Question

1. in a sample of mice in dr. rloes laboratory, 15% of mice have a nonsense mutation on their egfr gene and 10% of mice have a missense mutation on their egfr gene (none of the mice have both mutations). if there are 200 mice in the sample, how many do not have either a nonsense or missense mutation on their egfr gene? (a) 75 mice (b) 120 mice (c) 150 mice (d) 175 mice 89. how many integers between 200 and 1000 (inclusive) meet both of the conditions given in the statements below? 1. the product of the digits is odd. 2. the integer is divisible by 5. (a) 5 (b) 20 (c) 40 (d) 161 90. a botanist prepares circular beds with a radius of 5 inches (shown in white in the figure) to plant hybrid seedlings. she sprays a pesticide around the boundary of the beds in a strip 3 inches wide (shown in gray in the figure). what is the area of the ground that she sprays? (note: the figure is not necessarily drawn to scale.) (a) 9π inches² (b) 27π inches² (c) 39π inches² (d) 89π inches²

Explanation:

Step1: Find the radius of the outer - circle

The radius of the inner - circle is $r = 5$ inches and the width of the spray - strip is 3 inches. So the radius of the outer - circle $R=r + 3=5 + 3=8$ inches.

Step2: Use the formula for the area of a circle

The area of a circle is $A=\pi R^{2}-\pi r^{2}=\pi(R^{2}-r^{2})$.
Substitute $R = 8$ and $r = 5$ into the formula: $R^{2}-r^{2}=8^{2}-5^{2}=64 - 25=39$.
So the area $A = 39\pi$ square inches.

Answer:

C) $39\pi$ inches$^{2}$