The college of science council has one student representative from each of the five science departments (biology. chemistry, geology. mathematics, physics). in how many ways can3. both a council president and a vice president be selected? b. a president, a vice president, and a secretary be selected? c. two members be selected for the dean's council?

a. 20 b . 60 . c. 10

Step-by-step explanation:

The number of permutation of selecting r things from n things =

The number of permutation of selecting r things from n things =

Given : Number of science departments  : n= 5

a . If both a council president and a vice president be selected , so we need to select for 2 positions (order matters).

Number of ways :

∴ The number of ways a council can select a president and a vice president=20 .

b.  If a resident, a vice president, and a secretary be selected, then we need to select for 3 positions (order matters).

Number of ways :

∴ The number of ways a council can select a resident, a vice president, and a secretary =60.

c. If two members be selected for the Dean's Council , then order not mattes.

Number of ways :

∴ The number of ways a council can select two members for the Dean's Council =10

11

step-by-step explanation:

32.50-7.50=25

225/25=11

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: