Jetlag is a condition associated with crossing multiple time zones is experienced by sports tourists from Argentina travelling to Japan.
People who travel quickly between different time zones may experience jet lag, a sleep disorder.
Jet lag causes sporadic sleep problems. It occurs when signals from a new time zone cause the body's biological clock to become out of sync. Feeding times and light exposure are two examples of cues.
The term "jet lag" originated from the fact that it was uncommon to travel far and quickly enough to cause desynchronosis prior to the development of passenger jet aircraft. Propeller-driven travel was slower and covered less ground than jet flights, so it had a negligible impact on the issue.
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After how many years will the loan be half-paid?
A. 15 years
B. 18 years
C. 21 years
D. 24 years
suppose ax d b has a solution. explain why the solution is unique precisely when ax d 0 has only the trivial solution.
The solution of Ax = b is unique precisely when Ax = 0 has only the trivial solution, because Ax-b is consistent, its solution set is obtained by translating the solution set of Ax-0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
The correct answer is an option (b)
Let us assume that the equation Ax = b has a solution.
Now we need to show the solution is unique when Ax = 0 has only the trivial solution.
As we know Ax = 0 represents homogenous equation.
If Ax = b has a solution, it is unique if and only if every column of A is a pivot column. If every column of A is a pivot column, there are no free variables, and therefore the homogeneous equation has only the trivial solution.
Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
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The complete question is:
Suppose Ax = b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the trivial solution. Choose the correct answer.
A. Since Ax = b is inconsistent, its solution set is obtained by translating the solution set of Ax-0. For Ax-b to be inconsistent, Ax = 0 has only the trivial solution.
B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax-0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
C. Since Ax = b is inconsistent, then the solution set of Ax = 0 is also inconsistent. The solution set of Ax = 0 is inconsistent if and only if Ax = 0 has only the trivial solution.
D. Since Ax = b is consistent, then the solution is unique if and only if there is at least one free variable in the corresponding system of equations. This happens if and only if the equation Ax 0 has only the trivial solution.
peacock premium tv charges $5.00 per month plus a set-up fee. the total cost after 10 months was $65.00. write an equation in point-slope form to model this situation.
A point-slope form is an equation for a line, using a point and the slope of the line. So we have to find one x-coordinate and y-coordinate and write it in the form of (y-y₁) = m(x-x₁).
Here the total after 10 months is said to be 65 and number of months = 10. So we can calculate the set-up fee.
5 ×10 + x = 65
x = 65-50 = 15.
The only constant here is the set-up fee, 15.
Lets the number of months be x and total amount be y.
y- 5x = 15
Lets calculate the y intercept. x-term will be 0.
y+0 = 15
y = 15
Lets calculate the x-intercept. y term will be 0
-5x = 15
x = -3
Two points on the line are (-3,0) and (0,15)
slope = (15-0)/(0--3)
=15/3 = 5
So lets find out one point in the equation
If y=10,
10-5x = 15
-5x = 15-10
x = 5/-5 =-1
So a point on the line is (-1,10)
Point slope form,
(y-10) = 5 (x- ⁻1)
(y-10) = 5 (x+1)
So this is the point slope form.
y = 5x+15
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PLEASE HELP I WILL GIVE BRAINLIEST
For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
The image of the triangle DEF are formed by the following coordinates: D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).
How to dilate a triangle centered at a given point
In this problem we need to apply a rigid transformation known as dilation, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factorWe need to determine the image of triangle DEF. If we know that D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices of the triangle:
D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]
D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)
D'(x, y) = (4, - 2) + (- 3, 0)
D'(x, y) = (1, - 2)
E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]
E'(x, y) = (4, - 2)
F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]
F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)
F'(x, y) = (4, - 2) + (- 4.5, - 3)
F'(x, y) = (- 0.5, - 5)
The coordinates of the image of triangle DEF are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5)
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Things that have an equal an equal chance of happening are known as what?
Mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.
What is the probability theory?
