Basic Math Questions and Answers

Bob is at a friend s house and wants to run home His friend lives 12 miles away from his home Use the position time graph below to help answer the following questions Distance miles 07 10 What time interval s is Bob getting closer to home 0 3 14 12 10 5 15 03 5 10 8 5 7 10 10 5 Time hours 12 13 14 15

7 Nathaniel proves that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment His proof is shown below Given BP is the perpendicular bisector of AC Prove AQ CQ A Statements ZOPA ZQPC PQ PQ Q BP is the perpendicular bisector of AC PA PC APAQ APCQ 40 00 P C Reasons Given Definition of perpendicular bisector Right angles are congruent Reflexive Property of Congruence Corresponding parts of congruent triangles are congruent

Below is a position time graph of the O Connor Panthers in pursuit of a victory over the Marshall Rams Position yds 100 80 60 40 20 10 20 yards 30 40 50 60 Time s Find the total yardage traveled from 0 120 seconds 70 80 90 100 110 120

Let T RR and S R RP be linear transformations Then So T Rm RP is a linear transformation Moreover their standard matrices are related by So T S 7 Verify the result of the theorem above for the following S and T by finding the matrix of S o T by direct substitution and by matrix multiplication of S 7 X 5X2 Y1 P 2 Y Y a by direct substitution b by matrix multiplication 442

Vertex 2 O Is this a maximum or minimum The equation for the axis of symmetry is x The x intercepts are The range is y The domain is All Real Numbers for the graph below and

Find a basis B for the span of the given vectors

Find the standard matrix of the composite transformation from R2 to R Reflection in the y axis followed by clockwise rotation through 120

Area m 160 140 120 100 8878 80 60 40 20 5 10 15 Length of a Side m 20 The axis of symmetry is the vertical line that goes through the vertex The equation for a vertical line is in the form x a where a is the x value the line passes through For the graph above the axis of symmetry is x The x intercepts are where the function crosses or touches the x axis What are the x intercepts for this function Enter them as ordered pairs and The domain is the set of all possible input values x For quadratic functions the domain will be all real numbers This can be shown as o For this specific graph the domain would be 0 x 20 The range is the set of all possible output values y The range will be based on the y values covered by the graph This will change in each problem For this specific graph the range

Give a counterexample to show that the given transformation is not a linear transformation xy x x D O For example O For example T O For example 1 2 3 4 T 2 2 2 1 1 1 3 T For example 2 2 T T 2 2 O For example T 2 2

Find the standard matrix of the linear transformation 7y 5x 6y

a rare and precious metal has just been discovered on the planet Mars You and hundreds of other adventurers are traveling to the planet to stake your claim Each new explorer is allowed to claim any piece of land that can be surrounded by 20 feet of laser fencing You want to arrange your fencing to enclose the maximum area possible The only restriction the Mars colony adds is that each claim must be a rectangle Complete the table showing the length and width of a side and the area for each rectangle with a perimeter of 20 meters and whole number side lengths The first three have been done for you Length of a side m 0 1 2 3 4 5 6 7 Width of a side m 10 9 86 Area of the rectangle m 0 9 16

9 What is the degree of each polynomial function below a P x 0 08x 28 x C f x 5 x 3 x 2 x 7 b y 8x x 9 d y x 3 x 1 x 1

The following direct materials and direct labor data pertain to the operations of Laurel Company for the month of August Actual labor rate Actual materials price Standard labor rate Standard materials price a Costs Actual hours incurred and used Actual quantity of materials purchased and used Standard hours used Standard quantity of materials used Total materials variance Materials price variance Total labor variance Compute the total price and quantity variances for materials and labor Materials quantity variance Labor price variance 14 per hour 120 perton 13 50 per hour 121 per ton Quantities Labor quantity variance 3 900 hours 2 000 tons 3 950 hours 1 980 tons V

and the hill in line 50 represent a The transgressions of a divided history that they must overcome b The obstacles that older generations are facing with the new America c The violation of our founding fathers wishes for a better America d The debate about which route is better for this country wers 3x 23 What is implied in lines 52 54 a That our future depends on the past generations ability to overcome tragedy b That our future depends on our ability to accept and try to fix our past mistakes c Pride is stepping in the way of our ability to accept our history d History is repeating itself through our current generation 24 The personification in line 64 serves to a Show that the generations to come will look back at this moment to see what we are doing in the present b Emphasize that the past generations knew this moment would come for us to make the biggest difference c Justify that history and what we make of it is in the hands of those that came before us d Argue that history is not dependent on the decisions we will make 25 What does the idea of authoring a new chapter in line 70 represent a Write history as better than it actually was b To foster the love of reading as a means to educate the future c An opportunity to be and do something different d Rewrite the past in a light that paints it more hopeful

