3.6.2 Reflect the plane in the x-axis, and then in the line y = 1/2. Show that the resulting isometry sends (x,y) to (x,y+1), so it is the translation to.1. 3.6.3 Generalize the idea of Exercise 3.6.2 to show that the combination of reflec- tions in parallel lines, distance d/2 apart, is a translation through distance d, in the direction perpendicular to the lines of reflection. 3.6.4 Show, by a suitable picture, that the combination of reflections in lines that meet at angle 8/2 is a rotation through angle 0, about the point of intersec- tion of the lines. Another way to put the result of Exercise 3.6.4 is as follows: Reflections in any two lines meeting at the same angle 0/2 at the same point P give the same outcome. This observation is important for the next three exercises (where pictures will also be helpful).
The transformation as a whole is given by P → Q → R → S. A rotation through angle, about the intersection point of the lines, results from the combination of reflections in lines that meet at angle /2.
Two reflections across intersecting lines equal what?Two reflections across intersecting lines have the same composition as one rotation with the junction point as the centre of rotation.
By (0,-1/2), the initial translation is provided.
Given by is the reflection along the x-axis (x,-y)
By (0,1/2), the final translation is indicated. Hence, the transformation as a whole is provided by
(x,y) → (x,-y) → (x,-y+1/2) → (x,y+1)
This demonstrates that the resulting isometry moves the values of (x,y) by one unit in the positive y-direction to (x,y+1).
The whole transformation is provided by:
P → P + (0,d/2) → Q → Q - (0,d/2)
The total transformation is given by:
P → P + (d/2,0) → (x,-y) → (x,y) → Q
where Q is positioned (x,y). Adding the two transformations together, we obtain:
P → P + (0,d/2) → Q → Q - (0,d/2) = P + (d,0)
This demonstrates that a translation across distance d, in the direction perpendicular to the lines of reflection, results from the combination of reflections on parallel lines spaced d/2 apart.
The total transformation is given by:
P → Q → R → S
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A car hire company charged rs. C a day together with an additional rs. C per mile work out the total charge for hiring a car for 50 days and travelling 2500 miles during that time
The fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7.
Given that the charge for a 12 km ride is Rs. 89 and for a 20 km ride is Rs. 145, we can form two equations in terms of the fixed charge (c) and the charge per km (x).
Solving these equations, we get c = 5 and x = 7. Therefore, the fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7. To find the charge for a 30 km ride, we can substitute these values in the formula
c + 7x, which gives us 5 + 7x30 = Rs. 215.
89 = c + 12x ---------------(1)
145 = c + 20x -------------(2)
Solving equations 1 and 2, we get,
8x = 56
x = 7.
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Complete Question:
The car hire charges in a city comprised of a fixed charge together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs 145. What will a person have to pay for traveling a distance of 30 km?
how to rewrite the mixed number as an improper fraction. draw please help me bc it do tomorrow PLEASE HELP PLEASE IT DO TOMORROW.
Answer:
To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator of the fraction, then add the numerator. The resulting sum is the numerator of the improper fraction, while the denominator remains the same.
For example, to rewrite the mixed number 3 1/2 as an improper fraction, you would:
Multiply the whole number 3 by the denominator 2: 3 x 2 = 6
Add the numerator 1 to the product: 6 + 1 = 7
Write the sum 7 as the numerator of the improper fraction, with the denominator 2: 7/2
So, the improper fraction equivalent of the mixed number 3 1/2 is 7/2.
Step-by-step explanation:
The base of the pennant measures 3 inches and the height of the pennant measures 5 inches if austin is covering the pennant with paint how much of the surface will be covered?
Austin needs to cover 15 square inches of surface area with paint in order to finish the task.
The area of the pennant is the length times the width, which is 3 inches times 5 inches. This gives us 15 square inches of surface area to be covered. To calculate the amount of paint needed, we first need to calculate the area of the pennant. The formula for area is area = length x width. Plugging in the measurements for the base and height of the pennant, we get 15 square inches of surface area. This means that Austin needs to cover 15 square inches of surface area with paint in order to finish the task.
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The total revenue, in dollars, from the sale of x units of a product is given by 2200x R(x) = in(8x + 8) (a) Find the marginal revenue MR function. x In((8x+8)2200) – 2200x + ln((8x + 8)2200) in?(8x + 8)(x+1) MR = (b) Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) $ Interpret your result. O The cost of producing one additional unit is approximately this amount. O Selling one additional unit yields approximately this amount. O The total cost of producing 100 units is this amount. O The total revenue from selling 100 units is this amount.
