Answer:
x = 10°; Angle A = 84°
Step-by-step explanation:
Angle A + Angle B = 180
5x + 34 + 2x + 76 = 180
7x + 110 = 180
7x = 70
x = 10
Angle A: 5(10) + 34 = 50 + 34 = 84°
To draw a heart, one would be choosing 1 card of 13 possible hearts, and 0 from the remaining 39 non-hearts. With respect to the entire deck, one would be choosing 1 card from 52 total cards. So the probability of drawing a heart is

When Michelle replaces the card, the deck returns the normal, so the probability of drawing any card from a given suit is the same,

. In other words, drawing a spade is independent of having drawn the heart first.
So the probability of drawing a heart, replacing it, then drawing a spade is

.
The answer for this problem: Option C.
Answer:
It takes 22.52 years for the balance to triple in value.
Step-by-step explanation:
Continuous compounding:
The amount of money earned using continuous compounding is given by the following equation:

In which A(0) is the initial amount of money and r is the interest rate, as a decimal.
Interest rate of 5%.
This means that
, and thus:



Time for the balance to triple?
This is t for which
. So







It takes 22.52 years for the balance to triple in value.