In Bitcoin, the standard practice for a merchant is to wait for n confirmations of the paying transaction before providing the product. While the network is finding these confirming blocks, the attacker is building his own branch which contradicts it. When attempting a double-spend, the attacker finds himself in the following situation. The network currently knows a branch crediting the merchant, which has n blocks on top of the one in which the fork started. The attacker has a branch with only m additional blocks, and both are trying to extend their respective branches. Assume the honest network and the attacker has a proportion of p and q of tire total network hash power, respectively. 1. [10 pts] Let az​ denote the probability that the attacker will be able to catch up when he is currently z blocks behind. Find out the closed form for az​ with respect to p,q and z. Detailed analysis is needed. (Hint: az​ satisfies the recurrence relation az​=paz+1​+qaz−1​) 2. [10 pts] Compared with the Bitcoin white paper, we model m more accurately as a negative binomial variable. m is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success. Show that the probability for a given value m is P(m)=(m+n−1m​)pnqm.

Answer: FALSE

Step-by-step explanation:

                                   1500 decagram = 15 kg

                                      1 decagram = 0.01 kg

                                       1500 decagram = 1500/0.01 kg

                                                                   = 1500/100 kg

                                        1500 decagram = 15kg  

[tex] \Large{\boxed{\sf C = 31.40 \: inches}} [/tex]

[tex] \\ [/tex]

The circumference of a circle can be calculated using the following formula:

[tex] \Large{\sf C = 2 \pi r } [/tex]

Where:

[tex] \\ [/tex]

Since "a segment drawn from the center of a circle to a point on the circle" is actually the definition of the radius of said circle, we can take r = 5 inches.

[tex] \\ [/tex]

Applying our formula and using 3.14 for π, we get:

[tex] \sf C = 2 \times 3.14 \times 5in \\ \\ \implies \boxed{\boxed{\sf C = 31.4 \: inches = 31.40 \: inches}} [/tex]

Answer:

31.40 inches

Step-by-step explanation:

The circumference of a circle can be calculated using the formula:

Given:

Substitute the given value into the formula:

Simplifying the expression:

[tex]\therefore[/tex] The circumference of the circle is 31.40 inches.

A, C, and D. The angles that have a measure of 180-x are angles that have a measure of 180 minus the value of x. In this case, x is equal to mz1, so the angles that have a measure of 180-x are √3, √5, and √10.

Angle is a mathematical concept that is used to measure the amount of rotation of a line or a plane around a point. An angle is typically measured in degrees, which is the unit of angular measurement. Angles are used in many different fields of mathematics, such as geometry, trigonometry, and calculus. In geometry, angles are used to measure the size of a triangle, the size of a circle, or the angle between two lines. In trigonometry, angles are used to solve problems involving the length of sides and the measure of an arc. In calculus, angles are used to measure the rate of change of a function.

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Let's assume that the length of the rectangle is x cm.

According to the problem, the width is 1/2 of the length. Therefore, the width is 1/2 x cm, or (1/2)*x cm.

The area of the rectangle is given as 388 square centimeters.

We know that the formula for the area of a rectangle is:

Area = Length x Width

So, we can plug in the values we have:

388 = x * (1/2)*x

Simplifying this equation:

776 = x^2

Taking the square root of both sides:

x = √776 ≈ 27.87 cm

Therefore, the length of the rectangle is approximately 27.87 cm, and the width is (1/2)*x, or approximately 13.94 cm.

So the dimensions of the rectangle are approximately 27.87 cm by 13.94 cm.

Answer:

yytyyyyy

Step-by-step explanation:

The zeroes of the function are -12 and 5.

Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.

According to the question:

To find the zeros of the function

f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.

So we start with the equation:

x² + 7x - 60 = 0

Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:

x² + 7x - 60 = (x + 12)(x - 5) = 0

Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x + 12 = 0 or x - 5 = 0

Solving for x, we get:

x = -12 or x = 5

The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.

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The mean of the sampling distribution will be 3.54. Thus, the correct option is C.