Your answer is incorrect Hank Itzek manufactures and sells homemade wine and he wants to develop a standard cost per gallon The following are required for production of a 50 gallon batch 3 465 ounces of grape concentrate at 0 07 per ounce 54 pounds of granulated sugar at 0 40 per pound 60 lemons at 0 70 each 100 yeast tablets at 0 22 each 150 nutrient tablets at 0 14 each 2 600 ounces of water at 0 005 per ounce Hank estimates that 1 of the grape concentrate is wasted 10 of the sugar is lost and 25 of the lemons cannot be used Compute the standard cost of the ingredients for one gallon of wine Round intermediate calculations and final answer to 2 decimal places eg 1 25

A tire company produced a batch of 6 600 tires that includes exactly 6 430 that are non defective If 4 tires are randomly selected without replacement for installation on a car what is the probability that they are all non defective Round to three decimal places as needed

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A restaurant offers a 12 dinner special that has 4 choices for an appetizer 12 choices for an entr e and 3 choices for a dessert How many different meals are available when you select an appetizer an entr e and a dessert A meal can be chosen in Type a whole number 2 point s possible ways

possible A pair of dice is rolled What is the probability of getting a a sum greater than 5 b a sum less than 7 What is the probability of getting a sum greater than 5 Simplify your answer Type a fraction What is the probability of getting a sum less than 7 Simplify your answer Type a fraction

One baseball team played 25 games throughout their entire season If this baseball team won 15 of those games then what percentage of their games did they win Round your answer to the nearest whole number if necessary

5 Nancy went to her local zoo that featured 24 monkey exhibits If these monkey exhibits make up 75 of the zoo s exhibits then how many exhibits does the zoo have in total Round your answer to the nearest whole number if necessary P toot If these students are 60 of

18 The Current Population Survey is a monthly survey conducted by the US Census Bureau and the US Bureau of Labor Statistics to assess the strength of the US labor force In the March 2005 survey the men in California age 35 41 could be classified as employed unemployed or not in the labor force and as married widowed divorced separated or never married A two way table summarizing the results for these men is below Employed Unemployed Not in labor force Married 790 56 21 Widowed divorced or separated 98 11 7 Never Married b What test statistic can you use to test the claim 209 27 13 Test the claim that marriage status and employment status in men are associated at the 0 001 significance level Use the R printout on the following page to answer the following questions a Determine the null and alternative hypotheses for the given claim c Determine the value of the observed test statistic You may use the attached R printout You do not need to calculate the test statistic yourself d Test the claim that marriage status and employment status in men are associated at the a 0 01 significance level

Laura is participating in a 6 day cross country biking challenge She biked for 77 59 68 46 and 45 miles on the first five days How many miles does she need to bike on the last day so that her average mean is 57 miles per day miles X 3

Consider the following data set The temperatures F at a particular location for 30 days are 59 55 41 47 51 58 52 49 49 49 55 40 58 59 59 50 39 57 47 51 57 Draw a bar graph for the data set Frequency LL 50 55 60 65 35 Frequency 40 46 45 Temp A

https www webassign net web Student Assignm 8 8 Points DETAILS The financiar op Salaries Academic SMITHNM13 14 1 04 nall college shows the follo 1 400 000 68 000 195 000 31 000 50 000 1 744 000 Plant Operations Student activities Athletic programs TOTAL Draw a circle graph showing these expenses Expenses Student Activities 3 Academic

3 40 Points DETAILS Prepare a frequency distribution for the data set Height 63 64 65 66 67 SMITHNM13 14 1 60 Data set C The heights rounded to t 67 70 65 65 71 63 69 64 68 70 66 64 64 72 65 65 69 64 71 63 64 66 65 67 67 72 72 66 64 72 Frequency

O https www webassign net web Student Ass Data set A The annual wages of e 20 16 30 60 25 14 35 50 30 Frequency 3 2 14 16 18 20 25 30 35 Wages in thousands of

The amount of electricity used in a Heating and air conditioning 42 Miscellaneous 19 Water heater 11 Need Help Refrigerator 19 Clothes dryer 5 If in a certain month a home used 1 300 kWh kilowatt hours find the amounts of electricity used from the graph a The amount of electricity used by the water heater kWh b The amount of electricity used by the stove kWh Read It Stove 4 c The amount of electricity used by the refrigerator kWh d The amount of electricity used by the clothes dryer kWh Watch It

Consider the graph depicting U S trade Billions of dollars 280 240 200 160 120 80 40 0 1990 1995 2000 2005 2010 Year a What is being illustrated in this graph O United States and Canadian temperature from 1990 2010 O United States trade with Canada from 1990 2010 O United States and Canadian population from 1990 2010 O United States and Canadian hockey scores from 1990 2010 U S Imports from Canada Need Help Read It U S Exports to Canada b Did the United States have more imports or exports for the years 1990 2010 O The United States had more imports O The United States had more exports O The United States had the same number of exports and imports O This information is not displayed on the graph

A state s legislature was considering the funding of its parks system As part of the considerations a study was done to look at the number of unique visitors to a selection of the state s parks over the Memorial Day weekend The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of parks 10 9 8 7 6 5 4 3 2 1 0 120 to 269 270 to 419 420 to 569 Number of unique visitors a What is the class width 0 570 to 719 b One class is the least frequent How many parks are in this class 0 c According to the histogram what is the total number of parks 0

