Answer:
(a) 0.0001 or 0.01%
(b) 0.01 or 1%
Step-by-step explanation:
Since there are 10 possible numeric digits (from 0 to 9), and there is only one correct digit, there is a 1 in 10 change of getting each digit right.
The probability that if you forget your PIN, then you can guess the correct sequence
(a) at random:

(b) when you recall the first two digits.

It depends on what you mean by the delimiting carats "^"...
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for

.
In that case, you want to find the antiderivative,

Complete the square in the denominator:

Now substitute

, so that

. Then

which simplifies to

Now, recall that

. But we want the substitution we made to be reversible, so that

which implies that

. (This is the range of the inverse sine function.)
Under these conditions, we have

, which lets us reduce

. Finally,

and back-substituting to get this in terms of

yields
D=20/3 or in decimal form d=6.666, it keeps going
Rectangle diagonals are equal.
2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0
AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2 <span>
</span>BD = 2(a+1) = 2(0 + 1) = 2 <span>× 1 = 2
</span>
Ansver: AC = BD = 2