The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.

This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.

The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.

Thus, the correct option is C.

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It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.

There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.

However, some statistical tests may not be appropriate for this scenario.

The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.

In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.

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If the rectangle is 40 cm long, 30 cm wide, and 20 cm high, then its volume will be given as 24000 cubic centimeter.

Volume is defined as the space enclosed by the three dimensional figure in itself. No two dimensional object can have volume as volume can be determined only when the length, breadth and height of the figure is known and the value of height is missing in two dimensional figures.

The formula for volume of a cuboid which has rectangular faces is given as follows:

Volume of cuboid = Length × Breadth × height

Volume of cuboid = 40 × 30 × 20

Volume = 24000 cubic centimeter

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Refer to complete question below:

Find the volume of a rectangular cuboid whose dimensions are given as 40 cm long, 30 cm wide, and 20 cm high.

The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).

The fraction represents a portion or part of a whole.

There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.

The fractional distance traveled on day one = ²/₅

The remaining fractional distance = ³/₅ (1 - ²/₅)

The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)

The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)

Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.

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An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.

Inequality is an algebraic statement that two or more mathematical expressions are unequal.

Inequalities can be represented as:

The total amount received by the island = $32,000

The daily receipt of donations = $4,500

Let the number of days = x

Let the funds raised for aid = y

y ≤ 32,000 + 4,500x

Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.

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The null hypothesis (H0) proposed by the friend is H0: p^ = 0.24, where p^ represents the sample proportion of 25 year olds who are married. The alternative hypothesis (Ha) is Hα: p^ ≠ 0.24.

The error in the hypotheses is that the alternative hypothesis is not in line with the problem statement, which suggests that the 25% figure is incorrect.

The appropriate alternative hypothesis would be that the true proportion of 25-year-olds who are married is not equal to 0.25. Therefore, the correct alternative hypothesis would be Ha: p^ ≠ 0.25.

In summary, the correct set of hypotheses for this problem would be:

H0: p^ = 0.25 (Null hypothesis)

Ha: p^ ≠ 0.25 (Alternative hypothesis)

We would use a significance level and statistical test to determine whether we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.

The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."

In other words, if two non-zero numbers are multiplied, then the result is non-zero.

a)  We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.

b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.

c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.

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Answer:[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

Four fifths=4/5

two ninths=2/9

[tex]\frac{4}{5} *5*\frac{2}{9}=\frac{8}{9}[/tex]

Assuming you meant ( four fifths ) * 5 * ( two ninths ), the answer would be 0.88888888888.

If you meant 4/5 x 5 and then x 2/9, the answer would be 8/9, because 4/5 x 5 is 4, and 4 x 2/9 is 8/9.

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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the  correct area of the symmetrical object is option (B). 78 square inches.

If two more identical parts can be separated from a form and arranged in an orderly fashion, the shape is said to be symmetrical. For instance, when you are instructed to cut out a "heart" from a sheet of paper, all you need to do is fold the paper, draw one-half of the heart at the fold, and then cut it out. After you do this, you will discover that the second half precisely matches the first half.

In the first part of the object

Area of the object=½×H×Z

=½×13×6

=39 square inches

Given that object above is symmetrical through Z.

So, the area of 2nd part of object will also be 39 square inches

Hence total area is 78 square inches.

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Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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The required percent increase in the number of games won is approximately 18.2%.So, Option D) is correct.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

The percent increase in the number of games won can be calculated as follows:

[tex]$\text{Percent increase} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100%$$[/tex]

In this case, the old value is the number of games won last year, which is 11, and the new value is the number of games won this year, which is 13. Substituting these values into the formula, we get:

[tex]$\text{Percent increase} = \frac{13 - 11}{11} \times 100% = \frac{2}{11} \times 100% \approx 18.18%$$[/tex]

Therefore, the percent increase in the number of games won is approximately 18.18%.

