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Sphinxa [80]
2 years ago
12

Heyyy wanna help mee

Mathematics
2 answers:
Kipish [7]2 years ago
8 0

Answer: Only j = 2

============================================

Explanation:

Let's solve for j

\frac{96}{j} \ge 40\\\\96 \ge 40j\\\\\frac{96}{40} \ge j\\\\2.4 \ge j\\\\j \le 2.4

In the second step, I multiplied both sides by j. If j is a positive number, then the inequality sign will not flip. All of the answer choices are positive numbers, so we don't have to worry about the inequality sign flipping.

The last step shows that j = 2.4 or j < 2.4

So j is 2.4 or smaller.

Of the list given to us, only j = 2 fits the description, since something like j = 8 is not 2.4 or smaller.

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

If j = 2, then,

\frac{96}{j} \ge 40\\\\\frac{96}{2} \ge 40\\\\48 \ge 40\\\\

which is a true statement since 48 is larger than 40. This shows that j = 2 is a solution.

Something like j = 8 does not work because

\frac{96}{j} \ge 40\\\\\frac{96}{8} \ge 40\\\\12 \ge 40\\\\

which is false because 12 is not equal to 40 or larger than 40. This means j = 8 is not a solution. You should find that j = 12 and j = 3 lead to similar false statements.

Of the list given, j = 2 is the only solution.

masya89 [10]2 years ago
8 0
<h2><u>Answer:</u></h2><h2><u></u>\boxed{\boxed{\sf{j=2}}}<u></u></h2><h2><u></u></h2><h2><u>Solution Steps:</u></h2>

______________________________

<h3>1.) Solve using j = 12:</h3>
  • Plug in 12: \frac{96}{12} ≥ 40
  • Divide 96 by 12: =8
  • Compare: 8 ≥ 40

So this is False.

<h3>2.) Solve using j = 8:</h3>
  • Plug in 8: \frac{96}{8} ≥ 40
  • Divide 96 by 8: =12
  • Compare: 12 ≥ 40

So this is False.

<h3>3.) Solve using j = 2:</h3>
  • Plug in 2: \frac{96}{2} ≥ 40
  • Divide 96 by 2: =48
  • Compare: 48 ≥ 40

So this is True.

<h3>4.) Solve using j = 3:</h3>
  • Plug in 3: \frac{96}{3} ≥ 40
  • Divide 96 by 3: =32
  • Compare: 32 ≥ 40

So this is False.

______________________________

<u />

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a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is <u>$11,949.50</u>.

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<h3>How is the future value determined?</h3>

The future value can be determined using an online finance calculator.

Data and Calculations:

<h3>a) Compounded Semiannually:</h3>

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

<u>Result</u>:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

<h3>b) Compounded Continuously:</h3>

Using the formula A = Pert

Principal (P):  $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years):   8 years

<u>Result</u>:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is <u>$11,949.50</u>,  the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

Learn more about compounding interest at brainly.com/question/24274034

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