Math for george
A diameter of a circle has endpoints of (1, 4) and (5, 4). What is the equation of this circle?
(x - 3)² + (y-4)² = 4
What is the standard form of the equation of a circle with center (3, - 2) and radius 4?
(x-3)² + (y+2)² = 16
What is the equation of the circle in the diagram?
(x-3)² + (y-4)² = 4
Which equation describes a circle with center (4, -7) and radius 9?
(x-4)² + (y+7)² = 81
What is the equation of a hyperbola with center (4, 2), vertex (0, 2), and focus (9, 2)?
(x-4)²/16 - (y-2)²/9 = 1
The foci of an ellipse are located at (4, -3) and (4, 7). The major axis has a length of 16 units. Which of the following is an equation of the ellipse?
(x-4)²/39 + (y-2)²/64 = 1
A parabola has a focus of (4, 2) and a directrix of x= -2 Which equation can represent this parabola?
(y-2)² = 12(x-1)
class surveys 50 high school students and 50 elementary students to determine whether students take baths or showers. For which of the following two-way tables would the results indicate that being a high school student and taking baths are independent? Select all that apply.
- 25, 25, 25, 25 - 50, 0, 50, 0
A certain company requires at least a two-year college degree (called an associate's degree) as a condition of employment. The human resources manager looked through all of the personnel files to determine the highest degree employees at the company had. The results are shown below. Select two choices that are true about the highest degree that the employees received.
- If an employee is female, the probability that her highest degree is associate's degree is 24/68 - If an employee is male, the probability that his highest degree is an associate's degree is 20/54.
A researcher surveys 100 people that tasted two new flavors of yogurt to find their taste preferences. Each person surveyed tasted two yogurts. One was labeled A, and the other was labeled B. The student's results are represented in the two-way frequency table below. Which of the following statements are correct interpretations of the information represented in the two-way frequency table? Select THREE that apply.
- Only 50 people liked A. - Only 75 people liked B - Only 15 people did not like A or B
A hyperbola has foci (2,14) and (2,-12). One of the vertices of the hyperbola is located at (2,6). The equation of the hyperbola can be expressed as (y-P)²/ R² - (x-Q)²/3² = 1, where P, Q, R, and S are real numbers. Select each true statement regarding this equation.
- The Value of P is 1 and the value of Q is 2. - The value of R is 5 and the value of S is 12.
Brad is working on the landscaping around his house. He notices that working on his landscaping and whether or not it is raining are independent events. He also notices that he has been working on his landscaping for 2 out of every 5 days during the past month. Select TWO statements that may be true.
- The chance that Brad will work on his landscaping today is the same whether or not it is raining. - If it rained 10 days last month, Brad worked on his landscaping for 4 of those days
Marcos likes to run. However, during the next week, there is projected to be a lot of snow in his town. Select two choices that show that Marcos going for a run and snow falling in Marcos's town are independent events.
- The probability of Marcos running is the same whether or not it snows. - Marcos's decision to go running or not go running does not change if it is snowing.
Eve surveyed 48 students about whether or not they have a pet and what type of music they prefer from three genres. The table shows the results of her survey. Select THREE statements that are true.
- The probability that a student prefers rock music given that they have a pet is 6/13 - If a student prefers pop music, then there is approximately a 55% chance a student does not have a pet - The probability that a student prefers pop music given that they have a pet is less than the probability that a student prefers rock music given that they do not have a pet.
A group of 60 students are surveyed on whether or not they like baseball and whether or not they like the color green. The results of the survey are shown in the table below. Based on the data in the two-way table, which statements are true? Select THREE that apply.
- The probability that the students likes the color green given that the student likes baseball is equal to the probability that the student likes the color green - The events "A student likes the color green" and "A student likes baseball" are independent events - The probability that a student likes the color green is 0.25 and the probability that a student likes baseball is 0.8.
Consider right triangle ABC shown below. Which trigonometric ratios are equivalent to 5/13? Select ALL that apply.
- cos A - sin C
Right triangle PQR is shown. Which trigonometric ratios are equivalent to 3/5? Select ALL that apply.