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The value of the missing sides of the triangle given above include the following;

2.)X = 65°

3.) X = 60°

4.) X = 20°

ABC = isosceles triangle

AB = AC = 13 cm

BC = 11cm

There is an angle bisector at <A which divides lime BC into two equal parts at D.

BD = 11/2 = 5.5 cm

Cos∅ = adjacent/hypothenuse

Cos X = 5.5/13

cos X = 0.423076923

X = Cos -1(0.423076923)

X = 65°

The two diagonals divides the given rectangle into two opposite equilateral triangles which has each of its sides equal to 60°.

ABC = right angle triangle

Line D divides BC into two equal parts = DC and DB

BC = 16cm (opposite)

DC = 16/2 = 8cm

AB = 23 cm( adjacent)

AC = hypothenuse = BC²+ AB²

AC² = 16²+23²

= 256 + 529

= 785

AC = √785

= 28

<CAB = sin ∅ = opposite/hypothenuse

sin∅ = 18/28

= 0.642857142

∅= sin -1 (0.642857142)

∅ = 40°

Therefore X = 40/2 = 20°

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Answer:

8×21=168? That would make it 168=168? Or you could multiply even more to make 8×25 or somethin?

Step-by-step explanation: I don't know what answer ur looking for but there's some help

Answer:

x < 21.

Step-by-step explanation:

Given the equation: 8x < 168, solve the inequality.

First, make it as if it was an equality and solve x:

8x = 168  (Divide both sides by 8)

x = 21

That means x < 21.

In the following question, among the conditions given, Yes, the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day at the 0.01 level of significance.

This can be determined using a hypothesis test. The null hypothesis is that the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day, and the alternative hypothesis is that it does not.

A chi-square test for goodness of fit is conducted using the given data to test the null hypothesis. The results of this test show that the chi-square statistic is less than the critical value, indicating that the null hypothesis should be accepted and the distribution of service interruptions follows a Poisson distribution with a population mean of 1.5 interruptions per day.

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Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

Christian's company charges $0.8 per mile than Samantha's.

In Mathematics and Geometry, the rate of change can be calculated by using the following mathematical equation (formula);

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x for Christian's company;

Rate of change, m = (43.50 - 22.50)/(20 - 10)

Rate of change, m = 21/10

Rate of change, m = 2.1

Therefore, the difference between the charges by Christian's company and Samantha's company can be calculated as follows;

Difference in charges = 2.1 - 1.30

Difference in charges = $0.8.

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Answer:

The second figure.

Step-by-step explanation:

The first figure's perimeter is:

70 in + 42 in + 56 in = 168 inches.

And the second figure's perimeter is:

42 in + 33 in + 33 in + 64 in = 172 inches.

Therefore, Figure 1 < Figure 2.

a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.

b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.

c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.

d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.

e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.

f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.

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Answer:

do you have the graph to solve it?

Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth

Any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as: b ∈ (-90, ∞)

An inequality is a mathematical statement that compares two values or expressions using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Starting from the given inequality:

7 + (b/45) > 5

We can solve for b by first subtracting 7 from both sides:

b/45 > 5 - 7

Simplifying the right-hand side:

b/45 > -2

Multiplying both sides by 45 to isolate b:

b > -2 * 45

b > -90

Therefore, any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as:

b ∈ (-90, ∞)

For example, x > 5 is an inequality that states that x is greater than 5, while y ≤ 10 is an inequality that states that y is less than or equal to 10.

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EH=EF+FH, we can replace the found values ​​with EF and FH to get EH=12+7=19.

A line segment is a path between two measurable points. Line segments have a defined length so they can form the sides of any polygon.

To solve this problem, we can write EH in terms of EG and FH, taking advantage of the fact that F is between E and G, and G is between F and H. First, notice that EG+GF=EF. Substituting the given values, we get EF=9+3=12.

Then GF+FH=GH, so FH=GH-GF. Substituting in the given values, GH=10 and GF=3, so FH=10-3=7.

Finally, since EH=EF+FH, we can substitute the found values ​​into EF and FH to get EH=12+7=19. Therefore EH = 19

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