Basic Math Questions and Answers

19 cos 1020 20 tan 960

After recording the pizza delivery times for two different pizza shops you conclude that one pizza shop has a mean delivery time of 46 minutes with a standard deviation of 5 minutes The other shop has a mean delivery time of 42 minutes with a standard deviation of 19 minutes If you liked the pizzas from both shops equally well which one would you order from Why Choose the first shop The delivery time is more reliable because it has a lower standard deviation Choose the first shop The delivery time is more reliable because it has a lower mean Choose the second shop The delivery time is more reliable because it has a larger mean Choose the second shop The delivery time is more reliable because it has a larger standard deviation

Assume that a set of test scores is normally distributed with a mean of 78 and a standard deviation of 10 points On a separate piece of paper draw a normal distribution diagram and use the 68 95 99 7 Rule to find the percentage of test scores greater than 68 Select the correct answer below 84 50 34 16

A set of test scores is normally distributed with a mean of 100 and a standard deviation of 5 Use the 68 95 99 7 rule to find the percentage of scores in each of the following categories a Greater than 100 b Greater than 105 c Less than 95 d Less than 110 e Less than 90 f Less than 105 g Greater than 95 h Between 95 and 105 a The percentage of scores greater than 100 is 50 Round to one decimal place as needed b The percentage of scores greater than 105 is Round to one decimal place as needed

The resting heart rates for a sample of individuals are normally distributed with a mean of 67 and a standard deviation of 9 Use the 68 95 99 7 rule to find the percentage of heart rates in each of t following categories a Greater than 76 c Less than 76 e Greater than 67 g Greater than 49 b Less than 49 d Less than 85 f Less than 58 h Between 58 and 85 a The percentage of heart rates greater than 76 is Round to one decimal place as needed

Give the Five Number Summary for the number of Grizzly Bears in the previous question Low Lower Quartile Median Upper Quartile High

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximatin rectangle 12 10 8 6 4 1 1 2 4 y 2 2 4 Find the area of the region x 7 4 6 6 8 8 X X 2 4 6 8 10 12 y 3 6 6 8 8 X

5 Calculate the next two negative coterminal angles a 53 b 138

The scores on a psychology exam were normally distributed with a mean of 63 and a standard deviation of 5 A failing grade on the exam was anything 2 or more standard deviations below the mean What was the cutoff for a failing score Approximately what percentage of the students failed The cutoff for a failing score was Simplify your answer

Y NOTES ASK YOUR TEACHER Sketch the region enclosed by the given curves 1 y x y x 8 y 8 6 4 5 5 10 10 Find the area of the region X X 25 15 15 20 PRACTICE ANOTHER 20 25 25 X 8 6 y 8 6 4 5 5 10 10 15 15 20 20 25 25 X X

The scores on a psychology exam were normally distributed with a mean of 51 and a standard deviation of 5 About what percentage of scores were less than 41 The percentage of scores that were less than 41 was Type an integer or a decimal

V speed of a space shuttle that orbited Earth at an altitude of 682 km 5 646 X107 4

I can relate to many teenagers today by admitting the fact that I am a heavy social media user Over the past few weeks I have read many articles that have been headlining how influential social media is towards affecting people s personality and confidence From this I did not just become concerned about how I might be affected but also how it may affect other teenagers or even adults According to Whatls com social media is the collective of online communications channels dedicated to community based input interaction content sharing and collaboration Whatls 2016 All sounds very social however according to articles from USA Today Science Daily and Readers Digest have all made comments about how we humans are becoming narcissists Science Daily expressed individuals with narcissist syndrome to think of themselves as being exceptionally talented remarkable and successful Meaning they love to present themselves to other people and seek approval from them Gnambs 2017 Reading this article was shocking because I asked myself the question am I really that desperate This lead me to compose an investigation on whether social media was affecting two key expressive traits that being personality and confidence Even though we may be living in generation me where we could easily assume from that we are highly confident and mixed in personality types I believe that world only exists on social media because we have a screen to protect us from either the good or bad expression made by others This protection must have some deliberate affect towards our real confidence or personality traits The observation made above has allowed this investigation to find out whether the amount C Ca ex pe

