Geometry Questions

Use for questions 11 and 12 Of the 125 students enrolled at a dance studio 96 take ballet and 50 take jazz Of those that take ballet 28 also take jazz 11 Draw a Venn diagram to represent this information Ballet Jazz 96 28 50 125 13 If a point is placed at random on AE 12 If a dance student is chosen at random find each probability Give each answer as a fraction in simplest form a P ballet or jazz b P ballet but not jazz c P neither ballet nor jazz 14 A shuttle bus arrives at a hotel every 40 146 96 49

For questions 7 10 give each answer as a fraction simplest form decimal and percent 7 If a letter in the word MATHEMATICIAN is chosen at random what is the probability of choosing a vowel 9 If a card is selected at random from a standard deck what is the probability that it is a face card or an 8 8 A number from 1 30 is chosen at random What is the probability that the number is a two digit number and prime 10 If a card is selected at random from a standard deck what is the probability that it is an ace or a red card

Compound Events each answer as a fraction in simplest form 17 Each spinner below is spun once Find the probability of each event Green Blue Yellow Red Yellow 18 A month Blue Blue Green 9 8 7 10 6 1 2 4 3 a P blue then even b P not red then less than 7 c P green then at least 3

23 A number from 1 50 is chosen at random Find each probability as a fraction in simplest form a P odd less than 25 b P greater than 10 even 24 A letter in the grid below is chosen at random What is the probability that the letter is in the word BASKETBALL given that it landed in the shaded region ABCDE FGHIJ KLMNO PQRST

SU and VT are chords that intersect at point R S V x 6 x 1 n x 4 T What is the length of line segment VT O4 units 08 units 13 units O14 units

The circle is inscribed in triangle PRT P U 9 T S 5 R Which statements about the figure are true Select two options The perimeter of the triangle is 19 units TU TS PUTU The length of line segment PR is 13 units The length of line segment TR is 10 units

W 12 k 4 k N What is the length of line segment XZ O4 units 8 units 16 units 20 units

BD and AC are chords that intersect at point Y w 3 X Y 8 D S C What is the length of line segment AY O 2 units O 3 units O4 units O 6 units

Line segment BA is tangent to the circle 55 C A 120 What is the length of line segment BA Round to the nearest unit O 18 units O 65 units 88 units O 98 units

The circle is inscribed in triangle AEC A F B D C Which are congruent line segments Select two option OAB and CB OEF and ED ED and CD AF and EF CB and CD

R S T Line segment ST is congruent to which line segment OSK OKU OUT OTK

ndow elf Custom drapes are being fitted for a large circular window It is difficult to get these measurements but the window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame If the brace is extended upward it would go through the center of the shelf and the circle What is the diameter of the window Diameter feet

Circle O is inscribed in the given triangle 12 P 4 O R 6 What is the perimeter of the triangle O22 units O 30 units O 44 units O 60 units

What is the definition of postulate an assumption presumed to be true that is used as the basis for a logical argument B a statement that has been shown to be true by logical argument C a statement known to be false that is used as the basis for a logical argument D a statement that has been shown to be false by logical argument A

Use OP at the right to find the name of a minor arc whose measure is less than 82 D 829 P 68

A searchlight has a parabolic reflector that forms a bowl which is 13 in wide from rim to rim and 3 in deep If the filament of the light bulb is located at the focus how far from the vertex of the reflector is it round to at least 3 decimal places 13 3 Picture not to scale

Click here to watch the video Use the graph of y f x shown below to graph the function g g x f 2x y fix 8 0 CE KEE 4 5 0 0 SE DE 8 0yb

When a population grows past the ecosystem s carrying capacity what happens to the population OA The population starts to die off to return to carrying capacity OB Continues to grow OC The population grows then finds a new carrying capacity OD The population will go extinct due to lack of resources

A golfer tees off on level ground and hits the ball with an initial speed of 49 m sec at an angle of 33 above the horizontal Choose a coordinate system with the origin at the point where the ball is struck Remember to use the degree symbol if necessary Part 0 5 Part 1 of 5 a Write parametric equations that model the path of the ball as a function of time t in sec Simplify your answers as much as possible The parametric equations are X and y Osino cas

10 8 6 HERRE 4 2 8 9 6 4 2 CH 2 6 8 10 2 4 6 8 8 X 10 Q Write the standard equation for the hyperbola graphed above

se OP at the right to find the name of a minor arc whose measure is less than 82 C D 829 P 68 B 6 cm A

A factor that is necessary for the formation of a new species is OA different mating behaviors OB reproduction at different times OC geographic barriers OD reproductive isolation

What structural problem prevents adenine from pairing with guanine OA they lack the deoxyribose group OB they lack phosphate groups OC the bases are both short OD the bases are both long

The separation of populations by barriers such as rivers mountains or bodies of water is called QA genetic equilibrium B temporal isolation C behavioral isolation D geographic isolation

