Answer:
$610,297.11
Step-by-step explanation:
The problem seems to make several assumptions:
- contributions are made at the end of each year
- contributions and employer matching funds are not taxed until retirement
- the 15% tax rate applies to the account balance amount at retirement
Of these, the last is least likely to be true in the United States.
___
Based on the assumptions above, we compute the amount from the future value of the series of contributions, then subtract 15% from that result.
FV = P·((1 +r)^n -1)/r . . . . where P is the amount of each payment, r is the annual interest rate, n is the number of payments.
The amount deposited each year is ...
$4770 + 0.60·4770 = $7630
Then the future value after 34 deposits is ...
FV = 7630·(1.055^34 -1)/0.055 ≈ 717,996.60
When this amount is reduced by the assumed 15% tax rate, it becomes ...
$717,996.60 - 0.15·717,996.60 = $610,297.11
To find this answer you simply subtract eight from sixty-two, which gives you....
54!
So there are 54 student in the science club!
Hope this helps! :)
Answer: One-Half of the sweaters are blue.
Step-by-step explanation: Half of 6 is 3.
Okay, so your first one, number six. You have two shapes there, a cone and a circle. Now you have a full cone and a half of a circle. Let's start with the cone. The formula for the volume of a cone is πr²h/3. You have your height, that is 12, so get your paper out and plug that in. H = 12. Now, your radius is where it gets a bit tricky. Have you ever heard of the Pythagorean theorem? It's a²+b²=c². Look at the cone, but look at it like it's a two-dimensional shape. You see the triangle in the middle, ignore the rest and pretend it's only that triangle. You now have a right triangle, You know your height is 12, and by looking at the triangle adjacent to it, and know it's equal, you know that your hypotenuse (the longest side of your triangle) is 15. So plug that into the Pythagorean theorem. Now you have 12²+b²=15². Use algebra to work that out, and you're left with 9. So your radius is 9. Now plug that into your volume of a cone equation. The volume of the cone is about 1017.88. Now find the circle or sphere. The formula is 4/3πr³. Just plug in your radius and get your answer, which is 3053.63. Now cut that in half, as you've only got half a circle. Now you've got 1526.82. Now add that to the volume of your cone, and you've got your final answer. 2544.7, or about that. I used π on a calc, and not 3.14, so it might be a little different.
Do you think you can do the next one? Just look at your triangle in there. You've already got one side and a hypotenuse, so plug it into the Pythagorean theorem and get your last side. Then look at the little marks on there and you can see if places are the same. If you need help with it don't hesitate to ask. I'm staying up all night anyway. Homeschooled and behind, so I'm not going anywhere.
