29 24 21 28 24 25 26 28 29 27 21 22 23 24 25 29

Many colleges assign numerical points to grades as A 4 B 3 C 2 D 1 and F 0 Find the grade point average for the following semester grade report The grade point average is Round to the nearest hundredth C

Assume that in one of the classes the student has earned test scores of 77 83 51 78 and only one test remains a If the student needs a mean score of 70 to earn a C then what must the student obtain on the final test b If the student needs a mean score of 80 to earn a B then what must the student obtain on the final test a The student must obtain a Type a whole number on the final test to get a C

Find the range mean and standard deviation of the data set 16 16 16 16 16 16 16 16 D The range is Type a whole number

The mean number of hours that Raphael worked over the past four weeks is 39 25 If he works 42 hours this week what will the mean number of hours be that he will have worked over the five week period What is the five week mean Simplify your answer

K Find the range mean and standard deviation of the data set 18 14 18 8 8 10 5 6 The range is Type a whole number

The following bar graph compares women s and men s hourly wages in a recent year Percentage Earning Less than 7 50 per Hour Age 25 and older 20 to 24 16 to 19 Q Men Women 0 2 4 6 8 10 12 14 What percent of women ages 20 to 24 earned 7 50 or less per hour Read the graph to find the percentage of women ages 20 24 who earned less than 7 50 Type an integer or decimal rounded to the nearest tenth as needed

K Find the range mean and standard deviation for the data set 19 18 19 17 17 15 19 16 15 14 The range is Type an integer or decimal Do not round

Find the mean median and mode for the following distribution 4 9 10 9 3 8 11 13 11 14 What problem solving method should be used OA The Order Principle B The Splitting Hairs Principle OC Be Systematic D Guessing is OK Find the mean Select the correct choice below and fill in any answer boxes in your choice OA The mean is Type an integer or decimal rounded to one decimal place as needed OB There is no mean for these data

If the mean median and mode are all equal for the set 40 80 70 90 x find the value of x X Simplify your answer Type an integer or a decimal

distribution Click the icon to view the data table Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean is Round to two decimal places as needed CIE OB There is no mean for these data Domestic Receipts of Top 10 Movies Movie Title Movie A Movie B Movie C Movie D Movie E Movie F Movie G Movie H Movie I Movie J Total Gross millions 457 0 201 8 352 0 356 7 652 2 338 0 200 0 936 2 281 8 228 6 X

The frequency table describes the living arrangements for adults in a certain country Compute the relative frequencies and use them to construct a bar graph Construct a relative frequency table for the data Status Relative Frequency Living alone Living with spouse Child of householder Living with partner Other Total Type integers or decimals Round to three decimal places as needed Status Living alone Living with spouse Child of householder Living with partner Other Total Number in thousands D 59 214 209 411 18 223 67 190 99 947 453 985

F Use the given graph to find the mean median and mode of the distribution Find the mean Select the correct choice below and fill in any answer boxes in your choice OA The mean is Type an integer or a decimal OB There is no mean for this distribution SKELE

Last year Jarod left a job that pays 80 000 to run his own bike repair shop Jarod s shop charges 65 for a repair and last year the shop performed 5 000 repairs Jarod s production costs for the year included rent wages and equipment Jarod spent 60 000 on rent and 100 000 on wages for his employees Jarod keeps whatever profit the shop earns but does not pay himself an official wage Jarod used 30 000 of his savings to buy a machine for the business His savings were earning an annual interest rate of 4 percent Instructions Enter your answers as a whole number If you are entering any negative numbers be sure to include a negative sign in front of those numbers a What is Jarod s annual accounting profit 135000 b What is Jarod s annual economic profit 92900

The following data represent the modes of transportation to campus of 20 students in a math course Construct a frequency table a relative frequency table and a bar graph for the data bike bike walk skateboard car car bike walk car car skateboard bike bus car car car car bike walk bike Construct a frequency table for the data Transportation Frequency walk bike car skateboard bus Total 20 T

Find the mean median and mode for the following frequency distribution X 2 3 5 6 7 9 10 f 3 9 5 2 7 5 3 D Find the mean Select the correct choice below and fill in any answer boxes in yo choice OA The mean is Round to two decimal places as needed OB There is no mean for this distribution

Find the mean median and mode for the following distribution 5 6 5 1 3 8 9 7 10 Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean is Type an integer or decimal rounded to one decimal place as needed COLLE OB There is no mean for these data

K Find the mean median and mode for the following distribution 4 5 3 6 7 8 9 10 11 14 Find the mean Select the correct choice below and fill in any answer boxes in your choice OA The mean is Type an integer or a decimal OB There is no mean for these data

a What was the largest number of customers in the coffee shop and how often did it occur The largest number of customers was It occurred time s 12 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of Customers

Webby Inc is a web development company Webby s monthly production function for developing websites is given in the table below a Fill in the marginal product column Instructions Enter your answers as a whole number Programmers 0 1 2 3 4 5 6 Websites Marginal Product 0 2 6 14 20 24 26 b Marginal product diminishes after the Click to select programmer

How many ways can you get exactly 1 tail Construct a tree diagram Choose the correct diagram below OA Begin Quarter Dime Nickel H H H H Penny H T T T H T H H T There is are exactly Type a whole number H H H PNDQ HHHH HHHT HHTH HTTH HTTT THHH THHT THTH THTT TTHH H H TTHT T H TTTH TTTT way s to get 1 tail HHTT HTHH HTHT OB Begin Nickel H Penny H T T Dime H T H H Quarter H V V V V V V H T H HTH H T PNDQ HHHH THHH HTHH HHTT HHTH THTH HTTH HTTT HHHH HTTH THTH THTT TTHH THTT TTTH TTTT O C Begin Nickel H Penny H H Dime T T H T Quarter H V V V V V V V V H 7 T H T H T H H T PNDQ HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT

How many ways can you get exactly 1 tail Construct a tree diagram Choose the correct diagram below OA Begin Dime Nickel H H Penny H T T H T H H T L Quarter H T H H There is are exactly Type a whole number T H H PNDQ HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT T H way s to get 1 tail OB Begin Nickel H Penny H T Dime H T T H H T C Quarter V V V HTH TE V V V V V THTHE PNDQ HHHH THHH HTHH HHTT HHTH THTH HTTH HTTT HHHH HTTH THTH THTT TTHH THTT TTTH TTTT O C Begin Nickel H Penny H H Dime H H T H T T H H T Quarter H T V V V V H T H THE T PNDQ HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT

A storage container consists of a box of length 90 cm width 42 cm and height 34 cm and a lid in the shape of a half cylinder as shown in the diagram The lid fits the top of the box exactly The total exterior surface of the storage container is to be painted Find the area to be painted 42 a Find the area to be painted 3 90 34 diagram not to scale

Your insurance company has a policy to insure personal property Assume you have a laptop computer worth 1 600 and there is a 1 chance that the laptop will be lost or stolen during the next year What would be a fair premium for the insurance We are assuming that the insurance company earns no profit A fair premium for the insurance would be

K Assume that P A 0 4 P ANB 0 35 and the probability that neither A nor B occurs is 0 3 What is the probability of B P B Simplify your answer Type an integer or a decimal CITE

K An experiment and two events are given Determine if the events are independent or dependent Experiment Two dice one red one green are rolled Event A The total is greater than nine Event B The green die shows six The two events A and B are dependent independent

List all the ways to select two different members from S without repetition The order in which members are selected is important For example AB is not the same selection as BA S L M N P Q RIZA Identify the list of all the ways to select two members from S Choose the correct answer below A LM LN LP LQ MN MP MQ NP NQ PQ O B LL LM LN LP LQ MM MN MP MQ NN NP NQ PP PQ QQ OC LN LP LQ MN MP MQ NP NQ OD LM LN LP LQ ML MN MP MQ NL NM NP NQ PL PM PN PQ QL QM QN QP

K Assume that 2 cards are drawn from a standard 52 card deck Find the following probabilities a Assume the cards are drawn without replacement Find the probability of drawing 2 spades b Assume the cards are drawn with replacement Find the probability of drawing 2 spades a The probability of drawing 2 spades without replacement is Simplify your answer b The probability of drawing 2 spades with replacement is Simplify your answer STE

K If ten coins are flipped what is the probability of obtaining at least one head and at least one tail Consider the complement of the event before computing its probability P obtaining at least one head and one tail This question 1 point s possible Simplify your answer Submit tes

This question 1 point s possible A fish pond at a carnival contains 90 angelfish 88 cory cats 137 tetras and 135 goldfish If Marcelo picks a fish at random from the pond what is the probability that it is a angelfish The probability is Simplify your answer test

