The value of constant a is 2.45.
To find the value of the constant a, we need to make sure that the pdf (probability density function) is properly normalized. The pdf must satisfy the following property:
∫[a, ∞] f(x) dx = 1
In this case, we have pdf:
∫[a, ∞] (12/x^3) dx = 12∫[a, ∞] (1/x^3) dx
= 12 [-1/(2x^2)]ₐ∞
= 12 * (1/(2a^2))
= 6/ a²
Therefore, to ensure that the integral is equal to 1, we need:
6/ a² = 1
Solving for a:
a^2 = 6
a = ±√6
Since x is always positive, we have a = √6 ≈ 2.45.
So, the constant a is equal to 2.45.
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What is the best estimate of the area of the figure below?
The best estimate of the area of the figure given is 13 square units. The solution has been obtained by using the counting squares method.
What is counting squares method?
The number of squares inside the shape are counted in order to determine the area.
We are given a figure which has a number of squares enclosed in it.
So, the area of the figure = Number of squares enclosed
Area = 11 complete squares + 4 half squares
Area = 11 complete squares + 2 complete squares
Area = 13 square units
Hence, the best estimate of the area of the figure given is 13 square units.
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evaluate sin x cos y da where r [0, / 2][0, / 2]
According to trigonometry, the value of sin y cos x.
The term called trigonometry is defined as the type of mathematics that deals with the relationship between the sides and angles of triangles.
Here we know that the function is written as
=> sin x coy y
where r [0, 1/2] [0, 1/2]
Here by Using Fubini’s theorem we can write this as an iterated integral to get,
=> [tex]\int\limits^{1/2}_0\int\limits^{1/2}_0 {sinxcosy} \, da[/tex]
Here the Fubini's theorem states that the double integral over a region is equal to an iterated integral, which is computed in a similar manner with definite integrals of functions of single variable.
When we integrate the expression, then we get
=> [tex]\int\limits^{1/2}_0 {cos(1+y)sin(1+x)} \, da[/tex]
Again we have to integrate this one, then we get the value as,
=> sin y cos x.
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(a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of
(2+kx)²
where k is a constant. Give each term in its simplest form.
Given that the coefficient of x is 6 times the coefficient of x,
(b) find the value of k.
Answer:
3/2
Step-by-step explanation:
(a) The first three terms, in ascending powers of x, of the binomial expansion of (2 + kx)² are:
(2 + kx)² = 2² = 4
(2 + kx)² = 2 * 2 * kx = 4kx
(2 + kx)² = 2 * k² x² = 4k² x²
(b) If the coefficient of x is 6 times the coefficient of x, then 6 = 4k. Therefore, k = 6/4 = 3/2.
An object i traveling around a circle with a radiu of 14 centimeter. If in 20 econd a central angle of 1/2 radian i wpt out, what are the linear and angular peed of the object?
The circumference of the circle is given by C = 2 * π * r, where r is the radius. In this case, the circumference of the circle is 2 * π * 14 = 88 cm.
Let's call the linear speed of the object v. Then, in 20 seconds, the object travels a distance of v * 20. This distance is equal to the arc length of the central angle of 1/2 radian:
v * 20 = (1/2) * (C/2π) = (1/2) * (88/2π) = 22/π cm
Solving for v, we get:
v = (22/π) / 20 = 22 / (20π) cm/s
The angular speed ω can be found by dividing the central angle by the time it took to travel that angle:
ω = 1/2 / 20 = 1/40 rad/s
So the linear speed of the object is v = 22 / (20π) cm/s, and the angular speed is ω = 1/40 rad/s.
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Write the number five million four thousand three hundred
in standard form.e.g 2000=2x10*3
Five million four thousand three hundred can be written in standard form as 5,004,300.
