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labwork [276]
3 years ago
7

What lump sum must be invested at 9%, compounded monthly, for the investment to grow to $72,000 in 6 years?

Mathematics
1 answer:
lana [24]3 years ago
6 0

Answer: $42042.50

Step-by-step explanation:

We need to use algebra and equations.

A = P x (1 + (R/n)/100)^nt

our amount (A) is $72K

the number of times we compound the money (n) is 12 (12 months in a year, 'compounded monthly')

our rate (R) is 9 (9%)

our time (t) is 6 (6 years)

we need to find our principal/initial amount (p)

72000 = p x (1 + 0.0075)^12x6

p = $42042.50

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Sarah makes 5 ribbons the first day. On the second day she doubles the number of
sdas [7]
20 ribbons

Explanation:
1st day— 5 ribbons
2nd day—2 x 5 = 10 ribbbns
3rd day— 2 x 10 = 20

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3 years ago
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In a stack of 100 newspapers, the comic section is missing from 60 papers. Lexie buys two papers from the stack. What is the pro
Dimas [21]
<h2>Order does not matter no repetition:</h2><h2>40 papers contain the comic section:</h2>

<h3>Number of combinations:</h3>

40c2 = 780 \: combinations

<h3>Total number of combinations:</h3>

100c2 = 4950 \: combinations

p(a) =  \frac{780}{4950}  = 0.15757575757

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2 years ago
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Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common differen
pshichka [43]

Problem 1

<h3>Answer: Arithmetic, common difference = -4</h3>

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

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

  • term2 - term1 = -12 - (-8) = -12 + 8 = -4
  • term3 - term2 = -16 - (-12) = -16 + 12 = -4
  • term4 - term3 = -20 - (-16) = -20 + 16 = -4

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

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

Problem 2

<h3>Answer: Arithmetic, common difference = 5</h3>

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

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

  • -6+5 = -1
  • -1+5 = 4
  • 4+5 = 9

Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

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

Problem 3

<h3>Answer: Not arithmetic</h3>

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

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

  • term2 - term1 = 12 - 3 = 9
  • term3 - term2 = 48 - 12 = 36

The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

  • term2/term1 = 12/3 = 4
  • term3/term2 = 48/12 = 4
  • term4/term3 = 192/48 = 4

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

3 0
3 years ago
On the grid below, which point is located in the quadrant where the x-coordinate is a positive number and the y-coordinate is a
Ann [662]

Answer:

d

Step-by-step explanation:

d=(x, y) =(8,-4) so 4th quadrant

8 0
3 years ago
Please help me!!<br> (x+5) (x-2)<br> Any work out or help would be appreciated!!<br> Thanks! :)
Lostsunrise [7]

Answer:


Step-by-step explanation:

If you treat (x+5) as a single value and (x-2) as the values of x and +2, you can distribute (x+5) to x and +2: ( (x-5)*x + (x-5)*2 ). Then you can treat x-5 as the values of x and -5 and distribute those to the numbers next to them: (×^2 - 5x) + (2x - 10). This results in x^2 -3x - 10.


4 0
3 years ago
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