Question 10 options: A marine biologist is researching the population density of dolphins. The marine biologist counts 175 dolphins within a radius of 2.5 miles of a half circle off of Clearwater Beach.

What is the population density of the dolphins?

Use 3.14 for pi, and round to the nearest whole number.

Density = dolphins/mi2

9 dolphins/mi²

Step-by-step explanation:

area of circle = π x r² = (3.14)(2.5²) = 19.625 miles²

175/19.625 = 8.92 dolphins per square mile

Find the area of the half circle.

Area of half circle = 1/2 x pi x r^2

= 1/2 x 3.14 x 2.5^2

= 9.8125 square miles.

For the density divide the number of dolphins by the area:

Density = 175 / 9.8125 = 17.83

Rounded to nearest whole number the density is 18 dolphins per square mile.

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: