To determine Sally’s walking speed in kilometers per hour (km/h), we can use the formula for speed, which is: Speed = Distance / Time In this case, the distance Sally walked is 12 kilometers and the time she took is 14 hours. Plugging these numbers into the formula gives us: Speed = 12 km / … Read more
Understanding the Area Under the Normal Curve The area under the normal curve between two z-scores represents the probability of a data point falling between those two z-scores in a standard normal distribution. For the z-scores you mentioned, z = 1.0 and z = 2.0, we can calculate this using standard normal distribution tables or … Read more
When dealing with parallel lines in geometry, one fundamental rule is that parallel lines share the same slope. This means that if you have a line, let’s call it line k, with a given slope, any line that is parallel to it will have the exact same slope. In this case, we know that line … Read more
To simplify the rational expression \( \frac{t^2 + 4t}{32t + 8} \), we can start by factoring both the numerator and the denominator. Here’s how we can proceed: Step 1: Factor the numerator The numerator is \( t^2 + 4t \). We can factor out a common term, which is \( t \): \[ t^2 … Read more
The given sequence is 64, 16, 4. To find the 10th term, we first need to identify the pattern of the sequence. Looking at the sequence, we can observe the relationship between the consecutive terms: 64 divided by 4 equals 16. 16 divided by 4 equals 4. This indicates that each term in the sequence … Read more
The diameter of a circle is twice the length of its radius. This means that to find the diameter, you can simply multiply the radius by 2. In this case, if the radius is 8 cm, you can calculate the diameter as follows: Diameter = 2 × Radius Diameter = 2 × 8 cm Diameter … Read more
To find the first four terms of the sequence defined by a1 = 1 and an = 4 an-1, we will start by computing each term step by step: First term (a1): By the given condition, we have: a1 = 1 Second term (a2): Using the formula an = 4 an-1, we calculate: a2 = … Read more
To find the exact value of sin 255°, we can utilize the sine addition formula. First, let’s express 255° in terms of angles for which we know the sine values. We can rewrite 255° as: 255° = 180° + 75° Now, we can apply the sine addition formula: sin(A + B) = sin A cos … Read more
To determine the range of the function defined by the pairs (1, 5), (2, 8), (5, 3), and (13, 4), we need to look at the second value in each pair. The range of a function is defined as the set of all possible output values. For the input 1, the output is 5. For … Read more
To solve the expression 2×3 × 22 × 8 divided by x2, we can break it down into manageable steps. First, let’s simplify the numerator: 2×3: This term represents 2 multiplied by x cubed. 22: This is 2 squared, which equals 4. 8: This is simply 8. Now, we can combine these parts: The product … Read more