Math Questions

A local farmer is planting crops on his 30 acre farm He wants to plant at least 10 acres of com and at least 5 acres of soybeans The farmer believes he can make a profit of 80 per acre profit on the com and a profit of 60 per acre on the soybeans The farmer wants t maximize profit Which of the following is NOT a constraint in this situation Ox y 30 O x 10 Oy 25 OP 80x 6y

Question What is Xn X where X 11 14 67 5 36 99 Y 54 11 99 5 22 808 and Universal Set 2 45 90 22 11 444 14 99 808 67 8 54 36 5 Select the correct answer below O Y nx 2 45 90 22 444 14 808 67 8 54 36 O YnX 11 14 67 5 36 99 54 22 808 O Y nx 2 45 90 444 8 O nX 54 22 808

How many columns in Matrix C Matrix A 3 2 4 Matrix B 3 6 Matrix C 1 2 L A 1 1 1 2 3 1 8 C

The graph of an exponential function is given Select the function for each graph from the given options F x 6 22 g x 6 1 Drag each function given above into the area below the appropriate graph depending on which function is represented by which graph 19 20 Q 21 Q Ay Ay Q h x 6 1 G x 6 x H x 6 f x 6 G 23 Ay 40 24 Ay Ay Q

A sample of phosphorus was isolated and analyzed to determine the percent abundance of each isotope The results are recorded in the table below Isotope Phosphorus 29 Phosphorus 31 Phosphorus 32 Mass amu 29 31 32 Percent Abundance 5 71 24 Based on the data which statement gives the best reasoning for the average atomic mass for the isotopes of 31 14 amu Phosphours 31 makes up the majority of the sample so the average atomic mass should be close to 31 It is the sum of neutrons and electrons in the isotopes found in a sample It is the mean of all of the different isotopes of phosphorus present in the sample It is the total number of neutrons protons and electrons in the isotopes found in a sample of phosphorus

All changes An archery target is shown The length of a side of the inner square is 6 ft and the length of a side of the outer square is 11 ft If an arrow hits the target at random what is the probability hits the shaded region Round to the nearest percent 11 ft 6 ft

Question 3 1 Graph y c 4 5 5 4 3 2 1 4 3 2 1 1 2 3 4 5 Clear All Draw 1 2 3 k 4 5

John is in a club that collects annual dues In the first year that he was a member he paid 20 in club dues However the club dues increase by 2 each year Identify the function that describes the relationship between the number of years that John has been a member of the club and the dues he pays that year Of n 20 2 n 1 Of n 20 2 n 1 f n 20 2n f n 20 2 n 2

Line a passes through 3 1 and 1 7 Line b passes through 2 3 and 8 0 Line c passes through 1 9 and 5 3 Line d passes through 8 6 and 6 1 a b a c a d b c b d c d alb a c ald Obic bid

Fiona s Fashion Store is world renowned for its buttoned uniforms A collection of 36 shirts and 42 jackets contains 842 buttons A collection of 6 shirts and 7 jackets contains 137 buttons Each shirt has the same number of buttons and each jacket has the same number of buttons How many buttons are there in a Fiona s Fashion shirt and how many buttons are there in a jacket

The radius of a sphere is measured as 9 centimeters with a possible error of 0 025 centimeter a Use differentials to approximate the possible propagated error in cm in computing the volume of the sphere error t cm3 b Use differentials to approximate the possible propagated error in cm in computing the surface area of the sphere cm error t c Approximate the percent errors in parts a and b Round your answers to two decimal places volume surface area

The pany expression to represent the total number of rooms that Jake Lionel and Donald can paint together in one hour BIUX X Characters used 0 15000 15px A V E V Part F Find the nhor of rooms per hour that lake Linnel and Donald can paint working together if t is 6 hours

According to the graph of w below the line w 0 is also the H W 5 0 20 00 A neutral asymptote B vertical asymptote C horizontal asymptote D positive asymptote E negative asymptote W for H

