The required volume of the solid obtained by rotating the region is 56π/15 cubic units.
How we volume of the solid obtained by rotating the region?To find the volume of the solid obtained by rotating the region enclosed by y = x² and y = 5x about the line x = 0 using the method of disks or washers, we need to first determine the bounds of the region.
The intersection of y = x² and y = 5x occurs when x = 1, so the region to be rotated is the portion of the graph of y = x² that lies above y = 5x and to the left of x = 1.
Next, we use the method of disks (or washers) to find the volume of the solid generated by rotating the region about the x-axis. The method of disks involves dividing the region into thin vertical slices, approximating each slice as a disk, and finding the volume of the sum of these disks.
The volume of each disk is given by the formula V = πr²h, where r is the radius (distance from the center of the disk to the circumference) and h is the height (distance from the center of the disk to the x-axis). In this case, the radius is equal to the height of the slice and the height is equal to the difference between the maximum and minimum values of y in that slice.
The bounds of integration for the radius are x = 0 to x = 1. We integrate from x = 0 to x = 1, finding the volume of the sum of the disks:
V = π [tex]\int_0^1[/tex] (x² - 5x)² dx = π [tex]\int_0^1[/tex](x^4 - 10x³ + 25x²) dx
This definite integral can be solved to yield:
V = π × (x⁵/5 - 5x⁴/4 + 25x³/3) evaluated from x=0 to x=1
V = π × (1/5 - 5/4 + 25/3) = 56π/15 cubic units
So the volume of the solid generated by rotating the region enclosed by y = x² and y = 5x about the x-axis is 56π/15 cubic units.
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A base of a solid is the region bounded by y= e^{-x}, the x-axis, the y-axis, and the line x= 2....
The area of the base of the solid is equal to e^-2 - 2.
A base of a solid is the region bounded by y = e^-x, the x-axis, the y-axis, and the line x = 2.
To find the area of the base, we need to find the region that is bounded by y = e^-x, the x-axis, and the line x = 2. The x-axis and the line x = 2 act as boundaries, so we need to find the points where y = e^-x intersects these two lines. The x-axis is at y = 0, so the point of intersection is found by solving the equation:
0 = e^-x
Taking the natural logarithm of both sides, we get:
x = -ln(0) = ∞
The line x = 2 intersects y = e^-x at:
e^-x = 2
Taking the natural logarithm of both sides, we get: -x = ln(2)
And solving for x, we get: x = -ln(2)
So, the area of the base is the region bounded by x = -ln(2), x = 2, and y = e^-x. This can be found by integrating e^-x from x = -ln(2) to x = 2. The result is: A = ∫_{-ln(2)}^{2} e^-x dx = -e^-x |_{-ln(2)}^{2} = e^-2 - e^-(-ln(2)) = e^-2 - e^ln(2) = e^-2 - 2.
Therefore, the area of the base of the solid is equal to e^-2 - 2.
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Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S'. Which rule describes this transformation?
Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S' using the rule is (x, y) ⇒ (x + 8, y + 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Transformation can either be rigid like translation, rotation, reflection or it can be non rigid like dilation.
Translation is a rigid transformation because it preserves the shape and size. Translation is the movement of a point either up, left, right or down in the coordinate plane.
Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S'.
The rule is (x, y) ⇒ (x + 8, y + 7)
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A simple random sample of size n=59 is obtained from a population that is skewed left with u = 62 and a = 7. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? What is the sampling distribution of x? O A. No. The central limit theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. B. No. The central limit theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. C. Yes. The central limit theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.
D. Yes. The central limit theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n.
In this case, the x sampling distribution will be normal, with a mean equal to the population mean (u) and a standard deviation equal to the population standard deviation (a) divided by the sample size squared (n).
What is standard deviation?The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Here,
The central limit theorem asserts that, regardless of the form of the underlying population, as the sample size, n, grows, the sampling distribution of x becomes essentially normal, provided n is big enough (usually n >= 30). This is because, regardless of the form of the underlying population, the sum of independent random variables from the same population will tend to become regularly distributed. In this situation, the sampling distribution of x will resemble a normal distribution, with a mean equal to the population mean (u) and a standard deviation equal to the population standard deviation (a) divided by the sample size squared (n).
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then use your function to find the two roots. display ""x1"" and ""x2""
the two roots of the equation are x1 = -2.5 and x2 = -1.5.
x1 = -2.5;
x2 = -1.5.
Step 1: Calculate the discriminant
b2 - 4ac = (-2)2 - 4(2)(-3) = 4 + 24 = 28
Step 2: Calculate the roots
x1 = (-b + √D) / 2a = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5
x2 = (-b - √D) / 2a = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5
We start by calculating the discriminant, which is b2 - 4ac. In this case we have b2 = (-2)2 = 4 and ac = 2(-3) = -6, so the discriminant is 4 + 24 = 28. Then we calculate the two roots, x1 and x2, using the formula x1 = (-b + √D) / 2a and x2 = (-b - √D) / 2a. Substituting in the values we have, x1 = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5 and x2 = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5. Therefore, the two roots of the equation are x1 = -2.5 and x2 = -1.5.
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How many years is 1 billion seconds?
for an approximate result, divide the time value by 3.154e+7
so the answer is 31.71 calendar years
There are approximately 31.71 years in 1 billion seconds. The solution has been obtained by using the unit conversion.
What is unit conversion?
A unit conversion is used to express the same attribute in a different unit of measurement. Instead of using hours to represent time, you could use minutes, and instead of using miles to express distance, you could use feet. Measurements are frequently requested in one set of units, such as chains, but are given in another set, such as feet.
We are given 1 billion seconds which are to be converted into years.
We know that 1 second = 3.171e-8 years
So,
⇒1,000,000,000 seconds = 1,000,000,000 * 3.171e-8
⇒1,000,000,000 seconds = 31.71 years
Hence, there are approximately 31.71 years in 1 billion seconds.
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a coral reef is 5 miles due north of its closest point along a straight shoreline. a visitor is staying in a cottage that is 6 miles east of that point. the visitor is planning to go from the cottage to the coral reef. suppose the visitor runs at a rate of 8 mph and swims at a rate of 1 mph. how far should the visitor run to minimize the time it takes to reach the coral reef? round to two decimal places.
Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.
How far should the visitor run to minimize the time it takes to reach the coral reef?
Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.
distance swimming = root of x^2+5^2= root of x^2+25.
Times: time= distance / speed time running =6-x/8
time swimming =x^2+25/8 Total time
time running + time swimming:
T=6-x/8+x^2+25/8
The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.
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Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.
How far should the visitor run to minimize the time it takes to reach the coral reef?Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.
distance swimming = root of x²+5²= root of x²+25.
Times: time= distance / speed time running =6-x/8
time swimming =x²+25/8 Total time
time running + time swimming:
T=6-x/8+x²+25/8
The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.
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3 minus 1 over 3 to the power of 4 (I don’t know how to do this so can you please explain) please hurry
First, let's determine what (1/3) to the power of 4 is:
1/3 x 1/3 x 1/3 x 1/3 = 1/81
(1 x 1 x 1 x 1 = 1; 3 x 3 x 3 x 3 = 81)
1/81
Now what is 3 as a decimal?
We have to use the same denominator as 1/81 to be able to do a subtraction:
81 x 3 = 243
3 = 243/81
243/81 - 1/81 = 242/81
The answer is D.
Hope this helps! :) If you have any questions, let me know.
Solve the system by graphing
x+2y=3
-x+3y+7
This system of equations has been solved graphically and their solution is equal to the ordered pair (-1, 2).
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x + 2y = 3 ......equation 1.
-x + 3y = 7 ......equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II and it is given by the ordered pair (-1, 2)
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What is the volume of the region bounded by y=4x-x^2 and y=x^2 if rotated about the line x=4?
The volume of the region is 216.6 cubic units.
The volume of a three-dimensional object is the amount of space it occupies. When we rotate a two-dimensional region about a line, we obtain a three-dimensional object called a solid of revolution.
In this case, we are asked to find the volume of the solid of revolution obtained by rotating the region bounded by the curves y = 4x - x^2 and y = x^2 about the line x = 4.
To find the area of each slice, we need to find the radius of the disc.
In this case, the line of rotation is
=> x = 4,
so the radius of the disc at a point (x, y) on the curve is
=> 4 - x.
To find the height of the slice, we need to find the difference in y-values between the two curves at that x-value.
We can set the two curves equal to each other to find the x-values at which they intersect:
=> 4x - x² = x².
Solving for x, we find that x = -2 and x = 2 are the x-values at which the two curves intersect.
These x-values correspond to the y-values -2 and 8, respectively. Therefore, the height of the slice is
=> 8 + 2 = 10.