Triangle ABC has vertices A 3 2 B 1 3 and C 5 0 Write the coordinate notation for a translation of 6 units left and 9 units down Then write the coordinates of AA B C Part A Write the translation in coordinate notation Part B Write the coordinates of the image Show your work here

MatuloyDNE 7 Tameeka is in charge of designing a school pennant for spirit week What is the area of the pennant Example 3 31 1 ft 9 CLASS OF 2020 8 6 km TIGERS 6 ft Find the missing dimension of each triangle Example 4 10 b A 38 7 km2 8 Norma has an A frame cabin The back is shown below If the total area of the windows and door is 3 5 square yards how many square yards will she need to paint to cover the back of the cabin Example 3 12 642571 5 yd 6 75 in A 13 5 in h 8 yd

13 FIND THE ERROR A student is finding the height of the triangle Find the student s mistake and correct it 17h 68 h 4 meters 17 m A 68 m 15 CONSTRUCT AN ARGUMENT Mrs Giuntini s lawn is triangle shaped with a base of 25 feet and a height of 10 feet Is the area of Mrs Giuntini s lawn greater than 250 square feet Write an argument that can be used to defend your solution 14 CONSTRUCT AN ARGUMENT Determine if the following statement is always sometimes or never true Write an argument that can be used to defend your solution If a triangle and a rectangle have the same base and height the area of the triangle will always be greater 16 CREATE Draw and label a triangle with a base that is 3 times its height and has an area that is less than 50 square inches

12 B Apply the nearest neighbor algorithm to the graph above starting at vertex A Give your answer as a list of vertices starting and ending at vertex A Example ABCDA

rod connecting the piston to end of the crankshaft measures 12 cm What distance up and down in a cylinder rotates a wheel with radius 5 cm The must the piston travel to change the angle from 40 to 140 12 cm 40 Crankshaft 5 cm netry N Orlando

Given OS PR 21 22 Prove MO MT OP SR P M T Hint Use substitution property as a reason why z1 zMTO R

1 Would you use primary or secondary data in each situation Explain a To determine the percentage of fellow workers who drink at least one coffee a day 2 marks b To find the average weight of Canadian men 2 marks

Given TP VW lengths Find ST TV and PT as shown 10 T W

How many walks of length 10 are there from the green start to the red end node in the graph below START END

Find the lateral and total surface area for the figure round to the nearest tenth if necessary 23 4 LA SA

Use the given information and a calculator to find 0 to the nearest tenth of a degree if 0 0 360 cos 0 0 3150 with 0 in QIII sin 0 0 3168 with 0 in QIII sec 0 2 with 8 in QII sin 8 3 2 and 0 in QIV

number Area of smaller parallelogram 6 ft 4 The area of the larger parallelogram is Round to the nearest whole number as needed 00 2 ft 6 ft

For problems 4 6 use the figure below 3 Find the m 1

Can someone please explain the steps with a diameter of 4 feet and a height of 9 feet This trough is conical in shape and is filled with a liquid that weights tbs per cubic foot The depth of the liquid is at 7 feet What is the amount of work in ft lbs that is required to empty the conical trough by pumping the water over the top

A boy is flying two kites at the same time He has a 350 ft of line out to one kite and b 430 ft to the other He estimates the angle between the two lines to be 30 Approximate the distance between the kites

A woman standing on a hill sees a flagpole knows is 70ft tall The angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees Find her distance x from the pole S 1945 2060 ing on a hill sees a flagpole that she knows is 70 ft tall The angle ce x from the pole Round your answer to one decimal place ft

Complete the following sin 116 81 trig O Note that the given angles are in radians cos sin A op C

E 21 14 D B x 1 X What is the value of x O x 2 O x 3 O x 4 O x 6

Given Diagram as shown h 24 b 30 c 25 Find a K R r note K area triangle ABC B C h A D b R

x 2 Spl x 4 Which equation results from applying the secant and tangent segment theorem to this figure O x x 2 x 4 O x x 4 x 2 O x x 4 x 2 Ox 2x 4 x 2

3x Let 0 be the measure of an angle in radians in standard position with 0 Find the exact y coordinate of the intersection of the 2 11 terminal side of 0 with the unit circle given cos 0 sin 0 State the answer as a single fraction 16 The exact y coordinate is Simplify your answer including any radicals Rationalize all denominators Use integers or fractions for any numbers in the expression

41 in The area isin 49 in Find the area

Find the area of the regular polygon 041 Round to the nearest tenth as needed Area

A balloonist is directly above a straight road 1 8 miles long that joins two towns She finds that the town closer to her is at an angle of depression of 40 and the farther town is at an angle of depression of 38 How high above the ground is the balloon The balloonist is about miles above the ground 40 1 8 mi Not to scale answer to two decimal places as needed Round all intermediate values to four decimal places as needed

For problems 1 3 use the figure below Find the m1 Answer

What is the area of the regular polygon The area is m Round to one decimal place as needed