Answer:
g(x) = x² - 4x + 7
30 points to help me!
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
A taxi service charges $1.00 for the first 1/10 mile then $0.10 mile after that.
1. What is the cost of 3 1/10 mile
2. Is the relationship between distance traveled and price of the trip proportional? (yes or no)
1. cost of 3 1/10 mile for the taxi service charges: $0.40.
2. Relation is explained as direct proportional.
Explain about the improper fractions?The top number of an improper fraction is greater than (or equal to) that bottom number.
We have a certain number of pieces, which is the top number (called Numerator).The number at the bottom (the denominator) represents the quantity into which the total is divided.Using the example:
The steps below can be used to change a mixed fraction into an improper fraction:
Divide the fraction's denominator by the portion of the entire number.It is added to the numerator.The outcome should then be written on top of such numerator.Fixed taxi charge = $1.00 for the first 1/10 mile
Additional charge = $0.10 mile
1. cost of 3 1/10 mile
covert mixed into improper = (30 +1)/10 = 31/10
The cost of 31/10 miles.
= $1.00 * 1/10 + (31/10 - 1/10)*$0.10
= $0.100 + 30/10*$0.10
= $0.100 + $0.30
= $0.40
2. As the distance increases the price also increases.
Relation is explained as direct proportional.
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A rectangle's width is 1/2 of its length. its area is 388 square centimeters what are its dimensions
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.
Four fifths times five times two ninths
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.
a jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 40 cm3. if nickel plating costs $ 1 per cm2 and silver plating costs $ 12 per cm2, find the dimensions of the box to minimize the cost of the materials.
The dimensions of the box to minimize the cost of materials are 3.16 cm x 3.16 cm x 3.16 cm.
To minimize the cost of materials for the jewelry box with a square base, you will need to find the dimensions of the box. The volume of the box is 40 cm3. The sides of the box will be silver plated and cost $12 per cm2, while the top and bottom will be nickel plated and cost $1 per cm2.
Since the box has a square base, each of the sides has the same area and the total area of the box is four times the area of one side. To minimize cost, the sides of the box need to be as small as possible. The equation for the area of a square is A = l2.
We can use this equation to find the length of one side of the box. 40 cm3 = l2 x 4, so l2 = 10 cm2. The length of one side of the box is the square root of 10, which is approximately 3.16 cm.
Therefore, the dimensions of the box to minimize the cost of materials are 3.16 cm x 3.16 cm x 3.16 cm.
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9. Seven more than the quotient of a number b
and 45 is greater than 5.
Any number b greater than -90 will satisfy the inequality. We can express the solution in interval notation as: b ∈ (-90, ∞)
What is inequality?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).
According to question: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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1,500 decagrams = 150 kilograms.
True?
False?
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
Fractions MUST SHOW WORKING!!
Total seats in plane: 186
108+64+14
5/7 of 14 is: 10
14÷7= 2
2x5= 10
5/16 of 64 is: 20
64÷16=4
5×4= 20
5/9 of 108 is: 60
108÷9= 12
12x5= 60
60+20+10=90
90/186 of seats are being used
simplified: 15/31
No
Mps Support
In Exploration 3. 1. 1 you found the area under the curve f(t) =
between 1 and 3. What was the approximate area that you came up
with? [Select)
In calculus you will learn more about the significance of this activity. At
what x-value would you stop at to have an area of exactly 1?
[Select]
What is that number called? (Select]
The approximate area under the curve f(t) = 1/t when found between 1 and 3 is equivalent to option D: 1.1.
Calculating an integral is called integration. Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. One of the two primary calculus topics in mathematics, along with differentiation, is integration.
We can find the approximate area using the concept of integration as follows:
[tex]\int\limits^3_1 {1/t} \, dt[/tex]
We generally know that:
[tex]\int\limits^a_b {x} \, dx[/tex]= ㏑(x)
Therefore,
[tex]\int\limits^3_1 {1/t} \, dt[/tex]
= ㏑ (3) - ㏑ (1)
= 1.1, more specifically it would be 1.09.
From the table of logarithm, you can verify is equivalent to 1.1.
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Correct question is:
In Exploration 3.1.1 you found the area under the curve f(t)=1/t
between 1 and 3. What was the approximate area that you came
up with?
A. 1.3
B. .9
C. .7
D. 1.1
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume. The dimensions of box of maximum volume are __ in. (Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
The dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is 113.78 in³.
How to find the dimensions of the open rectangular box of maximum volume?The dimensions of the box can be found with the following steps:
First, determine the side length of the square that is to be removed from each corner of the cardboard box. Since this will be done uniformly on all four corners, let the side length be x. The dimensions of the cardboard box can then be written as:
Length = 19 in. - 2x
Breadth = 11 in. - 2x
Height = x
After folding the cardboard along the creases, the base of the rectangular box will be (19 - 2x) in. by (11 - 2x) in. with the height of the box being x in. The volume of the box can then be found by multiplying the base and height of the box, i.e.,
Volume = (19 - 2x) (11 - 2x) x
Let V(x) be the volume of the rectangular box in terms of x. Then:
V(x) = (19 - 2x) (11 - 2x) x
Simplifying,
V(x) = 4x³ - 60x² + 209x
The maximum value of V(x) can be found by differentiating V(x) with respect to x and equating the result to zero. Therefore,
V'(x) = 12x² - 120x + 209 = 0
Solving, V(x) has a maximum value when x = 19/3 - 2(2/3)√14 or x = 19/3 + 2(2/3)√14. The value x = 19/3 - 2(2/3)√14 is the maximum value because x must be less than 5.5, which is the minimum of 11/2 and 19/2 divided by 3, the upper bound for x. Therefore, the dimensions of the box are
Length = 19 - 2(19/3 - 2(2/3)√14) = 6.33 in.
Breadth = 11 - 2(19/3 - 2(2/3)√14) = 3.33 in.
Height = 19/3 - 2(2/3)√14 = 5.33 in.
Thus, the dimensions of the box are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is:
V = 6.33 x 3.33 x 5.33 = 113.78 in³.
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Let mz1 = x. Select all the angles that have a measure of 180 - x.
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.
What is angle?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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Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?
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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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
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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What is the circumference of the circle? Use 3.14 for π. circle with a segment drawn from the center of the circle to a point on the circle labeled 5 inches 31.40 inches 78.50 inches 15.70 inches 246.49 inches
[tex] \Large{\boxed{\sf C = 31.40 \: inches}} [/tex]
[tex] \\ [/tex]
Explanation:The circumference of a circle can be calculated using the following formula:
[tex] \Large{\sf C = 2 \pi r } [/tex]
Where:
C is the circumference of the circle.r is its radius.[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:
[tex]\large\rm{Circumference = 2 \cdot \pi \cdot Radius}[/tex]Given:
Radius = 5 inchesSubstitute the given value into the formula:
[tex]\large\rm{Circumference = 2 \cdot 3.14 \cdot 5\: inches}[/tex]Simplifying the expression:
[tex]\large\rm{Circumference = \boxed{\rm{31.40\: inches}}}[/tex][tex]\therefore[/tex] The circumference of the circle is 31.40 inches.
Hunters with dogs walked through the forest. If you count their legs, it will be 78, and if their heads, then 24. How many hunters were there and how many dogs did they have?
From the given data of hunters and do we find out there are 9 hunters and 15 dogs.
Let's assume that there were "h" hunters and "d" dogs.
Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:
2h + 4d = 78
We can simplify this equation by dividing both sides by 2:
h + 2d = 39
We also know that there were 24 heads in total, which includes the hunters and the dogs:
h + d = 24
We can now solve these two equations simultaneously to find the values of h and d.
First, we can solve for h in terms of d from the second equation:
h = 24 - d
We can substitute this expression for h in the first equation:
(24 - d) + 2d = 39
Simplifying and solving for d:
d = 15
Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:
h + d = 24
h + 15 = 24
h = 9
Therefore, there were 9 hunters and 15 dogs.
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A line has a slope of – 9 and passes through the point (1, – 3). Write its equation in slope-intercept form.
Answer:
yytyyyyy
Step-by-step explanation:
8x<168
The solution of the inequality is
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.
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
the graph represents the number of different tacos ordered for an office lunch. in total, how many tacos were ordered?
Answer:
do you have the graph to solve it?
U have 4/9 of a large bottle of cooking oil. U pour 3/5 of the cooking oil into a smaller bottle. How much of the entire large bottle did you pour in the small bottle?
You poured approximately 0.267 liters of cooking oil from the entire large bottle into the smaller bottle.
To find out how much of the entire large bottle of cooking oil was poured into the smaller bottle, we need to multiply the fraction of the large bottle that was poured into the smaller bottle by the total amount of cooking oil in the large bottle.
Given that you have [tex]\frac{4}{9}[/tex] of the large bottle of cooking oil, the fraction of the large bottle that you poured into the smaller bottle is [tex]\frac{3}{5}[/tex] of [tex]\frac{4}{9}[/tex]. We can find this fraction by multiplying [tex]\frac{3}{5}[/tex] by [tex]\frac{4}{9}[/tex]:
[tex]\frac{3}{5} * \frac{4}{9} = \frac{12}{45}[/tex]
Simplifying this fraction by dividing both numerator and denominator by 3, we get:
[tex]\frac{12}{45}= \frac{4}{15}[/tex]
Therefore, you poured [tex]\frac{4}{15}[/tex] of the entire large bottle of cooking oil into the smaller bottle. To find the actual amount, you can multiply this fraction by the total amount of cooking oil in the large bottle. For example, if the large bottle contains 1 liter of cooking oil, then you poured:
[tex]\frac{4}{15} * 1 = 0.267[/tex] liters.
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the weights of bunches of bananas in the grocery store are normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. a random sample of four bunches is taken and the mean weight is recorded. which of the following is the mean of the sampling distribution for the mean of all possible samples of size four? a.0.89 b.1.27 c.3.54 d.5.53
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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The supervisor at vector control wants your report of how the mosquito population is growing. Do you think your report is better supported by the table above or by a graph of the growth function as show below? WHY? Explain the reasoning behind your conclusion.
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
what is vector ?A vector is a mathematical concept that possesses both magnitude (or length) and direction. In physics, engineering, and other sciences, physical quantities with both a size and a direction, such as velocity, force, and acceleration, are frequently represented by vectors. In geometry, vectors can be represented as arrows, with the direction of the arrow indicating the vector's magnitude and the length of the arrow indicating its magnitude. In addition to being able to represent points in space and describe curves and surfaces, vectors may also be added, subtracted, and multiplied by scalars to create new vectors.
given
Based on the provided table and the growth function graph, I would argue that the report on the growth of the mosquito population is better supported by the graph.
On the other hand, there is no visual representation of the growth of the mosquito population in the table; it merely displays the data in a tabular format.
Although the table contains the same data as the graph, it is more difficult to understand and evaluate.
As a result, utilizing the graph of the growth function is preferable for describing the growth of the mosquito population .
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
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.
Thomas bought 120 whistles, 168 yo-yos and 192 tops. He packed an equal amount of items in each bag. A) What is the maximum number of bag that he can get?
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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A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
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The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
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.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).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
Inequality: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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Rectangle 40 cm long, 30 cm wide, and 20 cm high
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.
Find the area under the curve y = 2 x^-3 from x = 6 to x = t and evaluate it for t = 10 , t = 100 . Then find the total area under this curve for x ≥ 6 .
(a) t = 10
(b) t = 100
(c) Total area
The total area under the curve for x ≥ 6 is 449/4500.
The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:
We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]
Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.
Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6
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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.
In Bitcoin, when a merchant waits for n confirmation of a payment transaction before providing the product, there is a risk of a double-spend attack. In this situation, the network is aware of a branch crediting the merchant, which has n blocks on top of the one in which the fork started.
By simulating m as a negative binomial variable, P(m) = (m + n - 1m)pnqm can be used to more precisely compute this probability for a given value of m.
The attacker, on the other hand, has a branch with only m additional blocks. If we assume the honest network and the attacker have a proportion of p and q of the total network hash power, respectively, the probability of the attacker catching up when he is currently z blocks behind is given by az = paz+1 + qaz−1, where a is a constant.
To calculate the probability more accurately, we can model m as a negative binomial variable.
This 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.
The probability for a given value m is then given by P(m) = (m + n - 1m)pnqm.
Thus, when dealing with a double-spend attack in Bitcoin, the probability that the attacker will be able to catch up is given by az = paz+1 + qaz−1, where a is a constant.
This probability can be more accurately calculated by modeling m as a negative binomial variable, with the probability for a given value m given by P(m) = (m + n - 1m)pnqm.
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anyone know all the x's?
Answer:
Below.
Step-by-step explanation:
Yes.
-9 = 3/4x - 3 -6 = 3/4 x x = -8
-6 = 3/4x - 3 -3 = 3/4 x x = -4 (there's a pattern!)
0 = 3/4x - 3 3 = 3/4 x x = 4
3 = 3/4x - 3 6 = 3/4 x x = 8
Hope this helps!