Geometry I

When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent. What is the probability that Josephine hits a single or a double when she is at bat?

20 percent

The diagram shows the universal set U = {parallelograms}. Set A represents parallelograms with four congruent sides, while Set B represents parallelograms with four congruent angles. How many of the parallelograms fall into the category A B?

26

An oblique rectangular prism with a square base has a volume of 539 cubic units. The edges of the prism measure 7 by 7 by 14 units. How many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height?

3 units

Set V is all the unique three-digit numbers using the digits 1, 2, 3, 4, and 5. Which set would be considered a subset of set V?

A. Set W is all the unique three-digit numbers using the digits 1, 3, and 5.

Which pair of figures has the same number of faces as vertices?

C. rectangular pyramid and triangular pyramid

Which three-dimensional figure has nine edges?

C. triangular prism

An oblique square prism is shown. Which expression represents the volume of the prism?

C. x2(x - 2) cubic units

Which statements are true about x? Check all that apply.

1. x ∈ B ⋃ C 2. x ∈ B ∩ C 3. x ∈ A ⋃ C 5. x ∈ B 6. x ∈ C

Marina wants to install security cameras in her store, which has dimensions 48 feet by 48 feet. Each camera can view an area of approximately 128 ft2, with a viewing area shaped like a right triangle. How many cameras will be necessary to cover the entire store?

18

Fiona needs to chose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8. If she uses her initials, F, J, and S in order as the first three characters, and she does not use the same digit more than once in her password, how many different possible passwords are there?

20

A right square prism has a volume of 360 cubic units. Which could be the dimensions, in units, of the prism? Check all that apply

3 by 3 by 40 6 by 6 by 10 2.5 by 12 by 12 3.6 by 10 by 10

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 94,010 bushels of grain, resulting in a crop yield of 170 bushels per acre. To the nearest whole acre, how many acres were harvested?

553

S is a subset within a universal set, U. If S = {x, y, 4, 9, ?), which could describe U?

A. U = {keys on a keyboard}

Galina is finding the area of triangle RST. To do so, she follows the steps in the table. To solve the problem using these steps, what are the dimensions of the rectangle she should draw?

B. 3 units by 4 units

Which three-dimensional figure has the greatest number of faces?

B. octagonal pyramid

A cylinder has a radius of 1 inch and height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.

C.

An oblique prism has a square base and height of 3 centimeters. What is the volume of the prism?

D. 75 cm3

The universal set is the set of rational numbers. S is the set of integers. Which represents S^c?

D. {x|x is a rational non-integer}

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

102

In quadrilateral QRST, < RST measures (5x + 15)o. Angle TQR measures (4x + 3)o. What is the measure of angle RST

105

Evaluate the expression. 4! • 3!

144

Find P(Y|B) from the information in the table. To the nearest tenth, P(Y|B) =

0.4

Rhombus WXYZ is graphed on a coordinate plane. What is the perimeter of the rhombus?

20

The oblique pyramid has a square base. The volume of the pyramid is cm3

5

The volume of the sphere is 500/3 π cubic units.

5

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, a large farm harvested rice from 690 acres of farmland. The crop yield was 7,553 bushels per acre.

5.2 million bushels

Three out of nine students in the computer club are getting prizes for first, second, and third place in a competition. How many ways can first, second, and third place be assigned?

504

How many vertices does a triangular prism have?

6

The chords intersect at point U. What is the value of y?

6

A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches. Which could be the lengths of the diagonals of the rhombus?

6 in. by 8 in.

Use the Venn diagram to calculate probabilities. Which probability is correct?

A.

How do the areas of the parallelograms compare?

A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth

C. 235.5 cubic units

The oblique prism has a rectangular base with a width of 10 units and a length of 13 units. The top base extends 8 units to the right of the bottom base. What is the volume of the prism

1,950 cubic units

A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white?

15%

In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10. If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?

