Math Questions

If segment AC and segment BC are tangent to circle O find the value of x 0 x B x 20 C Enter

grap y f x 5 4 solid curve Sorry that s Incorrect Try again 10 5 5 0 5 10

An ice cream waffle cone can be modeled by a right circular cone with a base diameter of 6 6 cm and a volume of 54 45 cubic centimeters What is the height of the cone in centimeters 1 3 75 2 5 3 15 4 24 75

The graph shown here models the temperature t in degrees when the amount of snowfall s in inches increases during a winter day in Canada Which of the following gives realistic set of values for the domain for that day 1 40 20 10 1 O 10 0 t 32 20 30 40 S

Noel has an initial account balance of 4 000 For the next five months her account balance increases by 1 000 per month After that her account balance b decreases by 1 000 per month t Which statements are true for this situation The equation that models the account balance is b 11 000r 5 000 9 000 O The equation that models the account balance is b 11 000r 9 000 9 000 The equation that models the account balance is b 11 000t 9 000 4 000 Noel s account balance will be 7 000 in 3 months and 7 months Noel s account balance will be 7 000 in 7 months and 11 months

Lollipops are selling for 5 00 a pound Tootsie Rolls are selling for 2 50 a pound Wendy wants to spend exactly 80 to get a total of 30 pounds of candy How many pounds of each should she get Answer pounds of

Multiply and Divide Rationals Quiz Level G Anaya is viewing her bank account online She sees 3 entries for Monday each for 10 50 Write an expression to represent the total change in Anaya s account on Monday 10 50 3 10 50 3

9 Determine the amplitude A period P and phase shift PS of the function f x 8sin 2 x 4 10 OA 8 P n PS 4 10 O A 8 P n PS 4 10 O A 8 P n PS 4 10 O A 8 P n PS 4 10

Use the accompanying Venn diagram which shows the number of elements in region II to answer the following problem If n A 47 n B 45 and n U 77 find the number of elements in each of regions I III and IV Region I has 29 element s Region III has 27 element s 11 18

The value of a laptop t years after it is purchased is given by the decreasing function V where V t is measure in dollars The rate of change of the laptop s value in dollars per year is proportional to the laptop s value Which of the following differential equations with the correct description of constant k could be used to model the value of the laptop 1 point dVV where k is positive dt dv k dt V where k is negative V kV where k is negative It kt where k is positive

Find the total selling price 3 Mi Lynn Sato gave the sales clerk a 50 bill and a 5 bill and received 2 40 in change If the sales t rate in her community was 5 25 what was the item s total selling price

Raymond has a circular garden with a radius of 9 feet He wants to build a walkway that is feet wide around the garden A What will the area of the walkway be in square feet B C D 16T 25T 4 ft 81T 9 ft

At the gift shop they sell small greeting cards and large greeting cards The cost of a small greeting card is 2 15 and the cost of a large greeting card is 5 40 How much would it cost to get 2 small greeting cards and 5 large greeting cards How much would it cost to get a small greeting cards and y large greeting cards Total cost 2 small greeting cards and 5 large greeting cards Total cost a small greeting cards and y large greeting cards

The expression 10 000 0 90 represents the population of a town t years after 2000 Select the value from each drop down menu that best completes the sentence The population of the town by each year

Jenny Tarver purchases a 1 599 99 treadmill a 49 99 pair of walking shoes a 79 99 leather handbag 6 pairs of socks at 8 99 per pair and 2 pairs of running shorts at 19 99 each at the County Store in Bay Shore New York The state sales tax rate is 4 the county rate is 4 25 and the city transportation tax rate is 0 25 What is the sales tax on her purchases

Find the total selling price Remember that this price does not include the tax Johnny Most paid 255 25 total for a new solar panel If the sale tax rate is 9 in his community what was the panel s selling price

Find the surface area of the composite figure 6 cm 4 cm 15 cm 3 cm 5 cm SA cm 6 cm Enter

The number of people who visited a state park over the last nine years is recorded in the table 5 198 Year Visitors 1 452 2 360 3 348 Complete the statements describing the situation 4 302 The visitor data is best modeled by a function Based on the model the state park management should plan for 6 124 7 204 8 308 9 398 than 400 visitors next year

