The domain is defined as the complete set of values of variable x for which the function is valid. In this case, the x-axis illustrates time in seconds. Therefore, we must determine all possible time values over which distance can be covered or the function is defined. It’s noted that the sprinter completed the race in 11 seconds, and the start time is 0 seconds. Hence, the value of t ranges from 0 to 11. Therefore, the domain encompasses all real numbers from 0 to 11.
Using the Pythagorean theorem: In a right triangle where legs are labeled a and b, and hypotenuse is c. Given the triangle ΔXYZ has a right angle at Y, with angles YZX and ZXY both measuring 45 degrees, and ZY = YX = 12 cm. The task is to find the length of XZ.
The capacity is approximately 3.5 fluid ounces. In order to determine this, we need to compute the volume of a cone-shaped cup. The formula for the volume of a cone is: 1/3 * π * r^2 * h, where r equals the diameter divided by 2, which gives 1.35 inches, and h equals 3.3 inches. After substituting these values, we find the volume to be V = 1/3 * 3.14 * 1.35^2 * 3.3 = 6.3 cubic inches. To convert cubic inches to fluid ounces, we use the relationship that 1 fluid ounce is equal to 1.8 cubic inches. Therefore, x fluid ounces equal to 6.3 cubic inches leads to x = 6.3 / 1.8, which results in 3.5 fluid ounces.
Response:
Alan's survey aims to determine the art preferences among students at the local high school.
To conduct a thorough investigation, he needs to consider all students in the school as the target population since that is his goal.
Nevertheless, in many cases involving statistical studies, it's impractical to include the entire population. In such instances, a sample that accurately reflects the overall student body is employed.
This sample is a subset of the population and must share the same characteristics and attributes; otherwise, the findings may be skewed.
Thus, a feasible sample would consist of a specific number of students from each grade level, including freshmen, sophomores, juniors, and seniors. This approach ensures the sample accurately represents the larger population.
