Geometry Questions

Qo bo a Which formula would be used to find the measure of angle 1 O a b 2 a c O b c a b 6

53 R U N C 1 2 T S 47 What are the measures of angles 1 and 2 m21 m22

N M 62 O 138 L Shondra wants to find the measure of angle JKL Her work is started What is the measure of angle JKL 138 62 1 JKL m2JKL

5 Area setup 16 Measure of central angle 0 Length of apothem a Length of a side s Perimeter Area 15

Explore the properties of angles and arcs formed by two intersecting secants 1 Find the difference of arc measures mAC MDE m ZABC 28 mAC 80 mDE 24 A D E B

6 5 Result 1 4 2 3 10 11 The probability of winning a coupon at the grocery store checkout is 2 25 What is the probability of not winning Instrument For questions 9 15 give each answer as a fraction in simplest form 9 Natalie randomly answered the last three true or false questions on her math quiz What is the probability that she got at least two correct 13 A group of students were asked if they play a sport or play an instrument The results are shown in the Venn diagram below If one of these students is chosen at random find each probability a P instrument b P does not play a sport 14 4 15 A die was rolled 40 times The results of each roll is given in the table below If the die is rolled once more find the experimental and theoretical probability for each result Theoretical 10 5 7 12 8 Sport 555 18 Frequency 2 14 Out of 75 students 45 are taking Algebra 2 and 32 are taking Chemistry Sixteen students are taking both Algebra 2 and Chemistry If a student is chosen at random what is the probability that the student is taking Algebra 2 but not Chemistry 10 Two dice are rolled What is the probability that the sum on the two dice is less than 69 12 A number from 1 30 is chosen at random What is the probability that the number is not a prime number a P 5 c P both instrument and a sport b P 1 or 6 c P no more than 4 d P greater than 2 d P sport but not an instrument Experimenta

Which of these pairs of events are independent You remove a blue glove from a drawer without looking and do not replace it then remove another blue glove without looking You reach into a basket and draw a name for a prize return the name into the basket and then draw a second time for another prize Your CD player has a random mode that chooses songs randomly and plays each song once before repeating While listening to the CD player in random mode you hear track 5 first and then hear track 3 second You choose a member of the basketball team to be the center You choose a different member to be a forward None of the other answers are correct

Which of the following scenarios does NOT describe independent events Drawing two cards from a standard deck of cards without replacement that are both aces Rolling a fair number cube twice and getting 6 on both rolls Flipping a fair coin twice and getting heads on both flips Rolling a 3 on a fair number cube and flipping tails on a fair coin O None of the other answers are correct

Caleb and Drew are playing a game with a pair of dice Caleb needs a sum of 5 or greater to win What is his probability of winning on his next turn 03 0 0 1 0 WIN

Find the probability of getting the results shown on the spinners Express your answer as a fraction in simplest form 115 O 15 01 10 C WIT OF 00 5 2

Which of these pairs of events are dependent You flip a coin and get tails You flip it a second time and get heads You pull your friend s name out of a hat that holds 20 different names replace the name then draw out your friend s name again You spin a spinner divided into five equal parts and is numbered 1 5 You get a 3 on the first spin and then spin again and get a 2 on the second spin You remove a black sock from a drawer without looking and without replacing it then remove another black sock without looking None of the other answers are correct

An inelastic string of length 1 0m anchored to a point x has a stone tied to the end y how high does the stone rise when the string xy is inclined at 30 to the original vertical position

The numbers 1 30 are written down on pieces of paper and placed in a hat for students to to randomly select Event A is the probability of drawing a number between 1 and 10 A 1 2 3 4 5 6 7 8 9 10 Event B is the probability of selecting a number that is a multiple of 6 B 6 12 18 24 30 Calculate P A 3 10 24 3 12

Let U be the set of all integers from 1 to 20 Let A 1 3 6 9 12 15 18 and B 2 9 11 20 Which choice describes the set 4 5 7 8 10 13 14 16 17 19 O ANB OA B O AUB OA B

Use the Venn diagram to help with the following question What is the probability that a person will like both badminton and baseball 3 0 13 14 0 35 0 86 Badminton Boxing 13 2 19 20 12 15 Baseball 21 None of the other answers are correct

What is the probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube Assume the number cubes are fair and have six sides Express your answer as a fraction in simplest form O O 1 30 O 12 07 10 Cube 1 Cube 2

At a school carnival one of the booths has 12 plastic ducks floating in a tub of water Each duck has either a zero one or two printed on the bottom indicating the number of prize tickets you receive if you select that duck Six of the ducks have a zero on the bottom three of them have a one printed on the bottom and three of them have a two printed on the bottom If you randomly select a duck and then randomly select another duck without returning the first to the tub what is the probability that you will receive four prize tickets O 1 16 22 0

What is the probability of picking a 7 from a standard deck of 52 cards 1 13 O 4 13 01 0 MIN A

A grab bag contains 7 football cards and 3 basketball cards An experiment consists of taking one card out of the bag then selecting another card What is the probability of selecting a football card and then a basketball card if a the first card is not replaced b the first card is replaced Express your answers in decimal form If necessary round answers to the nearest hundredth a 0 23 b 0 21 a 0 09 b 0 49 a 0 21 b 0 23 a 0 49 b 0 09

table below shows the number of days that a meteorologist predicted it would be sunny and the number of days it was sunny Based on the data in the table what is the conditional probability that it will be sunny on a day when the meteorologist predicts it will be sunny Predicts sunny Does not predict sun Total 57 59 90 Not Sunny 570 20 590 Sunny Total 63 347 410 633 367 1000

Of 50 students going on a class trip 35 are student athletes and 5 are left handed Of the student athletes 3 are left handed Which is the probability that one of the students on the trip is an athlete or is left handed Athletes 0 2 0 5 0 74 0 8 Left handed

A grab bag contains 8 football cards and 2 basketball cards An experiment consists of taking one card out of the bag replacing it and then selecting another card Determine whether the events are independent or dependent What is the probability of selecting a football card and then a basketball card Express your answer as a decimal independent 0 18 dependent 0 04 dependent 0 64 O independent 0 16 None of the other answers are correct

Of 100 workers in a stadium 42 work in the concession stands and 88 are wearing name tags Of the workers in the concession stand five sixths are wearing name tags Which is the probability that one of the workers is in concessions or is wearing a name tag Works Concession 0 3 0 87 0 95 O 1 Is Wearing a Name

The diagram shows the sample space of all equally likely outcomes Find the probability of rolling two 2 s Express your answer as a fraction in simplest form 1611 1 6 1 36 M A 8

In a bag of 60 candies 36 are green and 45 have caramel in them If the events of picking a green candy and picking a candy with caramel are independent what percent of the green candies have caramel in them 25 60 O 75 100

A six sided number cube is rolled 350 times and the results are recorded as follows 58 ones 63 twos 52 threes 61 fours 60 fives and 56 sixes What is the experimental probability of not rolling a five Round to the nearest whole percent if necessary 83 93 17 7

A teacher asks two students in the class to think of a number between 1 and 100 Tell whether the events are independent or dependent Event A Brooke picks 23 Event B Shari picks 88 O dependent O independent O None of the other answers are correct

Find the value of h for the parallelogram Answer 24 36

3 Shortest Route Algorithm If you start at vertex A and use the Shortest Route Algorithm what would be the second path to be selected highlighted AB AC 25 points ACE A 4 8 D 2 4

Find the area of the polygon with the given vertices A 2 2 B 5 5 C 5 0 D 2 3

Find the value of h for the parallelogram 8 4

3 Shortest Route Algorithm What is the length shortest path from A to C in the graph below B 3 2 25 points 4 4 1 3 5 2 3 C

15 tan X Z 40 50 Y 30 X

4 34 32

Let p represent the focal length distance between the vertex and focus The vertex of a parabola is 1 4 and the focus is 1 4 The equation of the directrix is The value of niS 0 0 man A

The Ain Dubai is the world s largest ferris wheel The diameter of the wheel is 250 meters If there are 48 cabins to ride what is the distance between the cabins

Given right triangle ABC with altitude BD drawn to hypotenuse AC If BD 18 and DC 6 what is the length of AC A B 18 D 6 C

is problem p is in dollars and x is the number of units demand function for a certain product is p 190 2x and the supply function is p 33x 73 Find the producer s surplus at the equilibrium point Round x and p to two decimal places and your answer to the nearest cent

find the distance across a river a surveyor chooses points A and B which are x 200 ft apart on one side of the river see the figure She then chooses a reference point C on the opposite side of the river and finds that LBAC 82 and LABC 52 Approximate the cance from A to C Round your answer to the nearest foot ft A x ft 82 52 B

EM V Round your answer to the ne 2 S 13 5 The diagonal of a rectangle is 25 in The width is 15 inches What is the length

Suppose that the origin on a computer screen is in the lower left corner of the screen A target moves along a straight line at a constant speed from po 670 460 to point B 470 320 in 2 sec Part 1 of 2 a Write parametric equations to represent the target s path as a function of the time in sec after the target leaves its initial position The parametric equations are x 670 1001 and y 460 70t for 0 t 2 Part 1 2 Part 2 of 2 b Where is the target located 1 4 sec after motion starts The location of the target 1 4 sec after motion starts is

Find the area of the figure Sides meet at right angles 6 m 2 m 3 m 3 m 2 m 3 m 6 m m

O is the center of the regular hexagon below Find its perimeter Round to the nearest tenth if necessary 18

What is the value of y y Type an integer or a decimal 4 10

Find the area of the figure 8 m 5m 8m 6 m 5m

Find the area of the figure 15 cm 15 cm 11 17 cm 8 cm

Find the surface area of the figure below 8 yd 17 yd 17 yd 17 yd 14 7 yd

6 10 06 Review In circle K above the area of sector JKL 94 etermine m JKL to the nearest tenth of a degree A 94 in K O

Find the lengths and area A The length of the arc is yards Round to three decimal places as needed The area A of the sector is square yards Round to three decimal places as needed A 20 10 yd

Question 1 25 points Hamilton Circuits Paths Find a HAMILTONIAN CIRCUIT of the graph below C A B D E F G H ABCDEFGHI ICFGHDABE ABEDHGFCIA a circuit is not possible