A

Seventy-five percent of the flowers in the arrangement are roses and the rest are tulips. Of the tulips, 50 percent are pink. To the nearest whole percent, what is the probability that a randomly chosen flower from the arrangement is a pink tulip?

A. 13%

Given: Circle O; < A intercepts BC ; <D intercepts BC Prove: <A congruent <D Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Number 2 and 3 reasons are missing.

A. inscribed angles theorem

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

B.

The two-way table shows the ages of the players on different soccer teams. Which statement is true?

C. The probability that a randomly selected player on Team C is 10 years old is .

The corner of a rectangle is cut, creating a right trapezoid. What is the value of x?

D. 135o

A number cube has faces numbered 1 to 6. What is true about rolling the number cube one time? Check all that apply.

S = {1, 2, 3, 4, 5, 6} If A is a subset of S, A could be {5, 6}. If a subset A represents the complement of rolling a 5, its sample space is A = {1, 2, 3, 4, 6}.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is pir^2/4r^2 or pi/4 Since the area of the circle is pi/4 the area of the square, the volume of the cylinder equals

D.

Jasmine rolls a number cube 72 times. The number 2 is rolled 13 times and the number 3 is rolled nine times. To the nearest whole percent, what is the experimental probability of rolling a 2 or 3?

D. 31%

Which shape has a vertex that is also an apex?

D. pyramid

A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. The cross section can be which of these shapes? Check all that apply.

square triangle trapezoid

The pentagonal prism has a perpendicular distance of 14 units between the bases. The volume of the prism is 840 cubic units. What is the perimeter of the base?

30 units

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs. What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD? Express your answer in decimal form, rounded to the nearest hundredth.

0.07

A survey finds that 48% of people identify themselves as fans of professional football, 12% as fans of car racing, and 9% as fans of both professional football and car racing. Let event F be choosing a person who is a fan of professional football and let event C be choosing a person who is a fan of car racing. Which statements are true? Check all that apply.

1. P(F|C) = 0.75 3. P(C∩F) = 0.09 4. P(C∩F) = P(F∩C)

The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots. What is the probability of a customer buying carrots?

10

What is the volume of the cone? Use π ≈ 3.14.

12.56 cubic units

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen?

120

In the Venn diagram, consider U = {students in 10th grade at Lee High School}. The diagram shows the electives chosen by the students in the 10th grade. How many student chose to participate in the painting class?

17

A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver's licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver's licenses and take the bus to school every day. To the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a driver's license?

17%

The weather report states that the probability it will rain on Wednesday is 30 percent and the probability that it will rain on Saturday is 60 percent. What is the probability that it will rain on Wednesday and on Saturday?

18%

What is the volume of the right rectangular prism?

240

Twenty-two percent of the large pieces of mail that Rachel received this week were magazines and the rest were catalogs. Of the catalogs, 36 percent were for clothing. To the nearest whole percent, what is the probability that a randomly chosen large piece of Rachel's mail was a clothing catalog?

28%

The volume of the triangular prism is 54 cubic units. What is the value of x?

3

An oblique prism has a base area of 3x2 square units. What expression represents the volume of the prism, in cubic units?

36x2

Which polygon is a convex heptagon?

A

All freshmen, sophomores, juniors, and seniors attended a high school assembly. The total student attendance is shown in the table. Twice during the assembly, a student is chosen at random to assist with the presentation. After the first student has finished assisting, the student returns to the group and can be chosen a second time. What is the probability that the first student chosen is a senior and the second student chosen is a sophomore?

A. 11/320

Lori downloaded all the pictures she took at Rita's wedding into a single computer folder. She took 86 of the 134 pictures with her camera and the remainder of them with her cell phone. Of the pictures Lori took with her cell phone, one out of every five was blurry. To the nearest whole percent, what is the probability that when she opens a random picture from the computer folder, it will be a blurry picture she took with her cell phone?

A. 7%

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class. Which statement is true about whether A and B are independent events?

