Questions

Lesson 19 2 Checkpoint Checkpoint below Once you have completed the above problems and checked your solutions complete the Lesson Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 You want to reuse an old cookie tin can into a new decorative tin by spray painting the surface Find the surface area of the following cylinder below Use 3 14 for Round to the nearest tenth 6 in Dunich Butter Condi 10 in 2 If one 11 oz spray paint can provide coverage for up to 864 square inches will you have enough for two coats Explain your reasoning

N Your Turn 2 Find the surface area of each composite figure Use 3 14 for m Round Hint Scomposite prism surface area cylinder lateral area 3 cm 9 cm 9 in 2 cm 5 in 5 cm 4 cm 3 in 3 in 5 in 7 in 3 7 mm 0 3 mm 6 mm

Your Turn Find the surface area of each regular pyramid 1 10 2 6 cm 18 cm EXPLAIN 1B Finding the Surface Area of a Pyramid Read the section below and complete the following activity adapted from Lesson 19 3 If only the height altitude of a square pyramid is given one can use the Pythagorean theorem to determine the slant height The slant height of the square pyramid is the hypotenuse of the right triangle formed by the height and half the base length Recall the Pythagorean theorem formula which tells us that the relationship between the legs and the hypotenuse of every right triangle is a b c where a and b are the legs and c is the hypotenuse Finding the Surface Area of a Regular Pyramid if the slant area is not given Step 1 Find the slant height if it is not given Step 2 Find the lateral area RO Altitute Slant height

3 13 in Your Turn Find the surface area of each regular pyramid Round to the nearest tenth if necessary 1 2 8 ft 6fthed 8 in 8 in right Comp Leave your 6 ft 6 ft EXPLAIN 3 Finding the Surface Area of a Cone Read the section below and complete the following activity adapted from Lesson 19 3 A cone is a solid that has a circular base and a single vertex A right cone is a cone whose axis is perpendicular to the base The surface area of a cone is calculated by adding the lateral area to the base To calculate the lateral area of a right cone the slant height I must be known The slant height of a right cone is the distance from any point on circle of its base to the vertex see figure to the right It is not the same as the height of the cone becord ACCOGLODOG

A and B are mutually exclusive events P A 0 30 and P B 0 50 What is P A or B OA 0 80 OB 0 60 C 0 15 O D 0 20

Penguin Robin Snail Sparrow Pelican Bat Let event A The animal is a bird Let event B The animal can fly Which outcomes are in A and B V V A penguin robin sparrow pelican bat B robin sparrow pelican bat C robin sparrow pelican D penguin robin sparrow pelican

The surface Your Turn Each aluminum can is a right cylinder Find the total amount of aluminum needed to make the can Leave your answer in terms of 1 15 cm 6 cm 2 Pas 80 mm 72 mm

3 The volume of the cone is given Show the work necessary to find that the volume of the cone is V 78 776 3 mi Use 3 14 for I Show the work 28 mi lup 100 mi 4 Find the volume of the cone be wel stumises 14 m 14 m

A rigid bar ACE is supported by three vertical wires and is initially horizontal as shown in the figure Then a force P is applied at the center of the bar All wires are made from the same material with modulus of elasticity E 200 GPa and have the same cross sectional area A 10 mm You may assume that the deformations are small and that the stresses are within the elastic range for this problem 1 5 m B A 1 0 m D C P 1 0 m F A E 2 0 m Figure 3 1 Rigid bar supported by three vertical wires a Find the normal stresses and the axial displacements in the wires if P 15 kN b Knowing that AB is the critical wire and its yield stress is oy maximum P that can be applied 1500 MPa find the

You roll two number cubes Let event A The number rolled on the first cube is 6 Let event B The sum of the numbers rolled is 11 What does P BA represent A The probability that the sum is not 11 B The probability that the first number cube shows a 6 given that th sum is 11 C The probability that the first cube does not show a 6 D The probability that the sum is 11 given that the first number cub shows a 6

Your Turn Find the volume of each composite figure 1 16 m 16 m 10 m 4m 5m 2 8 ft 8 ft 8 ft

2 a Write the polynomial in standard form 8x 6x 3x b Identify the leading coefficient of the polynomia c Identify the degree of the polynomial

6 Classify each polynomial on the left by degree Polynomial 2p p 2x 5n 10n 10 6n 6 Constant Quadratic Quartic 60000

the volume he cylinder to the right has radius of 2 cm and height of 10 cm Give our answer in terms of it

5 Find the volume of the cone below 10 cm La 10 cm 6 Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches Use 3 14 for and round to the nearest tenth 7 Find the volume of the composite figure Use 3 14 for 7 and round to the nearest tenth The dimensions of the cylindrical conical tank are as follows The radius of the cylinder and cone 17 inches Height of the cylinder 50 inches Height of the cone 32 inches The volume of the cylinder and the cone is given Show the work necessary to find the volume of the composite figure a Show the work to find the volume of the cylinder is V 45373 in b Show the work to find the volume of the cone is V 9679 6 in c Use what you know about composite figures to estimate the volume of the cylindrical conical tank Optional Complete problems 2 5 7 9 10 15 23 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the fouthal

shapes 7cm 4cm Shape Polygons 3cm 3cm 4cm 11cm Circle 12 in 3cm 7cm Formula One sticky note is a two dimensional shape like all the previous shapes Describe or draw the shape you would get if you took a lot of sticky notes and stacked them perfectly on top of each other In this credit you will be learning about three dimensional shapes which are created by stacking many two dimensional shapes on top of each other like sticky notes Thinking about how a three dimensional shape is made may help you throughout the credit

Find the volume of each cone 1 Find the volume of the ice cream cone in cubic inches Use 3 14 for and round to the nearest tenth 2 Find the volume of the cone Use 3 14 for and round to the nearest tenth 24in 3 9 in

The gift box is a right prism Find the total amount of paper needed to wrap the box Do not count overlap 1 18 in 5 in 5 in

Your Turn Find the volume of each sphere Use 3 14 for and round to the nearest tenth 3 A spherical water tank has a diameter of 27m How much water can the tank hold to the nearest cubic meter U T 609M 3800 4 The diameter of an NBA basketball is about 9 inches How much air can it hold in cubic inches SPA

Find the volume of the composite figure Round to the nearest tenth 1 30 cm 15 cm 12 cm

Find the volume of each pyramid 1 A piece of pure silver in the shape of a rectangular pyramid has the dimensions shown below What is the volume of this piece of pure silver 2 5 cm 1 5 cm 1 5 cm

2 Find the volume of each figure 1 1 cm 4 cm 3 cm 5 cm 2 cm 4 cm

Use the Box Graphic Organizer to multiply 3x 1 x 5 Choose the correct values from each drop down menu X 5 3x 1

7 Match each polynomial with its end behavior 32 7x 8 2 3x 9x 2x 8x 5 x 8x 2x 5 DRAG DROP THE ANSWER Asz co f x o and As o 2 0 Asz o f z o and As o f x o As 2 f z and As o f x o As T 00 f x and As a too f x 0

You are given the polynomial 13x 5 6x x Part A Write the polynomial in standard form Part B Determine the degree of the polynomial

b 6 Answer 2 A 4 0 2 3 B 4 1 0 2 0 2 only 10 10 Part B What are the zeroes of the above polynomial function

Name the degree of each of the following polynomials Polynomials 17x 6 27 4x 7 No degree O 1st degree 3rd degree JA 5th degree KITTY KIN

6 Describe the end behavior of the function graphed below N 8 10 12 14 A As a o f x B As a f x o as a As x f x as x x x D As x 00 f x o as x f x o as x x o f x

State what you know about the given polynomial expressic 8x 24 5x7 12x The degree of this polynomial is There are 24 is called the in Standard Form terms in this polynomial

Task Classify each polynomial based on the the degree of the polynomial DRAG DROP THE ANSWER 3 x 12x 6x 7y 12y 3y 17 9 6 4x 16 X 9 3x 9x 12 Quadratic Linear Cubic Constant

Classify each polynomial by its terms DRAG DROP THE ANSWER 2p p 1 5n 10n 10 10a 8n 5n 2n 8n 9n 10 4 2a 8a Monomial Trinomial Binomial Other

Which type of polynomial is the following 3x 5 7y A binomial B trinomial c monomial

a Which statement describes the end behavior of the function f x 2a 16x 32x As a o f a o and as a f x 0 B As a o f x co and as a o f a As a f a oo and as a f a DAs a o f a oo and as a o f a 0 b Part B Based on its end behavior which graph represents f x 2a 16x 32x A 25 20 15 10 5 s 10

Use the dropdown options to fill in row 5 of Pascal s Triangle 1 11 121 1331 14641

Matthew knows that he can use the 6th row of Pascal s triangle to calculate the coefficients of the expansion a b Calculate the numbers in the 6th row of Pascal s triangle and hence write out the coefficients of the expansion a b 5 1 5 10 10 5 1 82 6 15 20 15 6 2 1 7 21 35 35 21 7 1 1 6 15 20 15 6 1 1 3 3 1

Use the Binomial Theorem to expand the polynomial a b then fill in the blanks a a b 6a 4 8 6

Directions Multiply the binomials using the box metho 3x 2x x 5

Use Pascal s Triangle to complete the expansion of y z y 4y z y z 4yz z

Given NQ is the bisector of LMNP and ZNMQ ZNPQ Prove A MNQAPNQ M N Q P

Simplify 2x 3y 4

Select the Quadratic Binom A x 3x B x 8 Cx 7 D 3x 2x 8

A clinical researcher predicts that a new therapy will reduce depression among patients The researcher knows that on average patients who receive the old therapy have a normal distribution of depression scores with average of 30 on the Beck Depression Inventory and a standard deviation of 4 In a very simple study the researcher randomly selects a depressed patient fromh a larger population and gives the patient the new therapy and then measures the patient s depression after the end of the therapy The patient receives a score of 23 What should the researcher conclude based on the results of a null hypothesis significance test using this sample of 1 person using the 5 steps of hypothesis testing with a one tailed 05 significance level Assuming that the analysis is performed correctly what is the appropriate interpretation of the results of the study The new therapy was effective the therapy reduced depression The new therapy was not effective the therapy did not change depression The new therapy was not effective the therapy increased depression The results of the study are inconclusive