Write the number five million four thousand three hundred in standard form?5,004,300 = 5 x 10^6 + 4 x 10^3 + 3 x 10^0.The number is composed of five millions (5,000,000), four thousand (4,000) and three hundred (300).In standard form, all numbers are written as a multiple of a power of ten. To convert the number to a multiple of a power of ten, the millions, thousands and hundreds are split apart. The millions is written as 5x10^6. This is because one million is equal to 10^6, and there are five millions. The thousands is written as 4x10^3.This is because one thousand is equal to 10^3, and there are four thousands. The hundreds is written as 3x10^0. This is because one hundred is equal to 10^0, and there are three hundreds. When the three parts are combined, the number is written as 5x10^6 + 4x10^3 + 3x10^0.This can be simplified to 5,004,300. This is the standard form of the number five million four thousand three hundred.To learn more about standard form refer to:
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Answer:
The number five million four thousand three hundred can be written in standard form as `5,004,300`. In scientific notation, it can be written as `5.0043 x 10^6`.
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find the equation of the line in slope-intercept form that is perpendicular to the line y=1/3x+4 containing the point (2,-3)
Step-by-step explanation:
Given eqn
y=1/3x+4
1/3x-y+4=0
eqn of line perpendicular to the given eqn.,
x+1/3y+k=0
since the reqd. line contains the point (2,-3)
2+1/3 (-3)+k=0
2-1+k=0
k=-1
so
x+1/3y-1=0
1/3y=1-x (in slope intercept form)
I NEED HELP ASAP!!!
How many boxes would Alan have to sell to earn less than $2050?
Answer: Alan would have to sell less than 540 boxes.
Step-by-step explanation:
A container hold 5 mL of fluid. Doe it hold more than or le than 500 mL of fluid?
The container holds 5 mL of fluid, which is less than 500 mL of fluid.
5 mL is much smaller than 500 mL, so the container holds less than 500 mL of fluid.
The numerator and denominator of a unit conversion factor have the same quantity in different units. Multiplying by a conversion factor has no effect on the number's inherent value because the factor is comparable to multiplying by 1.
The numerator is the intended unit, whereas the denominator is the supplied unit.
The primary guideline is to multiply when converting from a bigger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit. You will reduce the number, and as you are aware, division is all about reducing numbers.
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write an explicit formula for an, the nth term of the sequence 24,16,8
Answer:
f(n) = 32 - 8n
Step-by-step explanation:
24, 16, 8, 0
f(n) = 24 - 8 x (n-1)
f(n) = 32 - 8n
14oint
Nykai is scuba diving. She stops to look at a fish that is 10.0 meters
below the surface. Then she swims down 6.1 meters deeper to look
at a reef. If she then swims up 2.5 meters, what is Nykai's position in
relation the ocean surface (in meters)?
Answer:
Nykai's position in relation to the ocean surface is 13.6 meters. She started 10 meters below the surface, swam down 6.1 meters deeper, and then swam up 2.5 meters. Therefore, her position in relation to the ocean surface is 10 - 6.1 + 2.5 = 13.6 meters.
Step-by-step explanation:
Using the common denominator, what is an equivalent fraction for
?
The equivalent fraction is used such that operations like addition and subtraction can be done on fractions that don't have a common denominator.
What is an equivalent fraction ?
Equivalent fractions are those fractions that reflect the same value despite having numerators and denominators that differ.
According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction.
In their most basic form, all equivalent fractions are reduced to the same fraction. The equivalent fraction is used to enable operations on fractions without a common denominator, such as addition and subtraction.
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Quetion
Jack' pancake recipe call for 2 teapoon baking powder and 3 cup of flour. How much baking powder i needed if Jack ue 9 cup of flour
Jack will require 6 tsp of baking powder if he uses 9 c of flour.
Given: Jack's pancake recipe calls for 3 cups of flour and 2 teaspoons of baking powder.
The amount of baking powder required if Jack uses 9 c of flour is to be determined.
Solution:
For 3 c of flour, 2 tsp of baking powder is required
2/3 tsp of baking powder is required for 1 cup of flour.
We must now determine how much baking powder to use with 9 cups of flour.
2/3X9 tsp of baking powder is required for 9 cups of flour.
= 6 tsp
Jack will therefore require 6 tsp of baking powder if he uses 9 c of flour.
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The tallet tree in the world i in redwood California a of April 2019 if you’re tanding on the trail 220 feet from the bottom of the tree you have to look up it i 60° angle to ee the top how tall i the tree
The height of the tree is approximately 380.04 feet.
