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Margarita [4]
3 years ago
9

Elect the answer with BOTH correct answers (the product in standard form and the product in Scientific Notation). (8.08×106)×(7.

5×10−2)
A) 60,600;6.06×105
B) 60,600;60.6×104
C) 606,000;6.06×105
D) 606,000;60.6×104
Mathematics
1 answer:
kakasveta [241]3 years ago
3 0
Question: elect the answer with BOTH correct answers (the product in standard form and the product in Scientific Notation). (8.08×106)×(7.5×10−2)
A) 60,600;6.06×105
B) 60,600;60.6×104
C) 606,000;6.06×105
D) 606,000;60.6×104





Answer: a or b
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When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100
ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the <em>future value FV.</em>  

In order to see the rule of formation, let's see the value (in $) for the first few years

<u>End of year 0</u>

1,000

<u>End of year 1(capital + interest + new deposit)</u>

1,000*(1.09)+10  

<u>End of year 2 (capital + interest + new deposit)</u>

(1,000*(1.09)+10)*1.09 +10 =

\bf 1,000*(1.09)^2+10(1+1.09)

<u>End of year 3 (capital + interest + new deposit)</u>

\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)

and we can see that at the end of year 50, the future value is

\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}

The sum  

\bf 1+1.09+(1.09)^2+...+(1.09)^{49}

is the <em>sum of a geometric sequence </em>with common ratio 1.09 and is equal to

\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356

and the future value is then

\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564

The <em>present value PV</em> is

\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62

rounded to the nearest hundredth.

5 0
3 years ago
What is the value of y in the following system?
Vera_Pavlovna [14]

Answer:

x=2, y=1. (2, 1).

Step-by-step explanation:

y=3x-5

6x+3y=15

-----------------

6x+3(3x-5)=15

6x+9x-15=15

15x-15=15

15x=15+15

15x=30

x=30/15

x=2

y=3(2)-5=6-5=1

8 0
3 years ago
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