- cos P - sin R
The table below shows the types of goldfish in an aquarium at a pet store. Bill uses a net to catch a random fish from the aquarium. Which of these statements are true? Select all that apply.
- if Bill catches a fish with a plain tail, it has a 7/9 probability of being orange - if Bill catches a fish with a fancy tail, it has a 4/11 probability of being orange
A group of people are playing a game where they have to spin two spinners. To win the game, one spinner has to land on a certain number, and the other spinner has to land on a certain color. Each of the spinners has 6 equal areas that the arrow could land on. The first spinner has the numbers 1 through 6 in the areas, and the second spinner has the colors red, yellow, green, blue, purple, and orange. Select all of the choices that give the best chance of winning.
- one spinner landing on the numbers 1, 2, 3, 4, or 6 and the other spinner landing on the color red - one spinner landing on the number 1, and the other spinner landing on the colors red, yellow, green, blue, or purple - one spinner landing on the number 4, and the other spinner landing on the colors red, yellow, green, blue or purple.
Consider this right triangle. Select all trigonometric functions that are equivalent to the ratio x/y
- sin E - cos D
Three lettered balls are drawn at random from a jar containing six balls bearing the letters A - F. What is the probability that the three balls drawn will be B, D, F in that order?
1 in 120
If a man is thinking of a 5 digit number composed from the single digits 1,2,3,4,5,6 and 7 with each single digit used no more than once, what is the probability he is thinking of the number 43,561?
1 in 2,520
Jimmy rolls three dice at the same time. What is the probability all three dice will show the same number?
1/216
Jessica and Kyle each bought one of the 250 raffle tickets sold at the county fair. If two tickets will be drawn and awarded prizes, what is the probability that both Jessica and Kyle hold winning tickets?
1/31,125
Deb placed the seven tiles below into a bag. If Deb randomly draws the seven tiles from the bag, what is the probability she will draw them from the bag in alphabetical order?
1/5040
In a paper bag, 6 of the 18 marbles are blue. In a cloth bag, 1 of the 18 marbles is blue. If Stanley chooses one marble from each bag at random, what is the probability he will choose a blue marble from the paper bag and a blue marble from the cloth bag?
1/54
Steven and Emily are among 14 students in the math club. The club's advisor will randomly select two of the students to recruit new members at the school's extracurricular activity fair. What is the probability Steven and Emily will be the two students chosen?
1/91
At a school carnival, the math club hosts a booth for games. One of the games uses the spinner below, where each numbered section is of the same size. A student who correctly guesses the sum of the numbers that result when the spinner is spun twice receives a prize. Which number should a student guess as the sum to have the GREATEST chance of winning a prize?
10
Susan and Jake are two of seven people entered in a drawing to win a free pie. The bakery owner will randomly select five people to each win a pie. What is the probability that both Susan and Jake will win pies?
10/21
In the diagram below, mFG = 86° and m HKJ = 48°
10°
A grain silo is shaped like a cylinder with a height of 24 feet and a diameter of 10 feet. A farmer wishes to determine how many cubic feet of grain could fit in the silo. What is the maximum amount of cubic feet of grain that the silo could hold?
1884 cubic feet
In the figure below, circle O has a central angle of 120°. What is the area of the shaded sector of circle O in terms of r, the radius? Leave your answer in terms of pi.
2/3πr² square units
A triangular pond in the center of a shopping mall is sketched below. Which of these best represents the distance from A to C?
21.5 ft
A manufacturer is designing a new type of bowling ball. The bowling ball will have a weighted spherical core and a lighter outer layer of plastic around the core. The diameter of the entire bowling ball is 8.6 inches. The diameter of the weighted core is 5.66 inches. What is the volume of plastic the manufacturer will need to create the outer layer of the bowling ball?
238 cubic inches
What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?
24 cubic feet
A bottling company makes decorative bottles and ships them to their customers. Each bottle has a height of 13 inches and a radius of 2.5 inches. The manufacturer places each bottle in cylinder packaging and adds cushioning to the insides of the cylinder. The cushioning is an inch thick on each side of the bottle. If the height of the cylinder is the same as the height of the bottle, what is the volume of the cylinder used to package the bottles? (Round to the nearest whole number. Use pi= 3.14.)