Probability theory is a branch of mathematics that deals with the study of random phenomena. It provides a mathematical framework for analyzing the likelihood of different outcomes in a given situation, and for making predictions about future events based on past data.
Things that have an equal chance of happening are known as equally likely events or mutually exclusive events. In probability theory, mutually exclusive events are events that cannot happen at the same time; if one event occurs, the other cannot.
In general, mutually exclusive events are events that have no overlap between them and the sum of the probabilities of all mutually exclusive events is equal to 1.
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The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation( please help!!)
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = ln x
The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have
y - 12 = ln (x + 8)
y = ln (x + 8) + 12
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100 engines and the mean pressure was 5.5 lbs/square inch. assume the standard deviation is known to be 0.7 . if the valve was designed to produce a mean pressure of 5.3 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient evidence that the valve performs above the specifications.
Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch
Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch
To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.
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There's a 1/6 chance that a student will be in Miss Jones math class if there are 30 students in her class how many students are there at all
If there is a 1/6 chance that a student will be in Miss Jones's math class, if there are 30 students in her class, then 180 students will be there at all.
Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.
Total number of students present in the miss jones class = 30
The chance that a student will be in Miss Jones's math class = 1/6
Let x be the students are there at all
According to the question,
1/6 × x = 30
⇒x = 30 × 6
⇒x = 180
Hence, 180 students are there at all.
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A counter in Reagan's kitchen is 1 meter wide and 3 meters long. Reagan wants to replace the counter with a granite countertop, which would cost $185.00 per square meter. How much would the granite countertop cost?
The granite countertop costs $555
How much would the granite countertop cost?From the question, we have the following parameters that can be used in our computation:
Length = 3 meters
Width = 1 meter
Cost per square meter = $185.00
The cost of the granite counter is then calculated as
Cost = Length * width * Cost per square meter
substitute the known values in the above equation, so, we have the following representation
cost = 3 * 1 * 185
Evaluate
cost = 555
hence, the cost is $555
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which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?
Answer: The answer is D
Step-by-step explanation: I hope this helps!
The two similar rectangles shown below have a scale factor of 3:10
If the perimeter of the larger rectangle is 90 centimeters, what is the perimeter of the smaller rectangle?
The perimeter of the smaller rectangle would be 27 cm.
What is scale factor? How it is used in Dilating sides?Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically : K = a/b.Rewriting, we get : a = KbIf a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].Given is that two similar rectangles shown below have a scale factor of
3 : 10.
Since the two rectangles are similar, then the ratio of their corresponding perimeters will be constant.
We can write -
P{1}/P{2} = 3/10
P{1}/90 = 3/10
P{1} = (3 x 90)/10
P{1} = 27
Therefore, the perimeter of the smaller rectangle would be 27 cm.
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find the amount of rs 800000 for 2 years compounded annually and the rate being 9% during first year and 10% second year
Answer:
Amount = 800000×(1+0.09)2 = 800000×1.1881 = 946480
Amount = 800000×(1+0.1)2 = 800000×1.21 = 960000
help me please i need your help
Answer:
∞
Step-by-step explanation:
I don’t know just think it out. That is the explaination
How much money would you need to deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years? Round to the nearest cent.
The account balance after five years will be $10355.
What is compound interest?The interest that is paid on the principal and interest at regular intervals is known as compound interest. The difference between compound interest and simple interest starts to show after the first year, though.
The formula to calculate the compound interest is given below;-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
Given that deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years.
The account balance after five years will be:-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
[tex]A = 10000 ( 1+\dfrac{0.07}{1})^{5}[/tex]
A = 10000 x ( 1.07)⁵
A = $10355
Hence, the amount will be $10355.
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Is 13,14,15 a pythagonrean triples
Answer:
milk
Step-by-step explanation:
milk store is where your dad went
Question 32:
Write an equation in Slope-Intercept form for the
line that passes through (1,-3) and is parallel to
y+2 = 4(x-1)
The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.
For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.
