Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $3.
Answers
Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game
What is expected value?
Expected value is a concept used in probability theory to describe the average value or outcome of a random variable over many trials. It is calculated by multiplying each possible outcome of a variable by its probability, and then summing all of the products. This can help to estimate the most likely outcome or value of an uncertain event or situation.
The probability of selecting a face card from a standard 52-card deck is 12/52 or 3/13. The probability of selecting any other type of card is 1 - 3/13 or 10/13.
Kyd's expected value for this game can be calculated as follows:
(3/13) x (-$3) + (10/13) x $6 = $3.38
Therefore, Kyd's expected value for this game is $3.38.
North's expected value for this game can also be calculated as follows:
(3/13) x $6 + (10/13) x (-$3) = -$0.92
Therefore, North's expected value for this game is -$0.92.
Since Kyd's expected value is positive and North's expected value is negative, Kyd has the advantage in this game.
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Related Questions
In art class students are mixing blue and red paint to make purple paint. Deondra
mixes 6 cups of blue paint and 7 cups of red paint. Arun mixes 2 cups of blue paint
and 3 cups of red paint. Use Deondra and Arun's percent of red paint to determine
whose purple paint will be redder.
Deondra percent of red paint (to nearest whole number) =
Arun percent of red paint (to nearest whole number) =
O Deondra's purple paint will be redder.
O Arun's purple paint will be redder.
o The two purple paints will be equally red.
Submit Answer
%
%
attempt 1 out of 2
Answers
Arun's purple paint will be redder.
Define percentagePercentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.
Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:
7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.
Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:
3 / (2 + 3) × 100% = 60%.
Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.
Therefore, the answer is Arun's purple paint will be redder.
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A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answers
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth
Answers
Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)
Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).
The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,
A' = 2A
A'(8, -12) = 2×A(4, -6)
These facts are all you need to know to choose the correct answer (shown above).
Answer: 1/2
Step-by-step explanation:
I took the quiz!
Evaluate the expression for the given value.
–a – 7 for a = –4
A11
B–11
C3
D–3
Answers
Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
Answers
The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)
Calculating the composite functions (f/g)(x) and (f-g)(x)To calculate (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)
The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f/g)(x) is x ≥ 5/3.
To calculate (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)
The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f-g)(x) is x ≥ 5/3.
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Solve by using matrices.
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
X
= -66, y = [?], z =
Enter
Answers
The solution to the system of equations using matrices is x = 45, y = 15, and z = 30.
What is determinant of matrix?A scalar value that can be calculated from a matrix's elements is the determinant. When a square matrix is used to transform vectors, the determinant is a measurement of how much the matrix "stretches" or "shrinks" space. In linear algebra, the determinant is employed in a variety of operations, including as the computation of a matrix's inverse, the description of a matrix's eigenvalues and eigenvectors, and the resolution of linear equation systems. In specifically, the existence of a unique solution, the absence of a solution, or an unlimited number of solutions to a system of linear equations can be determined using the determinant of the coefficient matrix.
The given equation are:
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
Writing the equations in matrix form we have:
[tex]\begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]
Multiplying the inverse of the coefficient matrix we have:
[tex]\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 & -1 & 3 \\ -4 & 2 & 3 \\ 3 & -4 & 0 \end{bmatrix}^{-1} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix}[/tex]
Now,
[tex]\begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix}[/tex]
Multiplying this by the vector on the right-hand side gives:
[tex]\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 2/23 & 5/46 & -3/23 \\ 2/23 & 1/23 & 5/23 \\ -3/23 & -5/46 & 2/23 \end{bmatrix} \begin{bmatrix} 180 \\ 225 \\ 270 \end{bmatrix} = \begin{bmatrix} 45 \\ 15 \\ 30 \end{bmatrix}[/tex]
Hence, the solution to the system of equations is x = 45, y = 15, and z = 30.
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Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
Answers
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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Determine the interval(s) on which the function Is constant.
Write your answer as an interval or list of intervals.
When writing a list of Intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None* if applicable.
Answers
The intervals on which the function Is constant are [-4, -3] and [3, 6]
Determining the interval(s) on which the function Is constant.A function is considered constant over an interval if the function has the same output for all the inputs within that interval.
In other words, the function does not change over that interval.
Using the above as a guide, we have the following:
The function does not change over the intervals [-4, -3] and [3, 6]
Hence, the intervals are [-4, -3] and [3, 6]
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answers
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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Will mark brainliest if answer is correct
Answers
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
Answers
Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)
What is a Graph?A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.
In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.
For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.
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-4(2-x) less than or equal to 8
Answers
Answer: less than
Step-by-step explanation:
1. Dorie Sparrow, assistant manager of The Clothes Horse, Inc., must mark all clearance rack dresses back
to their regular selling price. She had marked all of them down 70%. What regular selling price does Dorie
need to sell a dress for that had been marked down to $104.98?
Answers
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
What is selling price?
Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.
If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.
Let P be the original selling price of the dress. Then:
0.3P = $104.98
Solving for P, we get:
P = $104.98 / 0.3
P = $349.93
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
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Need help with is question
Answers
Answer:
27.78%
Step-by-step explanation:
To calculate the percentage of the total spending that is on rent, we need to divide the amount spent on rent by the total amount spent, and then multiply by 100 to get the percentage.
Total spending = food + rent + other + fun
Total spending = $400 + $500 + $600 + $300
Total spending = $1800
So, the percentage of the total spending that is on rent is:
($500 / $1800) x 100% = 27.78%
Therefore, approximately 27.78% of the total spending is on rent.
Which statement explains the type of function that is represented by the equation y = x^2 + 9?
Answers
The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .
Describe Linear Function?A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.
The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.
A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
In the given equation y = x² + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.
Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.
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The complete question is :
Which statement explains the type of function that is represented by the equation y=x² +9?
A The function is linear because it contains more than one term.
B) The function is linear because the variable x is raised to the second power.
C) The function is nonlinear because it contains more than one term.
D) The function is nonlinear because the variable x is raised to the second power.
5. What is the perimeter of polygon XYDB?
Answers
option D 20 is correct answer .the perimeter of polygon XYDB is 20.
what is polygon ?
A polygon is a closed geometric shape made up of straight line segments connected end-to-end. It is a two-dimensional figure that has three or more sides and angles. Polygons can be classified according to the number of sides
In the given question,
To find the perimeter of polygon XYDB, we need to add up the lengths of all its sides. Since all side lengths are given as 5, we can simply multiply 5 by the number of sides to get the perimeter.
Polygon XYDB has four sides, so the perimeter is:
Perimeter = 4 × 5 = 20
Therefore, the perimeter of polygon XYDB is 20.
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Answer:
D. 20 cm
Step-by-step explanation:
Need help Asap please
Answers
Answer:
Summer for 9th Graders: 0.14
Fall for 10th Graders: 0.15
Spring overall total: 0.36
Summer overall total: 0.22
Fall overall total: 0.33
Winter overall total: 0.09
Step-by-step explanation:
Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.
However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency
What 2 numbers add up to 13 but multiply to -48??
Answers
Answer:
3 and -16
Step-by-step explanation:
To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:
1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48
We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:
3 x (-16) = -48
Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.
Answer: -3, 16
Step-by-step explanation:
Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
Answers
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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rewrite the equation in Ax +By = C. y -5 = 2(x - 1)
Answers
-2X + y = 3
y-5=2(x-1)
y=2x-2+5
-2x+y=3
How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answers
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.
Solve the equations using suntraction. Show all your work.
X-6y=11 and 2x-5y=1
Answers
To use this method, we need to choose one variable to eliminate. In this case, we can eliminate the variable "x" by multiplying the first equation by 2 and the second equation by -1, and then adding the two resulting equations. This will give us an equation in terms of "y" that we can solve, and then use the solution to find the value of "x".
Here are the steps:
Multiplying the first equation by 2, we get:
2x - 12y = 22
Multiplying the second equation by -1, we get:
-2x + 5y = -1
Adding the two resulting equations, we get:
-7y = 21
Dividing both sides by -7, we get:
y = -3
Now that we have solved for "y", we can substitute this value back into either of the original equations to find the value of "x". Let's use the first equation:
x - 6y = 11
x - 6(-3) = 11
x + 18 = 11
Subtracting 18 from both sides, we get:
x = -7
Therefore, the solution to the system of equations using the method of subtraction is:
x = -7 and y = -3.
Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Y′(−6, −1).
y-axis
x-axis
y = −1
x = 6
Answers
Answer:
To determine the line of reflection if the image of Y, Y′, is at (-6, -1), we need to find the perpendicular bisector of the line segment connecting Y and Y′. This perpendicular bisector will be the line of reflection.
The midpoint of the line segment YY′ is:
[(6 + (-6))/2, (-1 + (-1))/2] = (0, -1)
The slope of the line segment YY′ is:
(-1 - (-1))/(-6 - 6) = 0/(-12) = 0
Since the slope of YY′ is 0, the perpendicular bisector of YY′ is a vertical line passing through its midpoint (0, -1), which is the y-axis. Therefore, the line of reflection is the y-axis.
Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).
Answers
The equation of the normal plane is 4y = 4π, or equivalently, y = π.
What is osculating plane?The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.