The marginal revenue when 100 units are sold is approximately $17.12. Selling one additional unit at this point would yield approximately $17.12 in additional revenue.
To find the marginal revenue, we first need to find the derivative of the total revenue function with respect to x, which is the definition of marginal revenue:
R(x) = 2200x/(ln(9x+9))
Using the quotient rule, we get:
R'(x) = (2200(ln(9x+9)) - 2200x(1/(9x+9))(1/(9x+9)))/(ln(9x+9))^2
Simplifying this expression, we get:
R'(x) = 2200(9x)/(9x+9)^2ln(9x+9)^2
Substituting x=100, we get:
R'(100) = 2200(9(100))/((9(100)+9)^2ln(9(100)+9)^2 = $9.77 (rounded to the nearest cent).
Interpretation: The marginal revenue when 100 units are sold is $9.77. This means that selling one additional unit of the product will increase the total revenue by approximately $9.77.
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Complete question:
The total revenue, in dollars, from the sale of x units of a product is given by R(x)=2200x/(ln(9x+9)). Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) Interpret your result.
In the given the figure above, m∠BAC= 64° and m∠CBA=56°.
Part I: Find the m∠DEC .
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
I. The measure of angles DEC is: 60°
II. The theorems used are corresponding angles and triangle sum theorems.
What is the Triangle Sum Theorem?
We are given the following:
m∠BAC = 64°
m∠CBA = 56°
AB║CD
BC║DE
Considering triangle ABC, we have:
m∠BCA = 180 - m∠BAC - m∠CBA [triangle sum theorem]
Substitute:
m∠BCA = 180 - 64 - 56
m∠BCA = 60°
Therefore, based on the corresponding angles theorem,
m∠DEC = m∠BCA
Substitute:
m∠DEC = 60°
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use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. then compare this with the actual change in cost. (round your answers to two decimal places.)Function x-Value C = 0.075x^2 + 6x + 7 X = 10x-valuex = 10
The approximate change in cost corresponding to an increase in sales of one unit is 8.50. and actual change in cost is 8.25.
To answer this question, we need to use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. To do this, we need to calculate the derivative of the given cost function C = 0.075x^2 + 6x + 7.
The derivative of this function is dC/dx = 0.15x + 6. We can now use this derivative to approximate the change in cost when x is increased by one unit. This is given by dC/dx = 0.15(10) + 6 = 8.5.
To compare this with the actual change in cost, we can calculate the change in cost when x is increased from 10 to 11. This is given by C(11) - C(10) = (0.075x^2 + 6x + 7) | 11 - (0.075x^2 + 6x + 7) | 10 = 0.075(121) + 66 + 7 - 0.075(100) - 60 - 7 = 8.25.
Therefore, the approximate change in cost when x is increased by one unit (calculated by differentials) is 8.50 and the actual change in cost is 8.25. This shows that the approximate change in cost calculated by differentials is an accurate estimation of the actual change in cost.
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Alex and Sam both work for the same lawn-mowing service. The equation Y=20x gives the relationship between the amount Alex earns, y, by mowing for x hours. the table shows the amount Sam earns working different amounts of hours.
How much more does alex earn per hour, in dollars, than sam?
I NEED THIS ANSWER FAST! 20 POINTS POSSIBLE!
The amount more that Alex earn per hour more than Sam is $2.
How much more does Alex earn?A linear equation is an equation that has a single variable that is raised to the power of one. The general form of a linear equation is
y = mx + c
Where:
m = slope c = interceptThe linear equation that represents the amount that Alex earns is y = 20x. This means that for every hour worked, Alex earns $20. Looking at the table, Sam earns $18 for every hour worked. This can be represented with the equation : y = 18x
The difference in the amount earned = 20 - 18 = $2
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A 45° sector in a circle has an area of 13.75π cm².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
cm²
The area of the circle which contains the 45° sector as required to be determined is; 345.4 cm².
What is the area of the circle in discuss?As evident from the task content; A 45° sector in a circle has an area of 13.75π cm².
Hence, since the sector is 45° and the sum of angles in the circle would be 360°; it follows that the area of the circle is; 360/45 = 8 times the area of the sector.