To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)
So, using the point (1,-3) and the slope (4), we can write the equation as:
y - (-3) = 4(x - 1)
Simplifying this equation gives:
y + 3 = 4x - 4
Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:
y = 4x - 1
So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1
chris made 27 of the 45 putts while practicing golf. What percent of putts did he miss
Answer: The percent of putts that he missed is 60%.
Step-by-step explanation: You divide 27 by 45, and that equals 0.6. After that you multiply 0.6 by 100, which gets it to 60/60%.
in how many different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another?
There are 384 ways to arrange these given letters as per the given situation.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.
In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other. 2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.
The total number of arrangements is = 4! * 2 * 2 *2*2
The total number of arrangements is = 24 * 16
The total number of arrangements is = 384
Therefore, the Different ways to arrange these letters are 384.
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If you were to sketch a circle graph for the data shown in the table below, approximately what
fraction of the circle would represent food?
Vacation Expenses Budget
Expense Amount Budgeted
Activities=600
Food= 450
Souvenirs=270
The fraction of the circle that would represent food is given as 34.09
How to solve for the fraction that would represent foodThe data we have here is given as
Activities = 600
Food = 450
Souvenirs = 270
We would have to sum this up
600 + 450 + 270 = 1320
The proportion that represents food is given as 450
= 450 / 1320
= 0.3409
Then we would have to convert this to percentage
0.341 * 100
= 34.09
34.09 x 360 = 123 degrees
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can someone help me do #1 please
Answer:
All parts are below
Step-by-step explanation:
Seeing the first part asking for f(1). The equation f(n) lies above, so right here is plug and play. Since the n was replaced with a 1, we'll go to the table and find n and find 1.
Since it's the first number, looking directly below it is 7. Meaning f(1) = 7
Seeing common ratio... everytime n goes up 1, the value doubles, making r = 2/1 also known as 2
Now that we know f(1) is 7 and r is 2, we can plug it all in
f(n) = f(1) * (r)^n-1
Plugged in, it's f(n) = 7 * 2^1-1. 1-1 = 0. Anything to the power of 0 equals 1, which means 2^0 is 1
Multiplying 7 and 1 gives you 7, so
f(n) = 7
Geometric sequence is that f(n) = f(1) * (r)^n-1
Also known as f(n) = 7 * 2^n-1
For problem #2, try replicating all this and let me know how it goes
Which system of inequalities does (2,7) NOT satisfy?
● y ≥ 6x - 5
x + 2y ≤ 16
O y ≤ 6x-5
x + 2y ≥ 16
O x - 2y ≤-16
6x - y < 5
O у ≥ 6x - 5
X - 6y ≥ -54
Answer: (2,7) does not satisfy the system:
x - 2y ≤ -16
6x - y < 5
We can substitute the point (2,7) into the inequalities and see if they are true:
2 - 2*7 ≤ -16
-10 ≤ -16 which is false
6*2 - 7 < 5
5 < 5 which is also false
Since (2,7) does not satisfy both inequalities of the system, it is the correct answer.
Step-by-step explanation:
Mrs. Soriano baked 7 5/9 dozens of chocolate cookies. She gave 3 1/3 dozens to her friends. How many dozens of chocolate cookies were left ?
A. 4 3/9
B. 4 2/9
C. 4 5/9
D. 4 1/9
Answer:
4 2/9
Step-by-step explanation:
7 5/9 -3 1/3
68/9 -10/3
(68-30)/9
38/9
4 2/9
The middle school has 24 students less than 3 times the number of students at one of
the elementary schools.
The required equation is y=3x-24, where x is the number of elementary school students and y is the number of middle school students.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
Let x be the number of students in elementary school and y be the number of students in middle school.
y=3x-24
The required equation is y=3x-24 where x be the number of students in elementary school and y be the number of students in middle school.
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Find the height of the figure.
12. A = 12 m²
4.8 m
13. A 11.0625 m²
3.75 m
The height of the figure is 66 m².
How to find height?Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
27.5 × 4.8
= 132
132/2
= 66
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Explain in words how to solve an equation with a variable on both sides of the equation.