To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:
Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.Step 1: Find the first and second derivatives of the curve with respect to t.
x' = 2cos2t
y' = 1
z' = -2sin2t
x'' = -4sin2t
y'' = 0
z'' = -4cos2t
Step 2: Evaluate the derivatives at t = π.
x'(π) = 2cos2π = 2
y'(π) = 1
z'(π) = -2sin2π = 0
x''(π) = -4sin2π = 0
y''(π) = 0
z''(π) = -4cos2π = -4
So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.
Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.
The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:
n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩
Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.
The equation of the osculating plane is given by:
4(x - 0) + 0(y - π) + 0(z - 1) = 0
Simplifying, we get:
4x - 4 = 0
So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.
Step 5: Use the curvature vector to find the normal vector of the normal plane.
The normal vector of the normal plane is given by the curvature vector:
n' = κv = ⟨0, 4, 0⟩
Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.
The equation of the normal plane is given by:
0(x - 0) + 4(y - π) + 0(z - 1) = 0
Simplifying, we get:
4y - 4π = 0
So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.
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find the reduced radical 36^3/4 • 36^-1/4 (show explanation please)
Answers
Step-by-step explanation:
36^3/4 * 36 ^-1/4 = 36 ^( 3/4 - 1/4 ) = 36 ^1/2 = sqrt (36 ) = 6
Find the area of the trapezoid. 10 km 8 km 6 km
Answers
the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h
what is trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid
In the given question,
To find the area of a trapezoid, we use the formula:
A = (1/2) * (b₁ + b₂) * h
where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).
In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.
Using the Pythagorean theorem, we can find the length of the altitude:
a² + (b₁ - b₂)² = (2a)²
Simplifying and solving for a, we get:
a² + (b₁- b₂)² = 4a²
3a² = (b₁ - b₂)²
a = (1/√3) * |b₁ - b₂|
Since we know that the sum of the non-parallel sides is 10 km, we can write:
b₁ + b₂ = 10
Let's assume that b1 is the longer base, so we can write:
b₁ = 8 km
b₂ = 10 - b₁ = 2 km
Substituting these values into the formula for the altitude, we get:
a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km
Now we can use the formula for the area of a trapezoid to find the area:
A = (1/2) * (b1 + b2) * h
A = (1/2) * (8 + 2) * 2√3
A = 10√3 km²
Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).
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4. center (3, 6), tangent to the x-axis
Answers
The equation of the circle with center (3,6) and tangent to the x-axis is (x - 3)² + 36 = r²
Describe Tangent?In mathematics, a tangent is a straight line that touches a curve or surface at a single point and is perpendicular to the radius or line that passes through that point. The point of contact between the tangent and the curve or surface is called the point of tangency.
In geometry, the tangent to a circle is a straight line that intersects the circle at exactly one point. This point is called the point of tangency, and the tangent is perpendicular to the radius of the circle at that point.
The tangent is an important concept in calculus, where it is used to define the derivative of a function. The derivative of a function f(x) at a point x=a is defined as the slope of the tangent line to the graph of f(x) at the point (a, f(a)). This slope measures the rate at which the function is changing at that point.
If an equation is tangent to the x-axis, this means that it only intersects the x-axis at one point, which has a y-coordinate of zero. So, we need to write an equation of a circle with center (3,6) that intersects the x-axis at one point with a y-coordinate of zero.
Let the radius of the circle be r. Since the center of the circle is (3,6), the equation of the circle can be written in the form:
(x - 3)² + (y - 6)² = r²
Since the circle is tangent to the x-axis, we know that it intersects the x-axis at (x,0), where x is a point on the x-axis. Substituting y=0, we get:
(x - 3)² + (0 - 6)² = r²
Simplifying this equation, we get:
(x - 3)² + 36 = r²
So, the equation of the circle with center (3,6) and tangent to the x-axis is:
(x - 3)² + 36 = r²
Note that there are many possible values for r that would satisfy this equation, since we haven't specified the size of the circle. We only know that it is tangent to the x-axis and has center (3,6).
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The complete question is :
How do you write an equation with center (3,6), tangent to the x-axis?
A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answers
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
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Answers
Answer:
3,4,5 is the answer
Step-by-step explanation:
for the explanation using pythagoras theoem
[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]
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A car, van, truck and bike are all travelling in the same direction on the road. Each travels at a constant speed, but the speeds of the 4 vehicles may be different. At 10 am the car overtakes the van. At noon it overtakes the truck. At 2 pm it overtakes the bike. At 4 pm the truck overtakes the bike. At 6 pm the van overtakes the truck. When does the van overtake the bike?
Answers
Answer:
at 6 pm
Step-by-step explanation:
I'm 99.9% sure that it's correct, please tell me if I'm wrong