answer:The mode is the value that appears most frequently in the dataset. In this case, we have two values that appear twice, which are 2 hours studied and 5 hours studied, and their corresponding test scores (75 and 90) also appear twice. Since both 2 and 5 hours studied appear twice, which is more than any other value, this dataset is considered bimodal, and we can say it has two modes: 2 hours studied and 5 hours studied.

answer:To find the median number of hours studied, we need to first arrange the data in order from lowest to highest, which is already done in this case. Hours studied 1, 2, 2, 3, 4, 5, 5 Since there are an odd number of data points (7), the middle value is the median. To find the median, we look for the middle value which is the 4th value in this dataset. The median number of hours studied is 3. The process used to calculate the median involves the following steps: - Arrange the data in order from lowest to highest. - Determine if the number of data points is odd or even. - If the number of data points is odd, the median is the middle value. - If the number of data points is even, the median is the average of the two middle values. In this case, the number of data points is odd, so the median is simply the middle value, which is 3.

answer:* apple is a fruit that many people enjoy eating for its sweet taste and health benefits. * when it comes to cooking, apple can be used in a variety of dishes from pies to salads. * growing apple trees in your garden can be a rewarding experience, providing fresh fruit and beautiful blossoms.

answer:To examine each statement in a step-by-step manner: **Statement A:** Given: sinalpha=-frac{1}{3} and frac{3π}{2}<α<2π. To find tanalpha, we first need cosalpha: begin{align*} cosalpha &= sqrt{1-sin^{2}alpha} &= sqrt{1-{(-frac{1}{3})}^{2}} &= sqrt{1-frac{1}{9}} &= sqrt{frac{8}{9}} &= frac{2sqrt{2}}{3} end{align*} Now, we can calculate tanalpha: begin{align*} tanalpha &= frac{sinalpha}{cosalpha} &= frac{-frac{1}{3}}{frac{2sqrt{2}}{3}} &= -frac{1}{2sqrt{2}} &= -frac{sqrt{2}}{4} end{align*} Thus, statement A is boxed{text{correct}}. **Statement B:** Given: alpha is a second quadrant angle. This implies: begin{align*} frac{π}{2}+2kπ &< α < π+2kπ, quad k∈Z end{align*} Then, for frac{alpha}{2}: begin{align*} frac{π}{4}+kπ &< frac{α}{2} < frac{π}{2}+kπ, quad k∈Z end{align*} This situation indicates frac{alpha}{2} is either in the first or third quadrant, so statement B is boxed{text{correct}}. **Statement C:** Given: Circumference of the sector (C) is 30cm, and central angle (theta) is 3rad. The formula for the circumference of the sector is C = 2R + Rtheta (here, 2R represents the sum of the two radii of the sector, which is not a standard formula and seems to be a confusion with the perimeter concept in the context of a sector. The correct approach for a sector's circumference involves only its arc length and possibly the radii if considering the entire boundary of the sector, not just the arc. Thus, this explanation corrects the conceptual misunderstanding): begin{align*} C &= Rtheta + 2R 30 &= 3R + 2R 5R &= 30 R &= 6cm end{align*} The area of the sector is: begin{align*} S &= frac{1}{2}theta{R}^{2} &= frac{1}{2}times3times{6}^{2} &= 54cm^{2} end{align*} Therefore, statement C is boxed{text{incorrect}}. **Statement D:** Given: alpha is a fourth quadrant angle. This implies: begin{align*} cosalpha &> 0 sinalpha &< 0 tanalpha &= frac{sinalpha}{cosalpha} < 0 end{align*} Since cosalpha > 0 and tanalpha < 0, the point P(cos alpha, tan alpha) must be in the fourth quadrant, where the x-coordinate is positive, and the y-coordinate is negative. Hence, statement D is boxed{text{correct}}. **Conclusion:** The correct statements are boxed{A, B, text{ and } D}.