Geometry Questions

6 Alvaro is interested in the relationship between weather conditions and whether the downtown train runs on time For a year he records whether each day is sunny cloudy rainy or snowy as well as whether this train arrives on time or is delayed Here are his results Weather condition On time Sunny 167 Cloudy 115 Rainy 40 Snowy 8 Total 330 Delayed 3 5 15 12 35 Total 170 120 55 20 365 Which of the following statements is true A When the weather was rainy it was more likely for the train to be delayed than on time B The most delays came on snowy days C More than half of the delays occurred on rainy days D When the weather was snowy it was more likely for the train to be delayed than on time

In Exercises 5 9 you are asked to find all the specified roots of certain real or complex numbe Use exact values 5 Find all 8th roots of unity 6 Find all cubic roots of 27i 7 Find all quartic roots of 256

You spin the spinner twice 4 3 1 2 What is the probability of landing on a divisor of 42 and then landing on Simplify your answer and write it as a fraction or whole number

For a standard deck of playing cards find the probability to the nearest percent that a queen randomly selected from the deck is a diamond Do NOT include the percent symbol

sleep Do NOT include the percent symbol Question 2 To the nearest percent what is the probability that a student who got less than 6 hours of sleep failed the exam 2 pts

You have a standard deck of playing cards from which you randomly select a card Event D is getting a diamond and Event F is getting a face card jack queen or king What is the probability to the nearest percent that the diamond selected is a face card Do NOT include the percent symbol

A patrol car is parked 0 feet from a long warehouse see figure The revolving light on top of the car turns at a rate of 36 revolutions per minute How fast is the light beam moving in ft sec along the wall w beam makes angles of 0 45 0 60 and 0 85 with the line perpendicular from the light to the wall a 0 45 b 8 60 y ft ft sec ft sec c 85 Round your answer to two decimal places

Suppose that sin 21 Find the exact value of sin 1 if the angle lies in the same quadrant as 112 9x and the angle 21 lies in the same quadrant as

Given the diagram of the spinner describe how to change each sector of the spinner so that each of the outcomes A B C or D is equally likely A B C

Bonus Use the figure below to find the measures of the angles 1 2 7 3 4 5 6 7 8 9 54 1 118 96 2 4 5 28 79 24 8 9

5 4 6 Statements 1 2 22 Given FJGH is a rectangle Prove FH JG Use the bank below FGH and JHG are right angles 3 SALA FG JH SAS Reasons 1 2 FLUENIT 3 All right angles are congruent 4 5 6 F they are even Side Reflexive Property K 8 H

Given a segment with endpoints 10 3 and B 5 3 Find the coordinates of point CpM AC 2 between A and B so that the ratio CB 3 A 1 3 B 4 3 9 0 3 5 3

A guy wire for a radio antenna is anchored to the ground 21 feet from its base and forms a 70 angle with the ground How long is the guy wire A B C D 7 2 feet 22 3 feet 57 8 feet 61 4 feet

A tree casts a shadow that is 22 feet long at the same time a 4 foot fence post casts a shadow that is 3 5 feet long Use similar triangles to find the length of the tree A B C D 15 7 feet 19 3 feet 25 1 feet 63 6 feet

What is the value of 0 in the diagram below A B C D 32 2 40 2 49 8 57 8 13 11 8

If the cos 60 1 2 A B 2 3 2 2 3 C D 2 find the sin 30

What similarity criterion can be used to prove AABC AAED A D B AA acc D Ten ST

ve for pe2 monoH noitatibo a era lot to pinW 1 H A 3 B 4 C 9 L

Find the equation of the parabola described below Find the two points that define the latus rectum and graph the equation focus at 0 2 vertex at 0 0

A card is drawn from a deck of playing cards What is the probability of drawing a heart or the King of Spades

Drawing a diamond from a deck of cards drawing an 8 from a deck of cards O Overlapping Mutually Exclusive

A card is chosen from a standard deck of 52 cards What is the probability that the card chosen is a spade or a seven

A magazine contains fourteen pages You open to a random page What is the probability that the page number is three or seven

A six sided die is rolled What is the probability that the number rolled will be an even number or a 6

Finding Slope From a Graph Find the slope of each line 1 7 3 5 Ay A 0 0 B 2 1 A B 2 KU AT Vertical line A B m undefined

A bag contains 2 yellow balls 3 green balls 5 red balls and 6 black balls What is the probability of drawing a yellow or red ball if only one ball is drawn

Drawing a face card from a deck of cards drawing a 5 from a deck of cards O Overlapping O Mutually Exclusive

A basket contains three apples three peaches and four pears You randomly select a piece of fruit What is the probability that the fruit you choose is an apple or a peach

Rolling an odd number on a die rolling a 2 on a die O Overlapping Mutually Exclusive

