Network propagation: Assume a simple model for how quickly Bitcoin blocks propagate through the network: after t seconds, a group of miners controlling a proportion α(t) of the mining power has heard about the transaction, up to some point t max after which all miners will have heard about it. That is, α(t)=1 for all t≥tmax . Further assume that α(0)=0 and α(t) is monotonically increasing in t. Assume that blocks are found in a Poisson process with a mean time to find a block of β=600 seconds (λ=1/600). A stale block (likely to become an orphan block) occurs if some miner finds a block before news of the most recent block reaches them. a. Given the design of the Bitcoin P2P network, explain why an exponential propagation model (i.e. α(t)∝b t for some b) is a plausible model. Hint: Recall that the derivative of an exponential is another exponential function.

Answer:

-500

Step-by-step explanation:

(2a^4)^2

-----------------

a^0 a^5

We know ( xy) ^z = x^z y^z

so

(2a^4)^2 = 2^2 a^4^2

and x^y^z =x^(y*z)  so a^4^2 = a^(4*2) = a^8

(2a^4)^2 = 4 a^8

We know that a^0 = 1

4 a^8

-----------------

1 a^5

We know x^y / x^z = x^ ( y-z)

4 a^( 8-5)

4 a^3

Let a = -5

4 ( -5) ^3

4 ( -125)

-500

Answer:

He is right it is -500

Step-by-step explanation:

The number of compounding per year is\(N = 920(1+0.03)^4t\)

This can be calculated by making use of the formular;  920(1.03)^4t and use the  compound interest equation which is N=P( 1+r/n)^nt

We know that 12% was given as the rate per year, then to get the quarter rate we divide by factor of 4, which is  12/4= 3%

The compounding for t years = n*t = 4t where n=4.

and the Initial number of cars serviced=920

Then we can substitute the values into the above equation, we have Thus \(N = 920(1+0.03)^4t\)

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CHECK THE COMPLETE QUESTION BELOW:

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. 920(1.03) is the number of cars multiplied by 1.03. The quarterly rate of growth is 0.03 or 3%. The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The growth rate is 1.03. Exponent arrowRight Base arrowRight Coefficient arrowRight Rate arrowRight

Answer:

D

Step-by-step explanation:

ΔWXZ and ΔYZX

WZ ≅XY    {Given}

ZX ≅ ZX      {Reflexive property}

∠W ≅ ∠Y

But for SAS congruent the congruent angles should between congruent sides( WX & WZ should be congruent to ZY & XY respectively).

So it cannot be proved using SAS congruent

Answer:

Midpoint formula: (x1+x2/2, y1+y2/2)

Step-by-step explanation:

Take your x points and place them into the formula and then take your y points and do the same.

Answer:

(first)x+(second)x/2(fraction), (first)y+(second)y/2(fraction

Step-by-step explanation:

If you add the x values together and the y values together and divide them both by two you will get your x value for the midpoint and then your y value for the midpoint

9 minutes is the new standard time for the navigator iii.

What is statistics and example?

If a process improvement has changed the mean observed time for element 6 to 1.50 minutes, then

Element            1    2            3         4             5          6  

Mean obs. Time(t) 1.11   3.1    0.895  1.283333 1.565 1.5  

Normal time       1.0545  1.395 0.93975 1.283333 1.33025 1.65   Sum

Standard time   1.240588 1.641176 1.105588  1.509804 1.565 1.941176

   Sum    9.003333

New standard time = 9 minutes

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Answer:

Step-by-step explanation:

-2/5 and -1/5

Since -1 > -2

So, -2/5 < -1/5

(ii) -5/7 and -3/7

Since -5 < -3

So, -5/7 < -3/7

(iii)

2/9 and -5/11

Note :- That all positive fraction are greater than negative fraction.

So, 2/9 > -5/11

Answer:

81

Step-by-step explanation:

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.

Answer: 81

Step-by-step explanation:

Answer:

1. The union of angle 3 and angle 4

2. Angle 6 = 30°

The selling price of the jeans, after applying the 30% discount, is $41.93 and he discount on the jeans is $17.97, and the selling price of the jeans after the discount is $41.93.

To calculate the discount and the selling price of the jeans, we can use the information provided. The original price of the jeans is $59.90, and the store is offering a 30% discount on every purchase.

To find the discount amount, we multiply the original price by the discount percentage:

Discount = 30% * $59.90

Discount = 0.30 * $59.90

Discount = $17.97

So, the discount on the jeans is $17.97.

