Basic Math Questions and Answers

Assuming that boy and girl babies are equally likely what would be Kathy s probability of having exactly two daughters if she were to have four children altogether You may want to use a tree diagram to construct the sample space

Find all critical points of the given plane autonomous system Enter your answers as a comma separated list x 12 x v y y 14 y x x y

Write the given nonlinear second order differential equation as a plane autonomous system x x 2x 0 x y y Find all critical points of the resulting system x y

Here is a rectangle Explain why the area of the large rectangle is 2a 3a 4a Explain why the area of the large rectangle is 2 3 4 a

4 Read this invoice and de Terms 2 10 net 30

V Itranscript At 10 00 a m the number of bacteria in a jar is recorded The table below displays the pattern of growth of the bacteria Note that t 0 represent the starting time of 10 00 a m Time t minutes Answer 2 Points 0 1 2 3 Develop a function f t to model the number of bacteria at time t f t Number of Bacteria 20 80 320 1280 A Keypad Keyboard Shortc

Here is a bivariate data set X y 92 4 91 2 59 5 87 89 8 79 2 62 9 55 1 71 9 18 3 59 19 5 65 2 27 2 67 5 60 59 2 25 7 75 1 5 2 84 7 68 2 70 1 49 3 79 2 40 2 95 4 38 8 25 7 50 6 62 71 8 2 Find the correlation coefficient and report it accurate to three decimal places r What proportion of the variation in y can be explained by the variation in the values of x Report a percentage accurate to one decimal place

Itranscript Instructions for a chemical procedure state to mix salt baking soda and water in a 15 19 15 ratio by mass How many grams of baking soda would be required to make a mixture that contains 30 grams of water Answer 2 Points Key

Value 30000 25000 20000 15000 10000 5000 y 1 2019 16 400 2020 17 700 16 700 2021 2 3 Enable Zoom Pan 4 Year 5 6 X 1 correspond to the year 2017 Darnell has determined the slope intercept form of the equation for the line that passes through the presenting the value of his car in 2017 1 19 899 and the value of his car in 2021 5 16 700 to be y 799 75x 20 698 75

Darnell has recorded the estimated value of his car each year since 2017 Let x 1 correspond to the year 2017 Find the slope intercept form of the equation for the line that passes through the points representing the value of his car in 2017 1 24 700 and the value of his car in 2021 5 17 410 Round the slope to the nearest hundredth if necessary Value 30000 25000 20000 15000 10000 5000 y Year 2017 2018 2019 2020 2021 Value 24 700 22 410 20 400 18 400 17 410 Enable Zoom Pan

Growing linearly the balance owed on your credit card doubles from 600 to 1200 in 6 months If the balance were growing according to the exponential function f x 600 1 0 122 where x represents the number of months what would the balance be after 6 months Round your answer to the nearest cent Itranscript

Itranscript In 2020 the population of a city was 1 597 000 This was a 3 6 increase from 2019 The population is expected to continue to increase at the same rate per year Write a function f x to model the population where x is the number of years since 2020 Answer 2 Points f x Keyp Keyboard Shor

Use unit rates to determine the better buy and provide the unit price for your answer Round your answer to the nearest hundredth if necessary Itranscript Answer 2 Points 61 24 for 1000 business cards 10 75 for 250 business cards Selecting an option will enable input for any required text boxes If the selected option does not have any associated text boxes then no further input is required O 61 24 for 1000 business cards O 10 75 for 250 business cards per business card Keypad Keyboard Shortcuts per business card

Itranscript If the exchange rate from USD to euros is 1 1397 1 how much would 225 65 be worth in the United States rounded to the nearest cen Answer 2 Points Keyboard

Itranscript Suppose you got 80 of the questions on your last test correct If there were 110 equally weighted questions on the test what was your ratio of correct to incorrect answers on the test Write your answer in lowest terms Answer 2 Points Keypa Keyboard Shortc