Solve for x Assume that lines which appear to be diameters are actual diameters 16x 4 70 For your answer only put the number Do not type x R 42 Question 39 1 point Find the missing angle measure in the circle For lines that look like diameters can be assumed as the diameter for the circle 96

Vertices at 0 8 and 0 8 asymptote the line y 2x An equation of the hyperbola is 0 0 1 Use integers or fractions for any numbers in the equation Which of the following is the correct graph O A 13 13 OB 13 14 13 43 13 Q O C 13 13 13 13 OD Ay 13 H 13 13

Find the standard equation of the parabola whose vertex is 6 6 and whose directrix is y 4 Also find the focal diameter of each parabola The standard equation of the parabola is Simplify your answer Use integers or fractions for any numbers in the expression The focal diameter of the parabola is Simplify your answer XI

15 16 91 88 cos 64 isin 6 4 4 cos 45 isin 45 A 22 cos161 sm161 D 22 cos 19 sin 19 7 cos 30 sin 30 16 cos 75 isin 75 A 112 cos 45 isin 45 D 7 cos 135 isin 135 cos 135 isin135 16 B 352 cos 109 sin 109 C 22 cos19 sin19 E 84 cos19 Isin 19 17 3 cos 15 isin 37 94 B 23 cos 105 isin 105 E 112 cos 80 8 sin 80 8 A 12 cos 60 isin 148 C 0 75 cos 3 75 isin 32 25 E 81 cas 50 625 isin 1 874 161 C B x E y x 12 cos 105 1sin 105 B 81 cos 60 isin 148 D 81 sin 60 icos148 18 If a function is an odd function and x y is a point on its graph then which of the following will also 4 be a point on the graph A x D x y C x y

5 Find the area of the quadrilateral 5 100 8 6 7

Fencing with the length of 420 meters surrounds two identical playing fields with a common side The fields can be side by side and separated by a fence as shown in the figure Find the dimensions and the maximum area of each field The larger dimension of each field is meters The smaller dimension of each field is meters

Determine the standard equation of the ellipse Vertices at 2 3 and 4 3 focus at 3 3 Choose the correct equation below OA O C x 1 y 3 9 5 x 1 y 3 5 9 1 1 Next question OB x 1 2 y 3 9 5 1 OD x 1 y 3 1 5 9

Determine the sum Find the answer in simplest form 1 1 1 x 1 Enter the simplified sum in the box N Show Hints I

Write an equation of a line tangent to the graph 3x 3y2 75 at the point 4 3 4 0 v 3x 25 O X 4 O y x 1 7 7 O y x 3 4 O y x 25 3 3

Question Number 15 of 20 7th Grade Math A cylindrical paint can has a diameter of 12 centimeters and a height of 16 centimeters Which is closest to the volume of the paint can in cubic centimeters

An isosceles triangle ABC has legs of lengths 24 and a vertex angle that measures 36 degrees Determine the length of it s base BC to the nearest length

Find the exact value of arcsin 1 O arcsin 1 2 370 O arcsin 1 TU O arcsin 1 1 2 O arcsin 1 35

4 A bird is perched on top of a pole on a steep hill and an observer is located at point A on the side of the hill 110 m downhill from the base of the pole as shown in the figure The angle of inclination of the hill is 50 and the angle a in the figure is 9 Find the distance from the observer to the bird 110 m

and the eccentricity e and the distance d from the pole to the directrix of the conic 2 sin 8 4 Sketch and identify the graph Use a graphing utility to confirm your results 2 O q 1 1 1 24 1 D 6 4 2 n 2 2 8 2

Solve the equation for exact solutions in the interval 0 360 Use an algebraic method 4 sec 20 tan 0 8 tan 0

18 The first floor of a house is shaped like a rectangular prism and the second floor is shaped like a triangular prism The dimensions are shown on the following diagram If a 1000 BTU air conditioner can cool a house with a volume of air up to 1000 m3 can this air conditioner cool the house sufficiently 5 marks 14 m 4m Am

Find the area in square centimeters of a regular pentagon with an apothem of length a 4 4 cm and each side of length s 6 4 cm Use the formula A cm

llowing triangle with sides B 3 86 and C 4 35 Find the length of the entire bottom of the triangle A B 35 x C B h A Hint Break the triangle into two right triangles by drawing a line from the top corner directly downward Then find the height h and use this information to find angle B Then use this information to find a Finally find the length A You can solve this in any order you like I just find it easiest in this order

Three atoms with atomic radii of 4 0 5 0 and 6 7 are arranged as in the figure Find the measure of the angle at the center of atom B inside the triangle CID 40 A 67

ion 4 srt Chris covers her paper route which is 21 miles long by 7 30am each day If her average rate of travel were 1 mile per

Find the area of the circle given in the figure Use 3 14 O 103 cm O 1017 36 cm O 507 3 cm 300 cm 18 cm