Basic Math Questions and Answers

The four standard forms of categorical statements are all S are P some S are P some S are not P and all S are S Osome S are P all S are not P and some S are not P Ono S are not P no S are P and all P are S some S are P some S are not P and no S are P

What does the following Venn diagram represent All S are P O No S are P S O Some S are P O Some S are not P P

The figure below gives the results of compression test of a potato sample STRESS MPa 0 45 0 40 0 30 0 20 0 10 A 0 080 B 0 533 C 0 467 50 015 40 30 0 08 0 10 STRAIN mm mm or in int According to the figure the degree of elasticity is 20 10 STRESS lb in

A car rental company s standard charge includes an initial fee plus an additional fee for each mile driven The standard charge S in dollars is given by the function S 14 95 0 50M where M is the number of miles driven The company also offers an option to insure the car against damage The insurance charge I in dollars is given by the function I 5 70 0 15 M Let C be the total charge in dollars for a rental that includes insurance Write an equation relating C to M Simplify your answer as much as possible 0 C X

Trey and his wife are each starting a saving plan Trey will initially set aside 250 and then add 155 every month to the savings The amount A in dollars saved this way is given by the function A 155N 250 where N is the number of months he has been saving His wife will not set an initial amount aside but will add 395 to the savings every month The amount B in dollars saved using this plan is given by the function B 395 N Let T be total amount in dollars saved using both plans combined Write an equation relating T to N Simplify your answer as much as possible

Suppose a projectile is fired from a cannon with velocity vo and angle of elevation 0 The horizontal distance R 0 it travels in feet is given by the following R 0 vo sin 20 32 If vo 80 ft s what angle in radians should be used to hit a target on the ground 106 feet in front of the cannon 0 Do not round any intermediate computations and round your answer s to the nearest hundredth of a radian If there is more than one answer enter additional answers with the or button 0 rad or

For a fixed location the number of sunlight hours in a day fluctuates throughout the year Suppose that the number of daily sunlight hours in a particular location can be modeled by the following L t 12 2 9 cos 2 365 In this equation L t is the number of sunlight hours in a day and I is the number of days after June 21st So 1 0 means June 21st 1 1 means June 22nd 1 2 means June 23rd etc Suppose we start at 1 0 which is June 21s During the first 365 days when will there be 13 hours of sunlight Do not round any intermediate computations and round your answer s to the nearest day If there is more than one answer enter additional answers with the or button t days after June 21 st of D

A model rocket is launched with an initial upward velocity of 188 ft s The rocket s height h in feet after t seconds is given by the following h 1881 16 2 Find all values of t for which the rocket s height is 92 feet Round your answer s to the nearest hundredth If there is more than one answer use the or button ground 1 0 seconds or X

The temperature of a cup of hot coffee in degrees Fahrenheit can be modeled by the function T x 75 82 0 97 where x is the number of minutes after the cup of coffee has been poured into the cup Determine how many minutes it will take until the coffee reaches a temperature of 117 F The amount of time is A Less than 17 minutes B Between 17 and 20 minutes C Between 20 and 23 minutes D Between 23 and 26 minutes E More than 26 minutes

Solve for x A x 2 5 only x only B x C x 3 6 only D x 6 only E x 3 only log 5 x log 2 x 3

Determine the domain and range for the function g x log 3 8x A Domain 0 00 Range 0 00 13 00 B Domain C Domain D Domain m 100 3 8 8 318 E Domain 00 Range 0 00 Range Range 0 00 Range 0 00

4 Solve for x A x B x In 7 0 3 E x In 6 0 3 C x ln 4 0 3 D x ln 7 0 3 In 4 0 3 10 1 e 0 3 2

A blog surveyed 96 college students regarding which popular search engines they use regularly in their research and obtained the following information 10 use Site A Site B and Site C 21 use Site B and Site C 28 use Site A and Site C 35 use Site A but do not use Site B 80 use Site A or Site C 11 use only Site C 2 use none of these three sites How many of those surveyed use Site A How many do not use Site C Select the appropriate problem solving method A Guessing is okay OB Use the counterexample principle OC Look for patterns D Draw pictures How many students use Site A

Find the number of elements in sets A B and C using the given information Anc 0 n An B 6 n C B 4 n B C 10 n B U C 19 n A U B 18 Choose the appropriate problem solving method below A Draw pictures B Look for patterns OC Try a simpler version of the problem OD Try guessing Select the correct choice below and fill in the answer box es within your choice O A n A n B n C Simplify your answers OB There is an inconsistency caused by the given value of and the answers cannot be found

Find if possible the number of elements in sets A B and C using the given information If there is an inconsistency state where it occurs AnB 0 n An C 6 n B nC 5 n C A 6 n A C 4 n U 16 Select the correct choice below and fill in the answer box es within your choice O A n A n B n C Simplify your answers OB There is an inconsistency caused by the given value of and the answers cannot be found

For the given confidence level and values of x and 7 find the following x 44 n 96 confidence level 99 Part 1 of 3 a Find the point estimate Round the answers to at least four decimal places if necessary The point estimate for the given data is 4583 Alternate Answer 0 4583 Part 1 3 Part 2 of 3 b Find the standard error Round the answers to at least four decimal places if necessary

K O Points 0 of 1 There are 86 people protesting the destruction of the rain forests There are 37 males 22 of whom are students and 20 female nonstudents How many female students are protesting There are female students protesting Simplify your answer Save

Describe the set by referring to the numbered regions WOX NY What is are the number s for the region s describing the set W nx nY Type a whole number Use a comma to separate answers as needed

F Describe the set by referring to the numbered regions E What are the numbers for the regions describing the set E Type a whole number Use a comma to separate answers as needed

The formula for the volume V of a cylinder with radius and height h is as follows V nr h Suppose the height of the cylinder is 7 units shorter than the radius Rewrite V in terms of only It is not necessary to simplify

In the universal set U a b c h define subsets of cars with the characteristics shown to the right Describe the following set in words and then find the set P GUA Click on the icon to view the table of new car features Describe the set P GUA in words Choose the correct answer below O A The set of cars that are priced over 20 000 that have either a good safety rating or an antitheft package but not both OB The set of cars that are priced over 20 000 that do not have a good safety rating or do not have an antitheft package or do not have either C The set of cars that are priced over 20 000 that have neither a good safety rating nor an antitheft package D The set of cars that are priced over 20 000 that do not have a good safety rating or do not have an antitheft package but at least one or the other Identify the elements of the set P GUA Select the correct choice below and if necessary fill in the answer box to complete your choice OA P GUA Use a comma to separate answers as needed P price is above 20 000 C is compact G has a good safety rating A has antitheft package W warranty is at least three years OB P GU A is the empty set

K The accompanying table gives nutritional information for the following fast food items Monster m Monster with Cheese mc Bacon Cheeseburger bc Hamburger h Cheeseburger c Fish Sandwich fs and Ham Cheesy hc Find the set PUCUB Click on the icon to view nutritional information for the fast food items Identify the elements of the set PUCUB Select all that apply A hc C h E bc G mc P x x is an item that provides at least 30 of the MDA for protein C x x is an item that provides at least 10 of the MDA for calcium B x x is an item that provides at least 25 of the MDA for vitamin B1 A x x is an item that provides at least 15 of the MDA for vitamin A CLICH B c D fs F m H PUCUB is the empty set

K Find the set A UU U 1 2 3 4 5 6 7 8 A 1 4 5 6 Select the correct choice below and if necessary fill in the answer box to complete your choice OA AUU Use a comma to separate answers as needed OB AUU is the empty set

K Determine whether the following pair of sets is equivalent Justify your answer and 0 Are the two sets equivalent or not equivalent OA The sets are equivalent because the number of elements in 0 is 1 OB The sets are not equivalent because the number of elements in 0 is 1 OC The sets are not equivalent because the number of elements in 0 is 0 O D The sets are equivalent because the number of elements in 0 is 0

K Replace the with either E or to express a true statement Carl Friedrich Gauss y y is a living Cuban poet Carl Friedrich Gauss ty y is a living Cuban poet 8

During a certain year the national average price of regular gasoline was 2 17 or 217 cents per gallon Use the listing method to list the set of states G that had regular gasoline at a price greater than the national average Choose the correct answer below O A G AR NJ IL VT NH WV TN OB G AR NE MI WV NH VT IL NJ OC G IN MO RI TN OD G AR NE MI WV TN RI ALLER Price Per Gallon of Regular Gasoline in Cents 281 233 236 300 250 212 200 150 100 50 0 AR IN NE MIMO WV NH VT RI TN IL NJ 210 207 239 207 194 212 192 197 Q

