Math Questions

Omar owns a small business selling used books He knows that in the last week 102 customers paid cash 22 customers used a debit card and 10 customers used a credit card Based on these results express the probability that the next customer will pay with something other than cash as a percent to the nearest whole number

A coolant is injected into engine fluid causing the temperature of the engine fluid to decrease with respect to time at a rate that is proportional to the difference of the fluid s instantaneous temperature T and the fluid s original temperature To Select the differential equation that represents the relationship 10 points OdT c T T dt dt c T T T t T To T t To T

A small movie theater sells children s tickets for 4 each and adult tickets for 10 each for an animated movie The theater sells a total of 388 in ticket sales a If c represents the number of children s tickets sold and a represents the number of adult tickets sold write an equation that models the information shown above c Show that after multiplying both sides of the equation in a by 2 c 52 and a 18 is still a solution to this equation b Show that c 52 and a 18 is a solution to this equation not system d How can you interpret multiplying both sides of the equation by 2 in letter a in terms of ticket prices and total ticket sales

2 In December 2016 the Bureau of Labor Statistics issued a statement saying The Consumer Price Index increased 2 1 percent over the last 12 months to an index level of 241 43 What was the CPI in December 2015 6 pts

ur last submission is used for your score DETAILS LARCALC115 9 031 Find the derivative of the function h t h t t 30 sinh 6t

A chemistry student needs 20 0 g of tetrahydrofuran for an experiment By consulting the CRC Handbook of Chemistry and Physics the student discovers that 3 the density of tetrahydrofuran is 0 889 g cm Calculate the volume of tetrahydrofuran the student should pour out Be sure your answer has the correct number of significant digits

Challenge Find the value of x for which r s Then find m 1 and m22 m 1 70 2x m 2 81 3x The value of x for which r s is The figure is not to scale

Which square root equation shows a vertical compression a right horizontal translation and a downward vertical translation Oy x 4 5 Oy 2 x 1 2 Oy x 1 3 Oy 4 x 1 5

me graph Wh in blue Draw the graph of y f 3x shown in red by determining how a stretch or compression will transform the location of the indicated blue points Drag the movable red points to the desired coordinates Hint Drag the red dot to where you think it should be It will fall into the correct place if you are right You may click on a point to verify its coordinates Provide your answer below 74 6 5 4 3 2 1 A

A student dilates SW about point P using a scale factor of 7 5 The Image S W is created Which statements about P SW and S W must be true Select the two correct statements a If P is on SW then SW is parallel to S W If P is on SW then SW is perpendicular to S W If P is on SW then SW is the same line as S W d If P is not on SW then SW is parallel to S W If P is not on SW then SW is perpendicular to SW If P is not on SW then SW is the same line as S W

A factory makes candles Each candle is in the shape of a triangular prism as shown below If the factory made 90 such candies how much use in cubic centimeters If necessary refer to the list of geometry formulas 5 cm 9 cm 8 cm cm

5 A box has a width that is 2 inches greater than its height and a length that is 6 inches greater than its heig It s volume is given by the polynomial expression x 8x 12x where x is the box s height What is th box s volume in cubic inches if its height is 10 inches 1 1 812 3 182 2 1 920 4 2 180

7D Explain why the values of the trigonometric ratios only depend on the angle a and not on the particular lengths x y z q r and s Your answer 7E If y z 0 7 what is the measure of angle a to the nearest degree

Frequency 15 10 5 0 2 Histogram of Quality Defects 6 8 Defects per hour 10 12 n 80 X axis is giving midpoints so the first interval on left side bar shown is going from 1 5 defe 2 5 defects for its interval so based off that understanding answer the following Estimate the interval that contains the median The interval that contains the median is from to

1 Kristina walks from her house around the park to the store She is interested in taking a shortcut through the park to save time Approximately how far away from her house is the store if she were to follow the path shown by the dotted line in the graphic below HOUSE 80 m O 134 m O 128 m O 180 m 200 m PARK 100 m STORE

Drag each sign and value to the correct location on the image Each sign and value can be used more than once but not all signs and values will be used The vertices of an ellipse are at 5 2 and 5 14 and the point 0 6 lies on the ellipse Drag the missing terms and signs to their correct places in the standard form of the equation of this ellipse 6 5 8 2 OD 2 2 VOD 2 1

Math Journal What do the negative coordinates in the ordered pair 1 3 mean How can you use the signs of the coordinates to determine which quadrant 1 3 is in Include a graph in your response

Alan buys cheese from the local farmer s market The graph below shows the cheese cost in cents versus its weight in ounces Use the graph to answer the questions Cost cents 280 245 210 175 140 105 70 35 0 Weight ounces a What is the slope of the line 0 Y 8 08 X

Three gears in a machine are positioned relative to each other to form an isosceles right triangle as shown below 9 1 2 cm 8 What is the distance in centimeters between the centers of the gears located at B and C 5 8 4 12 13 14 15

Select the correct answer The value of m varies inversely as the square of n When 3 m 6 What is the positive value of n when m 13 5 OA 18 OB 4 OC 2 O D 9

Tasneem has a sample of 12 bags of candy She recorded the mass in grams of each bag Her data is shown 46 6 46 7 46 7 46 8 46 8 47 1 47 2 47 3 47 5 47 9 48 48 1 Aalia has a different sample of 12 bags of candy She recorded the mass in grams of each bag The median mass for Aalia s sample is greater than the median mass of Tasneem s sample Which dot plot could represent Aalia s data OA 46 8 OB 46 8 00 00015 47 47 O 47 2 474 47 6 47 8 Mass grams 47 2 474 47 6 47 8 Mass grams 48 48 OC O D 00 46 8 46 8 47 47 2 474 47 6 47 8 Mass grams 000 47 48 472 474 47 6 47 8 48 Mass grams

G 44 H 50 J 58 K 67 10 A 2 1 B 4 4 C 6 9 D 7 6 E 8 4 51 Radius OA of the circle shown below is perpendicular to AP The circle intersects OP at B The length of AP is 12 centimeters and the measure of ZAPO is 20 Which of the following values is closest to the length in centimeters of BP A B 20 12 20 P Note sin 20 0 342 cos 20 0 940 and tan 20 0 364 4

1 Solve each of the following systems by the Method of Elimination These two should be relatively easy Make sure to understand why a x y 7 x y 5 b 2x 5y 3 2x y 5 2 Solve each of the following systems by the Method of Elimination These will be slightly harder than 1 because you will have to alter one of the equations by multiplication a x y 15 b 2x 3y 17 4x 2y 30 5x 6y 32

Find the surface area of the composite figure 3 cm 12 cm 2 cm 10 cm SA 6 cm 8 cm cm Enter

Pythagoras and Esky both put 400 into a bank at the same time Pythagoras s bank calculates 5 interest compounded annually Esky s bank compounds continuously using 4 5 interested Who will have more after 10 years and by how much O Pythagoras will have 24 24 more O Esky will have 24 24 more O Pythagoras will have 21 24 more O Esky will have 36 15 more

61 Mary Bozo Lee Jan Jay and Nelly are on the academic challenge team The club advisor will assign students to 3 person teams at the next competition How many different 3 person teams can be formed from these six students

While on a beach your friend discovers a different genie This genie also offers two purses to choose from and he gives you the following graph to show how the money in each purse will grow The set of triangular marks that lie on a line represent values in Purse A and the set of square marks that make a curve represent those in Purse B 4 500 4 000 3 500 3 000 2 500 2 000 1 500 1 000 500 3 4 5 6 8 9 10 11 12 13 14 15 The genie is still deciding how many days he will let the money in the purses grow Ha and plan a strategy for picking the purse with the most money while the genie 1

29 Determine if the graph represents a polynomial function If it is a polynomial function then determine the number of turning points and the least degree possible This is not a polynomial Lines are not polynomials There are no turning points This graph is not a polynomial This is a piecewise defined function that is constructed with two lines rays Where the lines are connected there is a CUSP point polynomials are represented by graphs with smooth curves Yes this graph represents a polynomial This is a piecewise defined function that is constructed with two lines rays There is only one turning point as each line is a polynomial of degree one

Max is designing a hot tub for a local spa He wants the hot tub to have a diameter of 90 inches What is the approximate area required for the installation of the hot tub Use 3 14 for OA 282 60 in OB 6 358 50 in OC 12 717 00 in OD 25 434 00 in

Karen is buying pens and pencils for the new school year She wants to have no more than 25 writing utensils in all She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens Create a system of Inequalities to model the situation above and use it to determine how many of the solutions are viable OA None of the solution region is viable because there cannot be a negative number of pens or pencils OB The entire solution region is viable OC Part of the solution region includes a negative number of pencils therefore all solutions are not viable for the given situation on region includes a negative number of pens therefore not all solutions are viable for the given situation

Devin is painting a cone shaped centerpiece for the school dance The centerpiece has a diameter of 12 inches and slant height of 19 inches Devin needs to paint one centerpiece for each table There will be 12 tables at the dance The paint Devin uses comes in containers that can cover 500 square inches and cost 3 50 4 1 What is the total surface area that needs painting Round your answer to the nearest whole number 2 How many square inches of paint will Devin need for all the centerpieces 3 How many containers will Devin need 4 How much will it cost for Devin to paint all the centerpieces

Based on the triangles shown below Theodore claims that ATUV is transformed to AWXY with a scale factor of Is Theodore correct T 12 W 8 U X A B 24 16 18 12 Y V 3 Yes the triangles are similar with a scale factor of 21 No the triangles are similar with a scale factor of of 2

Three triangles that do not overlap are shown on the coordinate grid The coordinates of all vertices are integers Which statement is true A 5 4 3 2 1 0 3 4 5 D 2 B C 3 FAABD AEBA GACBD AEBA HAABD ADBC

22 In a recent survey 65 of those surveyed were in favor of a local school levy The margin of error was 2 How many people were surveyed Hint Use the Margin of error formula in the previous question Let ME 0 02 and p 0 65 Solve for n

56 Tasha is in the science club There are 21 students in the club Two of them will be picked at random to attend an awards banquet What is the probability that Tasha will not be randomly chosen to attend the banquet

A test is administered to 500 athletes to determine if they are using performance enhancing drugs PEDs It is assumed that a positive test result indicates that the athlete is using PEDs and a negative test indicates that the athlete is not using PEDs However the test is not 100 accurate so some errors occur The following table shows the test results for this group of 500 athletes Positive Test Result Negative Test Result How many athletes are using PEDs 7 050 53 Athletes Using PEDs 46 4 2 Athletes Not Using PEDs 7 443

1 Use a trigonometric ratio to find the length of x in the triangle Give your answer to two decimal places You may use the trigonometric functions of the Desmos scientific calculator https www desmos com scientific 28 9m X

48 Suppose you are comparing two populations and get the following statistics from random sampling n y SD population 1 population 2 35 100 11 9 5 0 4 0 5 Which sentence best describes this data a Strong evidence that the populations have differ ent means b The data is consistent with equal population

PART B Which of the following quotes regarding Narcissus s love for himself supports the answer to Part A A B C D But her great love increases with neglect her miserable body wastes away wakeful with sorrows leanness shrivels up her skin and all her lovely features melt as if dissolved upon the wafting winds Paragraph 3 He cannot move for so he marvels at himself and lies with countenance unchanged as if indeed a statue carved of Parian marble Paragraph 5 Nor food nor rest can draw him thence outstretched upon the overshadowed green his eyes fixed on the mirrored image never may know their longings satisfied and by their sight he is himself undone Paragraph 6 No more my shade deceives me I perceive Tis I in thee I love myself the flame arises in my breast and burns my heart Paragraph 6 In paragraph 5 the narrative point of view briefly shifts How does this shift of the text s narrative point of view affect the text as a whole Cite evidence from the text in your answer

Geometry Formula Sheet Given the similar triangles below AEDF A BAC set up an equation that you would need to solve in order to find the missing side x Do not solve the equation E x D 22 F B Figure is not drawn to scale 45 A 99 C

Question 3 of 46 Which of the following is a root of the polynomial function below F x x 6x 12x 7 OA 5 3 2 OB 5 3 2 O C 3 O D 6

7 On the dart board the center circle has a diameter of 2 inches What is the probability of hitting the shaded ring Round to the nearest hundredth A 0 01 B 0 29 C 0 30 D 0 45 11 5 in 5 in keb

Consider the following two prisms 14 7 6 15 Choose 1 answer 5 Sandra tried to use Cavalieri s principle to show that the two figures have the same volume The base areas are the same Therefore corresponding cross sections have the same area The prisms have the same height So the volumes must be the same What is the first mistake Sandra made 114 The base areas are not the same It isn t true that corresponding cross sections have the same area

From the observation deck of a skyscraper Meena measures a 45 angle of depression to a ship in the harbor below If the observation deck is 862 feet high what is the horizontal distance from the base of the skyscraper out to the ship Round your answer to the nearest tenth of a foot if necessary

15 The temperature inside of a storage building in degrees Fahrenheit can be modeled using the equation 4 pts A F t 8 3 cos 57 t 63 7 where t is the number of hours since midnight t 0 a At what temperature is the building at midnight Justify how you arrived at your answer Find min 8 3 cos 0 63 7 1 1 tegn 6 7 2 b How many hours after midnight does it take for the temperature to first reach its maximum value Justify how you arrived at you answer Need P 1 7 X 8 3 8 3 55 4 72 55 4 2 72

A high school gym teacher randomly selects a group of two players from three students to demonstrate a basketball drill during class The three students consists of two girls Andrea and Marta and one boy Davi The sample space of possible groups is listed below Let A be the event that the first player the coach chooses is a girl and B be the event that the second player is a boy What is P A or B the probability that the coach chooses a girl first or a boy second Group 1 Andrea Group 2 Andrea Group 3 Group 4 Group 5 Marta Marta Davi Marta Davi Andrea Davi Andrea

Whether the statement is true or false and explain why The empty set is a subset of every set HW Score 0 O Points 0 c Choose the correct answer below OA The statement is true The empty set is a subset of every set A since it has 0 as its only element B The statement is true The empty set is a subset of every set A since it is impossible to find an element of the empty set it has no elements that is not an element of the se C The statement is false The empty set has no elements and so all of its elements there are none do not belong to the nonempty set D The statement is false The empty set is a subset of every set A since it has 0 as its only element

This graph shows how the number of plants Maggie can have in her backyard is related to number of seed packets she purchases Plants in Maggie s backyard Total number of plants 10 9 B 55 43 2 HN 0 1 2 3 4 5 6 7 Number of seed packets 8 9 What is the rate of change Write your answer as a decimal or integer plants per seed packet X 10

Vector u PQ has initial point P 3 17 and terminal point Q 9 2 Vector v RS has initial point R 30 6 and terminal point S 8 18 Part A Write u and v in linear form Show all necessary work 4 points Part B Write u and v in trigonometric form Show all necessary work 8 points Part C Find 7u 4v Show all necessary calculations 3 points

A person s federal income tax rate is based on the amount of money that the person makes Income is broken into levels called tax brackets The table below shows the tax brackets for 2014 Taxable Income 0 9 075 9 076 36 900 36 901 89 350 89 351 186 350 186 351 405 100 405 101 406 750 406 751 plus If a Facebook engineer had a taxable income of 235 000 in 2014 how much income tax did the engineer owe that year 58 975 75 68 935 50 77 550 00 Tax 10 of taxable income 907 50 plus 15 of excess over 9 075 5 081 25 plus 25 of excess over 36 900 18 193 75 plus 28 of excess over 89 350 45 353 75 plus 33 of excess over 186 350 117 541 25 plus 35 of excess over 405 100 118 118 75 plus 39 6 of excess over 406 750 61 408 25