What unit of measurement is used to describe how far a set of values are from the mean?
The unit of measurement commonly used to describe how far a set of values are from the mean is called the standard deviation. Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to […]
How to Find the Lateral Surface Area of a Hexagonal Prism
To find the lateral surface area of a hexagonal prism, you will need to follow a straightforward process. A hexagonal prism has two hexagonal bases and six rectangular faces that connect the corresponding sides of the bases. The formula for the lateral surface area (LSA) of a prism is: LSA = Perimeter of the base […]
A Rational Number Can Always Be Written In What Form?
A rational number can always be written in the form of a fraction where both the numerator and the denominator are integers. More formally, it can be expressed as p/q, where p is an integer, q is a non-zero integer, and q ≠ 0. This means that any number that can be expressed in this […]
What is an Exponent?
An exponent is a mathematical notation that indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression 23, the number 2 is the base and the exponent is 3. This means that 2 is multiplied by itself a total of three times: 2 × 2 × […]
Prove that if one angle of a triangle is 90 then the other two add to 90
To prove that if one angle of a triangle is 90 degrees, then the other two angles must add up to 90 degrees, we can use the properties of triangles. We start with the basic fact that the sum of all interior angles in any triangle is always 180 degrees. This is a fundamental property […]
A sequence is defined by the formula fn = 1 + fn-3. If f4 = 22, what is f1?
To solve for f1 in the sequence defined by the formula fn = 1 + fn-3, we start by using the given information that f4 = 22. Using the formula: To find f4, we need f1 since it relies on the previous terms. From the formula, we can express f4 as: f4 = 1 + […]
How to Find the Angles Between Two Vectors?
To find the angle between two vectors, say vector a and vector b, you can use the formula derived from the dot product: cos(θ) = (a • b) / (||a|| ||b||) Where: θ = angle between the vectors a • b = dot product of vectors a and b ||a|| = magnitude (length) of vector […]
What theorem can be used to prove that the two triangles are congruent?
To prove that two triangles are congruent, you can use several theorems, including: SSS (Side-Side-Side) Congruence Theorem: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. SAS (Side-Angle-Side) Congruence Theorem: If two sides and the included angle of one triangle are equal […]
What is the 7th term of the geometric sequence where a1 is 1024 and a4 is 16?
To find the 7th term of the geometric sequence, we first need to determine the common ratio of the sequence. In a geometric sequence, each term can be represented as follows: an = a1 * r(n-1) Here, a1 = 1024 and a4 = 16. We can express a4 in terms of a1 and the common […]
Given the least squares regression equation y = 1202 + 1133x, when x = 3 what does y equal?
To find the value of y when x is 3, we need to substitute 3 into the regression equation. The equation is: y = 1202 + 1133x Now, replace x with 3: y = 1202 + 1133(3) This simplifies to: y = 1202 + 3399 Now, add those two numbers together: y = 4601 So, […]