A random sample of 16 pharmacy customers showed the waiting times below in minutes 27 19 31 20 17 23 Click here for the Excel Data File The 90 confidence interval 22 18 22 13 to 18 22 10 27 15 Find a 90 percent confidence interval for u assuming that the sample is from a normal population Round your standard deviation answer to 4 decimal places and t value to 3 decimal places Round your answers to 3 decimal places 14

Which manipulations to this equation maintain its balance 3z 3 12 Drag each tile to the correct location on the table For help see this worked example C Balanced 3x 3 12 3 Not Balanced 3x 3 1 2 3x 3 12 3 3 1 2 3x 3 3

lect the reason why these triangles are nilar If they are not select Not similar 8 10 12 5 7 6 25 B SAS D Not similar

5 The data provided is that for the depth of water in Cokato Creek as measured during a day long rainstorm D t is a differentiable function of time t t hour 0 4 8 12 16 20 24 D t in 32 36 38 37 35 33 32 a Find the approximate value of D 16 Indicate units of measure and explain its meaning in context of the problem 4 points b Cokato High School math students have determined that the function D t 35 3cos models the depth of the water during such rain events D t represents the depth of the creek in inches after t hours Use your graphing calculator to find D 16 and explain the meaning of your answer with appropriate units in context of the problem 4 points

The Harrington family belongs to a yacht club On Saturdays they take their sailboat out in the bay They usually spend about 3 hours sailing around This past Saturday they ended up at a point that was a 51 angle from the dock and 445 yards away How far east from the dock were they at this point boatdock O 280 04 yards O 549 53 yards O 345 83 yards O 330 26 yards boat N 4 W E S

5 Jesse drew a perpendicular line in the triangle below from B to the opposite side What is the next step to prove the Law of Sines B A b Find the sines of B and C Find the sines of A and B Find the sines of A and C a Set the sine of A equal to the sine of C C

Park rangers released 4 fish into a pond in year 0 Each year there were three times as many fish as the year before How many fish were there after x years Write a function to represent this scenario A f x 4 3 OB f x 3 4 OC f x 4 x D f x 3 x 4

Select the correct answer The graph of f x 1 10 8 6 4 2 What is the value of k has been transformed to create the graph of 9 x k y A 2 OB 0 O C 3 OD 3 10 8 6 A 2 2 T 6 8 10 O g 2 0 6 CO 8 10 X

Sherry bought 20 apples at the grocery store The Braeburn apples were 0 80 each and the Granny Smith apples were 0 65 each All together the apples cost 14 95 How many Granny Smith apples did she buy A 7 B 9 C 11 D 12 E 13

ve the figure below 45 ft 60 ft the figure answer the questions on the right 9 10 1 point In the figure we see that the cherry picker can reach a height of 60 feet off the ground which includes the 8 feet from the base when it is inclined to its maximum angle of 48 degrees What is the length of the arm of the cherry picker Enter your answer to 2 decimal places Type your answer 1 point If the cherry picker does not move can the angle of the arm change in a way that it can reach the top of the building 17 00 D type your answer

127GARAS 2 2008 Natasha conducted a survey to determine how many of the 215 workers in her office building use public transportation to get to work She surveyed 30 randomly selected workers who entered the office cafeteria throughout the day Of the 30 workers surveyed 9 used public transportation to get to work Which change to Natasha s survey process would make the data more reliable A Use a different sample size so the predicted number of workers who use public transportation is a whole number B Ask a randomly selected sample of people who use public transportation whether their office is in the building OC Randomly select the sample in the lobby of the building so workers who do not enter the cafeteria can be included Have workers complete a written survey so there is a written record of the responses D

Your parents have been advised to save 5 of their income for your college education which would include money for housing tuition books and fees Ho much would your parents have saved in one year following the recommended 5 they had an average household income of 48 948 Show your work 5 points

In a solar system two comets pass near the sun which is located at the origin Comet E is modeled by all measurements are in astronomical units Part A What are the vertices for the path of Comet E Show your work 4 points x 16 y 1 and Comet H is modeled by 400 144 Part B Which comet travels closer to the sun Give evidence to support your answer 5 points Part C What key feature does the sun represent for both comets Give evidence to support your answer 6 points x 13 y 25 144 1 where

