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crimeas [40]
2 years ago
8

A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.

Mathematics
1 answer:
skelet666 [1.2K]2 years ago
5 0

Answer:

The correct answer is a. $2275.28; b. 17.04 years

Step-by-step explanation:

Principal to be invested is $2000

Interest rate (r) per year is 6.5 quarterly.

Interest is calculated compoundly.

a. Time (t) for the investment is given to be 2 years.

Amount after two years is = Principal × ( 1+ \frac{r}{100n}) ^ {nt} where the value of n is 4.

⇒ A = 2000  × ( 1+ \frac{6.5}{400}) ^ {8}

⇒ A = $2275.28.

b. Now the value of A is given to be triple the principal = $ (3 × 2000).

Therefore we need to find the value of t.

⇒ 3 × 2000 =  2000  × ( 1+ \frac{6.5}{400}) ^ {4t}

⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)

⇒ t = 17.04

Therefore it would take 17.04 years for the principal to triple.

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Approximate the zeros of the function. Round to the nearest tenth if necessary. f(x) = 4x^2 + 4x - 35. Explain each step on how
svet-max [94.6K]
4x²+4x-35=0
factor: (2x+7)(2x-5)=0
2x+7=0, or 2x-5=0
2x=-7 or 2x=5
x=-3.5 or x=2.5

I don't see any rounding necessary in this case. 

when you factor ax²+bx+c, you take the two factors of a and the two factors of c, one factor of a times one factor of c, the other factor of a times the other factors, the sum of the two products make b.
in this case, the factors of 4 is 2 and 2, the factors of -35 is -5 and 7. I line them up in the following way:
2    -5

2      7
then I multiple them diagonally, the top left 2 multiplying the bottom right 7=14, and the other 2 multiplying -5=-10, 14 and -10 make a sum of 4.

if you don't get the desired sum, switch the factors up and down till you have the right combination. Note: Do not switch left and right. 

I hope this makes sense to you.
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3 years ago
Four times the largest of three consecutive odd integers is 36 more than the sum of the other
erica [24]

If you know how to solve word problems involving the sum of consecutive even integers, you should be able to easily solve word problems that involve the sum of consecutive odd integers. The key is to have a good grasp of what odd integers are and how consecutive odd integers can be represented.

Odd Integers

If you recall, an even integer is always 22 times a number. Thus, the general form of an even number is n=2kn=2k, where kk is an integer.

So what does it mean when we say that an integer is odd? Well, it means that it’s one less or one more than an even number. In other words, odd integers are one unit less or one unit more of an even number.

Therefore, the general form of an odd integer can be expressed as nn is n=2k-1n=2k−1 or n=2k+1n=2k+1, where kk is an integer.

Observe that if you’re given an even integer, that even integer is always in between two odd integers. For instance, the even integer 44 is between 33 and 55.

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It should be noted that for any positive integer, n, the expression of (x + y)^n will be C(n,0)x^n + C+n, 1)x^n-1 .... C(n, n)y^n.

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