Geometry Questions

Find the equations of the tangent lines at the point where the curve crosses itself Enter your answers as a comma separated list of equations x t 3 2t y t 2

O 1 3 1 2 1 6 O 1 4 Question 2 If a six sided die is rolled find the odds that the number will be a multiple of 2 2 1 2 p 2 6

Maggie used a standard deck of 52 cards and selected a card at random She recorded the suit of each card she picked then replaced the card The results are in the table below 1 4 13 50 1 2 Diamonds 7 10 Hearts What is the theoretical probability of selecting a heart Spades Clubs JK TILL JY JY I

Billy rolled a six sided die Each time he recorded the number rolled in the table below 1 3 5 18 5 12 Number on Die 7 15 1 2 3 4 5 6 Frequency 8 3 9 What is the experimental probability for rolling a number greater than 4 6 4 6

sweepstakes 1 500 499 1 1 499 499 500 Question 6 Maggie used a standard deck of 52 cards and selected a card at random She recorded the suit of each card she picked then replaced the card The results are in the table below O 7 10 Diamonds 3 10 Hearts Spades Clubs 2 pts JY HY HY I What is the experimental probability of selecting a heart

16 A tank is in the shape of a pyramid The base of the tank is a rectangle with length 3 feet and width 7 feet It is 9 feet high Find the volume of the tank

15 Popcorn is served in a conical container that has a radius of 3 inches and a height of 6 inches What is the volume of the small container

13 Find the volume of a cylindrical pool if the diameter is 20 feet and the depth is 6 feet

14 A fish tank is in the shape of a cylinder The tank is 22 feet deep and 40 feet in diameter Find the volume of the tank

The number of males and females enrolled in Oddability High School are listed per class in the table below Grade 9 10 11 12 107 207 20 207 35 207 Male 16 69 120 100 130 150 Female 150 If a student is chosen at random what is the probability that the student is female 100 110 175

Find the volume of the following 1 4 2 ft 11 cm 3 ft 11 cm 11 cm

1 6 Find the measure of the arc 1 AB A E D 40 B C AC L BE 2 ABC 3 ABD 4 BC

A ferris wheel is 19 meters in diameter and boarded from a platform that is 5 meters above the ground The six o clock position on the ferris wheel is level with the loading platform The wheel completes 1 full revolution in 6 minutes The function h f t gives your height in meters above the ground t minutes after the wheel begins to turn What is the amplitude What is the equation of the Midline What is the period The equation that models the height of the ferris wheel after t minutes is f t meters minutes meters How high are you off of the ground after 11 minutes Round your answer to the nearest meter meters

Rodrigo is organizing his CD collection He has 5 pop CDs and 85 other CDs If Rodrigo randomly selects one of his CDs what is the probability that it will be a pop CD Write your answer as a fraction or whole number P pop

Dwayne is making a gift during a pottery class at school He knows how to make 8 different items and there are 8 kinds of clay with which to make it How many different gifts can Dwayne make ich

20 You are planning to start a home business You decide to build a workroom in the shape of a rectangular prismin the backyard It will give you solitude to work and a place for cus tomers to see your products without disturbing your family in the house You price the mate rials needed and decide that the perimeter of the floor can be 64 ft in total Maximizing the floor area inside the workshop is your only objective What dimensions would you choose for the floor rounded to the nearest whole numbers You may know the answer already but provide a fully documented algebraic solution 5 marks

Oliver is deciding what to wear to school today There are 7 tops to choose from and 4 different pants How many different outfits can Oliver create outfit

Ken is buying a new set of DJ equipment Ken can afford one mixer and one turntable and is trying to decide among 3 different mixers and 8 different turntables There are 4 different speaker setups in Ken s price range How many different sets of DJ equipment can Ken buy sets

5 6 7 D Play Station B 8 00 Xbox 16 Nintendo 9 10 11 H 2 12 13 14 15 16 17 18 19 20 REQUIRED 1 A Video Game store Game Go is conducting a survey and asking each customer which current video game systems they own A customer named Justin said he only owns the latest Play Station and the latest Nintendo consoles In which region or regions would this place Justin in the VENN diagram 21 22 23

8 Find the area of the shapes below using addition or subtraction y a b 60 12 10 Wy 0 Seef X 3

on the board What is the probability that one dart hit the white area and the other dart hit the dark gray area white area 1 2 x 16 x 16 2 64 cm Dark area 3 14 x 16 2 200 96 cm 200 96 64 136 96 cm Area of square 16 256 cm p 64 256 x 136 96 256

Use for questions 8 11 A bag contains 20 slips of paper individually numbered 1 20 If a slip of paper and a letter in the word PENNSYLVANIA is chosen at random find each probability 8 P less than 15 then a vowel 9 P multiple of 4 then V 10 P at least 11 then N 12 Bella guessed on the last three questions on her science test If each question has five answer choices what is the probability she got all three correct 11 P a prime number then a consonant 13 It has rained two out of the past nine days Based on this data what is the probability that it will not rain for the next four days

Use for questions 1 3 There are 9 red markers 5 blue markers 14 yellow markers and 8 green markers in a pencil box A marker is chosen at random replaced then another is chosen Find

6 U B a sin b cos c tan E 32 4 cm Question 2 1 point For the diagram below which primary trigonometric ratio would you pick to solve the unknown value D 47 A a sin b cos c tan 6 cm

