A cinema seats 280 people. If 98 people are in the cinema, what percentage of the seats are filled?
To find out what percentage of the seats are filled, we can use the formula for percentage: Percentage = (Number of people in the cinema / Total number of seats) × 100 In this case, we have 98 people in the cinema and a total of 280 seats. So, we can substitute the values into […]
In circle O, angle AOB measures π/3 radians. What is the length of arc AB?
To find the length of arc AB in circle O given that the angle AOB measures π/3 radians, we can use the formula for the length of an arc: Arc Length = r × θ Where: r is the radius of the circle θ is the angle in radians In this case, we need to […]
Find the possible value or values of n in the quadratic equation 2n² + 7n + 6 = 0
To find the possible values of n in the quadratic equation 2n² + 7n + 6 = 0, we can use the quadratic formula: n = (-b ± √(b² – 4ac)) / 2a In our equation, the coefficients are: a = 2 b = 7 c = 6 Now, we need to calculate the discriminant […]
The sum of 6 consecutive integers is 519. What is the third number in this sequence?
To find the third number in a sequence of 6 consecutive integers that sum up to 519, we can start by letting the first integer be represented as x. This means the integers can be expressed as: x, x + 1, x + 2, x + 3, x + 4, x + 5 Now, we […]
It’s 3 PM: How Many Degrees Are in the Angle Between the Hour and Minute Hand?
To find the angle between the hour and minute hand at 3 PM, we can follow a simple calculation. The minute hand moves 360 degrees in 60 minutes. This means that every minute, it moves: 360 degrees / 60 minutes = 6 degrees per minute At 3 PM, the minute hand is pointing at the […]
Given the function f(x) = 0.5x^4 – 3, for what values of x is f(x) = 7?
To find the values of x for which f(x) equals 7, we start by setting the function equal to 7: 0.5x^4 – 3 = 7 Next, we can add 3 to both sides of the equation to isolate the term with x: 0.5x^4 = 10 Now, let’s divide both sides by 0.5 to solve for […]
What is the missing number in the series 1, 16, 81, 625, 1296?
The missing number in the series is 2401. Let’s break down the series first: 1 is 12 16 is 42 81 is 92 625 is 252 1296 is 362 Now, let’s identify the numbers that are squared: 1 = 12 4 = 22 9 = 32 25 = 52 36 = 62 If we look […]
Which Polynomial is Prime?
In the world of algebra, a polynomial is considered prime (or irreducible) if it cannot be factored into simpler polynomials with coefficients in the same field or ring. This means that there are no other non-trivial polynomials (other than itself and a constant) that multiply together to give the original polynomial. For example, in the […]
Find an ordered pair x y that is a solution to the equation x = 2y²
To find an ordered pair (x, y) that satisfies the equation x = 2y², we can choose a value for y and then calculate the corresponding value for x. For instance, if we let y = 1, we can substitute this value into the equation: x = 2(1)² This simplifies to: x = 2 So, […]
Select One of the Factors of 3x² + 10x + 3
To find one of the factors of the quadratic expression 3x² + 10x + 3, we can start by factoring it using the method of grouping or by using the quadratic formula. However, in this case, we will look for factors based on trial and error. The expression is of the form ax² + bx […]