Area of circle = 8 × 13.75π
= 8 × 13.75 × 3.14
= 345.4 cm².
Ultimately, the area of the circle is; 345.4 cm².
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Una varilla de plata mide 48 cm a 13°C. ¿Cuál es su longitud si se calienta hasta 500°C? (α=〖2x10〗^(-5) 〖°C〗^(-1)) ayuda se entrega a las 12 del medio dia
The length of the silver rod when heated to 500°C is approximately 48.47 cm.
To solve this problem, we can use the formula:
L₂ = L₁ (1 + αΔT)
where L₁ is the original length of the rod at temperature T₁, L₂ is the new length of the rod at temperature T₂, α is the coefficient of linear expansion of the material, and ΔT = T₂ - T₁ is the change in temperature.
We are given that the original length of the silver rod is L₁ = 48 cm at temperature T₁ = 13°C. The coefficient of linear expansion for silver is α = 2x10^(-5) °C^(-1). The change in temperature is ΔT = 500°C - 13°C = 487°C.
Substituting these values into the formula, we get:
L₂ = 48 cm (1 + 2x10^(-5) °C^(-1) x 487°C)
= 48 cm (1 + 0.00974)
= 48 cm (1.00974)
= 48.47 cm
Therefore, the length of the silver rod is approximately 48.47 cm.
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_____The given question is incorrect, the correct question is given below:
A silver rod measures 48 cm at 13°C. What is its length when heated to 500°C? (α=2x10^(-5) °C^(-1)).
I dont know how to do this
pls answer if u know with simple working
i dont know if u add 4 each time it didnt work for last questionn
The 3rd term of the linear sequence above is 14.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 18 - 22
Common difference, d = -4
For the third term, we have:
a₃ = a₁ + (n - 1)d
a₃ = 22 + (3 - 1)-4
a₃ = 22 - 8
a₃ = 14.
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A city bus collected $780 in fares in one day. The price of a regular fare was $0.80, and the price of a discount fare was $0.40. If a total of 1200 paid the fares on this bus, write a system of equations that represents this situation.
its b
i have covid and want to know what to do
Put the steps in order to solve this inequality 4x + 7 ⪯ 15
A. Subtract 7 from both sides of the inequality.
B. Divide both sides of the inequality by 4
C. Simplify; leaving only 4x on one side of the inequality.
D. Find your answer; x ⪯ 2
Answer:
C. Simplify
Step-by-step explanation:
1. Subtract 7 from both sides
4x +7 -7 < 15 -7
4x < 8
2. divide both sides by 4
4x/4 < 8/4
answer: x < 2
hope this helps
Which function is increasing?
A. F(x) = 5^x
B. F(x)=(0. 5)^x
C. F(x) = (1/15)^x
D. F(x)= (1/5)^x
In the given functions [tex]5^x[/tex] function is increasing because 5>1.
Let's first define functions so that we may better comprehend the monotonicity and rising and decreasing functions. In its simplest form, a function is a relationship between input and output in which each input is associated with exactly one outcome.
To better understand monotonicity and rising and decreasing functions, let's first define what a function is. A function, in its most basic form, is a relationship between input and output in which each input is connected to precisely one result.
During the duration of their whole domain, functions might alter, growing, shrink, or stay the same. Functions are both continuous and differentiable in the defined intervals.
Functions can change over the course of their entire domain, either increasing, decreasing, or remaining constant. In the specified intervals, functions are both continuous and differentiable.
We have all the functions that are exponential
So when we shall check all the given function
We observe that we have functions of the form:
f (x) = A[tex]b^x[/tex]
When
b > 1 The function grows
b <1 Function decreases
Hence [tex]5^x[/tex] function is increasing.
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Choose the expression that is equivalent to a fraction with four raised to the negative third power in the numerator and the quantity three raised to the negative second power times four squared end quantity in the denominator and the entire fraction is cubed
Answer: go look on yt there’s a good video on this one
Step-by-step explanation:
what is the answer to this?
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response as Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression.
what is polynomial ?Using just the methods of addition, elimination, and multiplication as well as ou pas integer exponents, a polynomial is a mathematical equation made up of variables and coefficients. A polynomial, for instance, is 3x2 - 2x + 5, where x has been the component and 3, -2, and 5 are now the coefficients. This polynomial's highest exponent is 2, which also happens to be its degree. Polynomials can have coefficients that are either constants or other polynomials, as well as many variables. Due to their usage in representing a variety of mathematical relations and functions, polynomials play a significant role in mathematics. Several disciplines, including algebra, algebra, geometry, and physics, make extensive use of them.
given
To make [tex]5x^2-x-8x^2 + 3x^3[/tex]simpler, we can rearrange the terms and join comparable terms:
[tex]0 + 3x^3 - x - 3x^2 = 5x^2 - 8x^2 + 3x^3 - x[/tex]
The following step is to factor the final three terms to remove a common factor of x:
[tex]3x^3 - x - 3x^2 = x\\(3x^2 - 1 - 3x)[/tex]
Hence, the abbreviated form is:
[tex]3x^2 - 1 - 3x^3 = 5x^2-x-8x^2 + 3x^3.[/tex]
Due to the fact that Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression, it is incorrect.
Due to their failure to simplify to the specified formula, options A, [tex]-5x^3+ x^2 = 0,[/tex] and D, [tex]3x^3 -3x^2 =6x[/tex], are likewise incorrect.
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response.
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The complete question is:-
Simplify: [tex]5x^2-x-8x^2 + 3x^3 = 5x[/tex]
OA.-5x3x2 = 0
B. 3x3 + x2 = 6x
C. 3x3 + x2 = 0
D. 3x3 3x26x
-
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How would i find percent of a number in this case 81% of 108 The work part i have the answer
To raise money for charity, Monica and her friends start the Pampered Pooch Pet Wash. The first day they are open, they forget to put up posters and only raise a little money. The next day, they hang posters all over the neighborhood and raise $55.50. In all, Monica and her friends raise $65.50 on the first two days they are open. Which equation can you use to find the amount of money a Monica and her friends raise on the first day?
55.50a = 65.50
a + 55.50 =65.50
a - 65.50 = 55.50
a - 55.50 =65.50
Answer:
Step-by-step explanation:
[tex]a[/tex] is the amount earned on the first day.
She earnt $[tex]$a[/tex] dollar on day 1, $55.50 on day 2, and $65.50 total in the 2 days.
So we get
[tex]a+55.50=65.50[/tex]
magine that party a is selling a car to party b. party a thinks there is an 80% chance the car will not break down in the first year, while party b thinks there is an 80% chance it will. design a contingency contract that could help them avoid an impasse over this issue.
The steps taken to design a contingency contract are valuating the potential outcomes, consequences and agree on terms of contract.
Identify the potential outcomes. Party A thinks that there is an 80% chance that the car will not break down in the first year, while Party B thinks that there is an 80% chance that it will. These are the two potential outcomes that need to be identified.
Determine the consequences of each outcome. Next, the consequences of each outcome should be determined. For example, if the car breaks down in the first year, then Party A may have to pay for repairs or reimburse Party B for the purchase price of the car. If the car does not break down, then no consequences need to be determined.
Agree on the terms of the contract. Finally, both parties need to agree on the terms of the contract. This may include how much Party A will have to pay if the car breaks down, how long Party B has to wait for reimbursement if the car does break down, and any other terms that are relevant to the situation. Once the terms have been agreed upon, the contingency contract can be signed by both parties, and they can proceed with the sale of the car.
A contingency contract could be designed to help them avoid an impasse over the issue of the car's breakdown. The contingency contract is a contract that is triggered by a specific event or circumstance, such as the car breaking down in the first year. This contract outlines what will happen if the event or circumstance occurs, and both parties agree to the terms in advance.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot it on -4
Step-by-step explanation:
Answer: -3
Step-by-step explanation:
Conner worked on Monday, M, and Friday, F, for a total of 12 hours. He charges $5 per hour on Monday and $8 per hour on Friday. If the total amount Conner received was $81, how many hours did he work on Monday
Conner worked 5 hours on Monday.
Let's use the letters "m" and "f" to denote the number of hours Conner worked on Monday and Friday, respectively.
Conner worked a total of 12 hours, and since we know this from the issue statement, we may write:
m + f = 12
Also, we are aware that Conner received $81 and charged $5 on Mondays and $8 on Fridays. Hence, we can write:
5m + 8f = 81
To determine one of the variables in terms of the other, we can utilise the first equation. To solve for "f," we obtain:
f = 12 - m
We can now solve for "m" by substituting this expression for "f" in the second equation:
5m + 8(12 - m) = 81
After simplifying and finding "m," we obtain:
5m + 96 - 8m = 81
-3m + 96 = 81
-3m = -15
m = 5
Conner spent 5 hours at work on Monday as a result.
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Given Matrices A and B shown below, find B - 2A. Let B - 2A = C.
The value of C(22) =
We need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.
Describe Matrix?In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used to represent linear transformations, as well as to solve systems of linear equations.
A matrix with m rows and n columns is called an m x n matrix. The individual entries of a matrix are denoted by a subscript, with the first subscript indicating the row and the second subscript indicating the column. For example, the entry in the second row and third column of a matrix A would be denoted by A[2,3].
Matrices can be added, subtracted, multiplied, and divided (by a scalar). Addition and subtraction of matrices is done element-wise, while matrix multiplication involves taking the dot product of rows and columns. Multiplying a matrix by a scalar involves multiplying every entry in the matrix by that scalar.
To find B - 2A, we need to multiply every element of A by 2 and then subtract the resulting matrix from B:
2A = [(-4)*2 (-3)*2 ; (-2)*2 (-3)*2 ; (-3)2 32 ; (-2)2 42] = [-8 -6 ; -4 -6 ; -6 6 ; -4 8]
B - 2A = [6 -9 ; 7 12 ; -3 -3 ; 2 -7] - [-8 -6 ; -4 -6 ; -6 6 ; -4 8] = [14 -3 ; 11 18 ; 3 9 ; 6 -15]
So C = B - 2A = [14 -3 ; 11 18 ; 3 9 ; 6 -15]
To find C₂₂, we need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.
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Consider a population of size N = 14,600 with a mean of μ = 156 and standard deviation of a = 23.
Compute the following z-values for sampling distributions of with given sarkple size. Round solutions to
two decimal places, if necessary.
The z-values of the sampling distributions are;
z = 2.27z = -2.09z = -2.2z = -3.33What is a sampling distribution?A sampling distribution is a probability distribution obtained through the repeated sampling of a specified population.
The z-value for a sampling distribution can be obtained using the formula;
[tex]z = \frac{\bar{x} -\mu}{\frac{\sigma}{\sqrt{N} } }[/tex]
Where;
[tex]\bar{x}[/tex] = The sample mean
μ = The population mean = 156
σ = The population standard deviation = 23
N = The sample size
The z-values for the sampling distributions are therefore;
1) The number of observations selected from the population, is 76, and the sample mean is; [tex]\bar{x}[/tex] = 162, we get the following z-value.
When, N = 76 and [tex]\bar{x}[/tex] = 162
[tex]z = \frac{162-156}{\frac{23}{\sqrt{76} } } \approx 2.27[/tex]2) The selected observations is 92, and the sample mean is; [tex]\bar{x}[/tex] = 151, we get the following z-value.
When, N = 92 and [tex]\bar{x}[/tex] = 151
[tex]z = \frac{151-156}{\frac{23}{\sqrt{92} } } \approx -2.09[/tex]3) The number in the random sample, N = 102 and the sample mean is; [tex]\bar{x}[/tex] = 151, we get;
When, N = 102 and [tex]\bar{x}[/tex] = 151
[tex]z = \frac{151-156}{\frac{23}{\sqrt{102} } } \approx -2.2[/tex]4) The number of observations in the random sample, N = 120 and the sample mean is; [tex]\bar{x}[/tex] = 149, we get;
When, N = 120 and [tex]\bar{x}[/tex] = 149
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A fish swims down at a rate of 12 ft per hour. If it started at the surface and swims for 6 hours where will it end up?
Answer:
Since the fish is swimming down at a constant rate of 12 ft per hour for 6 hours, the distance it travels can be found by multiplying its speed by the time:
distance = speed x time
distance = 12 ft/hour x 6 hours
distance = 72 ft
Therefore, the fish will end up 72 feet down from the surface.
Ben purchases 2 drinks and a bag of popcorn at the movie theater, for a total of $9.50. If x represents the cost of the drinks and y represents the cost of the popcorn, which equation represents this situation?
