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mariarad [96]
3 years ago
10

The Martian monetary system uses colored beads instead of coins. A blue bead is worth 3 Martian credits, and a red bead is worth

7 Martian credits. Thus, three blue beads are worth 9 credits, and a blue and red bead together are worth 10 credits, but no combination of blue and red beads is worth 11 credits. Using Induction, prove that for all n ≥ 12, there is some combination of blue and red beads that is worth n credits. Clearly state the type of Induction you have used to prove the problem
Mathematics
1 answer:
GalinKa [24]3 years ago
5 0

Answer:

"a" is showing the number of blue beads

"b" represents the number of red beads in a combination

let "n" show the number of credits.

We get the following equation:

n = 3a + 7b.

Now, we want to prove that for all n ≥ 12, there is some combination of blue and red beads that is worth n credits, there are a, b in N such that:

n = 3a + 7b

Hence we will prove this by induction.

Base Cases: n = 12.

Applying the formula clearly 12 = 3*4+7*0.

n = 13

Applying the formula clearly 13 = 3*2+7*1.

n = 14.

Applying the formula clearly 14 = 3*0+7*2.

<u>Induction Step:</u> Assume that for all 12<=k<n there are x, y in N such that

k = 3x + 7y. We will now prove that there are a, b in N such that n = 3a + 7b.

By the induction hypothesis we know that there are x, y in N such that n-3 = 3x + 7y.

Hence n = n - 3 + 3 = 3x + 7y + 3 = 3(x + 1) + 7y, so choosing a = x + 1

and b = y we see that n = 3a + 7b.

Therefore by induction, the claim is true for all n ≥ 12

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An investment banker deposited $50,000 in an account earning a nominal 6% per year compounded continuously. How much was in the
Orlov [11]

Answer:

The amount in the account at the end of three years will be $59,861.

Step-by-step explanation:

The formula to compute the amount at the end of <em>t</em> years, compounded continuously is:

A=P\times e^{t\times i}

Here,

A = Amount at the end

P = Principal amount

i = interest rate

t = number of years.

It is provided that:

P = $50,000

i = 6%

t = 3 years

Compute the amount in the account at the end of three years as follows:

A=P\times e^{t\times i}

   =50000\times e^{(3\times 0.06)}\\=50000\times 1.19722\\=59861

Thus, the amount in the account at the end of three years will be $59,861.

5 0
3 years ago
How do you solve even number between 300 and 400 it is divisible by both 5 and 9 how you solve it
BigorU [14]
The correct answer would be 360. you go through the multiples of 5 and 9
6 0
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Solve the inequality for x. Show each step of the solution. <br><br> 12x&gt;3(2x+4)-15
Leto [7]

Answer:

x<-2

Step-by-step explanation:

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Which equation has a constant of proportionality equal to 10? Choose 1 answer: Choose 1 answer:
Genrish500 [490]

Answer:

B

Step-by-step explanation:

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Have a great day!

3 0
3 years ago
Read 2 more answers
I need help on this asap thanks
lina2011 [118]
1st find the averages of each one:

Elizabeth average of reading in min =(18+36+15+45+88+57+12)/7 =38.71 min

Sam average of reading in min =(17+52+48+35+13+71+16)/7 =36 min


question:

1) No
2) YES. [the range is te difference between the largest & the smallest)
Eliz Range = 88-12 =76 & Sam's= 71-13 = 58

3) NO. Sam 71 min & Eliz 88 min

4) YES. Median Eliz =45 min. Median Sam =35 min
4 0
3 years ago
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