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Licemer1 [7]
3 years ago
8

Mario invested $5100 $ ⁢ 5100 at 13% 13 % to be compounded daily. What will be the value of Mario's investment in 2 2 years? Rou

nd your answer to the nearest cent, if necessary. Note: 365 365 days in a year and 30 30 days in a month.
Mathematics
1 answer:
Gennadij [26K]3 years ago
5 0

Answer:

lets see

Step-by-step explanation:

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Given: △FKL, FK=a, m∠F=45°, m∠L=30° Find: FL
drek231 [11]

The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL.  This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.

Find the lengths of FM and ML.  Then, FM + ML = FL

<u>FM</u>

ΔFKM (45°-45°-90°): FK is the hypotenuse so FM = \frac{a}{\sqrt{2}} = \frac{a\sqrt{2} }{2}

<u>ML</u>

ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = \frac{a\sqrt{2} }{2} , so KL = \frac{a}{\sqrt{6}} = \frac{a\sqrt{6} }{6}  

<u>FM + ML = FL</u>

(\frac{3}{3})\frac{a\sqrt{2}  }{2} + \frac{a\sqrt{6}  }{6}

= \frac{3a\sqrt{2} + a\sqrt{6} }{6}

8 0
3 years ago
Read 2 more answers
Alex is 12 years older than George. Carl is Three times older than Alex The sum of their ages is 68 Find the ratio of George’s a
earnstyle [38]

Ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

<em><u>Solution:</u></em>

Let "a" be the age of Alex

Let "g" be the age of George

Let "c" be the age of Carl

<em><u>Alex is 12 years older than George</u></em>

Therefore,

Age of Alex = 12 + Age of George

a = 12 + g

g = a - 12 ---- eqn 1

<em><u>Carl is Three times older than Alex</u></em>

Age of Carl = 3 x Age of Alex

c = 3a -------- eqn 2

<em><u>The sum of their ages is 68</u></em>

age of Alex + age of George + age of Carl = 68

a + g + c = 68 ----------- eqn 3

<em><u>Substitute eqn 1 and eqn 2 in eqn 3</u></em>

a + a - 12 + 3a = 68

5a - 12 = 68

5a = 12 + 68

5a = 80

a = 16

<em><u>Substitute a = 16 in eqn 2</u></em>

c = 3(16) = 48

c = 48

<em><u>Substitute a = 16 in eqn 1</u></em>

g = 16 - 12 = 4

g = 4

<em><u>Find the ratio of George’s age to Carl’s age to Alex’s age</u></em>

Ratio of George’s age to Carl’s age to Alex’s age = g : c : a

g : c : a = 4 : 48 : 16

Divide the above ratio by 4 to reduce to lowest terms

g : c : a - 1 : 12 : 4

Thus ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4

6 0
3 years ago
What value of x makes the equation true?
Rasek [7]

<em>Greetings from Brasil...</em>

Let's add all the values on one side and make it equal to the sum of all the other values on the other side

(- X) + (- X) + (- X) + (- X) + (- X) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1  =  X + X + X + (- 1) + (- 1) + (- 1) + (- 1) + (- 1) + (- 1) + (- 1) + (- 1)

- 5X + 12 = 3X - 8

- 5X - 3X = - 8 - 12

- 8X = - 20    x(- 1)

8X = 20

X = 20/8

<h2>X = 5/2</h2>

<em>or X = 2.5</em>

3 0
3 years ago
Account A and Account B both have a principal of $2,000 and an annual interest rate of 2%. No additional deposits or withdrawals
GuDViN [60]

Answer:

Account B earns more interest.

After 20 years, account B will have earned $171.89 more.

Step-by-step explanation:

Let's calculate the total for each account.

Account A:

Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:

A=P(1+rt)

Where A is the future value, P is the principal, r is the rate, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:

A=2000(1+0.02(20))

Multiply and add:

A=2000(1+0.4)=2000(1.4)

Multiply. So, the total amount of money in Account A after 20 years is:

A=\$2800

Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of 2800-2000=\$ 800

Account B:

Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:

B=P(1+\frac{r}{n}})^{nt}

Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:

B=2000(1+\frac{0.02}{1})^{(1)(20)}

Simplify this to acquire:

B=2000(1.02)^{20}

Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:

B\approx\$2971.89

Since our principal was $2000, this means that we earned an interest of approximately  2971.89-2000=\$ 971.89.

So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.

So, Account B earned more interest.

And it earned 971.89-800=\$ 171.89 more than Account A.

And we're done!

5 0
3 years ago
If a triangle has at least two congruent sides, it is an isosceles triangle. An equilateral triangle has three congruent sides.
Bingel [31]
B. An equilateral is an isosceles triangle
3 0
3 years ago
Read 2 more answers
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