Suppose Bob runs an ultra-lightweight client which receives the current head of the Bitcoin block chain from a trusted source. This client has very limited memory and so it only permanently stores the most recent block chain header (deleting any previous headers). Assume block header size is 80 bytes.


a. If Alice sent a payment to Bob, what information should she send to Bob to prove that her payment to Bob has been included in the block chain?

b. Assume Alice’s payment was included in a block k blocks before the current head and there are n transactions per block. Estimate how many bytes this proof will require in terms of n and k and compute the proof size for k=8, n=256.

c. One proposal is to add an extra field in each block header pointing to the last block which has a smaller hash value than the current block. As an example, see the figure below. Block 104 contains the hash of the previous block (block 103), 0x9645. However, block 104 also contains the hash of the last block with hash less than 0x9645, which is the hash of block 102, 0x8345. Similarly, block 103 contains the hash of the previous block (block 102), 0x8345. Block 103 also contains the hash of the last block with hash less than 0x8345, which is the hash of block 100, 0x3645. Explain how this scheme can be used to reduce the proof size from part (b).

d. What is the expected size of a proof (in bytes) now in terms of n and k? To simplify your analysis, you may use asymptotic (Big O) notation. What are the best-case and worst-case sizes?

Answer:

2

Step-by-step explanation:

Answer:

Y=0/0

Step-by-step explanation: since their is no fall or rise in the slope it is 0

First the 9

Then the 5:

The answer is x = 65 (option C)

a) To find the transition matrix from C to the standard ordered basis E, we can express the vectors in C as linear combinations of the vectors in E.

Let's represent the vectors in C as C1 and C2, and the vectors in E as E1 and E2.

C1 = -2E1 - 4E2

C2 = -E2

The transition matrix TEC can be obtained by arranging the coefficients of E1 and E2 as columns:

TEC = [[-2, 0], [-4, -1]]

b) To find the transition matrix from B to E, we need to express the vectors in B as linear combinations of the vectors in E. Let's represent the vectors in B as B1 and B2.

B1 = 4E1 - 7E2

B2 = 3E1 - 5E2

The transition matrix TEB can be obtained by arranging the coefficients of E1 and E2 as columns:

TEB = [[4, 3], [-7, -5]]

c) The transition matrix from E to B can be obtained by finding the inverse of the transition matrix from B to E:

TBE = (TEB)^(-1)

d) To find the transition matrix from C to B, we can express the vectors in C as linear combinations of the vectors in B. Using the same approach as before:

C1 = -2B1 - 4B2

C2 = -B1 - B2

The transition matrix TBC can be obtained by arranging the coefficients of B1 and B2 as columns:

TBC = [[-2, -1], [-4, -1]]

e) To find the coordinates of u = (1, 2) in the ordered basis B, we can use the equation [u]B = TBE[u]E:

[u]B = TBE * [1, 2]^T

f) To find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]C = (1, 2), we can use the equation [v]B = TBC * [v]C:

[v]B = TBC * [1, 2]^T

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The equation that represents the table, in slope-intercept form, is: y = -2x + 11.

The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:

Using two pairs of values from the table, (6, -1) and (9, -7):

Slope (m) = (-7 -(-1)) / (9 - 6)

Slope (m) = -6/3

Slope (m) = -2.

Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:

-1 = -2(6) + b

-1 = -12 + b

-1 + 12 = b

b = 11

To write the equation, substitute m = -2 and b = 11 into y = mx + b:

y = -2x + 11

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To convert a hexadecimal number to binary, each hexadecimal digit can be replaced by its four-bit binary equivalent.

The binary equivalent of each digit is obtained by using the place value of the digit in hexadecimal notation, and replacing it with the corresponding four-bit binary value. For example, to convert the hexadecimal number 80E to binary, we first convert 8 to 1000, 0 to 0000, and E to 1110. Then, we concatenate these binary values to obtain the binary expansion: 100000001110. Similarly, we can convert the hexadecimal numbers 135AB, ABBA, and DEFACED to binary by replacing each digit with its four-bit binary equivalent and concatenating the results.

a) (80E)16 = (100000001110)2

b) (135AB)16 = (1001101010101011)2

c) (ABBA)16 = (1010101110111010)2

d) (DEFACED)16 = (11011110111101011001110110101101)2

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Answer:

150 cm

Step-by-step explanation:

So the scale is 2 cm on the blueprint = 3.5 meters in real life.

