Math Questions

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

A circle is defined by the equation given below x y x 2y 0 What are the coordinates for the center of the circle and the length of the radius O A 1 4 units 1 1 2 units OC 1 1 2 units O D 1 1 4 units B

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

amie and Margie need to divide a couch and a hot tub Using the Method of Sealed Bids Jamie bids 530 on the couch and 160 on the hot tub while Margie bids 490 on the couch and 180 on the hot tub amie will get the couch and Margie will take the hot tub and will also get a little bit of money from Jamie To make the division fair how much money will Jamie have to give to Margie

Eugene has fifteen songs on his playlist If he uses the random mode on the music app to play all the songs which of the following represents the number of possible ways to order the songs Assume that the random mode does not play the same song more than once in a cycle O 15 O 1515 0 15 15 15

The two dot plots shown below indicate the number of pets owned by the students in two classes Class A and Class B Which class has the higher median Class A Class B I 2 2 3 4 Number of Pets 0 Number of Pets Class A has the higher median O Class B has the higher median The two classes have the same median 5 7 Not enough information is given to be able to determine which class has the higher median

The Ogden Senior High School chorus were invited to perform at the capital summer concert series To go the students need to convince th parents to pay 200 for the trip The chorus can afford to attend the concert as long as no more than one student s parents do not pay the Suppose there are 20 students in the chorus and each student has a 75 chance of convincing their parents to pay 200 What is the probability that the Ogden High School chorus makes it to the event 0 024

IV A light display has three colored lights each of which flashes on for an instant at regular intervals The yellow one flashes 15 times per minute the blue one flashes 6 times per minute and the red one flashes 12 times per minute You see all three lights flash on simultaneously How much longer must you wait before the three lights flash on simultaneously again The correct answer is 20 seconds Solve this problem and explain each step of your process so that a 5th grader will understand

Complete the following chart Standard Form 5700300 Word Form five thousand three hundred seventy thirty nine thousand seven hundred one

A rectangle will be rotated 360 about a line that contains the point of intersection of its diagonals and is parallel to a side What three dimensional shape will be created as a result of the rotation O A a cube OB a rectangular prism O C a cylinder D a sphere

9 A farmer has 5000 meters of fencing to enclose a rectangular field and subdivide it into three equal plots The enclosed area is to be a maximum Determine the dimensions of one plot of land to the nearest meter

Goldie Esparza buys 4 paper lanterns at 14 95 each 2 pi atas for 19 95 and 2 strings of white lights at 19 99 each The sales tax rate is 4 Norma Engel buys an inflatable canoe for 194 94 2 paddles for 44 95 and 9 energy hare 0 90 PTE

A force F with a magnitude length of 10 Newtons is applied to the point P at an angle of TT FS F with the horizontal as shown below Fv p FH Using trigonometry determine the horizontal component FH and the vertical component FV of the force Note that the triangle shown is a right triangle OFH 5 3 Newtons and Fy 5 Newtons OFH 5 Newtons and Fy 5 3 Newtons FH 5 2 Newtons and Fy 5 2 Newtons FH 5 3 Newtons and Fy 5 2 Newtons FH 5 2 Newtons and Fy 5 3 Newtons

9 Jenny is sitting on a sled on the side of a hill inclined at 15 What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds Show work

Farmer Ed has 650 meters of fencing and wants to enclose a rectangular plot that borders on a river If Farmer Ed does not fence the side along the river find the length and width of the plot that will maximize the area What is the largest area that can be enclosed The width labeled x in the figure is 162 5 meters Type an integer or decimal The length labeled 650 2x in the figure is 325 meters Type an integer or decimal The largest area that can be enclosed is Type an integer or decimal square meters CEL

The following graph shows the approximate relationship between speed in miles per hour and feet per second Answer parts a through e Feet per second AF 160 120 80 40 04 0 100 147 40 80 Miles per hour a Determine the slope of the line The slope of the line is 1 47 Type an integer or decimal rounded to the nearest hundredth as needed b Determine the equation of the line 120 M Q The equation of the line is F 0 Type an expression using M as the variable Use integers or decimals for any numbers in the expression Round to the nearest hundredth as needed