Apie is removed from your oven with an internal temperature of 165 F It is placed on your counter to cool The temperature of the room is 65 F If the temperature is 140 F after half an hour how much time will have passed when the temperature of the pie will be equal to 95 F Note Round to the nearest hundredth of an hour

at which jake Lionel the new rate is faster or slower and by how much BIUX X 15px Characters used 0 15000 paint part F with the rate at which jake Lionel and Wayne paint part C Determine whether AV A EEEEEE

Peter is writing about this excerpt from The Code Book A variation on the Trojan horse is a brand new piece of encryption software that seems secure but which actually contains a backdoor something that allows its designers to decrypl everybody s messages In 1998 a report by Wayne Madsen revealed that the Swiss cryptographic company Crypto AG had built backdoors into some of its products and had provided the U S Government with details of how to exploit these backdoors As a result America was able to read the communications of several countries Which of Peter s lines shows that he is using personal experience to understand the reading O Hidden messages can be shared through a backdoor in encryption software It reminds me of the way I leave my kitchen door open so the cat can come in Hidden messages can be shared through a backdoor in encryption software The author gives an example of this software helping the government O A Trojan horse is a type of encryption software but as the author explains it is not always 100 percent secure O A Trojan horse is a type of encription softuro which

Edna is fouled hard in an exciting basketball game It is ruled a flagrant foul and the opponent is tossed from the game As a result Edna is allowed to shoot two free throws She is a good shooter and on average makes 82 of her free throws Assuming independence between the 2 free throws what is the probability

The flight path of a rocket launched from the ground is modeled by y 0 25 60x x where y is the height of the rocket in meters from the ground and x is the time in seconds after it was launched Find the vertex of the parabola and explain what it represents in terms of the context 30 225 rocket reaches maximum height of 225 feet after 30 seconds 60 0 rocket lands at 0 feet after 60 seconds 30 225 rocket reaches maximum height of 30 feet after 225 seconds 60 0 rocket reaches 60 feet after 0 seconds

Of the 16 cards drawn from a standard deck of 52 cards 5 of the cards are spades Based on the cards that were drawn the and the difference of the experimental and theoretical probabilities of drawing experimental probability of drawing a spade is spade from a standard deck of cards is V 1

Given the following limit select all statements that must be true f 6 h f 6 h Select all that apply Of x is continuous at x 5 Of x is differentiable at x 6 lim f x exists x 6 lim f x f 5 x 6 None of the above lim h 0 5

A inanufacturer determines the relationship between the demand and price of an item to be x p 5200 where x is the number of items demanded at a price of Sp each If the price per is decreasing at a rate of 5 00 each week find the rate of change of the demand with respect to when the price is 40 per item Round your answer to the nearest integer if necessary d P 5 week a 90 items per week b 14 items per week c 3 items per week d 200 items per week e None of the above 540 2x 2p 0

Which of the following would not be a representation of the differentiable function f where f 5 3 6 points O The slope of y f x at x 5 is 3 O The instantaneous rate of change at x 5 of f x is 3 O f 3 h f 3 lim h 0 h 5 The slope of a line tangent to the graph of f at x 5 is 3

You have a bad habit of overpacking On an overnight field trip with the school you packed five shirts and one pair of jeans Two of your shirts are yellow and the other three are black What is the probability you randomly reach into your suitcase and pull out a yellow shirt 100 O 30 O 20 O 60

f x x 6x even O odd Oneither Sketch the graph of f If f is even or odd use symmetry to sketch its graph y 4 4 2 2 15 10 5 10 15 y 4 2 2 2 4 4 X X 4 4

On a piece of paper graph y2 x 1 Then determine which answer choice matches the graph you drew 5 A y 01 5 LO 3 2 0 1 5 O A Graph D OB Graph C OC Graph B O D Graph A 1 5 B 01 5 Ch 3 2 0 1 5 5 C 10 5 10 S 3 2 0 1 5 5 D 5 y 3 2 x 0 1 5

Find the surface area of the composite figure 3 cm 5 cm 4 cm 8 cm 8 cm 5 cm 7 cm 10 cm SA cm Enter