A. A and B are independent events because P(A∣B) = P(A).

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference. Which choice represents the sample space, S, for this event?

A. S = {ABC, ABD, ACD, BCD}

Figure ABCD is a square. Prove BD ≅ AC. What is the missing reason in the proof? 4. AB ≅ BC ≅ CD ≅ DA | Reason?

A. all sides of a square are congruent

Angle G is a circumscribed angle of circle E. What is the measure of angle G, in terms of x?

A. x° + x°

Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?

B.

The two-way table shows the number of books of each type in Eliza's home. What is the probability that a randomly selected reference book is hardcover?

B. 0.4

A solid right pyramid has a square base with an edge length of s units and a height of h units Which expression represents the volume of the pyramid?

B. 1/3 s^2h units3

The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. What is the probability that a person chosen at random from this group has brown or green eyes?

B. 13/25

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram

B. 4 cm and 7 cm

If events A and B are independent, what must be true?

B. P(A|B) = P(A)

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

B. rectangle

A parabola has a vertex at the origin. The focus of the parabola is located at (-2,0). Which is the equation for the directrix related to the parabola?

B. x = 2

The spinner is equally likely to land on any of the five sections. What is the probability that the spinner lands on an even number or on the unshaded section?

C.

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. What is the probability that his model rocket has landed in a grassy area?

C. 0.4

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

C. 102°

Points D, E, and F are on circle C and EF ≅ DF. What is the measure of ∠CDF?

C. 26°

Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Which number is missing from the two-way table?

C. 517

Which sets can be represented using the Venn diagram below?

C. A = {animals}; B = {mammals}

Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item. Which statement is true about whether A and B are independent events?

C. A and B are not independent events because P(A∣B) ≠ P(A).

Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel. For the events "shower gel" and "scented" to be independent, what must be shown to be true?

C. Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel. For the events "shower gel" and "scented" to be independent, what must be shown to be true?

Miriam is visiting five friends in her neighborhood, Louise, Mike, Nicole, Oscar, and Pascal. In each arrangement below, the first initial of each person's name represents that person's position as he or she is visited by Miriam. Which shows all the outcomes for this event if she visits with Nicole first and Louise last?

C. NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML

The angle measures of quadrilateral RSTU are shown. m∠R = (2x)° m∠S = (3x - 35)° m∠T = (x + 35)° The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

C. No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

Dayshawn can choose two of his four t-shirts to take on a weekend trip. If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, S, for the event?

C. S = {AB, AC, AD, BC, BD, CD}

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners?

C. S = {FGI, FIG, GFI, GIF, IFG, IGF}

An oblique square prism is shown. Which expression represents the volume of the prism?

C. x^2(x - 2) cubic units

Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them?

D.

The two-way table shows the number of houses on the market in the Castillos' price range. What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?

D. 0.8

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?

D. 38.2 m

A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

D. 5/12

A bag contains eleven equally sized marbles, which are numbered. What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?

D. 6/11

A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug. To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers

D. 86.7%

Which statement is true about whether C and Y are independent events?

D. C and Y are not independent events because P(C∣Y) ≠ P(C).

Consider the following sets. U = {all triangles} E = {x|x ∈ U and x is equilateral} I = {x|x ∈ U and x is isosceles} S = {x|x ∈ U and x is scalene} A = {x|x ∈ U and x is acute} O = {x|x ∈ U and x is obtuse} R = {x|x ∈ U and x is right} Which is a subset of I?

E

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile. How many deer live in the county? Round to the nearest whole number, if necessary.

5852

What is the measure of each exterior angle of a regular hexagon?

60

The volume of a solid right pyramid with a square base is V units3 and the length of the base edge is y units Which expression represents the height of the pyramid?

A.

Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram. Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie?

A.

Information about the students at Jackson High School is shown in the table. Which statement must be true?

A. Out of the 352 eleventh graders at the school, 173 of them are girls.

A solid right pyramid has a square base with an edge length of s units and a height of h units. Which expression represents the volume of the pyramid

B.

