Basic Math Questions and Answers

k in with 1 What c Goal 2 What is JL Explain 3 What triangles are similar to ADEF 4 What is the value of x x 6 P31

6 ETO What is the area of this triangle in square units Explain or show your reasoning

7 Find a solution for each equation a 25 a b b 8 C 10 1 000

Question 3 of 5 View Policies Current Attempt in Progress Sandhill Distribution markets CDs of numerous performing inventory 2 500 CDs with a unit cost of 8 00 During Marc March 5 March 13 1 850 9 00 4 000 10 00 March 21 March 26 During March 11 900 units were sold Sandhill uses a perio

41 15 The following table lists the mean monthly temperatures for Juneau and Fairbanks Alaska Averages u are listed in the far right column Perform a t test to determine if t differences are statistically significant p 0 05 Fairbanks 1 10 Juneau 25 44 33 35 40 Select one O p 0 15 The difference is not significant O p 0 15 The difference is significant 72 73 66 55 32 61 48 57 62 64 63 56 47 p 0 26 The difference is significant p 0 26 The difference is not 11 5 37 9 38 34 u 48 1

prove it is a trapezoid Quadrilateral Choose ABCD Midpoint E between A B 5 1 Midpoint F between C D 3 5 1 Midline EF BC AD 2 8 5 Midline EF BC AD 2 8 0 Quadrilateral ABCD is a trapezoid Check Respons Choose Concluded from the Midline Formula Lesson 8 Midpoint Formula Lesson 8 Given

6 There are k types of coupons Independently of the types previously collected coupons each new coupon collected is of type i with probability p 1 p 1 If n coupons are collected find the expected number of distinct types that appear in this set That is find the expected number of types of coupons that appear at least once in the set of n coupons

2 Consider the linear programming problem max 3x 2x x3 subject to 2x13x2 2x3 3 X x x3 5 1 T2 T3 20 a Write the problem in augmented form b Use the simplex method to solve the augmented problem Sl ell you licitly

Plot each of the following functions in separate graph papers Show tabulation for each piecewise function TWO questions must be done in TWO separate graph papers 1 f x x 4 x 3 x if x 3 if 3 x 2 if x 2 2 f x 2x 4 x 2 x 2 x 2 2 x 1 x 1

1 A simplified model for the movement of the price of a stock supposes that on each day stock s price either moves up 1 unit with probability p or moves down 1 unit with probability 1 p The changes on different days are assumed to be independent a What is the probability that after 2 days the stock will be at its original price

Let E be the solid below z 8 a y and above the square 2 2 2 2 Given the solid has a constant density of 4 find the moment of inertia of E about the z axis

power plant L Length underground in miles Length underwater in miles Minimal cost in dollars Z offshore facility X T D O A power line is to be run to an offshore facility as shown in the figure above The offshore facility is D 4 miles at sea and L 6 miles along the shoreline from the power plant It costs 550 per mile to lay a power line underground and 950 per mile to run the line underwater How much of the power line should be run underground and how much underwater to minimize the overall costs help numbers

A population of values has a normal distribution with 169 8 and 12 7 You intend to draw a random sample of size n 128 Find P73 which is the mean separating the bottom 73 means from the top 27 means P73 for sample means Enter your answers as numbers accurate to 1 decimal place Answers obtained using exact z scores or z scores rounded to 3 decimal places are accepted

Follow the steps in Ex 91 2 to prove the following on your paper Does the proof work out for f x g x too Type yes or no Correct spelling required Help Lecture 91 Ex 91 2 291 d dx Use the rule that lim f g x lim f x lim g x to prove that f g x f x

At Sea World San Diego kids are only allowed into the Air Bounce if they are between 37 and 61 inches tall They are only allowed on the Tide Pool Climb if they are 39 inches tall or under Must be Between 17 and 61 C MUST BE 39 OR UNDER a Represent the height requirements of each ride with inequalities b Show the allowable heights for the rides on separate number lines c Using inequalities and a number line describe the height of kids who can go on the

Fill in the blanks In the metric system a the commonly used unit to measure length is the b the commonly used unit to measure mass is the c the commonly used unit to measure liquid volume is d the commonly used unit to measure temperature is a The commonly used unit to measure length is the b The commonly used unit to measure mass is the curo liquid volume is the