Basically you can just divide the height of the building by 3.5 meters:

259/3.5=75

There are 75, 3.5 meters in 259 meters

Since 3.5 meters on the print is 2 cm

You need to multiply the number of 3.5 meters by 2:

75*2=150

150 cm

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

.5

Step-by-step explanation:

Answer:

a.220 ,

Step-by-step explanation:

I really don't know how I'ma gonna explain , I gave to type so that it can send sorrrryyy

Answer:

median<mode

Step-by-step explanation:

median is 18

mode is 19

so median<mode

plz mark as brainliest

Answer:

Percent increase = 25%

Step-by-step explanation:

Given that:

Old price of shoes = $65

New price of shoes = $81

Difference = 81 - 65

Difference = 16

Percent increase = \(\frac{Difference}{Old\ price}*100\)

Percent increase = \(\frac{16}{65}*100\)

Percent increase = 0.246 * 100

Percent increase = 24.6%

Rounding off to nearest whole number

Increase = 25%

Hence,

Percent increase = 25%

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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The coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4) is \((\frac{-17}{5} ,\frac{2}{5} )\)

Explanation :

the coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4)

Apply section formula to find coordinates of point Q

\((\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )\)

Ratio m:n is 2:3 and point R is (x1,y1) , point S is (x2,y2)

Substitute all the values inside the formula

\((\frac{2(2)+3(-7)}{2+3} , \frac{2(4)+3(-2)}{2+3} )\\\\(\frac{-17}{5} ,\frac{2}{5} )\)

The coordinates of point Q is \((\frac{-17}{5} ,\frac{2}{5} )\)

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The simplified expression of -15r + 3(2s - 4r) is 3(-9r + 2s)

The expression can be simplified as follows:

-15r + 3(2s - 4r)

open the brackets

-15r + 6s - 12r

let's combine the like terms

-15r - 12r + 6s

Therefore,

-15r - 12r + 6s

-27r + 6s

-27r + 6s = 3(-9r + 2s)

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Answer:

1 is H

2 is G

3 is B

Answer:

1 is G number 2 is F

Number 1 is G

Number 2 is F

To write an exponential function in the form y = ab^x that passes through the points (0, 9) and (10, 9216), we need to find the values of a and b.

The exponential function that satisfies the given conditions is y = 9 * (2^(x/5)).

Let's start by substituting the coordinates of the first point (0, 9) into the equation y = ab^x:

9 = ab^0

Since any number raised to the power of 0 is 1, we have:

9 = a * 1

This simplifies to:

a = 9

Now, substitute the coordinates of the second point (10, 9216) into the equation:

9216 = 9 * b^10

To solve for b, we can take the 10th root of both sides of the equation:

b^10 = 9216/9

b^10 = 1024

Taking the 10th root, we have:

b = 2

Now we have the values of a and b, so the exponential function that goes through the given points is:

y = 9 * (2^(x/5))

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Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.

To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.

tax rate = (tax / cost of bicycle) x 100%

tax rate = (32 / 400) x 100%

tax rate = 8%

Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.

tax on $700 bicycle = (tax rate / 100) x cost of bicycle

tax on $700 bicycle = (8 / 100) x $700

tax on $700 bicycle = $56

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Answer:

What does the serving consist of?

Step-by-step explanation:

Answer:

it depends on what the servings are

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

22.5 Cubic centimeters is the volume of the rectangular prism.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, A right rectangular prism has a length of 10 centimeters a width of 2.5 centimeters and a height of 0.9 centimeters

From the general formula of Volume of rectangular prism:

Volume = length * width * height

In our case,

Length = 10 cm

width = 2.5 cm

and height = 0.9 cm

thus, Volume = 10 * 2.5 * 0.9

Volume = 22.5

Therefore, the volume of the given rectangular prism is 22.5 Cubic centimeters.

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Answer:

32

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

The requried area of the given square is given as 31.36 ft².

A frame with a square shape i.e. all sides are identical and the measure of the angle between the side is 90°.

Here,
For a square with side a, the relation between the diagonal and side is given as,
diagonal = a√2
8 = a√2
a = 8/√25
a = 5.6 ft

The area of the square is given as,
Area = a²
       = 31.36 ft²

Thus, the requried area of the given square is given as 31.36 ft².

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Answer:

1

Step-by-step explanation:

listing the factors of both numbers

factors of 10 are 1, 2, ,5, 10

factors of 3 are 1, 3

the only common factor to both is 1

the greatest common factor is 1