Trigonometry involves the study of angles and their relationship to the sides of a right triangle
The tallest tree in the world is a redwood in California and if you're standing 220 feet from the bottom of the tree, you have to look up at a 60-degree angle to see the top. To find the height of the tree, we need to use a concept in mathematics called trigonometry.
The height of the tree can be found using the formula:
Height of tree = Distance from bottom of tree * tan (angle of elevation)
In this case, the distance from the bottom of the tree is 220 feet and the angle of elevation is 60 degrees. Plugging in these values into the formula, we get:
Height of tree = 220 * tan (60)
The value of tan (60) can be found using a calculator or a trigonometry table. The result is approximately 1.732. So the height of the tree can be calculated as:
Height of tree = 220 * 1.732 = 380.04 feet
So in summary, the height of the tree can be found by using the concept of trigonometry and the formula for the height of a tree based on the distance from the bottom of the tree and the angle of elevation to the top of the tree.
Complete Question:
2. The tallest tree in the world is a redwood in California (as of April 2019) If you're standing on the trail 220 feet from the bottom of the tree, you have to look up at a 60 degree angle to see the top. How tall is the tree? Draw the pic so that you know what you are solving for.
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If a circular object 1000 meters away subtends an angle of two arc minutes, then what is its diameter?a) 0.58 metersb) 0.29 metersc) 28647.9 meters
As per the angle of two arc minutes, the diameter is 16.67 meters.
The term diameter in math is known as a straight line passing through the center of a figure or body
Here we know that a circular object 1000 meters away subtends an angle of two arc minutes.
Here we know that that 1 minutes of arc is 60 seconds in other word it can be written as 1/60 minutes.
So for 2 minutes it can be written as
=> 2 x 1/60 = 1/30
Here we have know that the object is 1000 meters away, then the diameter is calculated as,
=> 1000/2 x 1/30
=> 500/30
=> 16.67
Therefore option (d) is coorect.
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what is the difference between mtm and most?
Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Maximum Operating Stress, or MOST, is the highest amount of stress to which a structure can be subjected without experiencing permanent deformation.
Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Structural analysis techniques, such as finite element analysis and structural testing, are often used to determine this. When designing and building a structure, MTM must be considered because it is crucial for structural safety. Maximum Operating Stress, or MOST, is the highest stress to which a structure can be subjected without experiencing permanent deformation. This is often decided by running a stress study on the structure and taking into account the materials that were utilised to build it. The building must be able to sustain the anticipated loads throughout its lifespan, which is of utmost importance. Additionally, it is crucial to prevent structural deterioration over time. When designing and building a secure structure, MTM and Most must both be taken into account.
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If the average weight of a panda is about 120kg, state what information you can deduce from the 40 pandas in the sample. Male pandas weigh, on average, between 80kg and 140kg, and females weigh, on average, between 70kg and 120kg. From the box plot, state the gender of the pandas in the sample
The box plot of the the gender of the pandas in the sample is illustrated below.
The term box plot in math is defined as a chart tool used to quickly assess distributional properties of a sample and the so-called box-and-whiskers plot shows a clear indication of the quartiles of a sample as well of whether or not there are outliers.
Here we have given that Male pandas weigh, on average, between 80kg and 140kg, and females weigh, on average, between 70kg and 120kg.
The the data for the box plot is written as,
=> 70, 80, 120 and 140.
By using this data we have plotted the box plot for the gender of the pandas in the sample.
And we have predicted the following values through it.
Minimum =70
Q1=75
Median =100
Q3=130
Maximum =140
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Solve each right triangle and show worked solutions.