To find the volume of the solid, we need to integrate the product of the area of the disc and its height over the interval from x = -2 to x = 2.
The area of the disc is given by
=> π * (4 - x)².
Therefore, the volume of the solid of revolution is given by the following integral:
V = π ∫[-2,2] (4 - x)² x 10 dx
Solving this integral, we find that the volume of the solid is approximately 216.6 cubic units
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HELPP THIS IS DUE AT 11:59
Answer: what grade u in?
Step-by-step explanation:
A bakery use 1/3 of a bag of chocolate chips to make three batches of cookies how much of the bags they use for each batch
PLS HELP I ONLY HAVE 10 POINTS SORRY
Solve the following pair of equations for the vectors u and v. Assume i = (1,0) and j = (0;1).
the solution to the pair of equations is u = (1,1) and v = (1,0).
u + 3v = (2,1)
3u + v = (3,2)
u = (1,1) and v = (1,0)
The first equation can be written as:
u + 3v = (2,1)
We can rewrite this equation as:
u + 3(1,0) = (2,1)
By substituting the values of i and j, we can solve for u:
u + (3,0) = (2,1)
u = (2-3,1) = (-1,1)
Now, we can substitute the value of u in the second equation:
(1,1) + v = (3,2)
By subtracting (11) on both sides, we can solve for v:
v = (3-1,2-1) = (2,1)
Therefore, the solution to the pair of equations is u = (1,1) and v = (1,0).
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15. In Houston, taxis charge $3 plus $.75 per mile for an airport pickup. How far from the airport can Courtney
travel for $12?
It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.M is 12.
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
3 + 0.75m = 12
(3/4)m = 9
m=12
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6.5 m far from the airport can Courtney travel for $12.
What is a linear equation?
It is referred to as the relationship between two variables, and a straight line is produced when the linear equation's graph is shown.
If there is just one variable in the equation, it is referred to as a linear equation in one variable.
A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
In Houston, taxis charge $3 plus $.75 per mile for an airport pickup.
3 + 75 m = 78
78 m / 12 = 9
m = 78 / 12 = 6.5 m
6.5 m far from the airport can Courtney travel for $12.
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Cada una de las gaseosas se va a repartir en seis vasos
Gaseosa grande 3 335,9cm3 y la gaseosa pequeña 1 550,
De la gaseosa grande quedaran _________ cm3
De la gaseosa pequeña quedaran _________ cm3
De la botella _______ quedarán mas liquido.
Answer:4
Step-by-step explanation:
4
Answer:
4
Step-by-step explanation:
Jevonte kicks a football. Its height in feet is given by h = -16t² +48t where t
represents the time in seconds after kick. Interpret the coordinates of the vertex in
context.
The x-coordinate (or t-coordinate) of the vertex is
The y-coordinate (or h-coordinate) of the vertex is
x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.
What is Coordinate System?Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given that Jevonte kicks a football. Its height in feet is given by h = -16t² +48t
where t represents the time in seconds after kick.
We have to find x-coordinate (or t-coordinate) of the vertex is time in seconds and y y-coordinate (or h-coordinate) of the vertex is the height of the football.
Hence, x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.
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How do you find the image under a linear transformation?
To calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.
What is linear transformation?A function from one vector space to another that respects the underlying (linear) structure of each vector space is called a linear transformation.
A linear operator, or map, is another name for a linear transformation.
The zero transformation and identity transformation are two significant illustrations of linear transformations.
An illustration of a linear transformation is the zero transformation, which is denoted by T(x)=(0) for every x.
Also linear is the identity transformation denoted by T(x)=(x).
Find the vector subspace in which the implicit equations are the homogeneous equations produced when the components of the linear transformation formula are equal to zero in order to compute the kernel.
This is the same as finding the null space of the linear transformation matrix.
Therefore, to calculate the kernel, locate the vector subspace in which the homogeneous implicit equations result from the linear transformation formula's component parts being equal to zero.
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what is the slope below
Answer:
The slope is 7/1
Step-by-step explanation:
The first valid point is at (-1,-4)
The second valid point is at (0,3)
You start at the (-1,-4) and you count up until you get at the same line as the next valid point, then you count over however many times it takes you to get to that point and in your case it would be up 7 over 1 so 7/1 and it is a positive slope
Can anyone solve 21x>5y+49x>2y>2-28x>2y?
Answer:
Step-by-step explanation:
i cant but someone can habha
Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls.
2
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
PLEASE HELP!!!
The pints of white paint molly used to paint her bedroom walls is 5.58 pints.
How many pints of white paint did molly use?Quantity of paint molly used for her bedroom walls= 9.3 pints
Fraction of blue paint= 2/5 of 9.3 pints
= 2/5 × 9.3
= 0.4 × 9.3
= 3.72 pints
Quantity of white paint = Quantity of paint molly used for her bedroom walls - Quantity of blue paint
= 9.3 pints - 3.72 pints
= 5.58 pints
Hence, Molly used 5.58 pints of white paint to paint her bedroom walls.
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Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) amplitude period horizontal shift b) Write an equation that represents the curve in the form y = a cos(k(x - b)).
The equation for the curve shown in the form y = a cos (k (x - b)). -2, 4π/3, -π/3 y = -2cos (4π/3(x + π/3))
Determine the horizontal shift, period, and amplitude.
Given:
1. The amplitude of a cosine graph is the maximum value of the graph. In this case, the amplitude is -2.
2. The period of a cosine graph is the length of one cycle. In this case, the period is 4π/3.
3. The horizontal shift of a cosine graph is the amount the graph is shifted to the left or right. In this case,
The absolute value of the horizontal shift is less than the period, so the horizontal shift is -π/3.
4. To write the equation of the graph in the form y = a cos (k (x - b)), we can use the information from the previous steps.
We know the amplitude is -2, the period is 4π/3, and the horizontal shift is -π/3. Therefore, our equation is: y = -2cos (4π/3(x + π/3)).
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One brick is 215 mm long. How many of these bricks, put end to end, WIll cover a 5.15 meter wall?
Answer:
24 bricks will cover a 5.15 meter wall
Step-by-step explanation:
1 meter = 1000 mm
5.15 meters = 5150 mm
5150/215 = 23.9534884
23 bricks will not be enough because 23 x 215 = 4945
24 will be the better option because 215 x 24 = 5160
So 24 bricks will cover a 5.15 meter wall
Joseph deposited $60 in an account earning 10% interest compounded annually. To the nearest cent how much will he have in 2years
Answer:
60
_
100 * 10=
Step-by-step explanation:
6% so that your answer
For this you will use
FV = PV (1+r)^t
FV = Future Value
PV = Present Value
r = rate
t or n = number of periods
$60 is PV
10% (.10) is rate.
2 years is number of periods.
FV = $60(1.10)^2
FV = $72.60
assume that t is a linear transformation. find the standard matrix of t.
If T is a linear transformation then the standard matrix of T is [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].
What is a matrix?
A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.
The transformation is given as - T : IR² → IR²
Take the (x,y) values as x(1,0) and y(0,1)
(x,y) = x(1,0) + y(0,1)
Apply the transformation -
T(x,y) = T[x(1,0) + y(0,1)]
Since T is a linear map then -
T(x,y) = x T((1,0)) + y T((0,1))
Now, substitute the values -
T(x,y) = x Te1 + y Te2
T(x,y) = x [e1 - 19e2] + y [e2]
T(x,y) = x e1 + e2(-19x + y)
Resubstitute the values back -
T(x,y) = x (1,0) + (0,1)(-19x + y)
T(x,y) = (x , -19x+y)
For T : IR² → IR²
T(x,y) = (ax+by , cx+dy)
Then A = [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
So, now the matrix A is -
A = [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex]
Therefore, the matrix is [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].
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Find the expression equivalent to
3(x+5)-2.
3(x+5)-2 is 3x + 13.
Knowing this information, all you have to do is find an equivalent expression to 3x + 13.
I'll see you in class tomorrow.
I'm kind of disappointed.
You were my favorite student too.
(and yes, I do have a secret undercover teacher account.)
Ten less than twice a number is equal to at least 52. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as the variable, and write the inequality so that the x term comes first.(1 point)
Answer:
x [tex]\geq[/tex] 21
Step-by-step explanation:
2x - 10 [tex]\geq[/tex] 52
2x [tex]\geq[/tex] 42
x [tex]\geq[/tex] 21
ind (f −1)'(a). f(x) = 3x3 3x2 5x 2, a = 2
function (f-1)(2) = 18 because the derivative of f at a = 2 is 18x2 + 10x.
