Sure, I'd be happy to walk you through the solutions step-by-step for each part of the question.
### 1. Image of the point [tex]$(-3,5)$[/tex] when rotated through [tex]$360^{\circ}$[/tex] about the origin
When we rotate a point [tex]$(x, y)$[/tex] in the coordinate plane by [tex]$360^{\circ}$[/tex] about the origin, the point returns to its original position because a full [tex]$360^{\circ}$[/tex] rotation is a complete circle.
Therefore, the image of the point [tex]$(-3, 5)$[/tex] after a [tex]$360^{\circ}$[/tex] rotation is:
[tex]\[ \boxed{(-3, 5)} \][/tex]
So the correct answer is:
C. [tex]$(-3, 5)$[/tex]
### 2. Probability of selecting a white ball
There are a total of 15 white balls and 25 black balls in the box. To find the probability of selecting a white ball, we first determine the total number of balls in the box:
[tex]\[ \text{Total number of balls} = 15 + 25 = 40 \][/tex]
The probability of selecting a white ball is the number of white balls divided by the total number of balls:
[tex]\[ \text{Probability} = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{15}{40} \][/tex]
Simplifying the fraction:
[tex]\[ \frac{15}{40} = \frac{3}{8} \][/tex]
Therefore, the probability that a randomly selected ball is white is:
[tex]\[ \boxed{\frac{3}{8}} \][/tex]
So the correct answer is:
D. [tex]$\frac{3}{8}$[/tex]
### 3. Number of oranges each student will get if shared among 30 students
Given that 50 students each got 15 oranges, first we calculate the total number of oranges:
[tex]\[ \text{Total oranges} = 50 \times 15 = 750 \][/tex]
If these 750 oranges are now shared equally among 30 students, each student will receive:
[tex]\[ \text{Oranges per student} = \frac{\text{Total oranges}}{\text{Number of students}} = \frac{750}{30} = 25 \][/tex]
Therefore, each of the 30 students will get:
[tex]\[ \boxed{25} \][/tex]
So the correct answer is:
D. 25