An equation that represents this situation include the following: D. y = -2x + 9.50.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the cost of the drinks and the cost of the popcorn respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent the cost of the drinks.Let the variable y represent the cost of the popcorn.Since Ben purchased 2 drinks and a bag of popcorn at the movie theater, for a total cost of $9.50, a linear equation that models the situation is given by this mathematical expression:
2x + y = 9.50
By making y the subject of formula, we have:
y = -2x + 9.50
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A right triangle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit and your answer 3 ft 3 ft 8ft 10ft
The area of shaded region is 45 square units.
How to determine the area of shaded region?The complete question is added as an attachment
The area of the shaded region is calculated as
Shaded region =Area of rectangle - Area of triangle
Using the above as a guide, we have the following:
Area of rectangle = 8 * 6 = 48
Area of triangle = 1/2 * 2 * 3 = 3
Substitute the known values in the above equation, so, we have the following representation
Shaded region = 48 - 3
Evaluate the difference
Shaded region = 45
Hence, the shaded region is 45 square units.
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The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? Enter your answer as a fraction.
Answer:
6/100=3/50
Step-by-step explanation:
The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.
The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.
To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.
Therefore, the probability of picking the same number from both bags is:
6/100
Simplifying this fraction by dividing both the numerator and denominator by 2 yields:
3/50
So the probability of picking the same number from both bags is 3/50.
The percent of carbon-14 remaining in a fossil can be found using the exponential expression (1/2)^t/5730 where t represents the age of the fossil in years. Rewrite the percent as an exponential expression with a base of 2
The percent of carbon remaining after 30642 years if, the half-life of carbon is 5730 years would be 3.1%
Total time is given: 30642 years
Half-Life of carbon-14 : 5730 years
After 1 half-life of the carbon-14 remaining carbon: 1/2
After 2 half-lives the carbon-14 remaining carbon : 1/4
After 3 half-lives the carbon-14 remaining carbon : 1/8
...
...
After n half-lives the carbon-14 remaining carbon : (1/2)^n
Number of half-lives in 30642 years: 30642 / 5730 ≈ 5 approx.
Amount of carbon remaining after 5 half-lives: 1/32
1/32 ≈ 0.031 = 3.1%
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help me with this question please
Answer:
2.50 p + 1.50p
Step-by-step explanation:
if you buy an item x amount of times you would times the two to figure out the total cost of that type of item then add with the other
11. Let X 1 ,…,X n,…∼iidBeta(1,β) and let Y n = 1≤i≤n min X i and Z n = 1≤i≤n
max Xi be the sample minimum and maximum of the first n observations. (a) Find the value b such that Yn → pb.
Therefore , the solution of the given problem of probability comes out to be -y^(β-1)/[(β-1)Β(1, β)] .
What is probability exactly?The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.
Here,
We are aware that X's PDF is provided by:
If x is between 0 and 1 and 0 otherwise, f(x) Equals 1/B
where represents the size factor.
The formula for Yn's cumulative distribution function (CDF) is
=> F(y) = P(Yn ≤ y) = [P(Xi > y)]ⁿ = [1 - P(Xi ≤ y)]ⁿ
Using the CDF of the beta distribution, we have:
=> F(y) = [1 - Β(1, β; y)]ⁿ
We can approximate Yn by a normal distribution with mean and variance given by the following formulas using the continuity adjustment and central limit theorem:
=> E(Yn) = Β(2, β; 1)/Β(1, β) and Var(Yn) = E(Yn) - [Β(1, β; 1)/Β(1, β)]²
Therefore, we have:
=> (Yn - E(Yn))/sqrt(Var(Yn)) → N(0,1)
With the formulas for E(Yn) and Var(Yn) substituted, we obtain:
=> (Yn - Β(2, β; 1)/Β(1, β))/sqrt[Β(2, β; 1)/Β(1, β) - [Β(1, β; 1)/Β(1, β)]²] → N(0,1)
We need to work out the solution to determine b:
where is the CDF's usual standard value.
After applying the limit and taking the logarithm of both sides, we obtain:
=> F(y) = lim n log[n] = lim n n log
=> [1 - B(1, β; y)] = lim n -n (y, n)/(1, n)
L'Hopital's law gives us:
=> lim n -d/dy [n -(1, y)/n -(1, y)] = lim nn y(-1), ((1, )) ^2Β(2, β; y)
=> -y^(β-1)/[(β-1)Β(1, β)]
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