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aivan3 [116]
3 years ago
11

Greg just purchased a house for $450,000. His annual homeowners insurance premium is $0.42 per $100 of value. If his annual prem

ium is divided into equal monthly payments, what will Greg have to pay on a monthly basis to keep his home insured? a. $1,890.00 b. $157.50 c. $1,575.00 d. $131.25 Please select the best answer from the choices provided A B C D
Mathematics
1 answer:
sveta [45]3 years ago
4 0

Answer:

\$157.50

Step-by-step explanation:

The computation of the amount pay on monthly basis is shown below:

But before that we need to find out the annual amount pay which is to be find out by applying the following formula

= Purchase\ value \times \frac {insurance\ premium}{percentage}

where,

Purchase value of the house is $450,000

Insurance premium is $0.42

Percentage is $100

Now put these values to the above formula

So, the annual amount pay is

= \$450,000 \times \frac {\$0.42}{\$100}

= \$1,890

Now the monthly paying amount is

= \frac{Annual\ amount\ pay}{total\ number\ of\ months\ in\ a\ year}

= \frac{\$1,890}{12\ months}

= \$157.50

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tino4ka555 [31]

a.

x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}

By Fermat's little theorem, we have

x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5

x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7

5 and 7 are both prime, so \varphi(5)=4 and \varphi(7)=6. By Euler's theorem, we get

x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5

x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7

Now we can use the Chinese remainder theorem to solve for x. Start with

x=2\cdot7+5\cdot6

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x=2\cdot7\cdot4\cdot2+5\cdot6

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x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6

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b.

x^5\equiv3\pmod{64}

We have \varphi(64)=32, so by Euler's theorem,

x^{32}\equiv1\pmod{64}

Now, raising both sides of the original congruence to the power of 6 gives

x^{30}\equiv3^6\equiv729\equiv25\pmod{64}

Then multiplying both sides by x^2 gives

x^{32}\equiv25x^2\equiv1\pmod{64}

so that x^2 is the inverse of 25 mod 64. To find this inverse, solve for y in 25y\equiv1\pmod{64}. Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that (-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}.

So we know

25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}

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and multiplying both sides by x tells us

x^5\equiv17x\equiv3\pmod{64}

Use the Euclidean algorithm to solve for x.

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that (-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}, and so x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}

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