Answer:
Step-by-step explanation:
Mathematicians stand on each other's shoulders. — Carl Friedrich Gauss We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
Answer:
(mn+n²)/(m+n)
Step-by-step explanation:
probability of blue marble= n/(n+m)
probability of red marble= m/(n+m)
probability that process stops = Probability of both blue + probability of both red= n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)
= (n²+m²)/(n+m)²
P(1st marbel is blue)= P(blue and red) + P(blue and blue)
= mn/(n+m) + n²/(n+m)
= (mn+n²)/(m+n)
P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)
= (mn+n²)/(m+n)
Answer:
Equivalent expressions
A) 
C) 
Step-by-step explanation:
Given expression :

Choices given :
A) 
B) 
C) 
D) 
To find the equivalent expression.
We will first evaluate the given expression.

⇒
[Quotient of a negative dividend and a positive divisor is always negative]
Evaluating each choice to select the equivalents.
A) 
⇒
[Quotient of a positive dividend and a negative divisor is always negative]
B) 
⇒ 
⇒ 
C) 
⇒
[Product of a positive and a negative is always a negative]
⇒ 
D) 
⇒
[Product of two negatives is always a positive]
⇒ 
∴ We see that the choices A and C are equivalent.
1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5