The inspiration of this mathematical investigation comes from an essential aid that helps me and my friend to get through the IB ice cream Whenever my friends and I are stressed about the workload from the IB we would work together with some ice cream by our side to cheer us up However it would always frustrate us when we concentrate on work for a long while only to find that the ice cream has melted Therefore when I had to come up with a topic for the Maths IA I thought it would interesting to connect calculus maths differentiation and integration an abstract concept to something that I not only love but also something that is real something that I can touch and see or even to eat Eventually I chose to do it on ice cream which is something I cannot live without I have always been a curious learner So when I came up with the idea I was very excited by it and started to think how ice cream melts In my observation I found out that ice cream melts faster when it is more exposed in the air In other words the rate at which the ice cream melts is actually proportional to its surface area I find that quite interesting and decided to look more into the 3D shapes of ice cream The aim of this investigation is to compare the melting rates of different solids of the ice cream It will be looking at basic solids of ice cream such as sphere hemisphere cubes and cuboids as stored in containers as well as some more interesting shapes i e platonic solids tetrahedron and dodecahedron The rate can be calculated by using calculus differentiation and integration I hope that through this exploration I can find the solid with the slowest and fastest melting rate and from that see if the abstract mathematics coincides with real life practicality

Find the slope of the line passing through the two given points 5 10 and 6 1 The slope is Type an integer or a simplified fraction

K In the given graph call the x intercept of each line p 0 and the y intercept of each line 0 q Identify the line s where pxq is negative Choose the correct answer below C c and d d This question 1 point s possible

State the y intercept and slope of the graph of the equation y 8x 6 The y intercept is 0 The slope is

This question 1 point s possible Solve the equation by using the rules for rewriting equations An approach that makes solving equations with fractions or decimals easier is to multiply each side of the equation by a suitable constant to make the coefficients easier to work with 0 6y 5 1 4y 3 Submit quiz The solution is y Type an integer or a decimal

K Identify the sequence as either arithmetic or geometric List the next two terms of the sequence 5 2 9 16 Is the sequence arithmetic or geometric OA Geometric OB Arithmetic List the next two terms in the sequence 5 2 9 16 Type integers or simplified fractions

A change equation together with a function value that is not the initial value are given Solve the equation dy dx In 2 y y 1 22 Express numbers in exact form Use symbolic notation and fractions where needed Give the equation in terms of y and x solution

Assume the nominal interest rate for an account is 9 per year Find the effective annual interest rate corresponding to each compounding period below Round your answers to four decimal places after writing each rate as a percentage a monthly b weekly c dally x x d continuously x

Megan bought a bag containing 50 Beads for 9 95 She received a 10 discount What was the discounted price of the beads 10 10 10 995 10 Discount Amount

2 or ever for It turns positive on 4 ion and eir own the field O a b C d a a d a C b a d b C C a b C d d b b d d The multiplication table above is defined on the set S a b c d 5 Is S closed under o misilgalam bue no 12 do dodamago vamaid ame 6 Compute a ob 7 Is o commutative in S Why or why not 11 gas chur 8 Is o associative in S Why or why not 9 Does S have an identity with respect to o If so what is it 2 aindes

The three sides of a right angle triangle are shown below What is the area of the right angle triangle A D A A A A 15 6 2 12 2 2 14 6 3 17 3 2 5 3 X 3 5

Question 3 Simplify the following expression 2x 1 2x y 1 A B C D 2y x 2y x 2y 2y 2y 2x 2x 2x y y

Perform the indicated operations and express the result in simplest radical form with rationalized denominators 2 C 15 2 15 4 25 2 15 6 15 4 15 15 3 15 15

Perform the indicated operation and express the answer in simplest form with rationalized denominator 2 6 5 3 6 4 5 A B 16 5 30 26 26 5 30 16 16 5 20 22 20 5 34 26 G

Evaluate the given expression 4 1 5 12 51 2 36 1 2 A B C D 13 10 26 5 10 26 36 10 Shey

Question 4 Simplify the given expression a 2 a 2 4 2 A B C D a 1 a a a 2 a 4 2a a 2 Story

Perform the indicated operation and express the result in simplest radical form with rational denominator 3x 2 3x A B y 6x 3xy 12x y 6x 3xy 12x y 6x 3 xy 12x y I 6x 3x y 12x y

