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sweet-ann [11.9K]
3 years ago
13

Imagine the United States only had two postage stamps, a 3 cent stamp and a 7 cent stamp. If you can put any number of stamps on

an envelope that you want, what amounts of postage can and cannot be paid for?
Mathematics
1 answer:
cricket20 [7]3 years ago
7 0

Answer:

  • not possible:  1, 2, 4, 5, 8, 11
  • possible: all others

Step-by-step explanation:

Obviously, all multiples of 3 and 7 can be paid.

1 cent can be added by adding a 7-cent stamp and taking away two 3-cent stamps. 2 cents can be added by adding three 3-cent stamps and taking away one 7-cent stamp. Hence any value more than 7 +2(3) = 13 cents can always be accommodated.

Amounts that are impossible:

  1, 2, 4, 5, 8, 11 cents

All other positive integer amounts are possible.

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Answer:

a = $80.3

b = $80

c = 4

d = 16

e = 4

f = 88

g = $132

h = 33%

i = 6

j = 30

k = 21

l = $90

m = $36

o = 21/50

p = 105

q = 7

r = 8 cm

s = 2.4

t = 4

u = 400cm

v = $280

Step-by-step Explanation:

==>Increasing $72 by 10% to get a

a = 110% of $72 = 110% × $73

a = 1.1 × 73

a = $80.3

==>a ($80.3) rounded to the nearest 10 to find b = $80

b = $80

==>Writing b (80) as the product of its primes I.e.

b = 2^{c} * 5

Thus, 80 = 2⁴ * 5

c = 4

==>Calculating c² = d

d = 4² = 16

d = 16

==> ²/8 of d = e

e = ²/8 × 16

e = 2 × 2

e = 4

==> e% of 2200 = f

f = 4% × 2200

f = 0.04 × 2200

f = 88

==>Converting £f to $ = g

If £1 = $1.5,

£88 = $g

1 × g = 1.5 × 88

g = $132

==> Converting \frac{g}{400} into % = h%

h = 132÷400 ×100

h = 0.33 × 100

h = 33%

==> √(h + 3) = i

i = √(33 + 3)

i = √36

i = 6

==> i × (3 + 2) = j

j = 6 × (3 + 2)

j = 6 × 5

j = 30

==> j% of 70 = k

k = j% × 70

k = 30% × 70

k = 0.3 × 70

k = 21

==> If k bottles = $63, 30 bottles = $l

21 bottles = $63

30 bottles = $l

21 × l = 63 × 30

21l = 1,890

l = 1,890/21

l = $90

==>If Tim and Mike (m) shares $90 in the ratio 3:2, Mike (m) would receive thus:

⅖ × $90 = m

m = 0.4 × 90

m = $36

==> √m + m = n

n = √36 + 36

n = 6 + 36

n = 42

==>Converting n% to fraction = o

Thus, o = 42/100

o = 21/50

==> o of 250 = p

p = 21/50 × 250

p = (21 × 250)/50

p = 21 × 5

p = 105

==> expressing p as a product of its primes i.e. p = 3 × 5 × q

105 = 3 × 5 × 7

Therefore, q = 7

==> Given a rectangle with dimensions of q cm and r cm, with an area of 56cm². Let's find r.

Area of rectangle = length × width = q × r

Area = 56 cm²

q = 7 cm

r = ?

56 = 7 × r

56/7 = r

8 = r

r = 8 cm

==> r × 0.3 = s

s = 8 × 0.3

s = 2.4

==> s ÷ 0.6 = t

t = 2.4 ÷ 0.6

t = 4

==> If t is in meters, converting t to cm will give us u

Since 1m = 100cm

4m = u cm

1 × u = 100 × 4

u = 400cm

==> Vikki (v) and John shares $u in the ratio 7:3. Thus, Vikki (v) would receive the following:

v = ⁷/10 × $400

v = 0.7 × 400

v = $280

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Answer:

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Step-by-step explanation:

Lines of best fit are used to try to make a correlation (relationship) about data that will either be positive (uphill), negative (downhill) or no correlation (points are scattered).  Correlation coefficients based off of a line of best fit will fall between -1 and +1 where -1 would represent a perfect negative relationship and +1 would represent a perfect positive relationship.  A correlation coefficient of 0 would indicate that there is no relationship.  So, if your data shows a correlation coefficient of 0.109, which is closest to 0 on a number line, then you can't be sure that your data has a very close relationship.


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