Kayla runs a small bakery in her town The following expression models the total amount of money Kayla s bakery earns in a particular mont where x represents the number of online orders in that month What does the constant term in the above expression represent O A 200 9x 1 900 OB OC OD The constant 900 represents the amount Kayla s bakery earns in a particular month when there are no online orders The constant 900 represents the maximum amount of money that Kayla s bakery receives in a particular month The constant 900 represents the maximum number of online orders Kayla s bakery receives in a particular month The constant 900 represents the amount Kayla s bakery earns from online orders each month

The amount of simple interest earned n varies jointly with the rate of interest r and the number of years t The simple interest earned is 225 when the rate of interest is 4 5 for 4 years Using the variables r and t find the equation that represents this relationship

Drag each tile to the correct box Match the text structure to the appropriate author s purpose description problem solution cause effect to describe important facts and details about the Declaration of Independence to recount why students can no longer carry backpacks and the impact it has on students to inform readers about the trouble with excessive screen time and possible ways to reduce it

Work must be shown to receive credit Recommended to work on problems on separate paper Answers are at the bottom 1 On average a U S smartphone owner between the ages of 18 and 24 sends and receives a total of 3853 text messages per month The number sent is 191 more than the number received On average how many text messages are sent and how many are received per month by a smartphone owner in this age group

An object is sighted from a helicopter at an angle of depression of 54 After the helicopter has traveled 9 0km horizontally the angle of depression to the same side of the object is 68 Determine the direct line distance at that point from the helicopter to the object 5 marks

ve buys last year s best selling novel in hardcover for 15 75 This is with a 25 discount from the original price What was the original price of the novel

Reena collects postage stamps to create an album The album has 14 pages The first five pages of her stamp album holds 4 stamps per page The remaining pages of the album have 14 stamps per page Which equation can be used to find the total number of stamps n On 5x 14 14 14 On 14 x 4 14 9 On 5x 4 9 x 14

On a map the endpoints of a straight fence are located at A 4 12 and B 8 22 Lisa plans to install a gate in the fence and wants the gate s hinges to be the same distance from both ends of the fence At what point on the map will the gate hinges be placed OA 0 2 OB 2 5 OC 6 17 OD 12 34

The price p in dollars and demand x for wireless headphones are related by x 8 000 0 15p The current price of 110 is decreasing at a rate 7 per week Find the associated revenue function R p and the rate of change in dollars per week of revenue R p 8000p 0 15p d dp dt R p 8 000p 3 dp dt 0 15p The rate of change of revenue is dollars per week Simplify your answer Round to the nearest dollar per week as needed

A high school chemistry teacher asks four student groups to determine the number of protons neutrons and electrons respectively present in an ion of Titanium Ti 2 Which student group provides the best answer Group one claims that there are 22 protons because this number identifies the element Ti they also claim there are 26 neutrons because when the protons and neutrons are added the number equals the atomic mass on the periodic table which is 47 87amu and there are 20 electrons because the ion has a 2 charge which indicates the atom lost two electrons Group two claims the number of protons is 26 because the number of neutrons is always the same when subtracted from the mass which is 48 the number of neutrons would then equal 22 and the number of electrons is 24 because the 2 charge indicates the atom gained 2 electrons O Group three claims that there are 22 protons in an atom of Ti so that means there are 24 neutrons because there is a 2 charge which indicates the atom lost 2 neutrons and there are 22 electrons because every atom has the same amount of protons and electrons Group four claims there are 20 protons because the atom lost 2 charges the number of neutrons is 28 because when added the number of neutrons and protons should equal 48 and there are 20 electrons because the number of electrons and protons should be the same

The following data show the list price x in thousands of dollars and the dealer invoice price y also in thousands of dollars for a variety of sport utility vehicles Find a linear equation that approximates the data using the points 16 5 16 1 and 20 0 18 3 Round to two decimal places as needed List Price Dealer Invoice Price 16 5 17 6 20 7 23 1 20 0 24 6 16 1 17 0 18 2 19 3 18 3 21 0 O A y 0 63x 5 73 OB y 0 63x 6 38 O C y 1 59x 10 21 O D y 1 59x 9 11