Algebra
A storage tank contains 14k^6 gallons of water. If 6k^6 gallons are pumped out, this expression represents the volume of water, in gallons, that remains in the tank.
What is 8k^6 gallons?
A triangular garden has side lengths of 15x^3 feet, 6x^3 feet, and 11x^2 feet. This is the perimeter, in feet, of the garden?
What is 21x^3 + 11x^2?
A commuter in a major city uses a pre-paid transit card to pay for train fares. The card initially has a balance of $150. Each round trip on the train costs $6.25. If the commuter only uses the card for these train trips, after how many round trips will the balance on the card be exactly $25?
What is 20?
A local nature reserve had an initial population of 12,000 birds. Each year, the population is estimated to be 90% of the population from the previous year. Which of the following function types best models the relationship between the bird population and the number of years since the initial population was measured?
Decreasing/Increasing Exponential/Linear
What is decreasing exponential?
This infinite, non-repeating number is derived by dividing a circle's circumference by its diameter.
What is pi?
𝑓(𝑥) = 12x^2 − 5𝑥 + 8 and 𝑔(𝑥) = 4x^2 + 9x − 15. This is (f+g)(x).
What is 16x^2 + 4x - 7?
A gardener is designing a rectangular herb garden that measures 7 feet by 9 feet. The gardener plans to place a straight wooden divider along the diagonal of the garden from one corner to the opposite corner. This is the length, in feet, of this wooden divider.
What is sqrt(130)?
A service technician's total earnings y, in dollars, for a job lasting x hours is given by the equation y = 25x−100, where 25x represents the labor charges and 100 is a one-time discount for a new customer. If the labor charges for a certain job where 25x=750, this is the value of y.
What is 650?
A small town has 500 households. A random sample of these households was surveyed to determine whether they would support the construction of a new community garden. Of those surveyed, 18% responded that they would support the construction of the garden. Based on this survey, this is the best estimate of the total number of households in the town that would support the construction of the garden.
What is 90?
Before creating the telephone, he dedicated his life to teaching the deaf, which directly inspired his acoustic research.
Who was Alexander Graham Bell?
A rectangular carpet has an area, in square feet, that can be represented by x^2 + 4x − 96, where x>8. Which of the following is an equivalent expression for the area of the carpet that displays the dimensions of the carpet as constants?
What is (x+12)(x-8)?
A right triangular plot of land is represented by triangle ABC on a map. The actual plot of land is represented by triangle DEF, which is similar to triangle ABC, where vertices A,B, and 𝐶 on the map correspond to vertices D,E, and F of the actual plot, respectively. The side lengths of the actual plot of land are 12 times the side lengths of the corresponding sides on the map. If the measure of angle A is 54 degrees , this is the measure of angle D?
What is 54 degrees?
A local theater group is selling tickets for a community play to raise money for new equipment. The group's goal is to collect exactly 1,200 dollars in total ticket sales. Adult tickets cost 15 dollars each, and student tickets cost 8 dollars each. This equation represents the number of adult tickets, x, and student tickets,y, the theater group must sell to meet their goal.
What is 15x + 8y = 1200?
A local print shop recorded the number of custom t-shirts ordered each day for 9 consecutive days. The list shows the number of orders received each 12, 25, 18, 46, 15, 27, 20, 14, 21. This is the median number of custom t-shirts ordered per day for these 9 days?
What is 20?
Famously used in architecture and nature, this ratio equals roughly 1.618 and is represented by the Greek letter Phi.
What is the Golden Ratio?
A function g is defined by g(x)=(256)^(x/4) . The function can also be written as g(x)=(1− n/100)^x , where n is a constant. This is the value of n.
What is -300? (Q Edited for no calculators)
Point G is the center of the unit circle. Point F is at (0,1) and point H is at ( −2sqrt(2) ,−2sqrt(2) ). This is one of the possible positive measurements of ∠FGH, in radians.
What is 3/4 pi or 5/4 pi
A projectile is launched vertically from a platform, and its height above the ground, in meters, ℎ h, after 𝑡 t seconds is modeled by ℎ(𝑡) = − 5𝑡^2 + 40𝑡 + 12.
If h(t) is graphed in the ty-plane, which of the following best describes the real-life meaning of the positive t-intercept of the graph?
What is when the projectile hits the ground?
A sample of 10th-grade students was selected at random from all 10th graders at a school. Based on the sample, it is estimated that the proportion of 10th graders who participate in at least one school club is 52% with a margin of error of 4%.
This/these of the following conclusion(s) is/are appropriate.
I. It is plausible that the proportion of all 10th graders at the school who participate in at least one school club is 49%. II. It is not possible that the proportion of all 10th graders at the school who participate in at least one school club is 57%. III. If the sample size is increased, the margin of error will likely decrease.
What is I and III?
Discovered by an Italian mathematician modeling rabbit populations, this sequence adds the two preceding numbers to get the next.
What is the Fibonacci sequence?
(48x+144)/8 − 15c = d(x−2) In that equation, c and d are constants and c>0. If the equation has infinitely many solutions, this is the value of c.
What is 450?
A rectangular billboard is positioned inside a circular spotlight's beam such that the four corners of the billboard lie on the circumference of the circular beam. The length of the billboard is 4/5 of the diameter of the circular beam. If the area of the billboard is 432 square feet, this is the diameter, in feet, of the circular beam.
What is 30 feet?
During a deep dive, a whale starts at the surface at t=0 minutes and returns to the surface at t=16 minutes. Its depth below the surface, in meters, is modeled by a quadratic function g(t) that has a maximum depth of 315.2 meters at t=8 minutes. According to the model, this is the whale’s depth, to the nearest meter, at t=10 minutes?
What is 296 meters?
Data set X consists of the lengths of 20 wooden beams and has a mean of 80 inches. Data set Y consists of the lengths of 30 wooden beams and has a mean of 90 inches. Data set Z consists of the lengths of the 50 wooden beams from data sets X and Y. This is the mean, in inches, of data set Z?
What is 86?
Moving beyond acceleration, physicists named the second, third, and fourth derivatives of acceleration by these three Rice Krispies mascots.
Who are Snap, Crackle, and Pop?