Measures of Central Tendency
The _______ is the mean of the two middle values in a dataset when there are an even number of values.
Median
In the expression 2x + 3, the number 2 is called the _______________________.
Numerical Coefficient / Coefficient
Simplify: (3x³ + 2x² - 5x + 1) + (2x³ - 4x² + x - 3) - (x³ + 2x² - x + 2) ________________________
4x3 - 4x2 -3x - 4
The formula for the square of a binomial (a + b) is ____________.
a2 + 2ab + b2
The expression x³ - 27 can be factored as (x - 3)(_______________) using the difference of two cubes technique.
x2 + 3x + 9
The mean of the scores 2, 4, 6, ___, and 10 is 6. What is the missing score?
8
The verbal phrase “3 less than twice the number x is 10” can be translated into algebraic expression _________.
2x - 3 = 10
Multiply: (3x² + 2x - 1)(2x² - 4x + 3). _________________________________
6x4 - 8x3 - x2 + 10x - 3
Find the product: (5-y)2
25-10y+y2
Factor completely: x⁴ - 16.
(x - 2)(x + 2)(x2 + 4)
A dataset has 11 values: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, x. If the mean is 12, what is the value of x?
22
"Twice the difference of a number and four, increased by seven" can be translated into the algebraic expression _______________.
2(x - 4) + 7
(x can be any letter)
A company has a total revenue of 6x³ + 12x² + 3x + 1000 and wants to divide it among its three departments. If the division is represented by the polynomial x + 2, what is the polynomial representing the revenue allocated to each department?
6x2 + 3 and a remainder of 994
Find the product: (9+b)(9-b)
81-b2
A rectangular garden has an area given by the polynomial x² + 5x + 6. If the length and width of the garden are represented by the factors of the polynomial, what are the possible dimensions of the garden?
(x + 3)(x + 2)
A company is assessing the performance of its sales team by examining the sales data from 10 representatives. Specifically, 3 representatives each sold 100 units, 2 sold 120 units each, 2 sold 150 units each, 1 sold 200 units, and 2 sold 250 units each. The company intends to evaluate the team’s performance using the mean, median, and mode of these sales figures. These statistical measures will be used to determine the team’s bonus distribution, their ranking within the organization, and to identify the most commonly adopted sales strategy. What is the mean?
154
To add polynomials, we combine _______________________ terms.
similar / like
A company's revenue from selling two products, A and B, is given by the polynomials 3x² + 2x + 1000 and 2x² - 4x + 500, respectively, where x is the number of units sold. If the company sells both products, what is the total revenue polynomial?
5x2 - 2x + 1500
Multiply: 2(x+10) using the binomial formula.
2x+20
A cube-shaped tank has a volume given by the polynomial x³ - 8. If the tank is filled with water, and the volume of water is represented by the factors of the polynomial, what are the possible dimensions of the tank?
(x - 2)(x2 + 2x + 4)
A company is assessing the performance of its sales team by examining the sales data from 10 representatives. Specifically, 3 representatives each sold 100 units, 2 sold 120 units each, 2 sold 150 units each, 1 sold 200 units, and 2 sold 250 units each. The company intends to evaluate the team’s performance using the mean, median, and mode of these sales figures. These statistical measures will be used to determine the team’s bonus distribution, their ranking within the organization, and to identify the most commonly adopted sales strategy. What is the median?
135
When 5x2 – 4x + 5 is subtracted from 10x2 + 4x – 4, the result is _____________________.
5x2+8x-9
A rectangular garden has a length given by the polynomial 2x + 3 and a width given by the polynomial x + 1. What is the polynomial representing the area of the garden and the path?
(2x2 + 5x + 3) square units
Each edge of a block of wood is 2 centimeters more than each edge of a block of copper. Use this information to write an equation modeling the volume of the wooden block.
(x3 + 6x2 + 12x + 8) cubic centimeters
A rectangular canvas picture measures 2 feet by 5 feet. The canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to 180 square feet. Find the uniform dimensions of the frame.
15 feet by 12 feet