4 16 Two soybeans are impacted against a steel surface Assume the impact is elastic and obeys the Hertz equations for contact between two solids This assumption is not valid Nevertheless insight can be gained by doing the analysis The equivalent radius of the first soybean is 0 251 cm and during the impact the maximum force reached is 22 1 N The equivalent radius is the radius of a sphere which has the same volume as the soybean The second soybean has an equivalent radius of 0 325 cm and during impact the maximum force reached is 37 0 N Assume the soybeans have the same modulus of elasticity 18 54 MPa and a Poisson s ratio of 0 35 For each soybean calculate the maximum normal stress developed during impact on the steel surface The maximum stress will develop at the point on the soybean where contact is first made between the soybean and the steel wall Compare the stresses experienced by the two soybeans Solution hints Assuming the soybeans are spherical calculate the radius of the contact circle a b from the force F and radius of the soybeans Then calculate the maximum contact stress Repeat the procedure for both small and large soybeans You will find that the stresses imposed on small and large soybeans are almost identical

Singers E nrique K aty R ihanna and B runo are performing a charity concert for world hunger and their order of appearance will be chosen randomly The outcomes in the sample space be represented as strings of letters such as ERBK or KERB Complete parts a through c below a How many elements are there in this sample space Type a whole number b Express the event Rihanna and Bruno perform consecutively as a set Choose the correct answer below A RBKE RBEK KRBE ERBK KERB EKRB B RBKE RBEK KRBE ERBK KERB EKRB BRKE BREK KBRE EBRK KEBR EKBR OC RBKE KRBE KERB BRKE KBRE KEBR OD BRKE BREK KBRE EBRK KEBR EKBR CE c What is the probability that Rihanna and Bruno perform consecutively Type an integer or a decimal

A typical bingo card is shown on the right The numbers 1 15 are found under the letter B 16 30 under the letter I 31 45 under the letter N 46 60 under the letter G and 61 75 under the letter O The center space on the card is labeled FREE The total number of different bingo cards is represented below P 15 5 xP 15 5 xP 15 4 xP 15 5 xP 15 5 Why is the number of different bingo cards possible not P 75 24 Choose the correct answer below B 5 7 2 11 9 OA Although there are numbers chosen from a set of 75 there are 25 locations on the bingo card OB Although 24 numbers are chosen from a set of 75 not every number can be used in every position OC The bingo card should use combinations or C 75 24 OD Since the FREE square cannot be moved the number of different bingo cards possible cannot be represented by either permutations or combinations 28 17 29 N 33 22 FREE 30 41 44 38 G 51 59 48 46 52 75 63 61 72 68

Consider the following loan purchase a refrigerator for 1 500 at 13 add on interest for 3 years Give the formula used to approximate the annual percentage rate or APR for an add on loan where r is the annual interest rate as a decimal and N is the number of monthly payments APR Determine the following values for this loan r 0 13 N Find the APR rounded to the nearest tenth of a percent for the loan

JARANTAMARAET Mamma s Pizza advertises a special in which you can choose a thin crust thick crust stuffed crust deep dish crust or cheese crust pizza with any combination of different toppings The ad says that there are almost 5 200 different ways that you can order the pizza What is the smallest number of toppings available Explain your thinking by referring to the fundamental counting principle The smallest number of toppings available is Type a whole number

Radio stations that are on the west side of a nation have call letters consisting of a K followed by four letters K can be used again How many different call letters of this type are possible There are different call letters that can be formed Simplify your answer

Assume you are rolling two dice the first one is red and the second one is green Use a systematic listing to determine the number of ways you can roll a total of 7 on the two dice In how many ways can you roll 7 ways

List all the ways to select two different members from S without repetition The order in which members are selected is important For example AB is not the same selection as BA S L M N P Q Identify the list of all the ways to select two members from S Choose the correct answer below OA LM LN LP LQ MN MP MQ NP NQ PQ B LL LM LN LP LQ MM MN MP MQ NN NP NQ PP PQ QQ OC LN LP LQ MN MP MQ NP NQ OD LM LN LP LQ ML MN MP MQ NL NM NP NQ PL PM PN PQ QL QM QN QP

How many different two digit numbers can be formed using the digits 6 8 3 4 and 5 with repetition For example 66 is allowed The number of different two digit numbers is

Use a calculator to evaluate an ordinary annuity formula nt A m A 1 F n 1 for m r and t respectively Assume monthly payments Round your answer to the nearest cent 150 6 35 yr

Use estimation to select the best response Do not calculate When using the average daily balance method for the month of September t is which of the following 31 365 1 12 30 365