3 Thomas wants to rent a carpet shampoo machine Store A charges a flat fee of 25 plus 8 for each day a customer keeps the machine Store B charges a flat fee of 30 plus 5 for each day a customer keeps the machine Which equation could Thomas use to find the number of days he could rent the machine from either store and pay the same amount A 8x 5x 55 B 25x 8 30x 5 C 8x 25 5x 30 D 8x 17 5x 25

Use a Venn diagram Let P Z 0 43 P Y 0 31 and P Z UY 0 56 Find each probability a P Z Y b P Z UY c P Z UY d P ZnY Complete the Venn diagram using the given probabilities region I represents region Il represents region III represents region IV represents Type integers or decimals S N Y ID IV

Two dice are rolled Find the odds in favor of rolling the following a A sum of 5 b A sum of 7 or 12 c A sum less than 8 d Not a sum of 8 a In reduced form the odds in favor of rolling a sum of 5 are to Simplify your answers

Suppose that 11 of a certain batch of calculators have a defective case and that 12 have defective batteries Also 5 have both a defective case and defective batteries A calculator is selected from the batch at random Find the probability that the calculator has a good case and good batteries The probability that the calculator has a good case and good batteries is Type an integer or a decimal

Second Parent Sickle cell anemia is an inherited disease in which red blood cells become distorted and deprived of oxygen A person with two sickle cell genes will have the disease but a person with only one sickle cell gene will have a mild non fatal anemia called sickle cell trait Using S to represent a healthy gene and s the sickle cell gene the table shows the four possibilities for the children of two Ss parents Find the probability that these parents give birth to a child who has sickle cell trait S S Ss SS P child has sickle cell trait Type an integer or a simplified fraction First Parent S S SS SS

One card is drawn from an ordinary deck of 52 cards Find the probabilities of drawing the following cards a A 10 or 5 b A red card or a 7 c A 5 or a red 6 d A heart or a black card e A face card or a spade a What is the probability that the card is either a 10 or a 5 Simplify your answer Type an integer or a fraction

Kristina Karganova invites 16 relatives to a party her mother 3 aunts 3 uncles 3 brothers 1 male cousin and 5 female cousins If the chances of any one guest arriving first are equally likely find the probabilities that the first gue to arrive is as follows a A brother or an uncle b A brother or a cousin c A brother or her mother www a Find the probability that the first guest to arrive is a brother or an uncle Type an integer or a simplified fraction

There were 2 468 427 deaths in a country in a certain year They are listed according to cause in the following table If a randomly selected person died in this given year use this information to find the following probabilities Complete parts a through c Cause Heart Disease Cancer Chronic lower respiratory disease Cerebrovascular disease Accidents Alzheimer s disease Diabetes mellitus Influenza and pneumonia All other causes Number of Deaths 597 681 574 749 138 084 129 472 120 853 83 492 69 078 50 091 704 927 a The probability that the cause of death wa heart disease The probability is Round to four decimal places as needed

The numbers 1 2 3 and 4 are written on slips of paper and 2 slips are drawn at random one at a time without replacement Find the given probabilities a The sum of the numbers is 7 b The sum of the number is 5 or less c The first number is 2 or the sum is 4 a The probability that the sum of the numbers is 7 is Type an integer or a simplified fraction

Use a Venn diagram Let P Z 0 52 P Y 0 28 and P Z UY 0 68 Find each probability a P Z Y b P Z UY c P Z UY d P ZnY a P Z nY Type an integer or a decimal www

A marble is selected at random from a jar containing 6 red marbles 2 yellow marbles and 4 green marbles What is the probability that the marble is red What is the probability that the marble is red www

Ajar contains 4 white marbles 3 orange marbles 2 yellow marbles and 5 black marbles If a marble is drawn at random find the probability that the marble is not yellow What is the probability that the marble is not yellow Simplify your answer Type an integer or a fraction

4 Recall that for any quadratic equation of the form ax bx c 0 with a 0 the b b2 4ac quadratic formula gives us that the smaller root is x 2a Consider the quadratic equation 2 x 0 1 123 1 4 3 6 a Compute using the formula above in four digit arithmetic with chopping b Suppose that the true four digit solution is a 0 0054 Compute the relative and absolute error of your above approximation c Now rationalize the numerator of the expression for r Use this new expression to compute for the quadratic equation above again in four digit arithmetic with chopping d Compute the relative and absolute error of this new approximation e Compare the error of these two approximations What in your own words is the source of the increased error in part b

5 Perform the following computations a exactly b using three digit chopping arith metic and c using three digit rounding arithmetic i 1 20 i d Compute the relative errors in part b and c

3 You are needing a force transducer for an experiment you are performing To make your transducer you have a rectangular bar that is 8 mm in width and depth i e it has a square cross section that is made from steel Young s modulus of elasticity You also have a displacement transducer that can measure displacements in the range of mm Answer the following questions a What is the largest force you can measure using this rectangular piece of steel considering that you don t want to exceed 50 of the yield strength i e maximum stress of 250 MPa b You want a transducer that can measure forces applied in one direction only What length of bar should you use so that you can measure a compressive load of 5 kN with maximum resolution For this problem assume you have maximum resolution if 5 kN of applied force causes deformation of 1 5 mm

1 a Describe intuitively i e in plain English what the Intermediate Value The orem IVT says b Use the IVT to show that there exists a solution to the nonlinear equation I cos z 21 31 1 0 on the interval 0 2 0 3

Find the third Taylor polynomial P3 x for the function f x x 1 about to 0 0 5 0 75 V1 25 and 1 5 using P3 x and compute the absolute Approximate errors

olve the fixed ends wave equation Utt4ux u 0 t 0 0 x t u t 0 Ju x 0 f x w T 0 a r

What is the volume of the composed figure 1 a 12 ft b 24 ft 6 ft 2 ft 2 ft 3 ft c 20 ft d 36 ft

Rural Tech Support paid 150 000 for a group purchase of land building and equipment At the time of the acquisition the land had a market value of 80 000 the building 48 000 and the equipment 32 000 Journalize the lump sum purchase of the three assets for a total cost of 150 000 the amount for which the business signed a note payable Record a single compound journa entry Record debits first then credits Select the explanation on the last line of the journal entry table Date Accounts and Explanation SCOOIS Debit Credit

noto Pro Ph reported the following figures on its December 31 2024 income statement and balance sheet Click the icon to view the figures Compute the asset turnover ratio for 2024 Round to two decimal places Net sales Data table Net sales Cash Accounts Receivable Merchandise Inventory Prepaid Expenses Property Plant and Equipment net Print 455 000 Dec 31 2024 Dec 31 2023 26 000 33 000 62 000 58 000 69 000 73 000 9 000 6 000 130 000 13 000 Deng X

A bacteria culture starts with 180 bacteria and grows at a rate proportional to its size After 6 hours there will be 1080 bacteria a Express the population P after t hours as a function of t P t b What will be the population after 8 hours bacteria c How long will it take for the population to reach 1690 Give your answer accurate to at least 2 decimal places heure

An equation of a parabola is given a Find the focus directrix and focal diameter of the parabola x y focus directrix focal diameter

b 52 5 4 3 2 1 y 54 et 1 3 2 1 1 2 Select Select 12 3 Select B

My Students To Put Their Laptops Away by Clay Shirky I teach theory and practice of social media at NYU and am an advocate and activist for the free culture movement so I m a pretty unlikely candidate for internet censor but have just asked the students in my fall seminar to refrain from using laptops tablets and phones in class I came late and reluctantly to this decision I have been teaching classes about the internet since 1998 and I ve generally had a laissez faire attitude towards technology use in the classroom This was partly because the subject of my classes made technology use feel organic and when device use went well it was great Then there was the competitive aspect it s my job to be more interesting than the possible distractions so a ban felt like cheating And finally there s not wanting to infantilize my students who are adults even if young ones time management is their job not mine Despite these rationales the practical effects of my decision to allow technology use in class grew worse over time The level of distraction in my classes seemed to grow even though it was the same professor and largely the same set of topics taught to a group of students selected using roughly the same criteria every year The change seemed to correlate more with the rising ubiquity and utility of the devices themselves rather than any change in me the students or the rest of the classroom encounter Over the years I ve noticed that when I do have a specific reason to ask everyone to set aside their devices Lids down in the parlance of my department it s as if someone has let fresh air into the room The conversation brightens and more recently there is a sense of relief from many of the students Multi tasking is cognitively exhausting when we do it by choice being asked to stop can come as a welcome change So this year I moved from recommending setting aside laptops and phones to requiring it 21 What is the author s main claim A Technology is negatively affecting classrooms across the country B Putting aside the distraction of technology can revitalize a classroom Students want an excuse to put down their mobile devices in class A learning environment with no phones is important to student success 22 The phrase laissez faire means A without interfering B not very strict

College by Denise Marie Ordway As tuition rises and the other costs of college go up campus administrators are forced to face a troubling reality Many college students don t get enough to eat In response hundreds of schools from community colleges to Ivy League universities have opened food pantries or stores selling subsidized groceries Many students ages 18 to 49 are not eligible for the federal government s Supplemental Nutrition Assistance Program also known as food stamps At Cornell University the student run Anabel s Grocery attracted about 2 000 unique customers within the first several months according to the student newspaper The store offers low cost groceries for all Cornell students and subsidies for those who qualify At the University of Central Florida students can pick up five free food items a day Portland Community College opened pantries on all four of its campuses and created a co op with free school supplies bus passes clothes and other items Academic research shows that a substantial percentage of college students experience food insecurity a lack of access to adequate amounts of food especially healthy foods The proportion appears to vary by institution type and among student groups with racial and ethnic minorities being most likely to skip meals or go hungry The research also suggests students who don t have enough food are more likely to have low grades and poor health 13 What is the primary purpose of the article A To highlight specific colleges who are doing more to help To emphasize that colleges need to do more to help students To convince the readers to help at their local food bank To show readers many college students need help getting enough food 4 Paragraph 2 provides support for the author s claim by listing colleges that are trying to help B explaining how the community can help

For the EBI Solar question select the correct answer If EBI Solar s Annual Sales at Cost is 2 500 000 and Aggregate average inventory value is 142 500 what is inventor turnover Considering they operate 52 weeks what is weeks of supply O 17 54 2 96 O 0 057 2740 O 17 54 17 58 O 2740 17 58 O 4 5 11 56

A poll of 1168 Americans showed that 46 6 of the respondents prefer to watch the news rather than read or listen to it Use those results with a 0 05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it Use the P value method Use the normal distribution as an approximation to the binomial distribution BECED Let p denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it Identify the null and alternative hypotheses Ho P H P Type integers or decimals Do not round Identify the test statistic Z Round to two decimal places as needed Identify the P value P value Round to three decimal places as needed State the conclusion about the null hypothesis as well as the final conclusion that addresses the original claim the null hypothesis There sufficient evidence to the claim that fewer than half of Americans prefer to watch the nou

For the manual car wash process what is the number of steps for each type of activity O None of the answers O Operation 50 Transport 25 Inspection 8 3 Delay 16 7 O Operation 25 Transport 50 Inspection 16 7 Delay 8 3 O Operation 50 Transport 50 Delay 8 3 Inspection 16 7

Find the critical z values Assume that the normal distribution applies Right tailed test x 0 02 Z Round to two decimal places as needed Use a comma to separate answers as needed

1 Given that AA B C is a dilation of AABC how are the angles and side lengths of the preimage related to the angles and side lengths of the image 2 What is the scale factor of the dilation shown D E G 10 00 F B D A 6 E B A C C 15 12 P

Assume that the normal distribution applies and find the critical z value s 0 09 H is 98 6 F Z Round to two decimal places as needed Use a comma to separate answers as needed

Find the critical value s for a left tailed z test with a 0 04 Include a graph with your answer The critical value s is are Round to two decimal places as needed Use a comma to separate answers as needed Draw a graph of the rejection region Choose the correct graph below A a 0 B CHCELA OC D A 0 NIN M 3 G G G

Which hypothesis test is used to test a claim concerning the population mean usin the sample standard deviation T Test Z Test