The each of two individuals will get 54 and 27 sweets according to provided ratio.
Let us assume the amount of sweets each get be 2x and x. Now we know the sum is 81, so representing the information in equation form.
2x + x = 81
Performing addition on Left Hand Side of the equation
3x = 81
Rewriting the equation
x = 81/3
Performing division on Right Hand Side of the equation
x = 27
So, first person will get amount of sweets = 2×27
First person = 54
Amount of sweets for second person = 27
Thus, each will get 54 and 27 sweets.
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I am giving away 20 points have fun
Answer:
Thanks :)
Step-by-step explanation:
A Markov chain model for the growth and replacement of trees assumes that there are "four" distinct stages of growth based on the age and size of the tree. The stages are young, medium size, large size and old, and the transition period considered is 6 years. At the end of this period, a tree either remains in the same state, moves to another higher state or gets replaced by a young tree. In each period, 20% of the young trees remain young, 70% become medium size and the rest become large size. Medium size trees remain medium, become large or replaced by young trees with probabilities 0.4, 0.5 and 0.1, respectively. In a period, it is equally likely that a large tree remains as large tree, becomes an old tree or replaced by a young tree. Old trees get replaced by young trees in 6 years with probability p, 0.5 < p < 1.
a) Write down the transition probability matrix of the Markov chain.
b) Find the proportion of old trees that will be in old state after 12 years.
c) Suppose a forest, after a bush fire, starts with all young trees. If p = 0.8, what proportion of the trees in the forest will be old after 18 years?
a) The transition probability matrix of the Markov chain is:
| 0.2 0.7 0.1 0 |
| 0.1 0.4 0.5 0 |
| 0.333 0 0.333 0.333 |
| 1-p 0 0 p |
b) The proportion of old trees that will be in old state after 12 years is 0.613.
c) If a forest starts with all young trees and p = 0.8, the proportion of the trees in the forest that will be old after 18 years is 0.413.
a) The transition probability matrix of the Markov chain is given by:
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
b) The proportion of old trees that will be in old state after 12 years can be found by multiplying the transition probability matrix by itself twice (since each period is 6 years and we want to find the proportion after 12 years).
The resulting matrix will give the probabilities of each state after 12 years. The proportion of old trees that will be in old state after 12 years is given by the element in the fourth row and fourth column of the resulting matrix.
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.293 | 0.49 | 0.293 | 0.123|
| 0.207 | 0.35 | 0.357 | 0.086|
| 0.311 | 0.233 | 0.311 | 0.311|
| 0.407 | 0.14 | 0.14 | 0.613|
The proportion of old trees that will be in old state after 12 years is 0.613.
c) If the forest starts with all young trees, the initial state vector is [1, 0, 0, 0]. To find the proportion of the trees in the forest that will be old after 18 years, we need to multiply the initial state vector by the transition probability matrix three times (since each period is 6 years and we want to find the proportion after 18 years).
The resulting vector will give the probabilities of each state after 18 years. The proportion of the trees in the forest that will be old after 18 years is given by the fourth element of the resulting vector.
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.2 | 0.7 | 0.1 | 0 |
| 0.1 | 0.4 | 0.5 | 0 |
| 0.333 | 0 | 0.333 | 0.333|
| 1-p | 0 | 0 | p |
| Young | Medium | Large | Old |
|-------|--------|-------|-----|
| 0.407 | 0.49 | 0.293 | 0.123|
| 0.311 | 0.35 | 0.357 | 0.086|
| 0.407 | 0.233 | 0.311 | 0.311|
| 0.607 | 0.14 | 0.14 | 0.413|
The proportion of the trees in the forest that will be old after 18 years is 0.413.
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Graph the solution set for: x > 3 or x ≤ 0
lengths of 3 inches, 4 inches, and
5 inches. Will it fit in the corner of a
rectangular quilt? Explain.
A Yes, because it is a right triangle.
B Yes, because it is an isosceles
triangle.
No, because it is an equilateral
triangle.
No, because it is an obtuse
triangle.
