Answer:
4,782,969
Step-by-step explanation:
9^7
Written in expanded form = 9 times 9 times 9 times 9 times 9 times 9 times 9
= 9 × 9 × 9 × 9 × 9 × 9 × 9
= 4,782,969
9^7 means multiplying 9 in 7 places
9^7 = 4,782,969
The sum would end us as: 2.33333333
The first misconception is that the balance shouldn't be paid off in full in order to boost the credit score. This is simply not true. You can pay off all of the balance and it will actually improve the score. The score reflects the ability to pay borrowed money back. A credit card is basically a micro-loan of sorts. So if George pays off the balance, he's paying back the credit card company and that tells the company (and others) that his ability to pay is good. Plus it tells about his priorities which is what the credit score indirectly indicates. Other companies will see that George can pay the money back, so they'll be more eager to lend to him.
The other misconception is that being late is fine and improving the payment habits is what brings up the score. This is murky gray area and somewhat true but also somewhat false. What happens is that if you are late then your score goes down by some amount. When you improve the payment habits, the score goes back up. Whether it goes back to the original value or larger depends on the situation. So the second claim George makes is technically true, but there's broader context to consider. It's similar to how if you shoot yourself in the foot in some videogame, and then let your foot heal up, then you're increasing health points. The first act shouldn't have needed to happen and it reflects a weird backwards thinking. If anything, it wastes time where George could have simply been improving the score (rather than decrease it only to increase it back).
The reality is that keeping up with the payments in a timely fashion is what keeps the credit score healthy. Once again, the score reflects someone's ability to pay back borrowed money. It applies to any kind of loan, which a credit card is a part of.
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In short, George is mistaken by two claims he makes
- Not paying off the balance in full improves the credit score
- Being late on payments, and then improving payment habits, will increase the credit score
When in reality keeping up with payments and paying off the balance will improve the credit score. There's no need to hinder oneself on purpose in the goal of improving from that contrived setback.
Side note: the credit card company wants you to carry a balance so they can charge interest on said balance. That's how they make most of their money. However, even if you go against the wishes of the credit card company, they won't ding you credit score points for paying off the balance in full.
Answer:
Step-by-step explanation:
This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically
θ/360 = a/A
Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have
θ/360 = a/(πr^2)
Solving for “a”:
a = π(r^2)θ/360
So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:
6a = 6π(r^2)θ/360
Which simplifies to
6a = π(r^2)θ/60
Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.
Finally, we substitute θ into our earlier formula to find that
6a = π(r^2)120/60
Or
6a = 2πr^2
So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.