K Replace the with either E or to express a true statement Vermont x x is a state north of Alabama Vermont x x is a state north of Alabama E

Chapter 6 LO1 2 Compare two assets returns and risks and decide about the preferred option 101 Di

IC VS unsystematic risks Wha

3 Explain how changes in the determinants of the aggregate demand component consumption gross investment spending government purchases and net exports affect the aggregate demand curve

Situation 1 Origami paper is always in the shape of a square If you take the top corner of either side of a 9 x 11 inch piece of paper and fold it to the lower opposite side and trim off the excess paper this creates the square that we need Then fold the top corner to the opposite corner to create a diagonal which is a typical first step to most origami designs Situation 2 You are the coach of the soccer team To start practice you want the players to do some running on the field The players have two options They can run from end to end the red line or they can do the diagonal the blue line Experiment with different heights and widths for your field Situation 3 You are trying to a build doghouse for your adorable Pomeranian The dimensions of the base of the doghouse will be needed Determine the length and width of your doghouse The roof of the doc that are the same length Decide the height of the roof

The value of a brand new car is 40 000 and the value depreciates 24 every year Write a function to represent the value of the car after t years where the quarterly rate of change can be found from a constant in the function Round all coefficients in the function to four decimal places Also determine the percentage rate of change per quarter to the nearest hundredth of a percent Answer Attempt 1 out of 2 Function f t

Describe or correct the error in solving the system of linear equations AND show your work to solve the system correctly Original system 2x Y 3x 2y Step 1 Solve one equation for one variable 2x y 5 becomes y 2x 5 Step 2 Substitute Step 3 Simplify BEEN M 5 5 S IE 54 4 2x 2x 5 5 2x 2x 5 5

A business pays 68 for a car seat and wants a 24 markup for operating expenses as well as a 6 markup for profit However customers think the car seats are ugly so they are not selling Management reduces the price of each car seat by 30 to get rid o them Find A the selling price B the reduced price C the percent markdown D Which applies to this situation profit operating loss or absolute loss E What is the amount of profit operating loss or absolute loss 4

15 15 58 A ball having a mass of 200g is released from rest at a height of 400 mm above a very large fixed metal surface If the ball rebounds to a height of 325 mm above the surface determine the coefficient of restitution between the ball and the surface 15 59 The 5 Mg truck and 2 Mg car are traveling with the free rolling velocities shown just before they collide After the collision the car moves with a velocity of 15 km h to the right relative to the truck Determine the coefficient of restitution between the truck and car and the loss of energy due to the collision 30 km h 10 km h Prob 15 59 15 60 Disk A has a mass of 2 kg and is sliding forward on the smooth surface with a velocity A 5 m s when it disk R which is sliding towards A at 15 62 subje perfe befor The s 15 63 restit one a collisi reach of eac

SENIOREN 2x 3y 11 1x 3y 1 What is the solution x y to the given system of equations O 1 4 O 4 1 4 11 O 11 4

4 3 pts 0 5 each Suppose you have a fair 4 sided die and three cards numbered 2 4 5 You roll the die and draw a card List the elements in a uniform sample space and compute the probabilities of the following events leave your answers in UNSIMPLIFIED form a The number on the card is bigger than the number on the die b The sum of the numbers is 6 c At least one of the numbers is 3 d The sun sum of the numbers is at most 4 e The product of the numbers is at least 10

Estimate each product Order the products from least to greatest 24 8 x 3 2 35 23 x 2 89 13 21 x 5 78 5 5 x 15 5 What strategies did you use Take It Further Use a geoboard and geoband if they help Reflect a Describe the pattern b Sketch the next 3 terms c Describe the 17th term and the 37th term Sketch them if you can 8 Assessment Focus Create two different number patterns Each pattern must contain the numbers 12 and 32 Describe each pattern in words Write the next 4 terms in each pattern 9 a Describe this pattern The pattern continues b How many squares would be in the 10th figure c What are the perimeters of the 4th figure and 5th figure d What is the perimeter of the 10th figure e How many squares are there in the figure with perimeter 72 f Could you make one of the figures using exactly 27 small squares Explain 10 Create two different number patterns that contain the numbers 16 20 and 25 Write the first 5 terms in each pattern number pattern

Pro Weave manufactures stadium blankets by passing the products through a weaving department and then a sewing department The following information is available regarding its June inventories Raw materials inventory Work in process inventory Weaving Work in process inventory Sewing Finished goods inventory Direct Weaving Direct Sewing Indirect The following additional information describes the company s manufacturing activities for June Raw materials purchases on credit Other actual overhead cost paid in cash Materials used Labor used Direct Weaving Direct Sewing Beginning Inventory 172 000 440 000 620 000 1 396 000 Indirect Overhead rates as a percent of direct labor Weaving Sewing Sales on credit 615 000 186 000 318 000 84 000 166 000 1 275 000 520 000 1 700 000 85 160 Ending Inventory 261 000 480 000 860 000 1 386 000 5 350 000 20 to record a raw materials purchases b direct materials used c indirect materials used d Che

8 Part 1 of 2 B points eBook Hint Print References 1 Compactou un Required information Unit Reconciliation Units to account for CAGNOLULLOU VUL Prepare the Molding department s production cost report using the weighted average method Note Round Cost per EUP to 2 decimal places Total units to account for Units accounted for Total units accounted for Equivalent Units of Production EUP 11 Units Direct Materials Complete EUP Conversion Complete EUP Chec

If you re eighteen you re eligible to vote But you re only seventeen You re not eligible to vote What is this argument Valid Invalid Strong Weak

3 Part 2 of 2 3 points TOTAL 10 Beginning work in process inventory Started and completed Ending work in process inventory Total Required information 2 Beginning inventory is 40 complete as to direct materials costs Ending inventory is 80 complete as to direct materials costs Beginning work in process inventory Started and completed Ending work in process inventory Total TUO ARRI O Units 36 000 54 000 18 000 108 000 et for the work you have completed so far It does not indicate completion Units 36 000 54 000 18 000 108 000 Direct Materials Percent Added 0 X 100 80 3 Beginning Inventory is 70 complete as to direct materials costs Ending inventory is 20 complete as to direct materials costs Direct Materials Percent Added IZARRI EUP 0 X 100 20 54 000 14 400 68 400 EUP 0x 0x 54 000 Return to question

Find the accumulated amount after 2 years if 3000 is invested at 5 year compounded continuously Round your answer to the nearest cent 3450 X What formula should you use to calculate the accumulated amount for the given account whose interest is compounded continuously Click the E need

Vertical Curves Given g 3 82 2 L 500 VPI Station of 100 00 Calculate the PC Stationing 100 00 47 95 9 00 97 50

A small publishing company is planning to publish a new book The production costs will include one time fixed costs such as editing and variable costs such as printing The one time fixed costs will total 69 936 The variable costs will be 9 25 per book The publisher will sell the finished product to bookstores at a price of 24 75 per book How many books must the publisher produce and sell so that the production costs will equal the money from sales books

7 points Vertical Curves Given 8 3 82 2 L 500 VPI Station of 100 00 Calculate the PT Stationing 100 00 102 50 54 65 90 50

Solve the given equation 0 7 8x The solution s is are x Round to three decimal places as needed Use a comma to separate answers as needed

The voltage across a certain inductor is V 18 91 30 0 50 0 135 0 80 0 150 0 Simplify this expression and find the magnitude of the voltage The magnitude of Vis Type an integer or a decimal rounded to two decimal places as needed CIB 80 0 150 0 Simplify your answer Type integers or decimals rounded to two decimal places as needed Use angle measures greater than or equal to 0 and less than 360

Use the drawing took s to form the correct answer on the provided graph Dilate the line segment by a scale factor of 2 with a center of dilation at the origin Draw the dilated segment on the provided graph Drawing Tools Select Point Line Segment Click on a tool to begin drawing Resel 2 16 12 10 8 CO 8 2 2 4 40 6 3 Delete 10 12 Undo 14 16

Question 6 A farm has a population of 100 alpacas in the year 2016 Farmers are concerned because the alpaca population is decreasing at the rate of 5 per year If the population continues to decrease at this rate how long will it take until the population is only 30 alpacas 15 p