In Unit 4 we are learning about graph theory For this discussion you will post at least twice 1 an initial post and then 2 a reply to a classmate For your initial post Select one of the statements below A A UPS driver trying to find the best way to deliver packages around town can model the delivery locations as the vertices on a graph and the roads between the locations as edges The best way for the driver to deliver the packages is an Euler path B Starting from my home I need to go to the post office the bank the medical clinic and the dry cleaners Because my goal is to run errands and return home using the shortest route I need to determine the minimum spanning tree C Using the shortest possible line length to connect ten towns with telephone lines involves finding the minimum cost spanning tree D Although the Nearest Neighbor Method does not always give the Hamilton circuit for which the sum of the weights is a minimum Kruskal s Algorithm always gives the spanning tree with the smallest possible total weight For the statement you selected answer the following questions 1 Identify the statement you selected Does the statement make sense 2 Explain your answer

From the list below select all FALSE propositions M x E ZI 2 x 2 CM The set 1 2 is the power set of MnZ OMCN The cardinality of MnZt is 2 Every subset of Mis infinite EM

x 3x 4 3x x 4 Factor the expression 3x 12 x 3 12 3x x 4x

16x 16x 40 40x JWS at 102 402 in factored form is 82 2x 5 8 2x 16x 5x 40x CLEA

m m 4m m 5m 20m Factor the expression 5m 20m m 5 20 5m m 4

Which statement about the greatest common factor of 36y2 and 16y is true 2y because that is a factor of both 36y and 16y t is 36y2 because that is the largest addend of the two terms CLEAR CHE It is 4y because that is the greatest term that is a factor o both 36y and 16y It is 144y2 because 36y2 and 16y are each factors of 144y2

Which expression is the greatest common factor of the two addends in 6k 15k 6k 26542

X X X Two of these models show a factored form of 6x2 Which model does NOT X X x x X X 2x 3x 6x X X X X X X X X X x x x x2 1x 6x 6x 4x 2x x x x x CLEAR x x 4x 2x 6x

2x 4 x 2x Factor the expression completely 2x 4x THIN 2 x 2 2x x 2

Which statement abou e greatest common factor of the two addends of 35x2 14x is true x is the GCF because it includes all the common factors of both 35x2 and 14x 7x2 is the GCF because it is a factor of both 35x2 and 14x 70x is the GCF because 14 and 35 are both factors of 70 and x and x are both factors of x 7 is the GCF because it is a factor of both 35x and 14x C

mich diagram best shows 5 4x 5 12x 15x 12x 15 x12x 15x x12x 47 ompletely factored 15X IS 3X 4x 4x 5x 3x12x 15x 4x 5 3 12x 15x

Select the negation of the following statement p r OA Par OB Par OC p r D 1 p

Mario loves to listen to music and is convinced that listening to music while taking a test helps him get higher test averages To prove this Mario conducts a study amongst his classmates in his AMDM class With the permission of his teacher he randomly selects 15 out of 30 students in his class to listen to music during their next test The remaining 15 students are not allowed to listen to music while they take their test He intends to compare the test scores from each group hoping to prove his hypothesis that listening to music while taking a test increases test scores What is the variable of interest in this study O test grades the class O Mario O survey

Hypothesis that most people already think is true O Alternative Hypothesis O Special Hypothesis O Null Hypothesis Science Hypothesis QUESTION 2 A treatment that has no effect however the subject s does not know this O Sugar O Sample Variable O Placebo QUESTION 3 E Experimental or Observational A group of students is interested in knowing if the number of times they can sink a basketball is related to th

B R G Q Match each equation with a graph above 2 0 85 2 1 26 2 1 5 2 0 74 4 1 26 K Question Heln a green G b orange 0 c red R d blue B e black K

A vehicle purchased for 27500 depreciates at a constant rate of 5 Determine the approximate value of the vehicle 12 years after purchase Round to the nearest whole number

Match the formula of the exponential function to its graph Graphs of Exponential Functions 17 k 5 4 3 2 1 17 MI N m 14 m 4 ry 3 M 14 A 3 4 Rot 2 H 4 24 M na S 16 day D 6 23 N A M O Formulas for the Graphs a f z 3 b z 3 c f x 2 d f x 27

22 gets shifted vertically 2 units Then type the new function Move the slider k so that the graph of y f x in the answer box 6 5 4 3 2 1 6 5 4 3 2 1 2 3 4 1 2 3 f x 2 O Don t forget to shift the graph vertically Using function notation i e f x enter the function that results fr O 4 5 k 0 00 10 1 6 1

R Match each equation with a graph above 2 2 22 G 22 2 B a red R b blue B c orange 0 d green G