Answer: A
Step-by-step explanation:
You can prove it by Pythagorean's Theorem, a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
It has to be a right triangle.
simplify the product using a table (5hrs+4)(3hrs+6)
Answer:
The polynomial is:
[tex]15h^2+42h+24[/tex]
Step-by-step explanation:
We have to simplify the expression which is given as:
[tex](5h + 4)(3h + 6)[/tex]
We have to simplify with the use of a table as:
3h 6
5h [tex]15h^2[/tex] [tex]30h[/tex]
4 [tex]12h[/tex] [tex]24[/tex]
Hence, the polynomial that is formed using this table form simplification is addition of all the entries in the table i.e.:
[tex](5h + 4)(3h + 6)=15h^2+30h+12h+24[/tex]
[tex](5h + 4)(3h + 6)=15h^2+42h+24[/tex]
Hence, the polynomial is:
[tex]15h^2+42h+24[/tex]
of 144 stamps that sierra and her brother collected, sierra collected 3 times as many stamps as her brother. how much did they each collect
To find out how many stamps Sierra and her brother each collected, we need to set up an equation and solve for the unknown variable.
Let's use "x" to represent the number of stamps that Sierra's brother collected.
According to the question, Sierra collected 3 times as many stamps as her brother. So, we can represent Sierra's number of stamps as 3x.
The total number of stamps that they collected together is 144, so we can set up the following equation:
x + 3x = 144
Now we need to solve for "x" to find out how many stamps Sierra's brother collected.
First, we'll combine like terms on the left side of the equation:
4x = 144
Next, we'll divide both sides of the equation by 4 to isolate the variable:
x = 36
So, Sierra's brother collected 36 stamps.
To find out how many stamps Sierra collected, we can plug this value back into the equation for Sierra's number of stamps:
3x = 3(36) = 108
So, Sierra collected 108 stamps.
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Label where the Equilibrium price, Equilibrium quantity, shortage and surplus exist on the graph for the market for
milk by placing the correct labels in the correct areas.
3
2.5
$ per
gallon 2
1 2 3
5 6 7
millions of gallons/week
:: Equilibrium Price :: Equilibrium Quantity
:: Shortage :: Surplus
The equilibrium quantity line (at the pοint 3 οn the quantity axis) is knοwn as the ‘surplus’.
What dοes the term equilibrium price mean?Equilibrium price is the price at which the supply and demand οf a gοοd οr service are equal. This means that the quantity οf gοοds being supplied tο the market is equal tο the quantity οf gοοds being demanded by the market.
The area οf shοrtage indicates the quantity οf milk demanded by cοnsumers that is greater than the quantity οf milk supplied by prοducers in the market. The area οf surplus indicates the quantity οf milk supplied by prοducers that is greater than the quantity οf milk demanded by cοnsumers in the market. The intersectiοn οf the equilibrium price and the equilibrium quantity lines indicates the market price and quantity at which the demand fοr milk is equal tο the supply οf milk in the market.
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The coordinates of two triangles
are shown in the table. Is XYZ a dilation of JKL? Write an
argument that can be used to defend your solution.
AJKL
J
K
L
(a, b)
(c,d)
(a, d)
X
Y
Z
AXYZ
(3a, 6b)
(3c, 6d)
(3a, 6d)
The argument for the dilation is that: No, in order for one figure to be dilated of another, both coordinates of all points must be multiplied by the same constant
How to determine the true statement about the dilationThe complete question is added as an attachment
From the attached table of values, we can see that:
The coordinates of x are multiplied by 3, while the coordinates of y are multiplied by 6
This means that
The figure is not properly dilated, because these coordinates must be multiplied by the same constant value
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20 points pls hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Answer:
Let x = the price of one shirt
Since he bought 3 shirts, he will pay three times the amount. Also, there is a discount. With the discount, the total cost is $63.
We can set up an equation to represent this scenario. Assuming we have a 30% discount as David said
3(x - 0.3x) = 63
Just so you understand, (x - 0.30x) is the sales price for one shirt. We apply this discount price 3 times because the discount is added for each shirt.
Solve for x from this equation to get the price for one shirt.
3(0.70x) = 63
2.1x = 63
x = 30
In February, Alec had 1,513 visitors to his website. In March, he had 1,400 visitors to his website. What is the percentage decrease of the number of visitors to Alec's website from February to March? If necessary, round to the nearest tenth of a percent. A. 9. 3%
B. 7. 5%
C. 8. 1%
D. 92. 5%
solution
1531-1400=113
decrease/original ×100
113/1513×100
7.46
round off to 7.5
Julia and her friends enjoy running long-distance races together. Julia's goal is to run faster than two of her friends in an upcoming 6. 2-mile race. The table shows the results of the last race that each runner finished. Assume they each run the race at the same rate they ran their last race. Complete the table. Who will finish first among the three friends, and by how much time will she beat the second-place finisher?
Julia will finish the upcoming 6.2-mile race first among her friends, beating the second-place finisher by 5 minutes and 42 seconds.
What is distance?Distance is the measure of how far apart two objects or points are. It is expressed in terms of length, area, volume, or time. It is a numerical measurement of how much space is between two points or objects. Distance can also be used to measure the length of a journey, or to measure the speed of an object moving over a certain period of time.
To calculate this, we can look at the table and compare the times of the last race each of them ran. Julia ran a 5-mile race in 32 minutes and 45 seconds, her first friend ran a 4-mile race in 28 minutes and 20 seconds, and her second friend ran a 4-mile race in 29 minutes and 15 seconds.
To calculate the time difference between Julia and the second-place finisher, we can compare the total time they would run the 6.2-mile race. Julia would run the 6.2 miles in 40 minutes and 45 seconds (32 minutes and 45 seconds for the 5-mile race plus 8 minutes for the additional 1.2 miles) and the second-place finisher would run the 6.2 miles in 41 minutes and 35 seconds (29 minutes and 15 seconds for the 4-mile race plus 12 minutes and 20 seconds for the additional 2.2 miles). The difference between the two times is 5 minutes and 42 seconds, so Julia would finish first and beat the second-place finisher by 5 minutes and 42 seconds.
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Work out (h+4)/(2)-(h+5)/(7) Give your answer as a single fraction in its simplest form.
The answer is (5h+18)/(14).
To work out (h+4)/(2)-(h+5)/(7) and give the answer as a single fraction in its simplest form, we will need to find a common denominator and then subtract the numerators.
Step 1: Find a common denominator. The common denominator of 2 and 7 is 14.
Step 2: Multiply the numerator and denominator of the first fraction by 7 to get (7h+28)/(14).
Step 3: Multiply the numerator and denominator of the second fraction by 2 to get (2h+10)/(14).
Step 4: Subtract the numerators: (7h+28)-(2h+10) = 5h+18.
Step 5: Place the difference over the common denominator: (5h+18)/(14).
Step 6: Simplify the fraction if possible. In this case, the fraction cannot be simplified further.
Therefore, the answer is (5h+18)/(14).
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Maya drinks 236 milliliters of milk with her lunch. Maya drinks 473 milliliters of milk with her dinner.
How many milliliters of milk does Maya drink in all?
Enter your answer in the box.
______________ milliliters
Answer:
709
Step-by-step explanation:
473 + 236 = 709
Find the sum: 16 + (-7) =
and thank you :)
Answer:
9
Step-by-step explanation:
since 16 is a positive number and the 7 is negative, it would basically be 16 - 7.
Math question 14 help
Plssss hellllppppp meeeeeeee
The areas of section 1, 2 and 3 are 8 inches square, 80 inches square and 8 inches square respectively.
The area of the trapezium is 96 inches square.
What is the area of the trapezium?Section 1 and 2 are right triangles.
Area of a right triangle = 1/2 x base x height
Height = 8cm
Base = (14 - 10) / 2 = 2cm
Area of a right triangle = 1/2 x 2 x 8 = 8cm²
Section 3 is a rectangle.
Area of a rectangle = length x width
8 x 10 = 80 cm²
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
= 1/2 x (10 + 14) x 8
1/2 x 24 x 8 = 96cm²
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For f(x)= 11x and g(x)= 1/11x, (fog)(x) and (gof)(x).Then determine whether (fog)(x) = (gof)(x). What is (fog)(x)?
(fog)(x)=____
The answer to the question "What is (fog)(x)?" is:
(fog)(x) = x
The first step in solving this problem is to find the composition of f and g, or (fog)(x). This is done by substituting the expression for g(x) into the expression for f(x):
(fog)(x) = f(g(x)) = f(1/11x) = 11(1/11x) = x
Similarly, we can find the composition of g and f, or (gof)(x), by substituting the expression for f(x) into the expression for g(x):
(gof)(x) = g(f(x)) = g(11x) = 1/11(11x) = x
Now, we can determine whether (fog)(x) = (gof)(x) by comparing the two expressions. Since both (fog)(x) and (gof)(x) are equal to x, we can conclude that (fog)(x) = (gof)(x).
Therefore, the answer to the question "What is (fog)(x)?" is:
(fog)(x) = x
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Mr. Jensen throws an eraser at a sleeping student. The equation that models the flight of the eraser is: h(t)=-16t^(2)+35t+6 The student hos his head laying on the desk about 3 feet off the ground. How long does it take for the eraser to hit the student in the head?
It takes approximately0.082 seconds for the eraser to hit the student in the head.
The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.
First, we will set h(t) equal to 3 and rearrange the equation:
-16t^(2)+35t+6=3
Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0
Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))
Simplifying further, we get:
t= (-35±√(1417))/(-32)
Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27
Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.
Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.
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Pls help!! Which graph represents the following ellipse.
A graph that represents the following ellipse (x + 1)²/16 + (y - 3)²/36 = 1 is: C. graph C.
What is the equation of an ellipse?Mathematically, the standard form of the equation of an ellipse is given by mathematical expression:
x²/a² + y²/b² = 1
Where;
a represents the major axis.b represents the minor axis.This ultimately implies that, the major axis of this ellipse is the x-axis. By critically observing the graph (see attachment), we can logically deduce the following values:
a = √16 = 4.
b = √36 = 6.
In conclusion, the standard form of the equation of this ellipse is given by (x + 1)²/16 + (y - 3)²/36 = 1.
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Please help me I am stuck what do I do I multiply?
Answer:
See below.
Step-by-step explanation:
I'm sure the question is asking to solve for ∠BDC, but we'll solve for all of the angles.
We should note that we have a Given Exterior Angle.
What is an Exterior Angle?An Exterior Angle is an angle that is formed by extended lines.
An exterior angle is equal to the combined sum of the two nonadjacent, and interior angles.
Using what we learned, ∠BCD and ∠CDB will equal ∠DBE°.
Let's turn this problem into an equation.
60° + ∠BDC = 120°
Subtract 60 from both sides.
∠BDC = 60°.
We can also identify that ∠CBD is a linear pair with ∠DBE.
A Linear Pair is 2 adjacent angles that add up to 180°. Linear Pairs are straight lines with one line intersecting in between.
Meaning that ∠CBD + ∠DBE = 180°.
∠CBD + 120° = 180°.
∠CBD = 60°.
We can identify that this triangle is an Equilateral Triangle. An Equilateral Triangles is a triangle that has all congruent sides and angles.
Our final answers are;
∠BDC = 60°.
∠CBD = 60°.
Solve the following equation for Ω over the interval [0, 2π), giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list.
cos(Ω) = - cos(2Ω).
Ω = _______
The solutions in radian units are:
Ω = 0.928, 2.213, 4.070, 5.355
The solutions should be entered as a comma-separated list:
Ω = 0.928, 2.213, 4.070, 5.355
The equation cos(Ω) = -cos(2Ω) can be solved by using the double angle formula for cosine. The double angle formula for cosine is cos(2Ω) = 1 - 2sin^2(Ω).
Substituting the double angle formula into the original equation gives:
cos(Ω) = - (1 - 2sin^2(Ω))
Rearranging the equation gives:
2sin^2(Ω) = 1 + cos(Ω)
Squaring both sides of the equation gives:
4sin^4(Ω) - 4sin^2(Ω) - cos^2(Ω) = 0
Using the identity cos^2(Ω) = 1 - sin^2(Ω) gives:
4sin^4(Ω) - 4sin^2(Ω) - (1 - sin^2(Ω)) = 0
Simplifying the equation gives:
4sin^4(Ω) - 3sin^2(Ω) - 1 = 0
Using the quadratic formula gives:
sin^2(Ω) = (3 ± √(9 + 16))/8
Solving for sin(Ω) gives:
sin(Ω) = ±√(7/8)
Taking the inverse sine of both sides gives:
Ω = sin^-1(±√(7/8))
The solutions in radian units are:
Ω = 0.928, 2.213, 4.070, 5.355
The solutions should be entered as a comma-separated list:
Ω = 0.928, 2.213, 4.070, 5.355
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1. (-3)² + (-2)² is equal to (A) (B) -13 -10 13. 25
The simplified form of the expression ( -3 )² + ( -2 )² is 13.
What is the simplified form of the expression?Given the expression in the question;
( -3 )² + ( -2 )²
To solve the expression (-3)² + (-2)², we first need to simplify each term inside the parentheses by multiplying each term by itself.
It involves squaring the values of -3 and -2, and then adding them together.
First, we can simplify;
(-3)² as (-3) x (-3), which gives us 9.
Similarly,
(-2)² can be simplified as (-2) x (-2), which gives us 4.
So, substituting these values back into our original expression, we get:
(-3)² + (-2)² = 9 + 4 = 13
(-3)² + (-2)² = 12
Therefore, (-3)² + (-2)² simplifies to 13.
Option C) 13 is the correct answer.
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Please answer this question
Answer: 1
Step-by-step explanation:
(6) + (8) ÷ 8 - 6
divide first then do left to right
6 + 1 - 6
7 - 6
1
Answer:
1
Step-by-step explanation:
t = 6 and d = 8
Rewrite the expression by replacing variables with given values:t + d ÷ 8 - 6 = 6 + 8 ÷ 8 - 6
First step is division.6 + 1 - 6
Then we follow from left to right and first add then subtract.6 + 1 - 6 = 1
en has 1 5 liter of juice. She distributes it equally to 3 students in her tutoring group. What fraction of the juice does each student get? Partition and shade the tape diagram to represent the amount of juice. 1 liter Nice! Partition the tape diagram to represent how Jen distributes the juice. 1 liter 1 5 Nice! Double shade to show the fraction of juice each students gets. 1 liter 1 5 Good work! Solve. Show the answer in an equation. 1 liter 1 5
Each student gets 1/3 of the juice.
What is Division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
Each student gets 1/3 of the juice.
Equation: 1/3 x 5 = 5/3 or 1 2/3 liters per student.
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Find the area of (a) A triangle if two sides have lengths 13 and 15 and the altitude to the third side has length 12 (b) A triangle whose sides have lengths 10, 10, and 16 (c) A triangle whose sides have lengths 5, 12, and 13 (d) An isosceles triangle whose base has length 30 and whose legs each have length 17 (e) An isosceles triangle whose base has length 20 and whose vertex angle measures 68° (f) An isosceles triangle whose base has length 30 and whose base angle measures 62° (g) A triangle inscribed in a circle of radius 4 if one side is a diameter and another side makes an angle measuring 30° with the diameter (h) A triangle cut off by a line parallel to the base of a triangle if the base and altitude of the larger triangle have lengths 10 and 5, respectively, and the line parallel to the base is 6
(a) The area of a triangle can be found using the formula A = (1/2)bh, where b is the base and h is the height. In this case, the base is one of the sides with length 13 or 15, and the height is the altitude with length 12. Using the formula, the area is A = (1/2)(13)(12) = 78 square units.
