What is the value of 324 + 435 + 546 when written in base 7?

1 answer:

6 0

<span>The sum of 324, 435, and 546 is 1305. If this number were to be expressed by the base of 7, we would need to figure out what value of exponent would satisfy the requirement. This can be done by setting up an equation where 7 to the power of x must equal 1305. Using logarithms, one can solve for x and find it to be 3.6866853. Thus the sum of the aforementioned numbers, expressed in by the base of 7, is 7^3.6866853.</span>

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How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $11,0

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Answer:

$8950.37

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.

Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:

$11,000 = P(1 + 0.07/2)^(2*3), or

$11,000 = P (1.035)^6

$11,000 $11,000

Solving for P, we get P = ---------------- = ------------- = $8950.37

1.035^6 1.229

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