5 PacBell 6 34 8 b C 6 55 d 5 Jose 1 99 4 Nel Cng 1 What is the coupon rate and maturity date for this bond a 5 The coupon rate is 6 the maturity date is 2034 8 1 The coupon rate is the maturity date is 2034 5 The coupon rate is 6 the maturity date is 2099 81 The coupon rate is 6 55 the maturity date is in 5 years

A distribution is given as X U 0 12 Find P x 3 Enter an exact number as an integer fraction or decimal

7 The rule that defines function is fix x 1 Complete the table Then sketch a graph of function f rent price dollars x 2 400 2 200 2 000 1 800 1 600 1 400 1 200 1 000 800 600 400 200 2 0 0 2 From Unit 4 Lesson 4 8 The scatter plot shows the rent prices for apartments in a large city over ten years 4 a The best fit line is given by the equation y 134 02x 655 40 where y represents the rent price in dollars and x the time in years Use it to estimate the rent price after 8 years Show your reasoning 123 4 5 6 time years 7 O 10 9 8 b Use the best fit line to estimate the number of years it will take the rent price equal 2 500 Show your reasoning

Quadrilateral ABCD is a kite What is AE D 13 12 A MU C B

Experiment You roll a die P 4 P 4 not 6 P 4 even P 4 greater than 2 P 4 less than 4 9 10 11 12 13 14 15 16 17 18 P odd P odd prime P odd 3 P odd even P odd greater than 1

In a survey of 2035 workers 73 reported working out 3 or more days a week What is the margin of error What is the interval that is likely to contain the exact percent of all people who work out 3 or more days a week Show all work

32 Determine if the function is a polynomial function If the function is a polynomial function state the degree and the leading coefficient If the function is not a polynomial state why x x 1 x 2 This is not a polynomial function because it is not written in the form f x ax bx rx sx t This is not a polynomial function because the factors are not all linear O This is not a polynomial function because there is no leading coefficient

Many large farms use center pivot irrigation which involves a sprinkler rotating around a central point as shown in the figure A particular system uses a sprinkler 120 meters long and rotates per hour What is the total area in square meters that the sprinkler will water in 5 hours S O 120 meters Enter your answer as a value rounded to the nearest whole number

The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale He decides to use a random number table to survey a simple random sample of 50 of the 250 employees Which of the following correctly labels the population of employees O000 250 O 001 250 O 0 250 1 250

Select the correct answer from each drop down menu A store owner must decide whether to continue stocking a particular brand of jeans in the upcoming year The graph shows the unit sales of this item in the years since the store started stocking it Sales of Jeans Pieces Sold thousands 12 10 8 S 2 3 The data is best modeled by a Based on the graph the store owner Year Complete the statements describing this situation function 15 6 continue stocking this particular brand of jeans

Moe plays a simplified version of powerball You either win the entire jackpot of 500 000 000 or you lose the cost to play i e 2 The probability of winning powerball is 1 out of 292 201 338 the probability of losing is thus 1 292 201 338 What is the expectedyolu

2 A group of 140 high school students were asked Do you play a musical instrument The results are shown in the table below F G 43 140 Males Females 43 67 Survey Results If a musician is selected at random what is the probability that the individual is a female student 43 75 Play a musical instrument 24 43 H J Do not play a musical instrument 15 28 41 32

Two straight fences meet at point A and a field lies between them A horse is tied to a post P by a rope of length r metres Point D is on one fence and point E is on the other such that PD PE PA r and DPE 0 radians This is shown in the following diagram The length of the arc DE shown in the diagram is 28 m 7d Hence find the size of D E 2 marks A new fence is to be constructed between points B and C which will enclose the field as shown in the following diagram IN 800 m B fence Point C is due west of B and AC 800 m The bearing of B from A is 195

Tori is creating an informal argument for the formula for the volume of a square pyramid To start she considered a cube with side lengths of 10 units Then Tori sliced through the center of the cube along its diagonals creating identical square pyramids Tori s diagram is shown below 10 How many square pyramids did Tori slice the cube into What is the height of each square pyramid units Pick all the expressions that can be used to represent the volume of the square pyramid 10 10 10 10 10 5 10 10 10 10 10 5 10 10 10 10 10 6

An object is moving at a speed of 95 kilometers every 7 5 weeks Express this speed in feet per day Round your answer to the nearest whole number Note you must use these exact conversion factors to get this question right Distance length Time 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 mile mi 5280 feet ft 1 meter m 100 centimeters cm 1 kilometer km 1000 meters m 1 inch in 2 54 centimeters cm 1 foot ft 0 305 meters m 1 mile mi 1 609 kilometers km 1 minute min 60 seconds sec 1 hour hr 60 minutes min 1 day day 24 hours hr 1 week week 7 days days 1 month month 30 days days 1 year year 365 days days

You are shopping for dinner for your family in a fast food restaurant but you are concerned about fat An informative menu gives you the following information Chicken sandwich Onion rings Hamburger 24 30 Item Grams of fat Fries 35 12 a How much total fat is in an order of 5 hamburgers 1 chicken sandwich 4 orders of fries and 4 orders of onion rings x 9 b Use a formula to express the total grams of fat F in an order of h hamburgers c chicken sandwiches forders of fries and o orders of onion rings F

Shift D Total Avg Head count 95 80 55 45 275 Total 16 14 8 4 42 Year to Date Turnover 90 Day 8 5 2 0 15 This Year 16 8 17 5 14 5 8 9 15 3 Last Year 16 2 11 1 9 8 10 3 14 3 Which shift will you focus your efforts on in order to reduce 90 day turnover during the second half of this year Shift A Shift B Shift C Shift D

Select the correct answer Cassidy is planning to obtain a loan from her bank for 210 000 for a new home The bank has approved Cassidy s loan at a fixed annual intere rate of 2 7 compounded monthly for 15 years Use the formula to determine Cassidy s approximate monthly payment P F p 1 1 1 OA Cassidy s approximate monthly payment will be 1 721 15 OB Cassidy s approximate monthly payment will be 1 474 58 OC Cassidy s approximate monthly payment will be 5 717 26 OD Cassidy s approximate monthly payment will be 1 420 11

The table below gives the retail sale of electricity in billions of kilowatt hours for the residential and commercial sectors of the United States Year 2000 2003 2006 2009 2012 2015 Residential billions of kilowatt hours 1 192 1 276 1 400 1 420 1 402 1 390 Let a represent time in years with 0 corresponding to 2000 and let y represent the corresponding residential sales Find the quadratic regression equation for the data y R x ax bx c with a rounded to the nearest hundredth 2 decimal places b rounded to the nearest tenth 1 decimal place and c rounded to the nearest integer Use this quadratic model above to answer this question Predict the residential retail sale of electricity in 2022 Round to the nearest billion of kilowa hours NOTE You may get the wrong answer if you do not use the quadratic model with coefficients rounded as described above billion of kilowatt hours

Guests are arriving for a show when the theater manager realizes he forgot to turn on the air conditioning The guests are very hot and uncomfortable At 2 04 p m the manager turns on the air conditioning It is 85 F in the theater a At 2 15 p m the manager announces that he has bad news Using average rate of change he predicts the theater will not cool off to a comfortable 70 F until 3 00 p m What calculations did the theater manager make What was the temperature at 2 15 p m Hint a 201 b As the air conditioner continued cooling the manager recorded these actual temperatures Time of day p m 2 04 2 15 2 24 2 32 2 37 2 53 3 01 3 18 3 27 3 40 Temperature F 85 78 76 73 72 71 70 70 79 What was the average rate of change after 3 00 p m until the temperature reached 70 F Why was the manager so far off in his prediction Hint b

Question 24 U Does the following graph have a maximum or minimum at its vertex What is the max min value Choose 2 2 3 O Minimum 3 pts Maximum

Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes SportsPlus a rival shoe manufacturer then came up with a design that it claims performs even better than Fastex s design A sports magazine decided to test the claims It created two groups of 15 randomly selected athletes each Members of both groups were pretested and determined to have equal athletic ability Additionally they followed the same nutrition plan and training program during the study The athletes did a 1 mile run to test the shoes The magazine found that the athletes who used Fastex shoes had reduced their 1 mile run time by an average of 3 and athletes who used SportsPlus shoes had reduced their 1 mile run time by an average of 2 Given the magazine s data collection method and findings what conclusion can be made The data collection method used was fair since both shoe designs were tested on identical parameters The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes O C The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better The data collection method used was random since the athletes in the two groups used two different shoe designs O A O B D

Rt L The electric current i in a circuit containing a resistance and an inductance see the figure below is given by In where I is the current at t 0 R is the resistance t is the time and L is the inductance Find how long in s it takes the current to reach 0 4 of the initial value of 0 751 A if 1 0 751 A R 7 61 2 and L 1 26 H E R The current changes from 0 751 A to 0 4 of 0 751 Ain Round to the nearest thousandth as needed S

ball is dropped from a height of 60 feet Each time it hits the ground It bounces two thirds of its evious height Find the total distance the ball has traveled before coming to rest 60 ft 40 ft 40 ft 26 7 ft 26 7 ft 17 8 ft 17 8 ft

Sales representatives at a car dealership were split into two groups One group used an aggressive approach to sell a customer a new automobile The other group used a passive approach The following table summarizes the records for 646 customers If one of these customers is selected at random determine the probability that the passive approach was used P Approach Aggressive Passive Total Sale 109 201 310 No Sale 246 90 336 The probability that the passive approach was used is Type an integer or a simplified fraction Total 355 291 646

Q2 2 Anna wants to mail a flag pole to her friend The flag pole is 5 feet long She has a box that is 1 ft by 1 ft by 4 ft Will the flag pole fit in the box Yes O O No Defend your answer using the Pythagorean theorem

Dan purchased a baseball glove for 63 50 If the sales tax is 8 25 what will be the total amount he will pay for the glove Dan heard about a quick way to find the total price of an item He was told that if sales tax is 8 25 he should simply multiply the price of the item by 1 0825 Check the first problem by using this method Carlos decides to buy two t shirts for 15 00 each and some socks that cost 5 99 each Which equation below shows the total cost y given in terms of the number of socks that were purchased p if a 8 5 sales tax was applied A 2 15 00 8 5 5 99 y B y 5 99p 15 00 085 C 1 85 5 99p 30 00 y D y 1 085 5 99p 30 00 0

carpool service has 2 000 daily riders A one way ticket costs 5 00 The service estimates that for each 1 00 increase to the one way fare 00 passengers will find other means of transportation Let x represent the number of 1 00 increases in ticket price Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least 12 000 Then use the nequality to select all the correct statements D W The price of a one way ticket that will maximize revenue is 7 50 100 2 1 500 10 000 1002 1 500 10 000 100x2 1 500 10 000 12 000 The maximum profit the company can make is 15 625 00 The maximum profit the company can make is 4 125 00 The price of a one way ticket that will maximize revenue is 12 50 12 000 12 000

To indirectly measure the distance across a river Mohal stands on one side of the river and uses sight lines to a landmark on the opposite bank Mohal draws the diagram below to show the lengths and angles that he measured Find PR the distance across the river Round your answer to the nearest foot R 150 ft 0 150 ft Answer 225 ft C Diagram is not to scale

7 Technology required What is the value of x D 3 40 X 50 E If necessary round your answer to the nearest tenth Do not include units units in your answer 2019 Illustrative Mathematics All Rights Reserved

The parallel dotplots below display the number of cars parked for several days in each of two parking lots Parked Cars by Lot Lots A B N 21 2 22 23 24 25 26 27 28 29 Number of Cars Which of the following statements is true O The range for the distribution of the number of cars is larger in lot A The range for the distribution of the number of cars is larger in lot B O There is a smaller standard deviation in the distribution of the number of cars in lot B The standard deviation in the distribution of the number of cars is the same for both lots

15 Identify whether each segment is an altitude an angle bisector a median or a perpendicular bisector SEE EXAMPLE 1 D A C a BD C CE E B 15 b FJ d KL L F 16 What is the value of KL SEE EXAMPLE 2 H K G H