Kieran is horseback riding. His horse can trot 470 yards in 2 minutes and 1,410 yards in 6 minutes when Kieran is riding. How fast, to the nearest integer, is Kieran riding if he continues at this rate?
Kieran can ride at 235 yd per min if he continues at this rate.
What is speed?Speed is a scalar quantity that refers to "how fast an object is moving."
Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time.
Given that, Kieran is horseback riding. His horse can trot 470 yards in 2 minutes and 1,410 yards in 6 minutes when Kieran is riding.
Here, the question is asking about how fast Kieran riding if he continues at the given rate,
That mean we have to find the speed,
Speed = distance / time
Therefore,
Speed of Kieran = 470 / 2
= 235 yd per min
Speed of Kieran = 1410 / 6
= 235 yd per min
Therefore, we can say kieran us riding for 235 yd in a minute.
Hence, Kieran can ride at 235 yd per min if he continues at this rate.
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Sofia is making a batch of slime using a recipe that includes glue, water, and a salt solution. She uses 7. 5 fl oz of glue. The amount of glue is 12. 5 times the amount of salt solution. There are 4. 2 less fluid ounces of salt solution than water.
How many fluid ounces of water does Sofia use to make the batch of slime?
Total amount of fluid ounces of water used by Sofia to make proportionate amount of slime is equal to 4.8 fluid ounces.
Let us consider 'x' amount of salt solution.
Amount of glue used by Sofia = 7.5 fluid ounces
Amount of glue = 12.5 times of salt solution
⇒ 7.5 = 12.5x
⇒ x = 7.5 / 12.5
⇒ x = 0.6
Fluid ounces of water used by Sofia to make the required batch of slime is:
Now, Amount of salt solution = Fluid ounces of Water - 4.2
⇒Fluid ounces of Water = x + 4.2
⇒ Fluid ounces of Water = 0.6 + 4.2
⇒ Fluid ounces of Water = 4.8 fluid ounces
Therefore, the fluid ounces of water used by Sofia with salt solution and glue to make a slime is equal to 4.8 fluid ounces.
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The value of a house increased by 6% the house then had a vaue of £26000 work out the value of the house before the increase
The value of the house before the increase is £1560
Now, According to the question:
Percentage basically means a part per hundred. It can be expressed in fraction form as well as decimal form. For example, if we say 25%, it means 25 out of 100. So, 25% is equivalent to the fraction 25/100 or 0.4 in decimal form.
"Information available from the question"
The value of a house increased by 6% the house then had a value of £26000.
Now, The expression will be :
= 6% of £26000.
= 6/100 × £26000.
= £1560
Hence, the value of the house before the increase is £1560.
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Find five consecutive odd integers whose sum is 85.
Answer:
13+15+17+19+21 = 85
Step-by-step explanation:
Hope you got it !
Answer:
The five consecutive odd integers whose sum will be 85 are 13, 15, 17, 19, and 21.
Step-by-step explanation:
To solve this problem, let's assume the first number is n.
Then the consecutive odd integers will be n+2, n+4, n+6, n+8
Thus we can write,
n+(n+2)+(n+4)+(n+6)+(n+8) = 85
In the next step add all the n's,
5n+20 = 85
Then transfer '20' from LHS to RHS,
5n = 85 - 20
5n = 65
Then in the next step '5' needs to be transferred to RHS,
n = 65÷5
n = 13
Therefore, n = 13
n+2 = 15
n+4 = 17
n+6 = 19
n+8 = 21
Thus the five consecutive odd integers are 13, 15, 17, 19, and 21.
PLEASE HELPPP
You are the grade 10 representative on the student council and you have been assigned the
task of finding a location to host a dance for the students of CISE. You have narrowed it down
to three options which are outlined below:
Ancient Abyss is a location that charges a $200 flat fee and $4 per person.
Beautiful Babylon is a location that charges a $99 flat fee and $6 per person.
Crazy Cleopatra is a location that charges a $280 flat fee and $3 per person.
Task:
You will analyze the three options and put together a proposal to submit to the student
council outlining your recommendations.
Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:
Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.
Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.
In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.