Answer:
P(X ≤ 3) = 0.9933.
Step-by-step explanation:
We are given that the random variable X has a binomial distribution with the given probability of obtaining a success
Also, given n = 5, p =0.2.
The above situation can be represented through binomial distribution;
where, n = number of samples (trials) taken = 5
r = number of success = less than equal to 3
p = probability of success which in our question is 0.20.
Let X = <u><em>A random variable </em></u>
So, X ~ Binom(n = 5, p = 0.20)
Now, the probability that X is less than and equal to 3 is given by = P(X ≤ 3)
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= 
= 
= <u>0.9933</u>
1 ) Area of the rectangle:
A = L x W
L = √(2² + 2²) = √8 = 2√2
W = √(6² + 6²) = √72 = 6√2
A = 2√2 x 6√2 = 24 units²
2 ) Area of a triangle:
RQ = 2 + 4 = 6 units
h = 4 units
A = ( 6 * 4 ) / 2 = 12 units²
3 ) The perimeter of Δ ABC:
AB = √(3² + 4²) = √25 = 5 units
BC = √(1² + 1²) = √2 = 1.4 units
AC = √(3² + 4²) = √25 = 5 units
P = 5 + 1.4 + 5 = 11.4 units
4 ) Area of the figure ( approx.):
A ≈ ( 8 * 8) - 6.25 - 8 - 2.5 ≈ 47.25
Answer: C ) 50 ft²
5 ) Area under the curve:
A ≈ 0.5 * 3 + 0.5 * 3.5 + 0.5 * 4 + 0.5 * 4.5 + 0.5 * 5 + 0.5 * 4.5 + 0.5 * 4 +
+ 0.5 * 3 ≈ 0.5 * 31.5 ≈ 15.6
Answer: B ) 15 units²
Answer:
y = - 3x² - 24x - 60
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 4, - 12 ), thus
y = a(x + 4)² - 12
To calculate a substitute (- 7, - 39) into the equation
- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )
- 27 = 9a ( divide both sides by 9 )
- 3 = a
y = - 3(x + 4)² - 12 ← in vertex form
Expand (x + 4)²
y = - 3(x² + 8x + 16) - 12
= - 3x² - 24x - 48 - 12
y = - 3x² - 24x - 60 ← in standard form
= - 3(x²
Answer:
A B and D
Step-by-step explanation:
Answer:
Complement of a Set If U is a universal set and A is a subset of U, then the set of all elements in U that are not in A is called the complement of A and is denoted Ac.
Step-by-step explanation:
