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2 years ago

Help please- Annuities - Find Time of Investment Algebra Two

Mathematics

1 answer:

suter [353]2 years ago

5 0

Based on the calculation below, the number of years it would be for Mia to have $34,000 is 29.1 years.

<h3>How do we find the period or time of investment?</h3>

The formula in the question is the formula for calculating the future value of an ordinary annuity and it can be rewritten as follows:

A = d((((1 + i)^n) – 1) / i) …………………………… (1)

Where:

A = $34,000

d = $850

i = 0.4% * number of months in a year = 0.4% * 12 = 4.8% = 0.048

n = number of years?

Substitute all the values into equation (1) and solve for n, we have:

$34,000 = $850((((1 + 0.048)^n) - 1) / 0.048)

$34,000 / $850 = (((1 + 0.048)^n) - 1) / 0.048

40 = (((1 + 0.048)^n) - 1) / 0.048

40 * 0.048 = ((1 + 0.048)^n) – 1

1.92 + 2 = (1 + 0.048)^n

3.92 = 1.048^n

Taking the log of both sides, we have:

Log3.92 = nlog1.048

0.593286067020457 = n 0.0203612826477079

n = 0.593286067020457 / 0.0203612826477079

n = 29.1379515370189

Rounding to the nearest of a year, we have:

n = 29.1

Learn more about the future value of an ordinary annuity here: brainly.com/question/17925440.

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(50 points and brainliest.Need help ASAP)

Aleksandr-060686 [28]

Answer: " 2x (2x - 1) (x + 1) " .

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Step-by-step explanation:

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Given:

f(x) = 9x³ + 2x² − 5x + 4 ;

g(x) = 5x³ − 7x + 4 ;

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What is: f(x) − g(x) ?

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Plug in: " 9x³ + 2x² − 5x + 4 " for: " f(x) " ;

and: " (5x³ − 7x + 4) " ; for: "g(x)" ;

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→ " f(x) − g(x) =

" 9x³ + 2x² − 5x + 4 − (5x³ − 7x + 4) " .

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Rewrite this expression as:

→ " 9x³ + 2x² − 5x + 4 − 1(5x³ − 7x + 4) " .

→ {since: " 1 " ; multiplied by "any value" ; is equal to that same value.}.

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Now, let us example the following portion of the expression:

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" − 1(5x³ − 7x + 4) "

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Note the "distributive property" of multiplication:

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→ a(b + c) = ab + ac ;

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Likewise:

→ a(b + c + d) = ab + ac + ad .

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As such:

______________________________________

→ " − 1(5x³ − 7x + 4) " ;

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= (-1 * 5x³) + (-1 * 7x) + (-1 * 4) ;

= - 5x³ + (-7x) + (-4) ;

= - 5x³ − 7x − 4 ;

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Now, add the "beginning portion of the expression" ; that is:

" f(x) " ; to the expression ; which is:

→ 9x³ + 2x² − 5x + 4 ;

→ as follows:

_______________________________________

→ 9x³ + 2x² − 5x + 4 − 5x³ − 7x − 4 ;

→ {Note that the: " - " sign; that is;

the "negative sign", in the term: " -5x³ " ;

becomes a: " − " sign; that is; a "minus sign" .}.

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Now, combine the "like terms" of this expression; as follows:

+ 9x³ − 5x³ = + 4x³ ;

− 5x − 7x = − 2x ;

+ 4 − 4 = 0 ;

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and we have:

______________________________________

→ " 4x³ + 2x² − 2x ".

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Now, to write this answer in "factored form" :

Note that among all 3 (three) terms in this expression, each term has a factor of "2" . The lowest coefficient among these 3 (three) terms is "2" ; so we can "factor out" a "2".

Also, each of the 3 (three) terms in this fraction is a coefficient to a variable. That variable takes the form of "x". The term in this expression with the variable, "x"; with the lowest degree has the variable: "x" (i.e. "x¹ = x" ) ; so we can "factor out a "2x" (rather than just the number, "2".).

So, by factoring out a "2x" ; take the first term [among the 3 (three) terms in the expression] —which is: "4x³ " .

2x * (?) = 4x³ ? ;'

↔ $\frac{4x^3}{2x} =$ ? ;

→ 4/2 = 2 ;

$\frac{x^{3}}{x} = \frac{x^3}{x^1} = x^{(3-1)} = x^{2}$ ;

As such: 2x * (2x²) = 4x³ ;

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Now, by factoring out a "2x" ; take the second term [among the 3 (three) terms in the expression] — which is: "2x² " .

2x * (?) = 2x² ? ;

↔ $\frac{2x^{2}}{2x} =$ ?

→ 2/2 = 1 ;

→ $\frac{x^{2}}{x} = \frac{x^2}{x^1}= x^{(2-1)} } = x^1 = x$ ;

As such: 2x * (x) = 2x²

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Now, by factoring out a "2x" ; take the third term [among the 3 (three) terms in the expression] — which is: " − 2x " .

2x * (?) = - 2x ;

↔ $\frac{-2x}{2x} =$ -1 ;

As such: 2x * (-1) = − 2x .

__________________________________________

So:

__________________________________________

Given the simplified expression:

→ " 4x³ + 2x² − 2x " ;

We can "factor out' a: " 2x " ; and write the this answer is: "factored form" ; as:

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"2x (2x² + x − 1 ) . "

Now, we can further factor the:

" (2x² + x − 1) " ; portion;

Note: "(2x² + x - 1)" =

2x² + 2x - 1x -1 = (2x -1) + x (2x - 1 ) =

(2x - 1) ( x + 1)

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Now, bring down the "2x" ; and write the Full "factored form" ; as follows:

_______________________________________

→ " 2x (2x - 1) (x + 1) " .

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Hope this helps!

Wishing you the best!

_______________________________________

7 0

3 years ago

Solve the inequality. q - 1 1/3 > -2 1/2

ioda

$\Leftrightarrow q>1\frac{1}{6}$

Step-by-step explanation:

$q-\frac {11}{3}>-2\frac{1}{2}$

$\Leftrightarrow q>-2\frac{1}{2}+\frac {11}{3}$

$\Leftrightarrow q>\frac{7}{6}$

$\Leftrightarrow q>1\frac{1}{6}$

6 0

3 years ago

In a study on the time that

krok68 [10]

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

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To solve this question, we need to find the confidence interval for the amount of time it takes the students to get the degree.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

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The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 80 - 1 = 79

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95% confidence interval

Standard level of confidence, we have to find a value of T, which is found looking at the t table, with 79 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.9905.