Question 5 1 point For the diagram below which primary trigonometric ratio would you pick to solve for the unknown value 3 8 cm R 37 a sin b cos c tan Question 6 1 point For the diagram below which primary trigonometric ratio would you pick to solve for the unknown value 2 8 m W 58

From the given figure find the length h Show all your steps to get full marks h 3 98cm 0 48cm R1 00cm 2 84cm

Expo sin 2u cos zu sin u 4 5 37 2 u 27t tan 2u

MANUSI Homework Members of the board of directors of an associatio N and city B The preference table for the 31 men criterion

You roll a 6 sided die What is P 6 or 1 Simplify your answer and write it as a fraction or whole nun

Check for Understanding 7 The triangle shown has vertices at A 3 1 B 1 2 and C 4 2 Find the area of triangle ABC 3 4 1 2 7 A A 22 8 4 A 16 2 A 4 4 7 14 unite16 4 12 unit 3 4 A T B 4 2 C 172

Practice 8 Find the area of the shapes below using addition or subtraction a b 60 putty A b h A R 11 66 11 R 66 89 unit c P A R A 9 4 18 9 4 18 31an 25 Z d WAY W 10 0 2 Y A 1 6 4 12 679 12 27 unit 2 32 7 A8 4 N A b h 4 8 1 8 34 A 32

All four sides of quadrilateral tangents of a circle then ABCD are PTET Nov 2011 1 AC AD BD CD 2 AB CD BC AD 3 AB CD AC BC 4 AC AD BC DB

Problem 2 50 points A population of 1 000 semiconductor wafers contains wafers made by three machines A B and C In the population 430 wafers are from machine A and 220 are from machine B A wafer will either meet or not meet a thickness specification For machine A 90 of its products confirm the thickness specification For machine B 15 of its products do not confirm the thickness specification For machine C 94 of its products confirm the thickness specification A wafer is chosen at random from the population A If the wafer is from machine A what is the probability that it is conforming B If the wafer is conforming what is the probability that it is from machine A C If the wafer is conforming what is the probability that it is not from machine C D If the wafer is not from machine C what is the probability that it is conforming

The drawing for a right triangular roof truss represented by AABC is shown in the accompanying diagram If LABC is a right angle altitude BD 4 meters and DC is 6 meters longer than AD find the length of base AC in meters A B D C

4 In circle L the length of MN 3 7 and m ZMLN 45 Find the area shaded below Express your answer as a fraction times T L N M

5 The accompanying diagram shows part of the architectural plans for a structural sup a building PLAN is a rectangle and ASL IN P 4 AN Which equation can be used to find the length of A S 1 LS AS AS SN 2 3 AS SN AS LN S N AS LS AS LS LS A Maz N

In the diagram below QM is an altitude of right triangle PQR PM 8 and RM 18 Solve for QM 8 M 18 R

Triangle RST is similar to AXYZ with RS 3 inches and XY 2 inches If the area of ARST is 27 square inches determine and state the area of AXYZ in square inches

2 Delroy s sailboat has two sails that are similar triangles The larger sail has sides of 10 feet 24 feet and 26 feet If the shortest side of the smaller sail measures 6 feet what is the perimeter of the smaller sail

1 The base of an isosceles triangle is 5 and its perimeter is 11 The base of a similar isosceles triangle is 10 What is the perimeter of the larger triangle

Homework The university administration has asked a g for improvement over the next year The cho summarized in the preference table

work Que e board of directors of a food company is holding an election t pansion to its corporate headquarters The 18 members of the mpanies Becker B DiMarco D LaChase L and Merende the right

1 1 Homework A family is trying to decide whether to go to Chicago C Kaccording to the following preference table Determine the Number of Votes 4 First Choice C Second Choice Third Choice ZO N 2 ZOON C 1 4 1 C N O O O N N C C

work Mathematics Department is holding an election for depa idates Clark C Jones J and Smith S mber of Votes 7 First J Second S Third C 10 4 8 S JC JC S C S J

nework The university administration has asked a group of stude arget for improvement over the next year The choices w center The votes are summarized in the preference table

ts Il Mode Live Online Class 362 omework 91 voters are asked to rank four brands of cereal A B C 45 25 12 Number of Votes First Choice Second Choice Third Choice Fourth Choice DABO A B C C D 2BCAD ooom 9 C D A B

In circle V m WVX 50 and the area 5 of shaded sector T Find the length of WY X Express your answer as a fraction times TT Y V W X C

9 1 the triangle Round decimal answers to C 14 B 56

4 A circle is inscribed in the square Find the area of the shaded region Round your answer to the tenths place A4414 4 2 16 16 in 12 04 0 r 2 in 4 in 4 in unod abnor abals fan to cansertbonent autt burkolme HD 2022461 2 88 5 A shape is constructed from a rectangle whose length is 10 inches and whose width is 8 inches along with a semicircle attached at the end What is the total area of this shape Leave your answer in terms of 10 in 1 80 32 1 12 5 2 18 3 3 21 7 4 28 6 3 80 8 4 96T 8 in 4 in Challenge 6 In the following diagram a quarter circle has been constructed using an isosceles right triangle whose legs measure 8 inches Which of the following represents the area of the shaded region rounded to the nearest tenth of a square inch 8 in 8 in

You are painting a jewelry box in the shape of a square pyramid How much paint will you need 10 in 13 in