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The half-life of a radioactive isotope is 4 .3 days. How long will it take to re

ID: 2894595 • Letter: T

Question

The half-life of a radioactive isotope is 4 .3 days. How long will it take to reduce the original amount to 1% (A) 3.2 days (B) 16 days (C) 29 days (D) 40 days Five fair coins are each flipped once. What is the probability that at least two of the coins will show heads? (A) 0.19 (B) 0.80 (C) 0.81 (D) 0.84 What is the determinant for the following 2 times 2 matrix? [1 3 4 2] (A) -10 (B) -5 (C) 9 (D) 10 What is the radius of a circle with the following equations? x^2 - 6x + y^2 - 4y - 12 = 0 (A) 3.5 (B) 4.0 (C) 5.0 (D) 6.0

Explanation / Answer

1)

0.01 =(0.5)^(t/4.3)

ln(0.01) =t/(4.3) *ln(0.5)

t= 4.3ln(0.01)/ln(0.5)

= 29

Option C is correct.

2)

P(x>=2) = 1- P(x=0)-P(x=1)

= 1-C(5,0)*(0.5)^5 -C(5,1)*(0.5)^5

=0.81

Option C is correct.

3)

2*1 -4 *3 = 2 -12 = -10

Correct option is A

4)

x^2-6x+y^2-4y=12

x² -6x +9 +y² -4y +4 = 12 +9+4

(x-3)² +(y-2)² =25

radius =25 =5

Option C is correct.