The expected length of the arc containing the point (1,0) is; π
How to solve Unit Circle Problems?First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.
The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.
Thus, we have;
L₁ + L₂ + L₃ + L₄ = 2π
Whereas, the expected value of several random variables is additive as;
E[ L₁ + L₂ + L₃ + L₄] = [EL₁] + [EL₂] + [EL₃] + [EL₄]
By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.
Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,
π/2 + π/2 = π
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Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Answer:
Mikaela's team scored 5.3 points, in whole number form 5.
Step-by-step explanation:
If Viktoria's team's score was 7, 2 more than twice is (7*2) +2.
(7*2)+2=16
16 is three times Mikaela's team's score. Reduced by three means just to divide.
16/3=5.3
Mikaela's team scored 5 points.
Hope this helps!
If not, I am sorry.
Answer:
8
Step-by-step explanation:
Make it into an equation.
2x+2=(3x7)-3
2x+2=21-3
2x+5=21
2x=16
x=8
8
What additional information could be used to prove that the triangles are congruent using aas or asa?.
Answer:
Two angles and a side
Step-by-step explanation:
In order to prove triangles congruent, you'd have to either have an angle, angle, and then a side in that exact order for AAS or you can have two angles and a side in the middle of them for ASA.
The figure below shows a large rectangle with a small rectangle cut out of it.
What is the area?
Answer:
40 square units
Step-by-step explanation:
The question gives that both the large shape and the small missing shape are rectangles. The formula for the area of a rectangle is [tex]A=bh[/tex] where "A" is the "Area", "b" is the "base" (bottom edge), and "h" is the height (side edge).
For rectangles, opposite sides (example: top & bottom) have the same length, so the top of the missing rectangle must also be 3.
To find the area of the figure, we must find the difference (subtraction) between the large rectangle (without a hole out of it) and the rectangular hole.
[tex]A_{\text{figure}}=A_{\text{large rectangle without hole}}-A_{\text{hole}}\\A_{\text{figure}}=(7)(7)-(3)(3)\\A_{\text{figure}}=49-9\\A_{\text{figure}}=40[/tex]
So, the area of the figure is 40 square units.
Answer:
40
Step-by-step explanation:
We can make a big square by making a line at the top open edge (as shown in the image attached below). We will first solve for [tex]A_{2}[/tex] and then [tex]A_{1}[/tex], and then finally solving for out answer by subtracting [tex]A_{1}[/tex] from [tex]A_{2}[/tex] .
[tex]A_{2}[/tex] is a square with side lengths of 7, so the area is 7 * 7 = 49.
[tex]A_{1}[/tex] is a smaller square with side lengths of 3, so the area is 3 * 3 = 9.
[tex]A_{2} - A_{1} = 49 - 9 = 40[/tex]
∴ Our final answer is 40
adam has 18 counters he gives 10 to lesleay how many of the 18 counters does lesleay get give your answer in simplest form
The fraction of the counters that Lesleay gets is 5/9.
What is the fraction?
A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. An example is 1/2.
The fraction of the counters that Lesleay gets = number of counters she gets / total number of counters
10/18 = 5/9
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wonder woman made a reglangular fence around her invisable airplane so it would not get hurt by her dog. her fence was 4ft long, 2 ft wide, and 3 ft high. how much material did she use t make her fence
Answer:
36 ft^2
Step-by-step explanation:
Perimeter = 4 + 4 + 2 +2 = 12 feet
12 feet x 3 feet high = 36 ft^2
There are 19 animals on the farm which contains hens and goats. There are 68 legs in total. How many goats are there on the farm?
Answer: 15 goats
Step-by-step explanation:
h = hens - they have 2 legs
g = goats - they have 4 legs
The equations would be:
h + g = 19
2h + 4g = 68
To solve this, I personally prefer substitution, we're isolating h since we need to find g:
h + g = 19
h = 19 - g
Now that we have h, we can plug this into the second equation:
2h + 4g = 68
2(19 - g) + 4g = 68
38 - 2g + 4g = 68
2g = 30
g = 15
There are 15 goats.
Adding onto this, 19 - 15 = 4, so there are 4 hens.
Calculate the area of the Parallelogram.
I will mark as brainliest, Please help quick!
Answer:
A = 42 cm²
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 6 and h = 7 , then
A = 6 × 7 = 42 cm²
For doing a certain a Job
Answer:
added in picture
Step-by-step explanation:
added in picture
Answer:
$71,744.53
Step-by-step explanation:
The earnings triple every day, so you can calculate them for the 15 days. For the total, you also have to add them up.
See the calculations in below picture.
i need help what's 8*3^2 i will mark brainiest if someone can answer it in 72-minute s
Answer:
72
Step-by-step explanation:
8 x 3² = 8 x 3 x 3
= 8 x 9
= 72
[P.S. If you meant (8 x 3)² the answer is:
(8 x 3)² = (24)²
= 24 x 24
= 576 ]
The following clues will help us identify a shape:
The shape has no right angles.
The shape has no pairs of sides of equal length.
The shape is not a triangle.
it is a circle
PLEASE MARK THIS AS THE BRAINLYEIST ANSEWER
please help I need so much help right now I feel like crying
Answer:
ok the first point there is (-4;-3)
the second point is(0;-6)
3(2x − 8) – 11x
equivalent to
Answer:
-5x - 24
Step-by-step explanation:
3(2x − 8) – 11x =
Distribute the 3.
= 6x - 24 - 11x
Combine like terms.
= -5x - 24
what is the area of aregular hexagon with side length of 10units square?
Answer:
h ≈ 259.81
Step-by-step explanation:
i used the hexagon calculator
Answer:
150 sqrt 3 = 259.8076 units^2
Step-by-step explanation:
Interior angles of hexagon = 120 degrees ....now look at the Right 1/2 of the hexagon... see illustration....this is a trapezoid...
One base is 10 units
the other labelled 'base' is
10 cos 60 + 10 cos 60 + 10 = 20 units
the height of this trapezoid is 10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)
the area of this trapezoid is then 1/2 ( 10+ 20) * 5 sqrt (3) = 75 sqrt 3
there are TWO of these trapezoids in the hexagon so total area is then
2 * 75 sqrt 3
150 sqrt 3
y = 3x - 5.1, (-1.2, -3.1)
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 3x - 5.1, (-1.2, -3.1)
we can plug in the point (-1.2, -3.1)
-3.1 = 3(-1.2) - 5.1
-3.1 = -3.6 - 5.1
-3.1 = -8.7
-3.1 does not equal -8.7 so this point is not on the line
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In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained.
a. What is the ratio of the number of milk cartons taken to the total number of milk cartons?
b. What is the ratio of the number of milk cartons remaining to the number of milk cartons taken?
Answer:
a. 73:100
b. 27:73
Step-by-step explanation:
total: 100
number remaining: 27
number taken: 100 - 27 = 73
a. taken:total = 73:100
b. remaining:taken = 27:73
#a
total milk cartons used=100-27=73
Total=100So the ratio is
73:100#b
It's already mentioned in question
The ratio is 27:737 times 36 = 21 times ?
help needed asap :)
Answer:
7*36=21*x
252=21x
x=12
Hope it helps!
Answer:
12
Step-by-step explanation:
Let x be the unknown number.
Method 1
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
[tex]\implies \sf 252 = 21x[/tex]
[tex]\implies \sf \dfrac{252}{21} = \dfrac{21x}{21}[/tex]
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
Method 2 (using mental arithmetic)
[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]
As 7 and 21 are both multiples of 7, divide both sides by 7:
[tex]\implies \sf 36=3x[/tex]
Divide both sides by 3:
[tex]\implies \sf 12=x[/tex]
[tex]\implies \sf x=12[/tex]
Which graph represents the following system of inequalities?
Answer:
D
Step-by-step explanation:
On graphing the 3 equations, we find that the central area (triangle) formed by the 3 inequalities is the solution.
Answer:
D
Step-by-step explanation:
When graphing inequalities:
< or > : dashed lines≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineGiven inequalities:
[tex]\begin{cases}y > \dfrac{1}{2}x-1\\\\y\leq -x+1\\\\y > -2x-1 \end{cases}[/tex]
From inspection of the given graphs, the red dashed line is the first inequality as it is the only inequality with a positive slope.
The blue sold line is the second inequality, as it is the only inequality with the sign that suggest a solid line.
Therefore, by process of elimination, the green dashed line is the third inequality.
Using the inequality signs and their definitions for shading, find the graph that has:
Shading above the red dashed lineShading below the blue solid lineShading above the green dashed lineThe only graph that matches these conditions is graph D
true or false 5x +11 = 7 is an expression
Answer: False
Step-by-step explanation: An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Expressions do not have an equal sign because they do not have an answer.
Which set of graphs can be used to find the solution set to 3e* > >-x?
The attached graph represents the solution set of [tex]3e^x > \frac 12^x[/tex]
How to determine the graph?The complete options are not given.
So, I would plot the graph that represents the solution set
The inequality is given as:
[tex]3e^x > \frac 12^x[/tex]
Start by splitting the inequalities as follows:
[tex]f(x) > 3e^x[/tex]
[tex]g(x) > \frac 12^x[/tex]
The above means that we plot the graphs of f(x) and g(x) to represent the solution set
See attachment
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Please Help Me! What is cos B?
Answer:
cos B = 0.4706
Step-by-step explanation:
The cosine of an angle in a right-angled triangle is the ratio of its adjacent side and the hypotenuse, so:
[tex]cos B = \frac{adjacent}{hypotenuse}\\\\cos B = \frac{8}{17} \\\\cos B = 0.4706[/tex]
Option B
Can someone help me with this, it’s urgent. It’s geometry.
Answer:
10. Ray ED and Ray EF (two rays)
11. DE and EF (two line segments)
Step-by-step explanation:
hope this helped
Answer:
Ray ED and Ray EF
DE and EF
Step-by-step explanation:
(6, -5) reflected aross the y axis
Answer:
Then the new point is (-6,-5)
Step-by-step explanation:
Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let represent the number of students who bought a cup of orange juice and represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
+ 3 = 76
+ = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables.
In order to eliminate one of the variables, subtract one of the equation from the other equation.
How to eliminate one of the variables?Given these equations:
o + 3s = 76 equation 1
o + s = 36 equation 2
Where:
o = number of orange juice bought
s = number of sandwiches bought
In order to eliminate one of the variables, subtract equation 2 from equation 1. The result is :
2s = 40
s = 20
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!!!!!!!!!!!!!!!!!!!help!!!!!!!
Answer: Answer below.
Step-by-step explanation: Attached is my work. Hope it is helpful!
Solve the system of equations: 3x + 6y=6 and 2y - 3x = 6.
Answer:
x = -1, y = 1.5
Step-by-step explanation:
3x + 6y = 6 -----> x + 2y = 2
-3x + 2y = 6 -----> -3x + 2y = 6
------------------
4x = -4
x = -1, y = 1.5
Pls Help! Will Give Brainliest for the right answer!
a. The survey method is unlikely to result in a representative sample
b. Interview people on all days of the week.
What is a Representative Sample?A representative sample is a sub-section of a larger population and has similar characteristics of the main group population.
a. The population of the study is the entire consumers that shop at the supermarkets who shop all days of the weeks. Therefore, asking only shoppers who shopped on Monday will most likely give you a bias response as most customers may select Wednesday. The sample doesn't represent the entire population.
b. A better survey method is picking samples on all days of the week and ask them.
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Two taps, *A* and *B* are of different sizes. Tap A fills a container with water in 3 minutes and Tap B fills the same container in 5 minutes. How much time Will it take if both the taps are turned on at the same time.
answer with working
A friend of yours, a senior, took the Graduate Record Exam in September and scored in the 99th percentile. In February, your friend took the same exam over again. This time your friend scored in the 90th percentile. As a research methods student, you told your friend that his/her lowered score was most likely due to:
His/her lowered score was most likely due to statistical regression.
How to determine the reason?The missing options in the question are:
A. compensation rivalry B. Demoralization C. Differential selection
D. Testing E. Statistical regression
From the question, we have:
September = 99th percentileFebruary = 90th percentileA change (whether higher or lower) in the score is caused by statistical regression.
This is so because several variables could attribute to the change in the score.
The relationship between these variables is referred to as statistical regression
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If f(x) = 3x^2 - x, find f(-2).
Answer:
14
Step-by-step explanation:
to find f(value), we plug that x value into the equation
so, if..
f(x)= 3x² -x
f(-2)= 3 · (-2)² - (-2)
f (-2) = 3 · 4 + 2
f (-2) = 12 + 2
f (-2) = 14
Answer:
14
Step-by-step explanation:
f(x) =3x^2-x
here,
f(-2)= 3(-2)^2 -(-2)
=3*4+2
=12+2
=14 Answer.
Solve a^5=?
Please thank and thank you
Answer:
341.8801
Step-by-step explanation:
