Basic Math Questions and Answers

All changes saved 5 You were painting a room in your house Unfortunately you lost the lid to the 5 gallon bucket of paint but you only used half of the paint You want to save the paint so you plan on transferring it to a new container The new container is shaped like a rectangular prism If there are originally 1 155 cubic inches of paint in the 5 gallon bucket is your container big enough to fit the paint that is left over Remember that half the paint is left in the bucket 12 in 8 in 5 in Yes the container is big enough There is 577 5 cubic inches of paint left and the new container is 480 cubic inches No the container is not big enough There is 577 5 cubic inches of paint left and the new container is 480 cubic inches No the container is not big enough There is 577 5 cubic inches of paint left and the new container is 960 cubic inches Yes the container is big enough There is 577 5 cubic inches of paint left and the new container is 960 cubic inches

Jennifer has written her own recipe for pot roast There is a proportional relationship between the weight in pounds of the pot roast x and the total cooking time in hours y Hours 10 9 8 7 6 5 4 3 2 1 2 3 5 Pounds 6 7 8 9 10 What is the constant of proportionality Write your answer as a whole number or decimal hours per pound

Anthony owns a small business selling bagels He knows that in the last week 3 customers paid cash 33 customers used a debit card and 34 customers used a credit card Based on these results express the probability that the next customer will pay with cash as a fraction in simplest form

What prism or other 3 dimensional shape would you use to model the tree trunk below Rectangular prism triangular prism square prism or cylinder If the height of the tree trunk is 13 ft and the radius is 1 5 ft what is the volume in cubic feet Round to the nearest tenth Enter your answer and also show your work to demonstrate how you determined your answer Review the rubric below to see how you will be evaluated

A graphic designer has created a piece of art for the side of a building The art is a circle with three sectors as shown in the figure The circle has a diameter of 10 feet The measures of the central angles of the three sectors have ratio 2 3 4 The designer wants to paint the smallest sector red If it costs 2 00 to paint each square foot which of the following is closest to the total cost to paint the smallest sector of the circle A B C 35 00 52 40 69 80 D 139 60

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 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

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

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

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

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

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

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

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

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

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

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

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

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

rag the tiles to the correct boxes to complete the pairs 53 75 13s 3 3 ewrite the rational expression 1 71 13 1 3 T S in the form 1 1 and then match qx x and b x to the correct expressions g 1 b I 1 4x 1 H 3 13 712 13 3 0

When Xochitl runs the 400 meter dash her finishing times are normally distributed with a mean of 84 seconds and a standard deviation of 2 5 seconds Using the empirical rule determine the interval of times that represents the middle 68 of her finishing times in the 400 meter race

Consider the following cylinder and cone A 10 10 4 4 Marcel 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 So the volur must be the same What is the first mistake Marcel made

6 page 193 Find the current balance of the following account Balance from Bank Statement 32 489 50 Checks Outstanding 3589 70 263 15 Deposits Not Yet Recorded 18 702 15 7269 78 Balance

A mother earned 13750 00 from royalties on her cookbook She set aside 20 of this for a down payment on a new home The balance will be used for her son s future education She invests a portion of the money in a bank certificate of deposit CD account that earns 4 and the remainder in a savings bond that earns 7 If the total interest earned after one year is 660 00 how much money was invested at each rate How much money was invested in the CD account Round to the nearest cent

A pendulum is swinging next to a wall The distance from the bob of the swinging pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function The function has period 0 8 seconds amplitude 6 cm and midline H 15 cm At time t 0 5 seconds the bob is at its midline moving towards the wall Find the formula of the trigonometric function that models the distance H from the pendulum s bob to the wall after t seconds Define the function using radians H t

A basic cellular package costs 40 month for 60 minutes of calling with an additional charge of 0 20 minute beyond that time The cost function C z for using z minutes would be If you used 60 minutes or less i e if if a 60 then C z 40 the base charge If you used more than 60 minutes i e z 60 minutes more than the plan came with you would pay an additional 0 20 for each of those z 60 minutes Your total bill would be C z 40 0 20 z 60 If you want to keep your bill at 50 or lower for the month what is the maximum number of calling minutes you can use

3 The graphs shows the amount of a chemical in a water sample at different times after it was first measured Select all statements that are true 2 400 50 2 000 1 600 1 200 800 400 chemical mg M 1 2 3 I time hours A The amount of the chemical the water sample is decreasing exponentially 4 5 B The amount of the chemical in the water sample is not decreasing exponentially C It is not possible to tell for certain whether or not the amount of the chemical is decreasing exponentially D When it was first measured there were 2 000 mg of the chemical in the water sample After 4 hours there were 100 mg of the chemical in the water

Stefan graphs quadrilateral BCDE on a coordinate plane The diagonals of BCDE intersect at point T Which methods could Stefan use to prove that BCDE is a rectangle Select all that apply Show that BT and DT are the same length Then show that CT and ET are the same length Show that BC and ED have the same slope and BE and CD have the same slope Then show that BC and BE have opposite reciprocal slopes Show that BC and ED are the same length BE and CD are the same length and BD and CE are the same length Show that BC and ED are the same length Then show that BC and ED have the same slope

What is the best way to combine these sentences It was a very close finish The crowd was delighted The bay mare won the race A The crowd was delighted because the baymare won the race and it was a very close finish B To the delight of the crowd the bay mare won the race in a very close finish C To the delight of the crowd and also in a very close finish the bay mare won the race

Question 4 of 15 To solve this system of equations Ayana isolated y in the first equation and then substituted for y in the second equation What was the result 2y 6x x y 4 A x 3x 4 OB x 6x 4 OC x 3x 4 O D x 6x 4

The points plotted below are on the graph of a polynomial Which of the following x values is the best approximation of a root of the polynomial Check all that apply A x 4 3 B X 6 C x 1 1 D X 1 7 E X 2 4 OF x 1

What is the degree of freedom for the critical t value of a population that has 450 sample differences 224 449 225 451

Interpret a p value of 0 005 This means that there is 0 005 probability for the null to be false O This means that the probability for observing the test statistic is 0 005 if the null is true O This means that there is 0 005 probability for observing the test statistic if the null is false This means that there is a 0 005 probability of a type Il error

3 Type the correct answer in each box Use numerals instead of words A company manufactures 2 000 units of its flagship product in a day The quality control department takes a random sample of 40 units to test for quality The product is put through a wear and tear test to determine the number of days it can last If the product has a lifespan of less than 26 days it is considered defective The table gives the sample data that a quality control manager collected 39 31 38 40 29 32 33 39 35 32 32 27 30 31 27 30 29 34 36 25 30 32 38 35 40 29 32 31 26 26 32 26 30 40 32 39 37 25 29 34 The point estimate of the population mean is and the point estimate of the proportion of defective units is Next 0

Omar paid 13 29 for a 7 03 kg bag of dog food A few weeks later he paid 13 58 for a 7 26 kg bag at a different store Find the unit price for each bag Then state which bag is the better buy based on the unit price Round your answers to the nearest cent Unit price for the 7 03 kg bag Unit price for the 7 26 kg bag The better buy sper kg sper kg The 7 03 kg bag The 7 26 kg bag Neither They have the same unit price