255 in³
A spherical-shaped ball that has a radius of 4 inches is currently deflated. How much air would it take to completely inflate the ball?
256π/3 in³
Jenna is getting a new cell phone number. What is the probability that NONE of the ten digits will be a 3?
3,486,784,401 / 10,000,000,000
Of 8 dogs in a kennel, 5 are male and 3 are female. If a trainer randomly chooses two dogs for a walk, what is the probability he will choose two females?
3/28
Marti is filling a 10-inch diameter ball with sand to make a medicine ball that can be used for exercising. To determine if the medicine ball will be too heavy after it is completely full of sand, she did some research and found that there is approximately 100 pounds of sand per cubic foot. How heavy will the medicine ball be after it is filled with sand, rounded to the nearest pound?
30 pounds
If arc HJ =66°, what is m<HIJ?
33°
You are standing 16 feet from the center of a circular swimming pool. The distance from you to a point of tangency is 25 feet. What is the approximate DIAMETER of the pool?
38 ft
The radius of Earth is 20,903,520 feet. Mark wants to make a model globe of Earth that is 70,000,000 of its actual size. What would be the volume of Mark's globe? (Round to the nearest tenth. Use 1 = 3. 14.)
38.2 ft³
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground?
39.0°
If mAB = 30° and mCD = 110°, find measure of angle E
40°
A bird feeder has a diameter of 3 inches and is composed of a cylinder and a cone. A diagram of the bird feeder is shown below. What is the volume of this bird feeder, to the nearest tenth of a cubic inch?
47.1
Marcus has been working on a large rubber band ball. When Marcus first measured the ball it had a diameter of 5 inches. Over the course of one year Marcus continued to add more rubber bands to the ball. After one year Marcus measured the rubber band ball, and it had a diameter of 15 inches. How much volume was added on to the rubber band ball? Round your answer to the nearest tenth.
541.7π inches ³
In circle P below, LOPM = 124° and line segments ON and MN are tangents to the circle. What is the measure of LONM?
56°
The ornament below is composed of two congruent square pyramids. Each square pyramid has base side lengths of 2 inches and a helght of 2.5 Inches. What is the volume, in cubic inches, of the ornament?
6 2/3
Darius has a cylindrical can that is completely full of sparkling water. He also has an empty cone-shaped paper cup. The height and radius of the can and cup are shown. Darius pours sparkling water from the can into the paper cup until it is completely full. Approximately, how many centimeters high is the sparkling water left in the can?
6.2 cm
A student has a box containing circular and rectangular shapes, as shown below. The student reaches in and randomly selects 2 shapes from the box one after the other, without replacing the first shape before selecting the second shape. The probability that the two shapes selected are both circles can be determined by which of the following expressions?
6/11 x 5/10
Triangle ABC is inscribed in a circle. The measure of arc AB is 126 degrees. What is the measure of Angle C?
63°
If arc WX = 40' and arc YZ = 92° find measurement of angle 3
66°
If the measurement of arc WX = 40 degrees and the measurement of arc YZ = 92 degrees, find the measurement of angle 3.
66°
Look at the tree shown in the diagram below. If θ = π/3, what is the height of the tree rounded to the nearest tenth of a foot?
69.3 feet
Find the area of the shaded sector. Round your answer to the nearest tenth. Use 3.14 for pi.
70.7 m²
Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof. What is the measure of the angle formed by the ladder and the ground?
71.8°
Two chords cross through a circle and intercept one another at a point on the circumference of the circle, forming an inscribed angle. The measure of the intercepted arc of the angle is 142°. What is the measure of the inscribed angle?
71°
A cylinder has a height of 5 centimeters and a radius of 2.3 centimeters. What is the volume of this cylinder?
83.10 cm³
A round basket designed to hold a potted plant is hanging on a porch as shown in the figure below. If the radius of the opening of the basket is 4 inches, what is the value of x to the nearest tenth of a degree?
