Answer:
x = 5
Step-by-step explanation:
The opposite sides of a rectangle are equal , then perimeter
2(- 2x - 6) + 2(4x + 4) = 16 ← distribute parenthesis and simplify left side
- 4x - 12 + 8x + 8 = 16
4x - 4 = 16 ( add 4 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Answer: 120
Step-by-step explanation:
The total number of digits from 1 to 9 = 10
The number of digits from less than 5 (0,1,2,3,4)=5
Since repetition is not allowed so we use Permutations , then the number of 3-digit different codes will be formed :-

The number of digits from greater than 4 (5,6,7,8,9)=5
Similarly, Number of 3-digit different codes will be formed :-

Hence, the required number of 3-digit different codes = 60+60=120
Answer:
8.89 feet
Step-by-step explanation:
The square of the side length is 79 ft², so the side length is the square root of that:
√(79 ft²) ≈ 8.88819 ft ≈ 8.89 ft
Answer:
a) P ( 3 ≤X≤ 5 ) = 0.02619
b) E(X) = 1
Step-by-step explanation:
Given:
- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:
Find:
a.Calculate the probability that 3 ≤X≤ 5
b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.

- The Expected Value can be determined by sum to infinity of CDF:
E(X) = Σ ( 1 - F(X) )

E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]
E(X) = 1