Basic Math Questions and Answers

Unit 5 Lesson 1 Cumulative Practice 1 Which expression equals 27 A B 2 2 2 2 2 2 2 C 2 7 2 2 2 2 2 2 2 D 2 7 2 Evaluate the expression 3 5 when x is 2 3 The graph shows the yearly balance in dollars in an investment account amount in dollars 5 000 4 000 3 000 2 000 1 000 OT 2 0 4 6 8 10 12 14 number of years a What is the initial balance in the account b is the account growing by the same number of dollars each year Explain how you know c A second investment account starts with 2 000 and grows by 150 each year Sketch the values of this account on the graph d How does the growth of balances in the two account balances compare

Isaiah had 6 inches of snow on his lawn It then began to snow at a rate of 2 inches per hour Assume no snow melted Answer the questions below regarding the relationship between the number of hours since snow began falling and the total amount of snow on Isaiah s lawn

Jack bought a car for 17 500 The car loses 750 in value each year Which equation represents the situation Oan 18250n 750 an 750n 18250 an 18250n 750 an 750n 18250

4 Jada rewrites 5 3 as 15x Do you agree with expressions Explain your reasoning 5 Investment account 1 starts with a balance of 200 and doubles every year Investment account 2 starts with 1 000 and increases by 100 each year a How long does it take for each account to double b How long does it take for each account to double again c How does the growth in these two accounts compare Explain your reasor 6 A study of 100 recent high school graduates investigates a link between their childhood reading habits and achievement in high school Participants are asked if they read books every night with another person wher were ages 2 to 5 as well as their grade average for all of their high school class The results are represented in the table A average B average C average D average read books nightly did not read books nightly 16 21 12 3 a What does the 21 in the table represent b What does the 10 in the table represent 10 14 16 8

24 16 8 0 0 A No 1 2 3 Does the graph represent a direct proportion B Yes the constant of proportionality is 16 C Yes the constant of proportionality is 8 D Yes the constant of proportionality is 4

points plotted below are on the graph of a polynomial In what range of x values must the polynomial have a root Check all that apply 5 A 2 5 to 1 5 B 2 5 to 3 5 C 3 5 to 4 5 D 1 5 to 2 5 E 5 5 to 6 5 F 1 5 to 0 5

5 50 Traffic flow at 1st Ave and High St is twice the traffic flow at 2nd Ave and Central Compare the graph of the traffic flow at 1st Ave and High St to the graph of the traffic flow at 2nd Ave and Central over time O The period of the graph of the traffic flow at 1st Ave and High St is four times as long as the period of the graph of the traffic flow at 2nd Ave and Central O The period of the graph of the traffic flow at 1st Ave and High St is twice as long as the period of the graph of the traffic flow at 2nd Ave and Central O The period of the graph of the traffic flow at 1st Ave and High St is equally as long as the period of the graph of the traffic flow at 2nd Ave and Central The period of the graph of the traffic flow at 1st Ave and High St is half as long as the period of the graph of the traffic flow at 2nd Ave and Central

Shapes Colors The percentage of employers who allow casual dress every day was 51 in 2001 and has decreased by about 3 percentage points per year Let p be the percentage of employers who allow casual dress every day at 1 years since 2001 Complete parts a through d CHEZEE a Find the slope of the linear model that describes this situation What does it mean in this situation The slope is The percentage of employers who allow casual dress every day has decreased by percentage points per year

Write the negation of the statement Everyone in the class was bored by the professor s lecture Choose the correct negation for the given statement Some people in the class were bored by the professor s lecture No one in the class was not bored by the professor s lecture Come people in the class were not bored by the professor s lecture O Everyone in the class was not bored by the professor s lecture x

8 Jerome has exemptions of 7 500 for dependents His deductions include 2 400 in allowable medical expenses and 450 for damage to his home caused by a hailstorm Jerome s taxable income if he has an income of 47 900 is a 10 350 b 37 550 c 40 400 d 58 250

12 3 More Factoring with Diagrams id niw Here are some polynomial functions with known factors Rewrite each polynomial product of linear factors Note you may not need to use all the columns in each dia For some problems you may need to make another diagram 1 A x x 7x 16x 112 x 7 Diagram X 7 x x 7x 0 11 2

Spinner Results Color Frequency Red 14 Blue 19 4 11 2 Green Yellow Purple the spinner is spun 900 more times about how many times would you expect to and on blue Round your answer to the nearest whole number

Select the correct answer from each drop down menu Each student in the class reported how long they slept last night The results are represented by the box plot below Hours Students Slept Last Night Complete the sentences about the box plot 5 7 8 9 10 Hours of Sleep The box plot shows how many A vertical line is drawn inside the box at the value of set Based on the box plot it is known that 6 V of sleep each student got last night This represents the 11 of the data

Challenge 5 The area of the circle is 40 square units Enter an angle WITHOUT the degree symbol to create a sector with an area of 17 square units Press Submit to check your work Submit

N Select the correct answer from the drop down menu Consider the equation and the graph 2 3 1 I 2 6 8 2 2 6 8 O 6 The approximate solution to the given equation after three iterations of successive approximations is when

The wooded area makes a right triangle in relation to the pond One side of the woods is 19 feet long and the other side is 7 feet long Find the distance acro the pond Answer as a decimal rounded to the nearest hundredth 19 Et 78

c Using the model in part a predict the population in 2029 Round your answer to the nearest million people million people Need Help 26 0 2 Points Read It DETAILS Watch It X PREVIOUS ANSWERS WANEFMAC7 2 2 080 MY NOTES ASK YOUR TEACHER A bacteria culture starts with 800 bacteria Two hours later there are 1 280 bacteria Find an exponential model for the size of the culture as a function of time t in hours f t 800 240t PRACTICE ANOTHE

5 14 points A calculator may be used The rate of change of the population of moose M t in the Boundary Waters Canoe Area Wilderness is directly proportional to 1200 M t for all t 0 t is the time in years and kis a constant of proportionality When t 0 the population is 300 a Write a differential equation that models this situation b Determine M t in terms of t and k c If M 4 600 find the value of k d Calculate M 8 and explain its meaning in context of the situation

A Naval Carrier dropped anchor off the coast The massive anchor drops at 3 5 m s and will be 52 5 meters under the surface of the water after 20 seconds How high above the surface of the water does the anchor begin to drop Round to the nearest meter

Dani had 200 in her savings account When she turned 18 the bank began charging her a 5 00 month fee Write a function in terms of a for the balance of her savings account if she doesn t notice the monthly fee Complete the following Use standard slope intercept form B o

11 You are rowing a boat on a lake at an angle of 35 from the perpendicular to the shore line headed in a straight line toward a village 3 miles down shore How far will you have to row a 2 3 miles b 4 9 miles c 5 7 miles d 7 0 miles 2014 2015 mo 3 miles 35

16 Norman s checking account reconciliation information is as follows Bank balance 304 79 Checkbook balance 206 19 Unreturned checks 110 17 Unprocessed deposits 12 58 When the account is reconciled the checkbook balance is a 206 19 b 207 20 c 303 78 d 304 79 S

18 There are 1 5 mg of iron in 8 ounces of apple juice If 18 mg are recommended for the RDA for iron the number of ounces that contain the RDA is a 27 ounces b 64 ounces c 96 ounces d 144 ounces

19 If the assessment rate is 46 and the tax rate is 37 84 per 1 000 of assessed value the property tax on a house with a market value of 170 000 is a 2 955 96 b 4 492 60 c 9 764 50 d 78 200 00

A baseball is hit towards the outfield following the equations a t 51 5t and y t 16t 105t 4 where x anc y are measured in feet and t is time measured in seconds A How long does it take for the ball to hit the ground Round your answer to the nearest second B How far has the ball traveled horizontally when it hits the ground Round your answer to the nearest foot C Eliminate the parameter by writing the parametric equations as a single rectangular equation D 330 feet away the outfield fence stands 20 feet high Is the ball going to clear the fence Justify your answer

be uneven because questions can be worth more or less including zero depending on your answer Match each number on the left with the correct description of the number on the right Answer options on the right may be used more than once This is an integer This is a rational number but not an integer 10 5 5 6 31 12 T Clear This is an irrational number Question ID 55855 Click and hold an item in one column then drag it to the matching item in the other column Be sure your cursor is over the target before releasing The target will highlight or the cursor will change Need help Watch this video

cylindrical vase has a circumference of about 62 8 centimeters and a height of 33 centimeters To the nearest cubic centimeter how m water will the vase hold OA OB O c OP 3 300 m3 5 183 m3 10 367 m 10 368 m3

Sonequa has two containers one in the shape of a cylinder and the other in the shape of a cone The two containers have equal radii and equal heights She investigated the relationship between the volumes of the cone and the cylinder by transferring water between the two containers Which of the following claims is most likely to be supported using the results of Sonequa s investigation A B C D The volume of a cylinder is two times the volume of a cone when the two containers have equal radii and equal heights because one full cylinder of water completely and exactly filled the cone two times The volume of a cylinder is three times the volume of a cone when the two containers have equal radii and equal heights because one full cylinder of water completely and exactly filled the cone three times The volume of a cylinder is two times the volume of a cone when the two containers have equal radii and equal heights because two full cylinders of water completely and exactly filled the cone one time The volume of a cylinder is three times the volume of a cone when the two containers have equal radii and equal heights because three full cylinders of water completely and exactly filled the cone one time

Ethan bought 3 pints of raspberries for 5 per pint and x pints of blueberries for 3 per pint The average 15 3x dollars per pint If the equation y 3 x 15 3x is graphed in the 3 x cost of all the berries he bought was xy plane what quantity will be represented by the y intercept of the graph O The total cost in dollars of all the raspberries Ethan bought O The average cost in dollars per pint of all the raspberries Ethan bought O The total cost in dollars of all the blueberries Ethan bought O The average cost in dollars per pint of all the blueberries Ethan bought

The table below gives the dimensions of a sculpture and a scale model of the sculpture Find the scale factor of the model to the real sculpture Write your answer as a fraction in simplest form Length inches Width inches Height inches Scale factor 0 Sculpture 12 00 8 16 Model 9 6 12

A chemist is performing an experiment by observing the effects when she combines two solutions She monitors the temperature of the combined solution over the course of eight hours and records it in this table Time hours 0 1 2 4 3 5 6 7 Temperature F 20 50 19 82 17 42 14 02 10 82 9 50 12 22 21 62 The chemist can model the temperature with a polynomial function During these eight hours over what interval is the temperature decreasing OA O B O C O D from hour 2 to hour 6 from hour 0 to hour 5 from hour 0 to hour 8 from hour 5 to hour 8 8 40 82

Problem 7 Suppose that a population P t follows the following Gompertz differential equation dP dt 3P 20 In P with initial condition P 0 110 a What is the limiting value of the population b What is the value of the population when t 2

ar Shakespea inctions on of a country increases at a rate of 1 5 annually and its current population is 430 000 h riple years ears ears e years Reset Next

109800 The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer A gardener makes a new circular flower bed The bed is fourteen feet in diameter Calculate the circumference and the area of the circular flower bed circumference 147 feet area 196 square feet circumference 147 feet area 49 square feet circumference 14 feet area 147 square feet circumference 7 feet area 49 square feet

You own a company that makes organs and pianos Each week you make at least 6 organs and at least 4 pianos You company cas make at most 16 of the instruments in a week The profit on a piano is 40 and on an organ it is 30 You wish to maximize profit The objective function for this situation is P 30x 40y What is the maximum profit 0 16 0 4 6 4 L 0 0 6 10 6 0 12 4 16 0

115 150 feet A security camera is set to record activities in a 115 sector of a parking lot as represented by the shaded region of the circle Which measurement is closest to the area of the parking lot recorded by this security camera 5 645 square feet 17 671 square feet 22 580 square feet 70 686 square feet

Write an inequality to represent each sit Professor Peterson is buying a writing desk The width of the desk must be less than 4 ft 1 3 An architect is measuring the height of every skyscraper in her hometown Her measurements show that each skyscraper is taller than 270 ft 2 A carpenter is using an air compressor that turns on when the internal pressure of the machine drops below 25 psi 4 A house has a thermostat to regulate the temperature The thermostat is set to turn the heat on when the temperature in the house is less than 65 F

Andres Michael bought a new boat He took out a loan for 24 010 at 4 5 interest for 4 years He made a 4 990 partial payment at 4 months and another partial payment of 2 660 at 9 months How much is due at maturity Do not round intermediate calculations Round your answer to the nearest cent Maturity value

An action movie was released two months ago and has been playing at a local movie theater The number of tickets purchased each week is shown in the table Week x Tickets y 1 2 3 4 5 6 7 8 348 402 476 500 520 534 540 545 Which equation best models the relationship between the number of weeks since the movie was released and the number of tickets purchased O y 345 x 1 82 y 82 x 1 345 y 362x 27 y 27x 362

2 The Venn Diagram below shows the number of boy scouts in a certain troop who have eamed the following merit badges camping swimming and first aid Camping 2 10 6 4 2 5 3 First Aid Swimming 7 a How many boy scouts have a first aid badge b How many boy scouts have a camping badge or a swimming badge c How many boy scouts have a camping badge and a first aid badge d How many boy scouts have a swimming badge but do not have a first aid badge e How many boy scouts do not have a camping badge f How many boy scouts are in the troop

What is the area of this figure 19 in 12 in 6 in 5 in 13 in 13 in 6 in 13 in Write your answer using decimals if necessary

Which of the following is a disadvantage to using tables Check all that apply A Graphs are much easier to work with for all problems B They organize the data C It is often difficult to solve complicated problems with tables alone D They force you to do every problem twice once with a table and once with an equation

Match each equation on the left to the mathematical property it uses on the right 1 4 3 1 4 3 commutative property of addition 2x 5 2 x 5 commutative property of multiplication 3 x 2 3x 6 associative property of addition 8 x 2 x 8 2 associative property of multiplication 6 5 3 3 6 5 distributive property

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

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

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