83.6°
In a plastic bag, 12 of the 25 marbles are yellow. In a cloth bag, 7 of the 25 marbles are yellow. If John randomly draws one marble from each bag, what is the probability that they are both yellow?
84/625
Two airplanes leave an airport at the same time, traveling on courses that have an angle of 125° between them. The diagram below shows the courses of plane A and plane B. If each plane travels 500 miles, how far apart are they to the nearest mile?
887 miles
The ornament below is composed of two congruent cones. Each cone has a base radius of 2 inches and a height of 3.6 inches. What is the volume, in cubic inches, of the ornament?
9.6π
In a right triangle, the tangent of angle A iS iz and the cosine of angle A is 15. Based on these values, what is the sine of angle A?
9/15
On a certain street of 50 houses, 20 houses have a 2-car garage, 10 have a 1-car garage, and 20 do not have a garage. If two houses are chosen at random, what is the probability that both houses have a garage?
9/25
Sandy is conducting a survey to determine the percent of students in her school that have been to the zoo or the museum located in her town. She finds that 40% of her classmates have been to the zoo, 30% have been to the museum, and 20% have been to the museum and the zoo. What is the probability that a randomly selected student in Sandy's school has been to either the museum or the zoo in her town?
90%
Aubrey marks a triangular play area in the back corner of her yard. The play area is represented below. Which of these best represents the measure of the largest angle of the play area?
92.2°
The Thompson Family made a circular cheesecake with a radius of 4 inches for dessert. The area of the cheesecake can be found by using the formula A = 7 • r2 or A = 1 • 42. Mrs. Thompson cut out a piece that has a central angle of 39°, as shown below. What is the formula for the area of the piece that Mrs. Thompson cut out?
A = 39/360 * π * 4²
The figure below shows circle O. Which formula can be used to determine the area of the sector bounded by central angle MON?
Asec = x*πr²/360
The diagram below represents a generic right triangle. Which statement BEST explains why the sine of an acute angle is equal to the cosine of the angle's complement?
Both sin A and cos B are equal to a/c
Jaimie takes a survey of his class to determine if having brown hair is independent of wearing a watch. There are 21 students in the class. He draws the Venn diagram, as shown above, to represent the information he has gathered. In his diagram BH represents the students that have brown hair and Wrepresents the students that are wearing a watch. Is having brown hair independent of wearing a watch?
Brown hair is independent of wearing a watch because P(W|BH) is not equal to P(W)
A spinner that consists of a dial and an arrow is used in a board game to indicate the number of spaces a player is allowed to move. When the dial is spun, there are four possible numbers the arrow can land on: 1, 2, 3 and 4, as shown above. When a player lands on a certain space on the game board they are allowed to spin the dial twice and move the total number of spaces as indicated by the sum of the numbers resulting from each spin. Each spin of the dial is a random event. After spinning the dial twice, one of the players moves a total of 5 spaces. Which statement correctly describes the event that occurred?
It was just as likely as any possible outcome
The two right triangles below both have an interior angle that measures 41°. Which statement BEST explains why the value of sin 41° is the same in both triangles?
The Triangles are similar because they have two interior angles in common. The proportions of corresponding sides of similar triangles are equal.
The equation below describes a circle. x² + 14x + y2 = 70
The center is (-7, 0) and the radius is √119.
The equation below describes a circle. x² - 10x + y² + 4y = 20 What are the center and radius of the circle.
The center is (5,-2) and the radius is 7
A circle drawn on a coordinate plane has the equation x² + y² + 8x - 8y + 24 = 0. Select each true statement regarding this circle.
The circle has a radius of 2√2 units The center of the circle is located at the point (-4,4) The equation of the circle can be written as (x+4)² + (y-4)²=8
Question: 56 A square pyramid has a height of 12 feet and a base with a length of 5 feet. In order to double the volume of this pyramid, which measurements could be changed? Select all that apply.
