What will the 6% sales tax be on purchases totaling $14,550?
To calculate the sales tax on a total purchase amount of $14,550 at a rate of 6%, you will need to multiply the total purchase amount by the sales tax rate. The formula to find the sales tax is: Sales Tax = Total Purchase Amount × Sales Tax Rate In this case, it would look […]
What is the slope of the function represented by the table of values below?
To determine the slope of the function from a table of values, we need to identify two distinct points from the table. A point can be represented as (x1, y1) and (x2, y2). The formula for the slope (m) is: m = (y2 – y1) / (x2 – x1) This formula calculates the rate of […]
What is the result of adding the system of equations 2x + y = 4 and 3x + y = 6?
To find the result of adding the two equations, we simply add the left-hand sides and the right-hand sides of the equations separately. The equations are: 1) 2x + y = 4 2) 3x + y = 6 Now, let’s add them together: (2x + y) + (3x + y) = 4 + 6 This […]
A fraction bears the same ratio to 17 as 37 does to 59. Find the fraction.
To find the fraction that has the same ratio to 17 as 37 does to 59, we can set up a proportion. Let’s denote the unknown fraction as x. The statement can be expressed mathematically as: Ratio 1: x / 17 = 37 / 59 Next, we can cross-multiply to solve for x: x * […]
If x² is a factor of x² + bx + b where b is a constant, what is the value of b?
To determine the value of b when x² is a factor of the polynomial x² + bx + b, we start by recognizing what it means for x² to be a factor. If x² is a factor of the expression, then we can express it as: x² + bx + b = x²(q(x)) for some […]
What is the solution to the equation 21x 3 14?
To solve the equation, we need to clarify the expression a bit more, as it is currently not in a standard mathematical format. Assuming the equation is supposed to be interpreted as: 21x = 3 + 14 First, we simplify the right side: 3 + 14 = 17 Now, the equation looks like this: 21x […]
Find the value of tan 1 tan 2 tan 3 tan 89
To find the value of tan 1° tan 2° tan 3° tan 89°, we can use some properties of the tangent function. One crucial property to consider is that tan(90° – x) = cot x, which means that tan 89° = cot 1°. Since cotangent is the reciprocal of tangent, we have: tan 89° = […]
How many multiples of 4 lie between 10 and 250?
To determine how many multiples of 4 lie between 10 and 250, we can follow a few simple steps. First, we need to find the smallest multiple of 4 that is greater than or equal to 10. We can do this by dividing 10 by 4: 10 ÷ 4 = 2.5 Since multiples must be […]
How to Determine if a Year is a Leap Year
To determine if a year is a leap year, you can follow a simple set of rules: A year is a leap year if it is divisible by 4. However, if the year is divisible by 100, it is not a leap year, unless: It is also divisible by 400, in which case it is […]
If p is the probability of success of a binomial experiment, what is the probability of failure?
In a binomial experiment, there are only two possible outcomes for each trial: success and failure. If we denote the probability of success as p, then the probability of failure can be determined using the complementary relationship between success and failure. The sum of the probabilities of all possible outcomes must equal 1. Therefore, if […]