Here is a graph of the function Use the graph to find the following If there is more than one answer separate them with commas a All local minimum values of b All values at which has a local minimum DO X

4 2 1 You have saved 400 350 and 340 so far After your next and final week of saving you want to have saved an average of 375 per week How much do you have to save to get a four week average of 375 per week

ABCD is a parallelogram and EF is parallel to AB Select all triangles are similar to triangle AEX 12 cm 8 cm D 2cm E O Triangle ADC Triangle CDA Triangle XFC Triangle CFX X B

Carl is making a garden that is half as long as it is wide He wants to cover 271 square feet with the garden Which equation best represents the situation if x represents the length of the garden Ox 2x 271 Oxx 271 Ox x 271 Ox 2x 271

Rachel walked 2 0 meters south Then she made a right hand turn and walked 16 0 meters west She turned right again and walked 24 0 meters north Then she turned eft and walked 36 0 meters west What is the magnitude of the overall displacement O 50 2m O 53 7m O 56 5m 629m

The World Bank forecasts growth of world trade to be 7 30 up from 21 80 in 2017 This change has caused Galapagos Islands Resort to analyze its current financial situation beginning with reconciling its accounts Galapagos Islands Resort received its bank statement showing a balance of 11 133 40 Its checkbook balance is 16 208 00 Deposits in transit are 4 039 00 and 7 225 00 There is a service charge of 47 00 and interest earned of 12 40 Notes collected total 2 466 00 Outstanding checks are No 1021 for 2 121 00 and No 1022 for 1 637 00 All numbers are in U S dollars Prepare Galapagos Islands Resort bank reconciliation Input all amounts as positive values Round your answers to 2 decimal places Galapagos Islands Resort checkbook balance Add Subtotal Deduct Reconciled balance BANK RECONCILIATION Bank balance Add Subtotal Deduct Reconciled balance

The salaries of six bank employees are 37 000 38 500 35 000 37 000 45 000 40 000 and 75 000 Which statement is true Both the median and mode are appropriate measures of center The mean median and mode are all appropriate measures of center Both the mean and median are appropriate measures of center The median is the only appropriate measure of center

The graph below represents one equation in a system of equations with the solutions 4 0 and 0 4 Determine which linear equation completes the system Oy x 4 o x y 4 O y x 4 x y 4 2 2 2 2 X

The measurement of a side of a square is found to be 9 centimeters with a possible error of 0 05 centimeter a Approximate the percent error in computing the area of the square X b Estimate the maximum allowable percent error in measuring the side if the error in computing the area cannot exceed 2 9 1 15

Apply Ana is bowling She pays 4 per game and 7 to rent shoes After three games each additional game is free Is the total cost to bowl a function of the number of games played Use a table or graph to help explain your answer

Parte Part 1 of 2 a Find the probability that both prizes are won by men The winning ticket is not replaced Enter your answer as a fraction or a decimal rour decimal places P both prizes won by men

Select the correct answer Each statement describes a transformation of the graph of f x 3 which statement correctly describes the graph of y fx 7 3 OA It is the graph of ftranslated 3 units up and 7 units to the left OB It is the graph of ftranslated 7 units down and 3 units to the right It is the graph of ftranslated 7 units up and 3 units to the right It is the graph of ftranslated 3 units up and 7 units to the right OC O D Reset Next

Joan s finishing time for the Bolder Boulder 10K race was 1 85 standard deviations faster than the women s average for her age group There were 380 women who ran in her age group Assuming a normal distribution how many women ran faster than Joan Round down your answer to the nearest whole number Number of women

The hawk population in a county is declining at a rate of 1 4 per year The population was 3800 in the year 2016 Which answer is the best prediction of the population in the year 2020 O 3541 O 3592 O 3643

You wake up one morning and find yourself wearing a toga and scarab ring Always a logical person you conclude that you must have become an Egyptian pharoah You decide to honor yourself with a pyramid of your own design You decide it should have height h 4470 and a square base with side 1210 S To impress your Egyptian subjects find the volume of the pyramid using integration