The three sides of a right angle triangle are shown in the image below What is the perimeter of the triangle A 6 2 2 6 B 4 2 2 6 6 2 2 3 C I X 2 2 2 6

Perform the indicated operation and express the result in simplest radical 1 6 3 2 3 2 1 6 B 1 6 1 3 3 2 A Jy

Simplify the given expression A B C D 4x2 2y2 x2 4x 2 v 2x y2 Jay

Use Lagrange multipliers to find the maximum and minimum values of f x y x 5y subject to the constraint if such values exist Round your answers to three decimal places If there is no global maximum or global minimum enter NA in the appropriate answer area Maximum x y 64 Minimum

nich digits replace A B and 25 31 21 2 A C 94 47 B 2

Fill in the missing cells in the following table Quantity of Output Q Units 0 1 23 45 67009 8 10 Total Fixed Cost TFC Dollars 200 200 200 200 200 200 200 200 200 200 200 Average Fixed Cost AFC Dollars Total Variable Cost TVC Dollars 0 30 50 60 65 75 95 125 165 215 275 Average Variable Cost AVC Dollars Total Cost Dollars Marginal Cost MC Dollars Average Total Cost ATC Dollars

12 10 Give a parametric representation for the surface consisting of the cap of the sphere x y z 16 for 2 2 z 4 Remember to include parameter domains

11 12 Use Green s Theorem to evaluate f xe dx x dy where C is the positively oriented boundary of the region bounded by the curves y x x 2 and the x axis You must use this method to receive full credit

8 10 Evaluate fff 15xydz dx dy where E is the region bounded by 0 y 1 y x 2y 0 z 2 x y

7 10 Evaluate the iterated integral TT TU SS si 0 x sin y dy dx by reversing the order of integration

9 10 Evaluate the line integral f xy 3 ds where C is the curve y x 0 x 1

3 Find the range of values for x 6x 18 TE 4x 2 0 5 W 42 X 44 L 10

Which answer lists the original data represented in the stem and leaf plot below 56789 5 6 2 23 3 7 83 8 52 58 58 63 63 70 80 97 52 58 58 63 63 97 52 58 63 97 52 58 58 63 63 7 8 97

A company determines that its weekly online sales S t in hundreds of dollars t weeks after online sales began can be estimated by the equation below Find the average weekly sales for the first weeks after online sales began S t 4e The average weekly sales amount is

Jessica rents a booth to sell her necklaces at a craft fair She uses the function p x c x k to determine the profit she will make if she sells different numbers of necklaces at the craft fair The expression part c x k of the function has c and k representing constants What did Jessica most likely use k to represent The cost to make each necklace The price she charges for each necklace at the fair The cost of participating in the craft fair The profit from participating in the craft fair

Solve the equation on the intervall 0 2x 12 sec x 16 0 of 10 po This question 3 points The solution set is Type an exact answer in terms of z Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression

Solve the equation on the interval 0 0 2x 2 sin 28 7 sin 0 5 0 Question 6 of 10 This quiz 30 point s possible This question 3 point s possible Sub What is the solution in the interval 0 0 2x Select the correct choice and fill in any answer boxes in your choice below OA The solution set is Simplify your answer Type an exact answer using x as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to separa as needed OB There is no solution

In this question we will use a spreadsheet to approximate the root of f x x 5 3x 3 9 using Newton s method with x0 1 The picture below shows a spreadsheet being used to perform the calculation A downwards arrow indicates the contents from the cell above will be copied down 1 2 3 4 A A1 B1 C1 B C Using a spreadsheet find the following values x1 ANSWER Give your answer to at least 3 decimal places x2 ANSWER Give your answer to at least 3 decimal places

4 Describe in proper order the transformations you would apply to the grap graph of your parabola STANDARD FORM TO VERTEX FORM 5 Use your graph in demos to list the a and c values of your parabola Calculate the b value by using the formula 2ah Write your relation in standard form using the values of a b and c and then complete the square to determine the vertex form a b C K4 The standard form of my relation is

Acme Industries had sales last year of 12 000 000 They had expenses of 9 755 000 They purchase several pieces of new equipment during the year that Cost 3 000 000 to purchase Had 1 100 000 related costs to set up install etc Has a salvage value of 750 000 in 5 years Using MACRS calculate the amount of tax owed 375 500 400 780 425 000 484 500