(b) The area of a triangle can also be found using Heron's formula, which is A = √[s(s-a)(s-b)(s-c)], where s is the semiperimeter of the triangle, and a, b, and c are the lengths of the sides. In this case, s = (10+10+16)/2 = 18, so the area is A = √[18(18-10)(18-10)(18-16)] = 80 square units.
(c) Using Heron's formula again, s = (5+12+13)/2 = 15, so the area is A = √[15(15-5)(15-12)(15-13)] = 30 square units.
(d) The area of an isosceles triangle can be found using the formula A = (1/2)bh, where b is the base and h is the height. In this case, the base is 30 and the height can be found using the Pythagorean theorem, h = √(17^2 - (30/2)^2) = 8. So the area is A = (1/2)(30)(8) = 120 square units.
(e) The area of an isosceles triangle can also be found using the formula A = (1/2)ab sin C, where a and b are the lengths of the two equal sides and C is the vertex angle. In this case, a = b = 20 and C = 68°, so the area is A = (1/2)(20)(20) sin 68° = 190.4 square units.
(f) Using the same formula as in (e), but with a = b = 30 and C = 62°, the area is A = (1/2)(30)(30) sin 62° = 675 square units.
(g) The area of a triangle inscribed in a circle can be found using the formula A = (1/2)ab sin C, where a and b are the lengths of the two sides and C is the angle between them. In this case, one side is a diameter with length 8 (2 times the radius of 4), another side has an unknown length, and the angle between them is 30°. The area is A = (1/2)(8)(b) sin 30° = 2b square units.
(h) The area of a triangle cut off by a line parallel to the base can be found using the formula A = (1/2)bh, where b is the length of the base and h is the height. In this case, the base is 10 and the height is 5 - 6 = -1, so the area is A = (1/2)(10)(-1) = -5 square units.
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Please help me on this
Answer:
232.5 units²
Step-by-step explanation:
Which direction is the arrow supposed to be pointing?
Answer:
Step-by-step explanation:
to the rieft
Create a Pandas crosstab to compare the number of players in each position by foot. Set normalize='all' and margins=True to view the data as a percent of the total. What combination of footedness and position is the most rare in our data?
To create a Pandas crosstab to compare the number of players in each position by foot, we first need to import the pandas library and then use the `pd.crosstab()` function with the appropriate parameters.
We can set `normalize='all'` to view the data as a percent of the total and `margins=True` to include row and column totals. Here's how we can do it:
```python
import pandas as pd
# Create a crosstab with the desired parameters
crosstab = pd.crosstab(df['Position'], df['Foot'], normalize='all', margins=True)
# Print the crosstab
print(crosstab)
```
To find the combination of footedness and position that is the rarest in our data, we can use the `idxmin()` function to find the index of the minimum value in the crosstab. Here's how we can do it:
```python
# Find the index of the minimum value in the crosstab
min_index = crosstab.idxmin()
# Print the combination of footedness and position that is rare
print('The most rare combination of footedness and position is', min_index)
```
The output of this code will show the combination of footedness and position that is the rarest in our data.
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find the value of x and y.
The value of x and y are 40° and 40° respectively
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
These are the few theorems of circle geometry
1. The angle at the centre is twice the angle at the circumference.
2. The angle in a semicircle is a right angle.
Angles in the same segment are equal.
3. Opposite angles in a cyclic quadrilateral sum to 180°
4. The angle between the chord and the tangent is equal to the angle in the alternate segment.
from triangle AOB,
angle 0 = 60° (opposite angles)
x = 180-( 80+60)
x = 180-140
x = 40°
x= y ( angle in the same segment are equal)
y = 40°
therefore the value of x and y are 40°
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What is the inverse of the following statement?
if two angles are not vertical, then they are not congruent
The inverse of the statement is if two angles are vertical, then they are congruent
How to determine the inverse of the statement?The statement from the question is:
if two angles are not vertical, then they are not congruent
Given a statement
If a then b
The inverse of the statement is
If not a then not b
To write the inverse statement using the above rule, we have the following statement
The inverse of the given statement is if two angles are vertical, then they are congruent
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