b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300 250 200 150 100 50 0 2 6 8 10 12 14 16 4 Distance cycled (miles)
Answers
Using the slope we know that the distance Keira traveled is 32 miles.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise).
Find the difference between these two points' x-coordinates (run).
Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
So, in the given situation:
c is calories burned and d is the distance.
Then,
x = kd
k is the slope = 200/10 = 20
Calories burned = 20 * distance cycled
When, c = 640:
640 = 20*distance
distance = 640/20
distance = 32 miles
Therefore, using the slope we know that the distance Keira traveled is 32 miles.
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Related Questions
Four fifths times five times two ninths
Answers
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.
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answers
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.
9. Seven more than the quotient of a number b
and 45 is greater than 5.
Answers
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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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?
Answers
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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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.)
Answers
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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the graph represents the number of different tacos ordered for an office lunch. in total, how many tacos were ordered?
Answers
Answer:
do you have the graph to solve it?
anyone know all the x's?
Answers
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!
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.
Answers
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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The manager of a computer network has collected data on the number of times that service has been interrupted on each day over the past 500 days. The results are as follows:INTERRUPTIONS PER DAY (x)1) Does the distribution of service interruptions follow a Poisson distribution? (Use the 0.01 level of significance.) 8Q2) Referring to the data in problem, at the 0.01 level of significance, does the distribution of service interruptions follow a Poisson distribution with a population mean of 1.5 interruptions per day?
Answers
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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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
Answers
[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?
Answers
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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1,500 decagrams = 150 kilograms.
True?
False?
Answers
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
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?
Answers
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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A line has a slope of – 9 and passes through the point (1, – 3). Write its equation in slope-intercept form.
Answers
Answer:
yytyyyyy
Step-by-step explanation:
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]
Answers
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
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?
Answers
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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Let mz1 = x. Select all the angles that have a measure of 180 - x.
Answers
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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Rectangle 40 cm long, 30 cm wide, and 20 cm high
Answers
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.
8x<168
The solution of the inequality is
Answers
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.
30 points to help me!
Answers
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
Fractions MUST SHOW WORKING!!
Answers
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
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
Answers
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?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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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)
Answers
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
Answers
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.
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
Answers
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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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
Answers
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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if (20x+10) and (10x+50) are altenative interior angle then find x
Answers
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]
A study suggests that the 25% of 25 year olds have gotten married. You believe that this is incorrect and decide to collect your own sample for a hypothesis test. From a random sample of 25 year olds in census data with size 776, you find that 24% of them are married. A friend of yours offers to help you with setting up the hypothesis test and comes up with the following hypotheses. Indicate any errors you see.H0p^=0.24Hap^≠0.24
Answers
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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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.
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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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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.
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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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