For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people who chose chicken as the main dish, 18 wanted potatoes. Of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. A total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish. Which two-way table correctly displays this data?

B.

Which circle has a central angle that measures 40°?

B.

A survey asked about the number of people who eat breakfast almost every day (B) and the number of people who buy cereal at least once a month (C). The results of the survey are shown in the Venn diagram. Given that a randomly chosen person eats breakfast almost everyday, what is the probability that the person also buys cereal at least once a month?

C.

Nadia's bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?

C.

A fast-food restaurant kept information about the drinks that were ordered along with the different-sized kids' meals, as shown in the table. Which statements are true? Check all that apply.

Milk was requested for 16 of the large-sized meal orders. Sixty-three of the orders of soda came with a regular-sized meal. A total of 124 large-sized meals were ordered.

Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY. The area of BXYC is 71.5 square units. What is the area of ABCD?

143 square units

A right cylinder has a radius of 2 units and height of 5 units. What is the volume of the cylinder? Round to the nearest tenth.

62.8 cubic units

The height of a right rectangular prism is three times the width of the base. The length of the base is twice the width. Which expression represents the volume of the prism in terms of w, the width of the base?

6w3 cubic units

Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair. Their names are placed in a hat, and four names are chosen at random to decide who attends the fair. What is the theoretical probability that Chandra will be chosen as one of the science fair participants?

80%

The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?

A.

The four diagonals of a cube are drawn to create 6 square pyramids with the same base and height. The volume of the cube is (b)(b)(b). The height of each pyramid is h. Therefore, the volume of one pyramid must equal one-sixth the volume of the cube, or

A.

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

A.

Students in a class were surveyed about the number of children in their families. The results of the survey are shown in the table. Two surveys are chosen at random from the group of surveys. After the first survey is chosen, it is returned to the stack and can be chosen a second time. What is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family?

A. 1/50

In the Venn diagram, consider U = {whole numbers 1 - 100}. Let A represent numbers that are perfect squares, B represent numbers that are perfect cubes, and C represent numbers that are perfect fourths. Which number(s) satisfy A ∩ C?

B. 1, 16, 81

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday's lunch. What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

B. 20%

A bag contains eleven equally sized marbles, which are numbered. Two marbles are chosen at random and replaced after each selection. What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number?

B. 24/121

Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is foot by foot and costs $0.45 per tile. The rectangular tile is 2 feet by foot and costs $0.80 per tile.

B. She should choose the rectangular tiles because the total cost will be $8 less.

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. What is the volume of material he must purchase

D. 8ft^3

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?

D. A^c = {x|x ∈ U and is an even positive integer}

Find each population density, to the nearest hundredth. Which statement is true?

D. Dish C and Dish D have approximately the same population density.

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?

D. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president. Which choice represents the sample space, S, for this event?

D. S = {PQ, QP, PR, RP, QR, RQ}

Two different cross sections are taken parallel to the base of a three-dimensional figure. The two cross sections are the same shape, but are not congruent. Which could be the three-dimensional figure? Check all that apply

cone triangular pyramid square pyramid

Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus?

A. 24 square units

A right triangular prism is constructed so that its height is equal to the leg length of the base. What expression represents the volume of the prism, in cubic units?

1/2 x^3

Holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the house. If order does not matter, in how many ways can she choose the plants for the front of the house?

36

Consider U = {x|x is a negative real number}. Which is an empty set?

B. {x|x ∈ U and x has a negative square root}

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units. What is BC, the height of the pyramid?

C.

The oblique pyramid has a square base with an edge length of 5 cm. The height of the pyramid is 7 cm. What is the volume of the pyramid

C.

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws. Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU?

C. (18 + 4)

Consider U = {x|x is a real number}. A = {x|x ∈ U and x + 2 > 10} B = {x|x ∈ U and 2x > 10} Which statements are true?

