PLEASE HELP ME I HAVE TWO MINUTES LEFT BE NICE

Mathematics

1 answer:

9966 [12]3 years ago

4 0

Since there are two vowels out of the six letters given, you have a 1/3 chance.

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Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.

anzhelika [568]

Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
$V_{0} =(1+ i_{a} ) ^{1}$
Where
$V_{0}$ = initial investment.
$i_{a}$ = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
$V_{0} =(1+ i_{q} ) ^{4}$
Where
$V_{0}$ = initial investment.
$i_{q}$ = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
$(1+ i_{a} )=(1+ i_{q} ) ^{4}$
Notice that we are not using the initial investment $V_{0}$ since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
$(1+0.07)=(1+ i_{q} ) ^{4}$
$1.07=(1+ i_{q} ) ^{4}$
$\sqrt[4]{1.07} =1+ i_{q}$
$i_{q} = \sqrt[4]{1.07} -1$
$i_{q} =0.017$
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.

6 0

3 years ago

Simplify the problem

Natasha2012 [34]

$\frac{6}{10x^2} \div \frac{6}{10x^3-60x^2} = \frac{6}{10x^2} \cdot \frac{10x^3-60x^2}{6} =\frac{1}{10x^2} \cdot \frac{10x^2(x-6)}{1} =x-6$