MarvelUS is a service that streams shows and movies over the internet As a new subscriber Gary counted the number of episodes that are available through the service for a selection of his favorite shows The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of shows 10 9 8 7 6 5 4 3 2 5 to 10 17 to 22 11 to 16 Number of episodes available a What is the class width 1 23 to 28 b How many shows have from 5 to 10 episodes available 1 c How many shows have 11 or more episodes available 0

Complete the table by substituting in the given x values into the function below For the next few problems we will use the parent function f x x f x 4 x 4 x f x 4 2 1

Kimberly Richard and Cindy are helping with the selection of tiles for the entrance to Village Park and the parking lot Kimberly selected her preferred tile which is shown in the diagram with measurements in inches 6 Find x 2x 3 alig nat 3x 6 3x Unit 4 QPA 2x 3 2x 1 x 4 5 What is the most descriptive name for the shape of this file Justify your answer 3x audinarh 7 What is the length of the longer sides What is the length of the shorter sides

Richard could not decide on one tile so he selected several all of which can be modeled as quadrilateral ABCD A F D 8 Suppose one of the selected tiles represented as ABCD is a parallelogram How can you prove ABCD is a rectangle by comparing another segment to BD 9 Suppose one of the selected tiles represented as ABCD is a rhombus How can you prove that ABCD is a square using the segment AD

For the parking lot Kimberly Richard and Cindy decide to angle the parking spaces as shown in the diagram Cindy wants to find the size of a parking space measured in feet 7x 11 Find x 5x 6 3x 3x 7x 4x 3 3x 2 10 What is the most descriptive name for the shape representing the parking space Explain 12 What is the length of the longer side What is the length of the shorter side

4 Benny receives a 20000 salary for working as an agent If Benny has to spend 15000 o his salary on expenses each year then what percent of Benny s money does he have to spend Round your answer to the nearest whole number if necessary

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit Assume that revenue R x and cost C x are in thousands of dollars and x is in thousands of units R x 9x 3x C x x 4x 3x 1 The production level for the maximum profit is about units Do not round until the final answer Then round to the whole number as needed The profit is about Do not round until the final answer Then round to the whole number as needed

estion 18 of 20 1 point Question Attempt 1 of 3 9 12 needs to borrow 10 000 She can borrow the money at much total interest would Bethany pay at 6 5 simple in much total interest would Bethany pay at 5 interest co interest

Let p represent any number in the interval 6 22 Rewrite the possible values for p in inequality notation TRA P Type integers or decimals Do not round

In the sentence below the highlighted coordinating conjunction FANBOYS is Last night Dorothy Vaughan went to the movies and ate out at the diner

10 A school librarian ordered new books for the library Of the new books ordered are science are biography and the rest of the books are fiction What fraction of the books ordered are fiction 11 A B C D A 3 B 1503100 8 The model below is shaded to represent an expression D 4 Which expression represents the model 11 15 1 3 C 3 x 2 55 2 15 3x2 110 10 2 2 5 3x2 55 1 5 528

problem Use the following graph to find y when x 4 Q Q 6 4 2 o 2 complete this 2 X 57 When x 4 y

2 1 5 Solve the following equation x 3 x 1 C 5 marks

4 Solve the following equation 3 1 x 2 X 1 5x T 3 marks

21 Brightspace Assignment tion 7 of 10 1 point Question Attempt 1 of 1 2 PALING INSINIZ jors 3 4 5 e between cities A and B on a map is 12 25 in The

Find the charge q t on the capacitor and the current i t in the given LRC series circuit L 1 h R 100 C 0 0004 f E t 20 V q 0 0 C 0 4 A q t 2 250 50t i t e e 50t 18 50t 2 5 4 180t te A 250 C Find the maximum charge on the capacitor Round your answer to four decimal places

CritEek is a website where fans of horror films go to write movie reviews On the website s home page there is a display of the number of movies reviewed by a selection of the site s top critics The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of critics 10 9 8 7 6 5 4 3 2 7 to 14 39 to 46 15 to 22 31 to 38 23 to 30 Number of movie reviews a One class is the most frequent How many critics are in this class 11 b What is the class width 0 c How many critics have 22 or fewer movie reviews

A sample of 44 customers was taken at a local computer store The customers were asked the prices of the computers they had bought The data are summarized in the following table Number of computers 17 12 15 Price in dollars 1400 1600 2150 Find the mean price for this sample Round your answer to the nearest dollar X

The heights of 8th graders are modeled using the normal distribution shown below The mean of the distribution is 67 1 in and the standard deviation is 1 7 in In the figure v is a number along the axis and is under the highest part of the curve And u and w are numbers along the axis that are each the same distance away from v Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded and find the values of u v and w 62 64 Percentage of total area shaded Choose one U 66 V 68 W 70 72

A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit Find the angle of depression of the light to the nearest minute The angle of depression of the light to the nearest minute is ii EXT Employee exit angle of depression 0 angle of elevation 51 6ft 39 56ft