A clinical researcher predicts that a new therapy will reduce depression among patients The researcher knows that on average patients who receive the old therapy have a normal distribution of depression scores with average of 30 on the Beck Depression Inventory and a standard deviation of 4 In a very simple study the researcher randomly selects a depressed patient from a larger population and gives the patient the new therapy and then measures the patient s depression after the end of the therapy The patient receives a score of 23 What should the researcher conclude based on the results of a null hypothesis significance test using this sample of 1 person using the 5 steps of hypothesis testing with a one tailed 05 significance level Which critical value should be used for this test Hint make sure it matches your research hypothesis 1 64 1 64 1 64 1 96 1 96 1 96

Visit an area within your vicinity Identify at least one type of ecosystem and be able to explain ecosystem you have chosen Take a picture s or selfie of it 60 points Photo or Model of Student Ecosystem Content Vocabulary Poor 5pts did not accurately and neatly display model of ecosystem Organization 74 or fewer of concepts are described correctly demonstrating little knowledge of ecosystem terms and concepts Fair 10 pts Student displayed ecosystem below the expectations of the instructor lacking either neatness or accuracy 75 85 of concepts 85 94 are to described concepts correctly described demonstrating fair correctly knowledge of demonstrating ecosystem terms and concepts writer Organization and structure detract from the message of the Paragraphs are disjointed and lack transition of The thoughts The Organization and structure of the paper is not easy to follow Paragraph transitions need are unclear paper is inadequate excessive Good 15 pts Student somewhat displayed the ecosystem with accuracy and neatness paper is length inadequate excessive in length of are Excellent 20 pts Student exceeded the expectations of the instructor by accurately and neatly displaying the ecosystem model 95 100 of are concepts described correctly Score demonstrating high knowledge of good knowledge of ecosystem terms ecosystem terms and concepts and concepts Organization and structure of the paper is somewhat easy to follow Paragraphs contain transitions The paper s length is acceptable some Organization and structure of the paper are clear and easy to follow Paragraphs contain appropriate transitions The paper s length is appropriate for ideas expressed TOTAL

A clinical researcher predicts that a new therapy will reduce depression among patients The researcher knows that on average patients who receive the old therapy have a normal distribution of depression scores with average of 30 on the Beck Depression Inventory and a standard deviation of 4 In a very simple study the researcher randomly selects a depressed patient from a larger population and gives the patient the new therapy and then measures the patient s depression after the end of the therapy The patient receives a score of 23 What should the researcher conclude based on the results of a null hypothesis significance test using this sample of 1 person using the 5 steps of hypothesis testing with a one tailed 05 significance level What are the characteristics of the comparison distribution H D shape Choose Choose Choocal

This is a new question unrelated to the previous scenario In a research study If the critical value is 1 96 and the calculated sample Z score is 2 05 the correct decision is to fail to reject the null hypothesis reject the null hypothesis accept the research hypothesis fail to accept the research hypothesis

Devise a preference schedule with three candidates such that the sequential runoff method violates Fairness Criterion 4 Explain your work Choose the correct answer below OA First Second Third OC First C A B 4 CAB3 A B Second B A Third C C 4 3 HE CABS CBAS C OB First Second A Third B 4 OD First C Second B Third A 4 BAC3 C A B 3 C B A 5 C B A 5

Suppose the sequential runoff method is used on the following preference schedule Is Fairness Criterion 3 satisfied Is fairness criterion 3 satisfied O A Criterion 3 is not violated so candidate C should win the second election B Criterion 3 is violated if the 8 voters in the first colum move B above A C Criterion 3 is violated if the 5 voters in the third column of Le table move C above A O D Criterion 3 is not violated so candidate A should win the second election First Second Third A B C 7

Suppose the plurality method is used on the following preference schedule Is fairness criterion 4 satisfied Is fairness criterion 4 satisfied No O Yes First Second Third

K Explain in words why the plurality method always satisfies the criterion If a candidate receives a majority of the first place votes that candidate should be the winner Choose the correct answer below OA The plurality method always satisfies this criterion because the plurality method is where the candidate with the most first place votes wins OB The plurality method always satisfies this criterion because the plurality method is where the candidate who wins the most pairwise one on one contests is the winner of the election OC The plurality method always satisfies this criterion because the plurality method is where points are awarded according to the rank of each candidate on each ballot first second third and the candidate with the most points wins OD The plurality method always satisfies this criterion because the plurality method is where the two candidates with the most first place votes have a runoff and the winner of this runoff is the winner of the election