- Will give brainliest -
The solution for each right triangle are:
(a) BC = 13.9 units, AB = 11.9 units
(b) XZ = 17.5 units
How to solve each right triangle?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
(a) Using trigonometric ratio
sin 31.2° = 7.2/BC (Sine = opposite/hypotenuse)
BC = 7.2/sin 31.2°
BC = 13.9 units
tan 31.2° = 7.2/AB (Tan = opposite/adjacent)
AB = 7.2/tan 31.2°
AB = 11.9 units
(b) XZ = √(14.4² + 10.0²) (Pythagoras theorem)
XZ = 17.5 units
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Determine whether each value for x would make the inequality, -12x < 36, true or untrue.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-12x < 36}[/tex]
[tex]\huge\textbf{DIVIDE \boxed{\rm{\bf -12}} to both sides:}[/tex]
[tex]\mathsf{\dfrac{-12}{-12}x < \dfrac{36}{-12}}[/tex]
[tex]\huge\textbf{SIMPLIFY it:}[/tex]
[tex]\mathsf{x < \dfrac{36}{-12}}[/tex]
[tex]\mathsf{x > -3}[/tex]
[tex]\large\text{It is a(n) \boxed{\rm{o p e n e d}} circle SHADED to the RIGHT of your number line}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x > -3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
10. A pipe can fill a cistern in 6 hours. Due to a leak in the bottom it is filled in 7 hours. When the cistern is
full, in how much time will it be emptied by the leak?
Multiple Choice Questions (MCQs)
M
Ti
Answer:
7 hours.
Step-by-step explanation:
This is a rate problem. We can start by using the formula: Rate x Time = Quantity.
The rate at which the cistern is filled is the quantity of water in the cistern divided by the time it takes to fill it. So, the rate at which the cistern is filled is 1 (the cistern is full) / 6 hours = 1/6 cistern/hour.
Similarly, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / the time it takes to empty it. So, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / 7 hours = 1/7 cistern/hour.
Since we know the rate at which the cistern is filled and the rate at which it is emptied, we can find the time it takes for the cistern to be emptied by dividing 1 (the cistern is full) by the rate at which it is emptied.
Therefore, the cistern will be emptied in 1 / (1/7 cistern/hour) = 7 hour.
out of 9799 wistles that a company manufactured, some were rejected for shipment to stores because they did not pass the quality controll standards of the company. estimate the number of wistles that did not pass
1862 are the number of wistles that did not pass.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that out of 9799 wistles that a company manufactured
19% were rejected for shipment to stores because they did not pass the quality controll standards of the company.
We have to find the number of wistles that did not pass
To find this we have to find 19% of 9799
19/100×9799
0.19×9799
1861.81
Hence, 1862 are the number of wistles that did not pass.
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Based on the scatter plot below, which is a better prediction for x when y = 42?
Based on the scatter plot below, better prediction for x when y = 42 is 53.
What is scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events. Scatter plots are used to demonstrate how much one variable affects another by plotting data points on a horizontal and vertical axis. Each row in the data table is represented by a marker, the location of which is determined by the values in the columns.
Here,
The scatter plot below shows that the better estimate for x when y = 42 is 53.
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Question in the picture
Answer:
Week 7
Step-by-step explanation:
Connie will have $170 in week 7, because in 3 weeks she will add $30 to her account.
Ling will have $117.5 in week 7, because in 3 weeks he will add $4.50 to his account.
170-117.5=52.5
52.5 is greater than 50, so it satisfies the question.
How do you find D when Diagonalizing a matrix?
The matrix D is important because it is the diagonal representation of the matrix A, which makes it easier to work with and understand.
When diagonalizing a matrix, the goal is to find a diagonal matrix (D) that is similar to the original matrix (A). This means that the matrix D will have the same eigenvalues as the matrix A and will be represented in a more simplified form.
To find the matrix D, you must first find the eigenvalues of the matrix A. These eigenvalues can be found by solving the characteristic equation, which is found by setting the determinant of the matrix (A - λI) to zero, where λ is the eigenvalue and I is the identity matrix.
Once the eigenvalues are found, you can then find the eigenvectors, which are non-zero vectors that satisfy the equation
=> Av = λv,
where v is the eigenvector.
Once you have both the eigenvalues and eigenvectors, you can then arrange them into the matrix D, where the eigenvalues are on the main diagonal and the eigenvectors are the columns.
To make sure that D is diagonal, you may need to scale the eigenvectors so that the entries are integers. This is called normalizing the eigenvectors.
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Please answer this picture (it’s khan btw)
Answer:
first statement
Step-by-step explanation:
each day breakfast is longer
a theater production group is making frames to support wall-like props. three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.a right triangle is shown. the lengths of the 2 sides are 10 feet and 3 feet. the angle opposite to side with length 3 feet is x.what is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?