From December 2007 through March 2012 researchers at the University of Pittsburgh studied a new medication to treat osteoporosis in frail elderly women The researchers administered a daily dose of the medication or a placebo by injection along with calcium and vitamin D supplements Then the researchers measured the hip and spine bone density of each patient at 12 and 24 months Results were published in the Journal of the American Medical Association JAMA in April 2015 This is an example of which type of study observational study experiment

Application 1 A rocket is tossed from a platform and follows a parabolic path through the air The height of the rocket in meters is given by h t 3t2 10t 8 where t is measured in seconds a How high is the rocket off the ground when it is thrown b For what times is the height of the rocket above 10m Round to 2 dec places 1 mark 3 marks

arble jar below Assuming that you keep each marble after you pick one out what is the probability of pulling out a yellow marble then a blue and then a red YOU MUST SHOW WORK TO RECIEVE FULL CREDIT a 1 point work shown 1 point correct final answer 27 TOTAL 30 ON FILL

Solve the following problem Be sure to make a diagram of the situation with all the given information labeled If a 76 0 foot flagpole casts a shadow 54 0 feet long what is the angle of elevation of the sun to the nearest tenth of a degree

G H For this question make sure to type your answers using proper notation symbols capitalization as needed and include the word Point or Plane accordingly 1 Name three points that are not collinear 2 Name two opposite rays 3 Give another name for JH 4 Name two different planes that contain HL 5 Use Desmos Geometry tool to sketch two planes that intersect with each other at a side Label your planes using the points on each plane Save your image drawing and include it here with your workcheck

Write the statement using symbols Let p be you live in the city of Nashville and let q be you live in Virginia If you do not live in Virginia then you do not live in the city of Nashville Op q Op q O p q Oq p 09 p O q p Submit Answer

3 0 d Solve SHOW YOUR WORK Solve SHOW YOUR WORK Camille has 20 stuffed cats and 15 stuffed Bila and Clarence are training for a marathon dogs which she wants to divide into identical Lila runs 12 kilometers at a time while Clarence with no stuffed animals left over prefers to run in blocks of 3 kilometers At the end of a month they realize that they have run same total number of kilometers What is the smallest number of kilometers that each must have run groups What is the greatest number of groups Camille can place her stuffed animals into HINT GCF Find the factors of 15 then the factors of 20 This will give you the GCF This is the answer T Gef 5 Wor HINT LCM Find the least common multiple of 12 and 3 The answer to this is the answer to the problem 1cm 121m O

For the following distribution decide whether you expect the mean median or mode to give the best representation of the center of the distribution and explain why Daily snowfall in Omaha in January Choose the correct answer below OA The mean because it takes into account all days regardless of the amount of snow OB The median because it is easier to calculate C The mode because it will find the most common snowfall amount s OD The mean because it is the most commonly understood measure of center OE The median because it is unaffected by outliers such as extreme storms OF The mode because there can be more than one

An investment company advertised that last year its clients on average made a profit of 9 Assuming that average refers to the mean which of the followi claims must be true based on this information Note More than one statement could be true If none of the statements is true mark the appropriate box Last year at least one of their clients made a profit of exactly 9 Two years ago some of their clients made a profit of at least 9 Last year the number of their clients who made a profit of 9 or more was equal to the number of their clients who made a profit of 9 or less Last year all of their clients made a profit of at least 9 Last year at least one of their clients made a profit of less than 15 None of the above statements are true X

In the diagram below MN is parallel to JK If MN is 3 more than JM ML 14 and JK 15 find the length of JM Figures are not necessarily drawn to scale State your answer in simplest radical form if necessary L M J N K O

Jon has quarters dimes and nickels in his pocket The value of his money is 1 75 There are two more dimes than quarters and twice as many nickels as dimes How many nickels does he have Inickels