C. 8 ∉ A; 8 ∈ B

A city's bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized. The population of City A, in Texas, is 29,455 and covers an area of 19.42 mi2. The population of City B, in Alabama, is 34,890 and covers an area of 25.4 mi2. Which city's residents are more likely to use public buses? Explain.

D. The residents of City A are more likely to use public transportation because the city has the highest population density.

Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups. Which statements about the situation are true? Check all that apply.

Set X has 10 possible groupings. Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} There are three ways to form a group if persons A and C must be in it.

Fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers. Let the five towels be represented by A,B,C,D, and E. If Fiona chooses towel A for herself, which statements about the possible outcomes for her brothers' towels are true? Check all that apply.

She has four choices for the first brother's towel and three choices for the second brother's towel. ABC, ABD, ABE, ACD, ACE, and ADE are the possible outcomes. If Fiona did not choose towel A for herself, there would be more outcomes.

An oblique prism is created using rhombuses with edge lengths of 25 units. The area of one rhombus is 600 square units. The perpendicular distance between the bases is 24 units. What is the volume of the prism?

14,400 cubic units

Consider the following sets. U = {ordered pairs on a coordinate plane} A = {ordered pair solutions to y = x} B = {ordered pair solutions to y = 2x} Which ordered pair satisfies A ∩ B?

A. (0, 0)

A briefcase has a three-digit lock code that does not include zero as a digit. What is the probability that the lock code consists of all even digits if the same digit is not used more than once in the lock code?

A. 24 out of 504

A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?

B.

A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. Which statements are true about Yuri's experiment? Check all that apply.

The theoretical probability of spinning any one of the five colors is 20%. The theoretical probability of spinning green is equal to the experimental probability of spinning green. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 9,396 bushels of soybeans, resulting in a crop yield of 40.5 bushels per acre. To the nearest whole acre, how many acres were harvested?

232

Helena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning. In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon?

24

What is the area of triangle RST?

9

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?

A.

Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking. What subset, A, represents the complement of the event in which Joe plays in the first match?

A. A = {KL}

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75. Which packaging should the company use to minimize cost? Explain.

A. The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.

A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is pir^2/4r^2 or pi/4 Since the area of the circle is pi/4 the area of the square, the volume of the cone equals

B.

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches

B.

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the height of the triangular base of the pyramid?

B.

The height of a cylinder is equal to the diameter of the base. What expression represents the volume of the cylinder, in cubic units?

B.

What is the difference of the volumes of the two oblique pyramids, both of which have square bases? Round the volumes to the nearest tenth of a centimeter.

B.

What is the approximate base area of the resulting three-dimensional figure?

B. 113 sq. cm

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag. What is the probability that two vowels are chosen?

B. 25/144

A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindrical container can hold 126 beads. The wooden container costs the company $0.70, while the plastic container costs $0.40. Which container should the company use to minimize cost? Explain.

B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

Which statement regarding these four states is true?

B. The state with the second lowest population has the lowest population density.

April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs. What is the complement of April choosing five pop CD

B. choosing five CDs where all of them are not pop

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units. Which expression represents the volume of the prism, in cubic units?

B. x^3 + 3x^2

The rectangle shown is rotated about line k. What is the approximate base area of the resulting figure?

C. 79 sq. in.

The table shows information about Town A in Illinois and Town B in Florida. If the two towns have the same population density, which must also be true?

C. Town B has a population of approximately 5,138.

The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the rotation and what is the approximate circumference of the base?

C. a cone with a base circumference of about 63 mm

The area of rectangle ABDE is 270 square inches. The rectangle is rotated about a line that passes through points C and F. Which best describes the resulting three-dimensional shape?

C. a cylinder with a base radius of 9 inches

Which events are independent? Check all that apply.

Roll a number cube, and then roll the same number cube again. Flip a coin, and then flip the coin a second time. Draw a card from a deck, replace it, and then draw a second card.