What are the two numbers if their sum is 36 and one number is 3 times the other?
To find the two numbers, let’s define the first number as x. According to the problem, the second number is 3 times the first number, which would be 3x. We know the sum of the two numbers is 36, so we can write the equation: x + 3x = 36 Combining like terms gives us: […]
Which of the following numbers is a multiple of 6?
To determine which number is a multiple of 6, we should remember that a number is a multiple of 6 if it can be divided evenly by both 2 and 3. First, let’s break down what it means to be divisible by 2 and 3: Divisibility by 2: A number is divisible by 2 if […]
Do You Include the Median When Finding the Upper and Lower Quartiles?
When calculating the upper and lower quartiles in a data set, whether to include the median depends on how we define the quartiles, but generally, the median is not counted when finding quartiles. The lower quartile (Q1) is the median of the lower half of the data set, while the upper quartile (Q3) is the […]
What is the percentage increase from 60 to 75?
To calculate the percentage increase from 60 to 75, you need to follow these steps: First, find the difference between the new value (75) and the old value (60). This is done by subtracting the old value from the new value: Difference = New Value – Old Value = 75 – 60 = 15 Next, […]
How do you prove sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b)?
To prove the identity sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b), we can start by using the unit circle and some basic trigonometric properties. Consider two angles a and b represented on the unit circle. The coordinates of a point on the unit circle corresponding to angle a are given by […]
How many terms are in the expression 5m² mn 4n 7?
To determine how many terms are in the expression 5m² mn 4n 7, we first need to properly interpret and separate the individual parts of the expression. The expression contains the following components: 5m² – This is one term. mn – This is another term. 4n – This is yet another separate term. 7 – […]
What is the area of the sector that is not shaded 12 24 120 144?
To find the area of the sector that is not shaded, we first need to understand the context of the problem, which presumably involves a circle and some shaded portion of it. Let’s say you have a circle and it’s divided into sectors. To find the area of the complete sector, you would typically use […]
What is the area of a rhombus with diagonals of 6cm and 8cm?
The area of a rhombus can be calculated using the formula: Area = (d1 × d2) / 2 where d1 and d2 are the lengths of the diagonals. In this case, we have: d1 = 6 cm d2 = 8 cm Substituting the values into the formula gives us: Area = (6 cm × 8 […]
Solve for x: 3x = 15
To solve the equation 3x = 15, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 3. Here’s how it works step by step: Start with the original equation: 3x = 15. Divide both sides by 3: x = 15 / […]
Divide 1400 into three parts such that the 1st part is 2/3 of the 2nd part and the ratio between the 2nd and 3rd part is 4:5. Find each part.
Let’s denote the three parts as A, B, and C. According to the problem: The total sum of the parts is A + B + C = 1400. The first part, A, is 2/3 of the second part, B. This gives us the equation: A = (2/3)B. The ratio between the second part and the […]