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3 years ago

9

If you deposit ₱10,000 into an account that earns 5% annual interest compounded semiannually, how long will it take until there

is ₱12,000 in the bank account

1 answer:

emmainna [20.7K]3 years ago

8 0

Answer:

t = 3.69 ≈ 3. 7 years

Step-by-step explanation:

Given :

P = 10,000

r = 5%= 0.05

A = 12,000

n = 2 ( because it is compounded semi - annually )

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

$12000 = 10000(1 + \frac{0.05}{2})^{2 t}\\\\1.2 = ( 1 + \frac{0.05}{2})^{2t}\\\\1.2 = (1.025)^{2t}\\\\log \ 1.2 = 2t \ log \ 1.025\\\\2t = \frac{log 1.2 }{log 1.025} \\\\2t = \frac{0.1823}{0.0247}\\\\2t = 7.3805\\\\t = 3.69$

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Please help me with these two math problems that I do not quite understand. This is urgent!

g100num [7]

Answer:

1) $a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19$

2) $a_{10}=4+8(10-1)\Rightarrow a_{10}=76$

Step-by-step explanation:

1) To write an Arithmetic Sequence, as an Explicit Term, is to write a general formula to find any term for this sequence following this pattern:

$a_{n}=a_{1}+d(n-1)\Rightarrow \left\{\begin{matrix}a_{n}=n^{th}\: term\\a_1=1st \: term \\d=\: difference\\n=n^{th}\, term\end{matrix}\right.$

<em>"Write an explicit formula for each explicit formula A(n)=-1+(n-1)(-2)"</em>

This isn't quite clear. So, assuming you meant

Write an explicit formula for each term of this sequence A(n)=-1+(n-1)(-2)

As this A(n)=-1+(n-1)(-2) is already an Explicit Formula, since it is given the first term $a_{1}=-1$ the common difference $d=-2$ let's find some terms of this Sequence through this Explicit Formula:

$a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19$

2) $(4,12,20,28, ..)$ In this Arithmetic Sequence the common difference is 8, the first term value is 4.

Then, just plug in the first term and the common difference into the explicit formula:

$a_{10}=4+8(10-1)\Rightarrow a_{10}=76$

6 0

3 years ago

Which number is a solution of the inequality?

padilas [110]

we know that

A number is an inequality solution if the number satisfies the inequality

<u>Part 1)</u> $10.6 < b$

rewrite the inequality

$b > 10.6$

The answer Part 1) is the option D $14$

Because $14$ satisfies the inequality

$14 > 10.6$ -----> is true

<u>Part 2)</u> $m > 7/12$

The answer Part 2) is the option A $1$

Because $1$ satisfies the inequality

$1 > 7/12$ -----> is true

<u>Part 3)</u> $8< x(7-x)$

we're going to verify every case

<u>case A)</u> For $x=2$

substitute the value of x in the inequality

$8< 2(7-2)$

$8< 10$ ------> is true

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The number $2$ is a solution

<u>case B)</u> For $x=8$

substitute the value of x in the inequality

$8< 8(7-8)$

$8< -8$ ------> is not true

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The number $8$ is not a solution

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substitute the value of x in the inequality

$8< -1(7-(-1))$

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<u>case D)</u> For $x=0$

substitute the value of x in the inequality

$8< 0(7-0)$

$8< 0$ ------> is not true

therefore

The number $0$ is not a solution

therefore

The answer Part 3) is the option A $2$

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