Match each graph with its equation 4 3 3 2 1 2 F LA 1 2 3 4 5 5 5 4 3 4 3 7 LG E 2 T tim 42 43 5 5 4 3 2 4 4 F 2 234 12 2 3 4 4 a d a y 2 b y 2 c y 2 d y 2

For the function f x 4 4 calculate the following function values f 2 2 f 0

4 Find the area of the parallelogram determined by the vectors 2 2

115 teens were randomly surveyed about their social media usage Twenty two only used Snapchat fourteen only used Instagram and nine only used Twitter Seven teens use Snapchat and Twitter and six used Instagram and Twitter Thirteen students used all three social media platforms while eighteen of the students surveyed did not use any of these social media platforms Draw a venn diagram and show how many teens in the survey use both Snapchat and Instagram but not Twitter QUESTION 21 In a recent survey of 705 teens 300 said they have a sister and 383 teens have a brother One third of those teens with a sister also have a brother What is the probability that a teen has a sister or brother What is the probability that a teen has a sister or no siblings What is the probability that a teen has a brother no siblings

Inside a bag there are 3 green balls 2 red balls and 2 yellow balls Two balls are randomly drawn without replacement Calculate the probability of drawing one green ball and one yellow ball The tree diagram has been started 2 6 3 7 2 7 2 7 G R Y 2 6 2 6 G Y R

Jason has two pairs of black shoes and three pairs of brown shoes He also has three pairs of red socks four pairs of brown socks and six pairs of black socks If Jason chooses a pair shoes at random and a pair of socks at random what is the probability that he chooses shoes and socks of the same color Complete the tree diagram to find the probability Shoes Socks ZIM mlin 24 37 65 13 Black Brown 1 VSE 54 Red Brown Black Red Brown Black

You must burn 3 500 calories while exercising to shed one pound of excess body fat You can usually burn 100 calories while walking a mile at a fast pace How many miles would you have to walk per day in a week to shed two pounds show work 2 pts

A hydraulic jump occurs in 12 ft wide rectangular channel If the flow rate is 370 cfs and the downstream depth is 4 5 feet determine 1 the upstream depth 2 the loss of energy in the jump 3 the Froude number before and after the jump and 4 critical depth in the channel

Use the information below to answer the ques 82 people vote yes 81 people vote no 45 people vote both 145 total people voted Yes No How many people voted neither Answer 45 27

Parallelogram PQRS is made up of Isosceles Triangle RST and Trapezoid PORT Find the area of Parallelogram PQRS 5 in P 11 in 18 in S

Trapezoid RSTU is made up of three triangles and Triangle TUV is an isosceles triangle Find the area of Trapezoid RSTV If the area of Trapezoid RSTU is 13 square centimeters 8 cm RM4 SK MV 30 cm U 19 cm T

2 A math tutor makes 15 00 per hour in the tutoring lab at her school She earns an additional 7 50 more per hour overtime for any hours worked which exceed her normal 40 hr work week b Write a piece wise function to describe the tutors weekly pay P h in terms of hours h 6 points

4 The population P t of a culture of the bacterium Pseudomonas aeruginosa is given by P t 1718t 82 000t 10 000 where t is the time in hours since the culture was started a Determine the time at which the population is at a maximum Round to the nearest hour 5 points b Determine the maximum population Round to the nearest thousand 5 points Blank 1 Blank 2 A A

Suppose a farmer in Georgia begins to grow peaches He uses 1 000 000 in savings to purchase land he rents equipment for 70 000 a year and he pays workers 110 000 in wages In return produces 200 000 baskets of peaches per year which sell for 3 00 each Suppose the interest rate on savings is 2 percent and that the farmer could otherwise have earned 25 000 as a shoe salesman What is the farmer s economic profit The peach farmer earns economic profit of What is the farmer s accounting profit The peach farmer earns accounting profit of Enter your response as an integer Enter your response as an integer

6 The following equation models a runner s speed f x in ft sec x represents time in seconds after the start 10x 10 F x X of a race round all answers to the nearest tenth a Approximate the runners speed after 6 seconds 3 points b Approximate the runners speed after 100 seconds 3 points Blank 1 Blank 2 A

Which of the following commands will throw an error for all vectors x all refers to the almost infinitely many possible vectors in R x c 0 5 0 5 2000 O x c 0 5 0 5 2 x c 0 5 0 5 2 x c 0 5 0 5 2