Answer: a) No, b) 0.78, c) No.
Step-by-step explanation:
Since we have given that
P(A) = 0.7
P(B) = 0.2
P(A∩B) = 0.12
(a) Are A and B independent? Explain.
Since P(A).P(B) = ![0.7\times 0.2=0.14](https://tex.z-dn.net/?f=0.7%5Ctimes%200.2%3D0.14)
And P(A∩B) = 0.12
P(A∩B) ≠ P(A).P(B)
So, they are not independent.
(b) Compute P(A or B).
![P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=0.7+0.2-0.12\\\\P(A\cup B)=0.9-0.12\\\\P(A\cup B)=0.78](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%29%3DP%28A%29%2BP%28B%29-P%28A%5Ccap%20B%29%5C%5C%5C%5CP%28A%5Ccup%20B%29%3D0.7%2B0.2-0.12%5C%5C%5C%5CP%28A%5Ccup%20B%29%3D0.9-0.12%5C%5C%5C%5CP%28A%5Ccup%20B%29%3D0.78)
(c) Are A and B mutually exclusive? Explain
Since P(A∩B) ≠ 0
So, they are not mutually exclusive.
Hence, a) No, b) 0.78, c) No.
Answer:
The triangle should be 16 inches wide.
Step-by-step explanation:
![\text {Use the Pythagorean Theorem to solve for the leg.}\\a^2 + b^2 =c^2](https://tex.z-dn.net/?f=%5Ctext%20%7BUse%20the%20Pythagorean%20Theorem%20to%20solve%20for%20the%20leg.%7D%5C%5Ca%5E2%20%2B%20b%5E2%20%3Dc%5E2)
What we know:
- One of the legs measures 12 inches.
- The hypotenuse is 20 inches.
We need to solve for b. Solving for a while b is 12 would also be acceptable.
![12^2 + b^2 = 20^2 \text { OR } a^2 +12^2=20^2](https://tex.z-dn.net/?f=12%5E2%20%2B%20b%5E2%20%3D%2020%5E2%20%20%5Ctext%20%7B%20%20OR%20%20%7D%20%20%20a%5E2%20%2B12%5E2%3D20%5E2)
We will use the first equation.
![12^2 + b^2 = 20^2\\12 * 12 = 144\\20 * 20 = 400\\\\\boxed {144 + b^2 = 400}](https://tex.z-dn.net/?f=12%5E2%20%2B%20b%5E2%20%3D%2020%5E2%5C%5C12%20%2A%2012%20%3D%20144%5C%5C20%20%2A%2020%20%3D%20400%5C%5C%5C%5C%5Cboxed%20%7B144%20%2B%20b%5E2%20%3D%20400%7D)
![\text {Subtraction property of equality: }\\144-144+ b^2 = 400-144\\\boxed {b^2 = 256}\\\\\text {Take the square root of 256: }\\\sqrt{256}=\sqrt{b^2} \boxed {16 = b}](https://tex.z-dn.net/?f=%5Ctext%20%7BSubtraction%20property%20of%20equality%3A%20%7D%5C%5C144-144%2B%20b%5E2%20%3D%20400-144%5C%5C%5Cboxed%20%7Bb%5E2%20%3D%20256%7D%5C%5C%5C%5C%5Ctext%20%7BTake%20the%20square%20root%20of%20256%3A%20%7D%5C%5C%5Csqrt%7B256%7D%3D%5Csqrt%7Bb%5E2%7D%20%5Cboxed%20%7B16%20%3D%20b%7D)
The triangle should be 16 inches wide.
Answer:
(x - 3)² + (y + 1.5)² = 15.25
Step-by-step explanation:
Centre: midpoint of the diameter
(h,k) = (0+6)/2, (1-4)/2
= (3, -3/2)
Radius = ½(diameter)
Diameter = sqrt(6² + (-4-1)²)
sqrt(61)
Radius = sqrt(61)/2
Equation:
(x - h)² + (y - k)² = r²
(x - 3)² + (y + 1.5)² = 15.25
350-15%= 297.50 so he lost 15% in the 2months if u want to break it down further u can:
350- 5%= 332.25
332.25-10%= 299.00 ur choice and depends how far ur teacher wants u to break it down.
14. The student is not correct because ...
Ex. 14:6 if you add one to