We can find out how a function is changing at a specific point by looking at its derivative. We are required to calculate (f-1) in this scenario (2). We must first get the derivative of the given function, f(x) = 3x3 + 3x2 + 5x2, in order to perform this. The derivative of each term can be used to achieve this, giving us 9x2 + 6x + 10x. The derivative of f at a = 2 is equal to 18x2 + 10x when this is evaluated at a = 2. Now, by putting the derivative equal to 0 and finding x, we may calculate (f-1)(2). Thus, we obtain x = -1/9. Once this value has been entered, the original method returns (f-1)(2) = 18.
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Please help me with these questions!!!
The value of f + g when function f(x) = 3x³- 6x g(x) = x² + 8x - 9 is 3x³ +x² + 2x - 9.
What is a function?
Function can be defined in which it relates an input to output.
Given functions ,
f(x) = 3x³ - 6x
g(x) = x² + 8x - 9
So,
f+g = 3x³ - 6x + x² + 8x - 9
= 3x³ +x² - 6x + 8x - 9
= 3x³ +x² + 2x - 9
So , f+g = 3x³ +x² + 2x - 9
Therefore, The value of f + g when f(x) = 3x³ - 6x g(x) = x² + 8x - 9 is
3x³ +x² + 2x - 9
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the titanic sunk more than 100 years ago. below is a summary of the class and fate of each passenger. show the use of an appropriate conditional probability formula to calculate the following: class survived died total first 201 123 324 second 118 166 284 third 181 528 709 total 500 817 1317 (a) if the passenger died, what is the probability they were in third class? (b) find the probability that a passenger survived given that they were in first class.
(a) The probability that a passenger who died was in the third class is 528 / 817.
we can find the probability by using the formula:
P(Third Class | Died) = P(Third Class and Died) / P(Died)
Where,
P(Third Class and Died) = the joint probability of a passenger being in third class and dying
P(Died) = the probability of a passenger dying regardless of class.
We can find P(Third Class and Died) by adding the no. of passengers in third class who died (528) and then dividing by the total no. of passengers (1317)
P(Third Class and Died) = 528 / 1317
Now we can find P(Died) by adding the no. of passengers who died (817) and dividing by the total no. of passengers (1317)
P(Died) = 817 / 1317
By using the values we got, we can find P(Third Class | Died):
P(Third Class | Died) = P(Third Class and Died) / P(Died) = 528 / 817
So, the probability that a passenger who died was in the third class is 528 / 817.
(b) The probability that a passenger survived given they were in first class is 201 / 324
we can find the probability by using the formula:
P(Survived | First Class) = P(Survived and First Class) / P(First Class)
Where,
P(Survived and First Class) = joint probability of a passenger surviving and being in first class.
P(First Class) = probability of a passenger being in first class regardless of survival.
We can find P(Survived and First Class) by adding the no. of passengers in first class who survived (201) and dividing by the total no. of passengers (1317)
P(Survived and First Class) = 201 / 1317
Now we can find P(First Class) by adding the no. of passengers in first class (324) and dividing by the total no.of passengers (1317):
P(First Class) = 324 / 1317
By using the values we got, we can find P(Survived | First Class):
P(Survived | First Class) = P(Survived and First Class) / P(First Class) = 201 / 324
So, the probability that a passenger survived given they were in first class is 201 / 324.
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what is the largest possile sample you can take and still be able to calculate the standard deviation of the sampling distribution of p^
The largest possible sample space for a standard deviation is infinity as the number of observations can be infinity.
What is Standard Deviation ?The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean.
There are several mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.
The standard deviation is significant because it reveals the degree of dispersion of the values in a particular dataset. Every time we examine a dataset, we look for the following metrics: the dataset's geographic center. The mean and median are the two metrics most frequently used to gauge the "center."
The largest possible sample space for a standard deviation is infinity as the number of observations can be infinity.
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hich of the following is a case in which the area bounded by two curves is most easily found by integrating with respect to y?
The parabola and line's intersection can be easily determined which the area bounded by two curves is most easily found by integrating with respect to y. So the option A is correct.
We can readily locate the area by looking at the following sketches; the first sketch, integrating with respect to x, is in figure one.
The curve in the first illustration is a parabola and a line, as you can see.
The parabola and line's intersection can be easily determined.
The area between the curves is then calculated using the formula
A = integration from a to b [(higher curve) - (lower curve)] dx,
which means that the first sketch represents the right response.
So, the first option A is correct one.
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