What number is needed to complete the pattern below: 5, 10, 3, 15, 20, 13, 25, 30?
The missing number in this pattern is 18. To understand why, let’s break the sequence down into two interleaved sequences: The first sequence is: 5, 10, 15, 20, 25 The second sequence is: 3, 13, 30 The first sequence consistently adds 5: 5 + 5 = 10 10 + 5 = 15 15 + 5 […]
In a unit circle, the radian measure of the central angle is equal to the length of what?
In a unit circle, the radian measure of the central angle is equal to the length of the arc that it subtends on the circle. A unit circle is defined as a circle with a radius of one unit, typically centered at the origin of a coordinate system. When you measure an angle in radians, […]
What is the perimeter of the base of a right pentagonal prism with a height of 14 units and a volume of 840 cubic units?
To find the perimeter of the base of the right pentagonal prism, we can start by using the formula for the volume of a prism: Volume = Base Area × Height In this case, we have the height (h) as 14 units and the volume (V) as 840 cubic units. We can rearrange the formula […]
What word is used to define the slope of a vertical line?
The word used to define the slope of a vertical line is undefined. In mathematics, the slope of a line is calculated as the change in the vertical coordinate (rise) divided by the change in the horizontal coordinate (run). For a vertical line, all the points share the same x-coordinate, meaning there’s no horizontal change. […]
What is the area under the standard normal curve to the right of z = 1.43?
The area under the standard normal curve to the right of z = 1.43 can be found using standard normal distribution tables or a calculator that provides cumulative distribution function (CDF) values for the normal distribution. First, we need to find the cumulative area to the left of z = 1.43. This value represents the […]
Why is 120 Degree the Highest Exterior Angle for a Regular Polygon?
The highest exterior angle for a regular polygon is 120 degrees because it relates directly to the number of sides the polygon has. To understand this, we first need to know how to calculate the exterior angle of a regular polygon. The formula to find the exterior angle (E) of a regular polygon is given […]
What fraction of natural numbers from 102 to 113 are prime numbers?
To determine what fraction of the natural numbers from 102 to 113 are prime, we first need to identify the prime numbers within this range. The natural numbers between 102 and 113 are: 102 103 104 105 106 107 108 109 110 111 112 113 Now, we’ll check each of these numbers for primality: 102: […]
What are some examples of acute and obtuse angles?
Acute angles are angles that measure less than 90 degrees. Here are two examples: Example 1: 45 degrees Example 2: 30 degrees On the other hand, obtuse angles are angles that measure more than 90 degrees but less than 180 degrees. Here are two examples: Example 1: 120 degrees Example 2: 150 degrees Understanding the […]
Which statement is true about fx 6x 5 2?
The statement that is true about the function f(x) = 6x + 5 can be determined by analyzing its properties such as its slope, intercepts, and behavior as x varies. First, let’s look at the slope of the function, which is the coefficient of x. In this case, the slope is 6. This tells us […]
What is the slope of the line represented by the equation y = x + 3?
To find the slope of the line given by the equation y = x + 3, we need to identify the form of the equation. This equation is in the slope-intercept form, which is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y […]