Use the median home values in Mississippi and Hawaii adjusted for inflation shown in the table below Assume that the house values are changing linearly Year 1950 2000 Mississippi 25 200 71 400 Hawaii 74 400 272 700 In what state have home values increased at a higher rate Select If the trends were to continue what would be the median home value in Mississippi in 2010 Select If we assume the linear trend existed before 1950 and continues after 2000 the two states median house values will be equal in what year Select

1 Angle 3 and Angle 6 are examples of which type of angle pair Lines A and B are parallel lines cut by a transversal Use the lines and the angles formed to answer the questions below Corresponding angles 4 Which of the following angles would not be congruent o the measure of 27 42 23 26 Alternate interior angles Same side interior angles Vertical angles 28 f the m27 115 find the asure of 115 0 115 2 Angle 1 and Angle 5 are examples of which type of angle pair ABIGAIL The two angles must be on opposite sides of the transversal Same side exterior angles Alternate interior angles Vertical angles Corresponding angles 5 Which of the following is an example of corresponding angles 28 and 24 25 and 27 21 and 27 D 23 and 25 8 If the m25 is 63 find the measure of 43 MALIK The two angles could be corresponding angles A B m27 3 Angle 6 and Angle 7 are examples of which type of angle pair Alternate exterior angles Same side interior angles Vertical angles 27 and 28 22 and 23 21 and 27 26 and 24 Corresponding angles 6 Which of the following is not an example of supplementary angles lejandro drew two parallel lines cut by a transversal He measured two of the angles that both measured 86 Circle the name of any student who made a true statement wo angles 9 If the mz1 is 57 find t measure of 26 FLETCHER The two angles coule be a linear pair

A hospital has been tracking the number of incidents of heart disease it treats each year for several years The data is shown below Year Heart Disease Incidents 2012 2013 2014 2015 80 83 84 89 a The data is approximately linear Use the data from 2012 and 2015 to find an equation for the linear model Use these variables t years after 2010 so 2015 would be t 5 n number of heart disease incidents b Using this model predict the year in which the number of heart disease incidents will reach 107 The year

In a certain Algebra 2 class of 28 students 9 of them play basketball and 17 of them play baseball There are 6 students who play neither sport What is the probability that a student chosen randomly from the class plays both basketball and baseball

Order Sandostatin octreotide acetate 40 mcg subcut Q 6h Read the label in the figure If the recommended dose is 100 600 mcg d in 2 4 divided doses titrate to response is the prescribed dose safe If the prescribed dose is safe how many milliliters will you administer Select one O a Yes 0 8 mL O b No the dosage is not safe O c Yes 0 5 ml O d Yes 1 2 mL

5 34 Husbands and wives The mean height of American women in their twenties is about 64 3 inches and the standard deviation is about 2 7 inches The mean height of men the same age is about 69 9 inches with standard deviation about 3 1 inches Suppose that the correlation between the heights of husbands and wives is about r 0 5 310 a What are the slope and intercept of the regression line of the husband s height on the wife s height in young couples Interpret the slope in the context of the problem b Draw a graph of this regression line for heights of wives between 56 and 72 inches Predict the height of the husband of a woman who is 67 inches tall and plot the wife s height and predicted husband s height on your graph c You don t expect this prediction for a single couple to be very accurate

apital Expansion Jester s Burger Hut plans to expand by opening several new restaurants e chain operates two types of restaurants drive through and full service A drive through restaurant costs 111 000 to construct requires 7 employees and has an expected annual revenue of 205 000 A full service restaurant costs 184 000 to construct requires 17 employees and has an expected annual revenue of 565 000 McJester s has 3 250 000 in capital available for expansion Labor contracts require that they higher no more than 325 employees Licensing restrictions require that they open no more than 25 new restaurants Let x be the number of drive through restaurants and let y be the number of full service restaurants in this expansion Let R be the expected annual revenue in dollars resulting from the expansion McJester s wants to maximize the expected revenue Set up the linear programming problem Answer the following questions about this linear programming problem for some values a and b Find a and b Round to the nearest integer a Select 325 25 b 205000 184000 17 565000 111000 7 The objective function is R ax by a for some values a and b Find a and b Round to the nearest integer Select b Select 184000 205000