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alexdok [17]
3 years ago
6

One day, a king left his castle with a bag of silver coins to wander his kingdom. to the first peasant he met, he gave one-half

of the coins plus two more. A little later, he met another peasant to whom he also gave one-half of his coins plus two more. Walking on, he met a third peasant and again gave half his coins plus two more. FInally, the king went home with two coins left in his bag. How many coins did he have to begin with? Create an algebraic equation. Please explain why.
Mathematics
2 answers:
tresset_1 [31]3 years ago
8 0

Answer:

The king left his castle with 44 silver coins.

Step-by-step explanation:

A king left his castle with a bag of silver coins and he gave his coins to 3 peasants in an order. Finally he went home with two coins left.

To solve this question we calculate it in reverse order.

Finally the king has in his bag = 2 coins

Before it he met third peasant king had =

= (2+2) × 2

= 4×2 = 8

Before the king met third peasant, he had 8 coins.

Before he met Second peasant king had :

= (8+2) × 2

= 10 × 2 = 20

Before he met second peasant king had 20 coins.

Before he met first peasant he had :

= (20+ 2) × 2

= 22 × 2 = 44

Before King met first peasant he had 44 silver coins.

galina1969 [7]3 years ago
6 0
Are there any options on what type of problem u want?
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<u>Step-by-step explanation:</u>

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Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.
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Answer: The length is 13cm and the width is 7cm

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = W*L

In this case we have:

L = (2*x + 9) cm

W=(3*x + 1) cm

Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

A = (6*x^2 + 29*x + 9) cm^2

now we remove two squares with sides of x cm

The area of each one of these squares is (x cm)*(x cm)  = x^2 cm^2

Then the area of the figure will be:

area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2

area = (4*x^2 + 29*x + 9) cm^2

Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

0 =  (4*x^2 + 29*x + 9) cm^2 - 83 cm^2

0 = (4*x^2 + 29*x - 74) cm^2

Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)}  }{2*4} = \frac{-29 \pm 45}{8}

Then the two solutions are:

x = (-29 - 45)/8 = -9.25  (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

The other solution is:

x = (-29 + 45)/8 = 2

x = 2

Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

Width = (3*2 + 1)cm = 7cm

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Required information Skip to question NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to re
pogonyaev

The result for the given 14 length bit string is-

(a) The bit strings of length 14 which have exactly three 0s is 2184.

(b) The bit strings of length 14 which have same number of 0s as 1s is 17297280.

(c) The bit strings of length 14 which have at least three 1s is 4472832.

<h3>What is a bit strings?</h3>

A bit-string would be a binary digit sequence (bits). The size of the value is the amount of bits contained in the sequence.

A null string is a bit-string with no length.

The concept used here is permutation;

ⁿPₓ = n!/(n-x)!

Where, n is the total samples.

x is the selected samples.

(a) Because there are exactly three 0s, its other digits have always been one, hence the total of permutations is equal to;

n = 14 and x = 3 digits.

¹⁴P₃ = 14!/(14-3)!

¹⁴P₃ = 2184.

Thus, the bit strings of length 14 which have exactly three 0s is 2184.

(b) Because it is a bit string with 14 digits and it can only have digits 0 or 1, we must choose 7 0s and the remaining 7 1s, hence the number possible permutations is equal to;

n = 14 and x = 7 digits.

¹⁴P₇ = 14!/(14-7)!

¹⁴P₇ = 17297280.

Thus, the bit strings of length 14 which have same number of 0s as 1s is 17297280.

(c) The answer is identical to problem a, but the rest of a digits could be either 0 or 1, hence it must be doubled by 2¹¹ because there are 11 digits, each of which can be one of two options;

= 2184×2¹¹

= 4472832

Thus, he bit strings of length 14 which have at least three 1s is 4472832.

To know more about permutation, here

brainly.com/question/12468032

#SPJ4

The correct question is-

How many bit strings of length 14 have:

(a) Exactly three 0s?

(b) The same number of 0s as 1s?

(d) At least three 1s?

3 0
1 year ago
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