The length of the base could be increased to 10 feet The height of the pyramid could be increased to 24 feet
The ingredients of five different smoothies are shown below. Smoothie #1: pineapple, banana, strawberry, apple Smoothie #2: banana, strawberry, orange Smoothie #3: pineapple, banana, strawberry Smoothie #4: strawberry, orange, blueberry Smoothie #5: pineapple, banana, orange, mango A customer picks a smoothie at random. Which probability and interpretation is correct?
The probability that the customer chooses a smoothie made with blueberries or oranges is 3/5. This can be represented as 3/5 + 1/5 - 1/5
A biologist is studying species of lizards that live in the desert. He wants to determine how the temperature affects the number of each species he observes. The two-way table shows his data.
The probability that the species observed is a western band gecko and the temperature is above 100°F is equal to the product of each individual event.
A circle is graphed on a coordinate plane. The circle has center (-2,4) and has a radius of 5. The equation of the circle can be expressed as x² + y² + Ax + By + C = 0, where A, B, and C are integers. Select each true statement.
The value of B is -8
A group of people are playing a game where they have to spin two spinners. To win the game, one spinner has to land on a certain number, and the other spinner has to land on a certain color. Each of the spinners has 6 equal areas that the arrow could land on. The first spinner has the numbers 1 through 6 in the areas, and the second spinner has the colors red, yellow, green, blue, purple, and orange. Select all of the choices that give the best chance of winning.
a pink, white, or green gumball dropping out when she turns the knob.
Which value below is equivalent to sin 74°?
cos 16°
Right triangle QRS is pictured below. Which equation gives the correct length of side RS?
cos 31° = RS/24.8
Justin was asked to write six different equations based on the triangle below. Four of the six equations that Justin wrote are correct. Which four of the equations are correct?
cos(30) sin(30) cos(60) tan(60)
Consider triangle DEF,shown below, where d is the length of the side opposite D, e is the length of the side opposite <E, and f is the length of the side opposite LF. In triangle DEF, LE= 37°,d = 8 units, and f= 11 units. Which of the following equations represent a correct application of the Law of Cosines which can be used to determine the length of a side in triangle DEF? Select all that apply.
d² = e² + f ²- 2(e)(f)cos(∠D) 121 = 64+e²-(16e)(cos(∠F))
Circle O is shown below. Which of the statements below are correct? Choose all that are correct.
m∠ACB = 44° mAC = 156* mBAC = 58°
Which of the following is the formula for the number of possible permutations of k objects in a set of n objects?
nPk = n! / (n-k)!
Which trigonometry equation about the angles π/3 radians and π/6 radians are true? Choose all that are correct
sin (π/3) = 2 sin (π/6)
Look at the equilateral triangle shown below. Which of these correctly represents the values for sin θ and sin ø
sin θ = √3/2 and sin Ø = 1/2
A flagpole casts a 13-foot shadow on the ground when the sun is at a 68° angle of elevation. Which of the following expressions can be used to determine the height (h), in feet, of the flagpole? (Assume the flagpole is perpendicular to the ground.)
tan 68° = h/13
Based on the figure below, the ratio of x/y is equivalent to which trigonometric function?
tan B
A parabola has a directrix of x = - 1 and a focus of (-3, -2). Select ALL options that represent the equation of the parabola.
x = -1/4(y+2)²-2 x=-1/4y²-y-3
Ben keeps flour in a container shaped like a cylinder. The top of the flour is level, and is 1.5 inches below the top of the container. There are about 14.44 cubic inches In one cup. Which expression represents the number of cups of flour in the container?
x(4²)(11-1.5) / 14.44
What is the equation of an ellipse centered at the origin with a horizontal major axis of length 12 units and with foci at (-4, 0) and (4, 0) ?
x²/36 + y²/20 = 1
Gabriella created a parabola with a directrix of y= -2 and a focus of (-2, 0). Which equation represents the parabola Gabriella created?
y + 1 = 1/4(x+2)²
How many radians are in 1 degree?
π/180
Triangle GIH is similar to triangle KJL. Select the angle whose tangent equals 6/8
∠G
Triangle G/H is similar to triangle KJL. Select ALL angles whose tangent equals 6/8
∠G ∠K
