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MaRussiya [10]
3 years ago
14

Let P (n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The goal is to sh

ow, using strong induction, that P (n) is true for all integers n ≥ 18.
Mathematics
1 answer:
natulia [17]3 years ago
7 0

Complete Question

Let P (n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true for n ≥ 18.

Show statements P (18), P (19), P (20), and P (21) are true, completing the basis step of the proof.

Answer:

P(18) is true

P(19) is true

P(20) is true

P(21) is true

Step-by-step explanation:

a. When n = 18

18 cents can be formed using two 7cents and one 4cents

i.e. 2 * 7 + 4 = 18

So, P(18) is true

b. When n = 19

19 cents can be formed using one 7cents and three 4cents

i.e. 1 * 7 + 3 * 4 = 19

So, P(19) is true

c. When n = 20

18 cents can be formed using five 4cents

i.e. 5 * 4 = 20

So, P(20) is true

d. When n = 21

18 cents can be formed using three 7cents

i.e. 3 * 7 = 21

So, P(21) is true

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Solve the following word problem: Kay made 5 less phone calls today than Stephanie. If together they made 21 calls, how many cal
professor190 [17]
Answer:
Kay made 8 phone calls
Stephanie made 13 phone calls

Explanation:
Assume the number of phone calls that Stephanie made is x.
We are given that:
Kay made 5 phone calls less than Stephanie.
This means that:
Kay made x-5 phone calls

We know that the total number of phones is 21.
This means that:
21 = x + x - 5

Now we solve for x as follows:
21 = x + x - 5
21 = 2x - 5
2x = 26
x = 26/2
x = 13

This means that:
Stephanie made x = 13 phone calls
Kay made x - 5 = 13 - 5 = 8 phone calls

Hope this helps :)
5 0
3 years ago
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A pair of sneakers are on sale for $51.00. This is 75% off the original price. What was the original price of the shoes?
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4 0
3 years ago
X² + y² = 34<br>x + y =8​
Nataly [62]

Step-by-step explanation:

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How many times does forty-two go into eight hundred twenty?
tankabanditka [31]
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