What is the difference between a rate and a unit rate?
A rate is a ratio that compares two quantities of different units. For example, if you travel 150 miles in 3 hours, the rate would be written as 150 miles/3 hours. This tells you how many miles you travel for every hour spent. A unit rate, on the other hand, is a specific type of […]
Give a function that is positive for the entire interval (3, 2)
To find a function that is positive for the entire interval (3, 2), we need to ensure that the function does not take any negative values for any point within that interval. One such function is the exponential function, f(x) = e^(x). This function is positive for all real numbers, and thus it will certainly […]
What is 20 of 10?
To find what 20 of 10 is, we can interpret this phrase as asking for 20% of 10. To calculate this, we multiply 10 by 0.20 (since 20% is equivalent to 0.20 in decimal form). So, the calculation looks like this: 10 x 0.20 = 2 This means that 20 of 10 is 2. It’s […]
Which are the solutions of x² + 5x + 8?
To find the solutions for the quadratic equation x² + 5x + 8 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In our case, the coefficients are: a = 1 b = 5 c = 8 Now, we can calculate the discriminant (b² – 4ac): b² […]
What is 6 5 as a mixed number?
To convert the improper fraction 6/5 into a mixed number, we start by dividing the numerator (6) by the denominator (5). 1. **Perform the Division**: When we divide 6 by 5, it goes 1 time (1 x 5 = 5) with a remainder of 1. So we can express it as: 6 ÷ 5 = […]
What is the circumference of a circle with a radius of 6?
The circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference and r is the radius. In this case, the radius r is 6. Plugging this value into the formula gives: C = 2π(6) Calculating this, we find: C = 12π To get a numerical approximation, we […]
Example of an Integer That is Not a Whole Number
In mathematics, an integer is any whole number that can be positive, negative, or zero. However, when we talk about whole numbers, we refer specifically to non-negative integers, which include zero and positive integers only. Therefore, an example of an integer that is not a whole number would be -3. This number is indeed an […]
What is 19 6 as a mixed number?
To convert 19 6 into a mixed number, we first recognize that the expression represents a whole number and a fraction. In this case, the number before the space (19) is the whole number, and the number after the space (6) represents an integer that needs to be expressed as a fraction. Since we have […]
What shape has 4 sides?
A shape that has four sides is called a quadrilateral. Quadrilaterals can come in various forms, including squares, rectangles, trapezoids, and rhombuses. Each of these shapes has its unique properties, but they all share the common characteristic of having four sides. For example, a square has equal sides and all right angles, while a rectangle […]
The number one followed by one hundred zeros is known by which name?
The number one followed by one hundred zeros is known as a ‘googol.’ The term ‘googol’ was coined in the 1930s by mathematician Edward Kasner, who was looking for a way to illustrate the concept of very large numbers. He asked his nine-year-old nephew, Milton Sirotta, to come up with a name for this immense […]