To calculate the selling price of the jeans after the discount, we subtract the discount from the original price:

Selling Price = Original Price - Discount

Selling Price = $59.90 - $17.97

Selling Price = $41.93

Therefore, the selling price of the jeans, after applying the 30% discount, is $41.93.

In conclusion, the discount on the jeans is $17.97, and the selling price of the jeans after the discount is $41.93.

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Answer:

90

Step-by-step explanation:

first you do 11 + 11 =22

23+45=68

now im postitive you add 68 and 22 and get you final answer which is ...

90

Answer:

1 23/45

Step-by-step explanation:

Start by multiplying numerators and denominators to get the LCD in all fraction denominators

=11×45/11×45+23×11/45×11

Then rewriting the equation with the equivalent fractions

=495/495+253/495

With like denominators we can operate on just the numerators

=495+253/495

=748/495

Simplifying the answer

=68/45

=68/45

=1 23/45

The line of intersection between two planes can be represented by symmetric equations. In this case, the symmetric equations for the line of intersection are:

x = 0

y = -c

z = c

To find the symmetric equations for the line of intersection,

first we set up a system of equations using the normal vectors of the planes.

The normal vector of Plane 1 is [5, -2, -2].

The normal vector of Plane 2 is [4, 1, 1].

Let's call the direction vector of the line of intersection "d = [a, b, c]".

Next, we set up a system of equations using the dot product between the direction vector and the normal vectors of the planes.

For Plane 1: [5, -2, -2] ⋅ [a, b, c] = 0

For Plane 2: [4, 1, 1] ⋅ [a, b, c] = 0

Simplifying these equations, we have:

5a - 2b - 2c = 0

4a + b + c = 0

Solving the system of equations,

Multiplying the second equation by 2, we get:

8a + 2b + 2c = 0

Adding this equation to the first equation, we eliminate b and c:

13a = 0

a = 0

Substituting a = 0 back into the second equation, we find:

0 + b + c = 0

b + c = 0

b = -c

Therefore, the direction vector of the line of intersection is d = [0, -c, c], where c can be any real number.

Then, write the symmetric equations for the line of intersection.

We can choose a point on the line of intersection as the origin, which gives us the point (0, 0, 0).

Thus, the symmetric equations for the line of intersection are given below:

x = 0, y = -c, z = c

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Answer:

Y= -1.5x+3

Step-by-step explanation:

(Y-Y1)=m(x-x1)

0-3=m(2-0)

m= -1.5

Y= -1.5x+B

when y=3 and x=0 b=3

Answer:

So, plug in those x values for "x" in the expression f(x)

0, 5

1, 8

2, 11

3, 14

4, 17

Answer:

Step-by-step explanation:

Pls check

To determine the number of aardvarks that were there last year, we will have to use the formula for exponential growth. Exponential growth is a type of growth that increases in size exponentially over time.

The formula for exponential growth is given by the equation:

\(Nt = N\times(1 + r)^t,\)

where N₀ is the initial population, r is the annual growth rate, t is the time in years, and Nt is the population after t years.Let's use this formula to find the number of aardvarks last year. Given that the current population of aardvarks is 756, and the growth rate is 8%, we can write the equation as

\(:Nt = N \times (1 + r)^t756 = N \times(1 + 0.08)^1So, N = 756 / (1 + 0.08)^1\)

Now, we need to find the population of aardvarks last year, which is t = 1 year before.

Thus, plugging in t = 1, we get

:\(N = 756 / (1 + 0.08)^1N= 700\)

Hence, there were 700 aardvarks last year.

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Answer:

y = -3 and x = -3

Step-by-step explanation:

The given identity is verified as follows:

Starting with the left side of the equation: tan(A - B)

Using the trigonometric identity for the difference of two angles, we have:

tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

This matches the right side of the equation: (tan A - tan B) / (1 + tan A tan B)

To verify the given identity, we need to manipulate the left side of the equation using trigonometric identities and simplify it until it matches the right side of the equation.

Starting with the left side, we have tan(A - B). Using the trigonometric identity for the difference of two angles, we can express this as (tan A - tan B) / (1 + tan A tan B).

By applying the identity for the difference of two angles, we can rewrite tan(A - B) as (tan A - tan B) / (1 + tan A tan B). This is because tan(A - B) is equivalent to the ratio of the difference of the tangent values of the angles A and B, divided by 1 plus the product of the tangent values of angles A and B.

After simplification, we see that the left side of the equation matches the right side of the equation, (tan A - tan B) / (1 + tan A tan B).

Therefore, the given identity is verified.

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Answer:

-25

Step-by-step explanation:

sorry for the mistake

​

The inequality to represent the problem is x + 1.25y ≥ 2000 and it's graph is attached below

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in mathematics. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

Let;

a) The inequality to represent the situation can be expressed as

1x + 1.25y ≥ 2000

This is further expressed as;

x + 1.25y ≥ 2000

b) The graph of the inequality x + 1.25y ≥ 2000 is attached below.

c) The possible solutions are at (2000, 0) and (0, 1600)

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The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).

        z = x₁ + 2x₂ = (0) + 2(3/4)

                    = 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0

                        z = x₁ + 2x₂ = (3) + 2(0) = 3

The maximum value of the objective function z is 3, and it occurs at the point (3, 0).

Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.

maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function,

        evaluate the objective function at each corner of the feasible region:

                                (0, 0), (3, 0), and (2, 5).

                          z = x₁ + x₂ = (0) + 0 = 0

                          z = x₁ + x₂ = (3) + 0 = 3

                           z = x₁ + x₂ = (2) + 5 = 7

The maximum value of the objective function z is 7, and it occurs at the point (2, 5).

Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.

maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.

To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:

To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).

                         z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4

                      z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6

                      z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19

The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.

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Answer: 84 square inches.

Step-by-step explanation:

Side A of shaded: 5+3+3 = 11

Side B of shaded: 3+3+3= 9

11x9= 99

99-(3x5{normal rectangle area})= 84

On Sunday mornings, Jason enjoys reading the sports. The structure is supported by a pillar at each corner.

The sentence depicts a building that is supported at each corner by something. The word for such a supporting structure is "pillar," which refers to a vertical, upright support that is frequently employed to hold up a building or other structure.

The other possibilities do not fit the sentence's context as well. "Column" is a word that sounds similar to "pillar" and may work, but it is normally used to indicate a vertical support that is more slender and decorative than a pillar.

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Answer:  The graph is shown below. It is nonlinear

==========================================================

Explanation:

I used GeoGebra to make the graph. Desmos is another option I recommend.

The equation we graph is y = (1/2)^x since we're splitting the paper in half each time. This is an exponential decay function. Note how the curve slopes downhill when moving to the right.

It appears the curve touches or crosses the x axis; which is misleading. Instead, the curve is getting closer and closer to this horizontal asymptote. It will never reach the x axis. Think of it like an electric fence.

As the graph indicates, we don't have a straight line. Therefore, the function isn't linear. It's a nonlinear curve.

rate of cooling of the turkey in minutes is 41.13545

The formula for finding the rate of cooling of a roasted turkey is provided in the question. It is given as:T(t) = Ae^kt + TsThe following are the variables:• T(t) represents the temperature of the turkey at time t• A represents the initial temperature of the turkey• k is the cooling rate• Ts is the temperature of the environmentNow, using the values given in the question, we can get the rate of cooling of the turkey as follows:T(t) = Ae^kt + TsLet us replace the variables with the given values:159 = A*e^(0.5k) + 75 => A*e^(0.5k) = 84 => A = 84/e^(0.5k)Let us substitute the value of A in the initial equation:T(t) = Ae^kt + Ts => 190 = A*e^(k*0) + 75 => 190 = A => A = 190So, we can get the value of k using the values of A from the above two equations:84/e^(0.5k) = 190 => e^(0.5k) = 84/190 => e^(0.5k) = 0.4421052631578947 => k = (ln0.4421052631578947) / 0.5 = -0.4662195477817674So, the equation for the temperature of the turkey as a function of time is:T(t) = 190e^(-0.4662195477817674*t) + 75To find the rate of cooling of the turkey, we need to take the derivative of the above equation with respect to t, which gives:dT/dt = -87.75877428502014*e^(-0.4662195477817674*t)This is the rate of cooling of the turkey. To find the rate of cooling in minutes, we substitute t = 0.5 in the above equation and simplify to get:dT/dt = -41.135453873444264Therefore, the rate of cooling of the turkey in minutes is 41.13545 (accurate to at least 5 decimal places).

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Answer:

A coefficient is a number multiplied by a variable.

Answer:

its being multiplied by a variable when it is being multiplied by a letter

Step-by-step explanation:

a variable is a symbol, usually a letter, that represents a number

Ex.

x in 5x (5 times x)