In the right-angled triangle, the value of x is 16.7 degree.
In the given right-angled triangle, the angle x can be determined using the trigonometric function of tangent. As length of the two legs is 3 feet and 10 feet, and the angle between hypotenuse and the 10 feet leg is x. In a right-angled triangle, the tangent of an angle is the ratio of opposite side to adjacent side. Hence,
Tan Ɵ = Opposite side/Adjacent side
As Ɵ = x, opposite side = 3ft, and adjacent side = 10 ft,
Tan x = 3/10
Tan x = 0.3
x = Tan^(-1) (0.3)
x = 16.7 degree
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y = 3x + 4y, x + 2y = -1 using substitution
Answer:
x = 1
y = -1
Step-by-step explanation:
y = 3x + 4y
3x + 3y = 0
So, we have 2 equations that are
3x + 3y = 0
x + 2y = -1
Times the second equation by -3
3x + 3y = 0
-3x - 6y = 3
-3y = 3
y = -1
Now put -1 in for y and solve for x
x + 2(-1) = -1
x - 2 = -1
x = 1
Let's check
1 + 2(-1) = -1
1 - 2 = -1
-1 = -1
So, x = 1 and y = -1 is the correct answer.
a particle's position is given by = − 5 meters. at what time is its velocity zero? give your answer to the nearest unit.
At t = ±0.6 seconds its velocity will be zero.
When an object is moving, its velocity serves as a measure of how quickly its location is changing as it is seen from a given point of view and as time is measured using a specific unit of measurement.
The velocity of a particle is the derivative of its position with respect to time, so to find the velocity we need to take the derivative of x with respect to t.
dx/dt = 20 - 15t^2
To find when the velocity is zero, we set dx/dt = 0 and solve for t:
0 = 20 - 15t^2
15t^2 = 20
t^2 = 20/15
t = ±√(20/15)
So, the velocity is zero at approximately t = ±0.6 seconds.
Correct Question :
a particle's position is given by = 20t − 5t^3 meters. at what time is its velocity zero? give your answer to the nearest unit.
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Maria mixes cream and milk in a ratio of 2 parts cream and 3 parts milk.
She uses 8 liters of cream in her mixture.
How many liters of mixture in
all does she make?
How many liters of milk does she use for the mixture?
Answer:
If Maria uses 2 parts cream and 3 parts milk, then for every 2 parts of cream, she uses 3 parts of milk.
Since she uses 8 liters of cream, we can find the total volume of mixture by finding the equivalent volume of milk that she used.
To find the equivalent volume of milk, we multiply the volume of cream by the ratio of milk to cream:
8 liters * (3 parts milk) / (2 parts cream) = 12 liters
So Maria used 8 liters of cream and 12 liters of milk for a total volume of 20 liters.
find a solution to the initial value problem, [hint: interpret the left-hand side of the equation as the derivative of the product of two functions.]
The value of a in the equation in the simplest form will be 17 / 6.
We are given an equation:
x³ / x^(1/6) = x^(a)
We need to evaluate the left hand side to find the value of a in the equation in simplest form.
We know that:
x^ (a) / x^ (b) = x^ ( a - b)
Using this, we get that:
x^ (3 - 1/6) = x^ (a)
x^ (17/6) = x^ (a)
By comparing the bases, we get the value of a as:
a = 17 / 6.
Therefore, the value of a in the equation in the simplest form will be 17 / 6.
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a frustum of a right circular cone is formed by cutting a small cone off of the top of a larger cone. if a particular frustum has a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches, what is its lateral surface area? (the lateral surface area of a cone or frustum is the curved surface excluding the base(s).)
The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches
The lateral surface area of the frustum is calculated using the given formula:
Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii² + height²)
Lower base radius of frustum = 6 inches
Upper base radius of frustum = 3 inches
Height of frustum = 4 inches
Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]
= π × 9 × √[(9 + 16]
= 9π × 5
= 45π sq. inches
Hence, the lateral surface area of the given frustum is 45π sq. inches
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