If two events A and B are mutually exclusive, what does the special rule of addition state?
When two events A and B are mutually exclusive, it means that they cannot occur at the same time. In probability, the special rule of addition for mutually exclusive events states that the probability of either event A or event B occurring is simply the sum of their individual probabilities. This can be expressed mathematically […]
If FG 2 Units, FI 7 Units, and HI 1 Unit, What is GH?
To find GH, we can interpret the relationships between these segments in the context of geometry or algebra. Assuming FG, FI, and HI are parts of a larger figure or sequence, we often look for patterns or proportional relationships. In this case, if we treat these lengths as segments along a line or in a […]
What is the prime factorization of 50?
The prime factorization of 50 is 2 × 5 × 5 or 2 × 52. To explain this, we start by dividing 50 by the smallest prime number, which is 2. Since 50 is even, we can easily divide it: 50 ÷ 2 = 25 Now we are left with 25. The next step is […]
Which of the following expressions correctly determines that x is greater than 10 and less than 20?
To determine if a variable x is greater than 10 and less than 20 at the same time, you need to use a logical AND condition. The correct expression is: 10 < x && x < 20 This expression checks two conditions: first, it verifies that x is greater than 10, and second, it checks […]
Find the value of a and b in x² + 16x + a + b²
To find the values of a and b in the expression x² + 16x + a + b², we start by rewriting the quadratic part. The expression can be grouped as follows: x² + 16x Next, we can complete the square for the quadratic term: 1. Take the coefficient of x, which is 16. 2. […]
If JM = 5x + 8 and LM = 2x + 6, which expression represents JL?
To find the expression that represents JL, we first need to understand that JL can be expressed in terms of JM and LM. If we consider the two segments, JM and LM, as two parts of a larger segment JL, we can set up the equation: JL = JM – LM Next, we can substitute […]
What is the arc length when 8 pi over 3 and the radius is 5 cm?
To find the arc length, we can use the formula: Arc Length = r × θ where r is the radius and θ is the angle in radians. In this case, the angle given is 8π/3
If the point A(7, y) lies on the graph of the equation 5x + y = 8, then what is the value of y?
To find the value of y when the point A(7, y) lies on the equation 5x + y = 8, we substitute x with 7 in the equation. The equation can be rewritten as: 5(7) + y = 8 This simplifies to: 35 + y = 8 Now, to isolate y, we subtract 35 from […]
How to Select One of the Factors of the Expression 4x² + 5x + 6?
To find one of the factors of the expression 4x² + 5x + 6, we can start by looking for two numbers that multiply to give the product of the coefficient of the quadratic term (4) and the constant term (6), which is 24, and at the same time, add to equal the coefficient of […]
Find the Vertex, Focus, Directrix, and Focal Width of the Parabola x = 10y
To analyze the parabola given by the equation x = 10y, we can rewrite it in the standard form of a parabola. This equation can be rearranged to: y = (1/10)x This indicates that it opens to the right, and it is in the form of x = 4py, where p is the distance from […]