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il63 [147K]
3 years ago
15

What is the equation for continuous growth or compound interest

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
4 0

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

Step-by-step explanation: A = P(1 + \frac{r}{n})^{nt}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

From the web

The compound interest formula is ((P*(1+i)^n) - P), where P is the principal, i is the annual interest rate, and n is the number of periods.

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A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid
Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = 2 \times width

Base area = lb

= 2x^2

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}

Now, cost is

= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}

now we have to minimize C(x)

So, we need to compute the C'(x)

= 52x - \frac{648}{x^2}

C"(x)  = 52x - \frac{1,296}{x^3}

now for the critical points, we will solve the equation C'(x) = 0

= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}

C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0

So, x is a point of minima that is

= (\frac{648}{52} )^\frac{1}{3}

Now, Base material cost is

= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}

= 139.75

Side material cost is

= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3}  }

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0
3 years ago
Can someone please help me, someone who's serious lol. PLEASE
klemol [59]

Question 11.4.10

Add up everything in the first row

13+31+24 = 68

We have 68 people with high school only education. Out of this group, 24 are conservative

So we have 24/68 = 6/17 represent the probability of selecting a conservatives person given they have high school only education.

<h3>Answer:  6/17</h3>

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

Question 11.4.15

There are 269+485 = 754 males.

Of this group, 485 are not associates.

Therefore, 485/754 = 0.64 approximately

We focus on the males only because of the phrasing "given that the recipient is male".

<h3>Answer:  0.64 </h3>

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

Question 11.4.16

Refer to the diagram below. Let's say we had 1000 people surveyed. This means we have 1000 in the bottom right corner to represent the grand total.

40% have a pet now currently and also had a pet in the past, so we have 0.40*1000 = 400 people go in the upper left corner of the table. This is the "have a pet now" row and "had a pet in the past" column.

60% do not have a pet now, so 600 people don't have a pet currently. This is the total for row 2. This must mean 1000-600 = 400 people do have a pet currently. This is the total for row 1.

The missing value in row 1 must be 0 because 400+0 = 400. Also, if a person has a pet now, they likely had it in the past as well. To be honest, the wording to set up the time scale for this problem is vague. What does it mean "in the past"? Do the researchers mean in the previous month? Year? It's not clear. Anyway, the first row consists of 400, 0 and 400 in that order.

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

Then we're told that 85% have had a pet in the past. So 0.85*1000 = 850 people had a pet in the past. This goes at the bottom of the "had a pet in the past" column. This leaves 1000-850 = 150 people who didn't have a pet in the past.

Lastly, 15% of the 1000 people surveyed don't have a pet in the present and they didn't have it in the past either. Since 15% of 1000 = 0.15*1000 = 150, we will write 150 in the second entry of row 2. Notice how 0+150 = 150 for the second column. Every row should add up to the entry in the "total" column, and every column should add up to the entry in the "total" row to help check we have the correct table set up. Lastly, notice how 400+600 = 1000 and 850+150 = 1000 to further verify the table.

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

By this point, the table is completely filled out. We're told "given the respondent had a pet". We only focus on the "had a pet in the past" column. 400 people have a pet now out of 850 who had a pet in the past.

Therefore, 400/850 = 0.47 approximately

<h3>Answer: 0.47</h3>

4 0
2 years ago
1. Slope of line 1: 5/12<br> Slope of line 2: 12/5<br> Parallel<br> Perpendicular<br> Neither
ad-work [718]

Answer:

     

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the answer to
katovenus [111]

Answer:

y\geq2

Step-by-step explanation:

1. switch sides

2. distribute

3. simply (combine like terms) in this case it would go to 22y

4. add 48 to both sides

5. simplify

6. divide

y\geq2

6 0
3 years ago
!!!!!!!!! PLEASE HELP !!!!!!!!!!<br><br><br> Solve x² - 6x - 7 = 0
sesenic [268]

Answer:

x = 7, -1

Step-by-step explanation:

4 0
3 years ago
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