Perimeter: 36.84 feet
Let’s start with the easy part...all the rectangle pieces 6 x 3 = 18 feet
We know from subtracting the rectangle length (6ft) from the total length (12 ft) that the diameter of the circle is 6ft.
Circumference = diameter x pi
= 6 x 3.14 = 18.84
We have the circle split into 2 halves, but the circumference remains the same
18 + 18.84 = 36.84
A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is: (8, 16, 20, 24)
If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is: (1/8, 1/6, 1/3, 2/5, 2/3)
If a code is chosen at random, the probability that D is in the code but is not in the first position is: (1/8, 1/6, 1/3, 2/5, 2/3)
90-52=38
38=3x-5
3x=43
x=14.3
Answer:
2.2 - 0.4
Step-by-step explanation:
1. Approach
To divide by imaginary number, one must take the fraction and multiply the complex conjugate of the denominator. A complex conjugate is a complex number with its imaginary unit multiplied by (-1). Once one multiplies both the numerator and denominator by the complex conjugate, then the denominator should be a real number (this is because the complex numbers act like binomials when multiplied, and hence the difference of square property works). Now all one has to do is divide every term in the numerator by the real number in the denominator.
2. complex conjugate
As mentioned above, to solve this problem, one has to multiply the numerator and denominator by the complex conjugate of the denominator. That is the complex number in the denominator with its imaginary until multiplied by (-1).
Complex number in the denominator;
(-8 - 6i)
complex conjugate;
(-8 + 6i)
3. Multiplying
Now, one has to multiply the problem's numerator and denominator by the complex conjugate of the denominator. Since a number over itself in fraction format is the same as multiplying by (1), one is allowed to do this;

Multiply

Distribute

4. Simplifying
Now all that is left is to simplify and divide to find the quotient.
=
=
Remember the rotations of
, 
Simplify further

Divide
2.2 - 0.4