The mathematical expression does not seem clear but I have made an attempt to make sense of what is implied.
Answer:
<em>a</em> = 4, <em>b</em> = 2, <em>c</em> = 16, <em>d</em> = 9
Step-by-step explanation:

Solving the first part of the question by indices,

Comparing the rightmost term with the second term in the question,
<em>a</em> = 4, <em>b</em> = 2
Solving on,

Comparing with the final term in the question,
<em>c</em> = 16 and <em>d</em> = 9
Therefore,
<em>a</em> = 4, <em>b</em> = 2, <em>c</em> = 16, <em>d</em> = 9
Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes

.
The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.
The probability of selecting one coin is

Part A:
To find <span>the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.
P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.
Thus

</span><span>P(B) means that the first envelope contains a quarter AND the
second envelope contains a quarter
</span><span>Thus

Therefore,

Part B:
</span>To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime<span>, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.
</span><span>

</span><span>

</span><span>
Therefore,

</span>
Answer:
Option c. 18 withdrawals is correct
Step-by-step explanation:
Gareth has to invest = $2,000
His local bank gives 2.2% annual interest and gives him the ability to make ATM withdrawals without any charges.
In an online savings gives 4.85% annual interest, but charges $3 every time he makes an ATM withdrawal.
Let us find the amount of interest earned from the local bank.
The amount of interest earned from Local Bank = 2.2% of 2000
=
× 2000
= 0.022 × 2000 = $44
The amount of interest earned from online savings = 4.85% of 2000
=
× 2000
= 0.0485 × 2000 = $97
As it is given that savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.
so we need to make x withdrawals from both accounts such that:
97 - 3x = 44
Let us solve for x.
Upon subtracting 97 from both sides of or equation we will get,
97 - 97 - 3x = 44 - 97
3x = -53

x = 17.666 rounded to 18
Therefore, Gareth must make 18 ATM withdrawals every year for the local savings account to be a better deal than the online savings account.
Answer:1. C 3. 52
Step-by-step explanation: