To approximate the area of the region under the curve y = 5x using upper and lower sums with the given number of subintervals, we need to find the width of each subinterval and evaluate the function at the endpoints of each subinterval.
The width of each subinterval is given by:
Δx = (b - a) / n
where b and a are the upper and lower limits of integration (in this case, 2 and 1.718, respectively), and n is the number of subintervals (in this case, 10). So:
Δx = (2 - 1.718) / 10 = 0.0282
Now we can find the upper and lower sums using the formulae:
Upper sum = Σ[f(xi*)Δx], where xi* is the largest value of f(x) in the ith subinterval
Lower sum = Σ[f(xi)Δx], where xi is the smallest value of f(x) in the ith subinterval
For the upper sum, we evaluate f(x) at the right endpoints of each subinterval:
f(1.746) = 8.73
f(1.774) = 8.87
f(1.802) = 9.01
f(1.83) = 9.15
f(1.858) = 9.29
f(1.886) = 9.43
f(1.914) = 9.57
f(1.942) = 9.71
f(1.97) = 9.85
f(1.998) = 9.99
So the upper sum is:
Upper sum = [8.73 + 8.87 + 9.01 + 9.15 + 9.29 + 9.43 + 9.57 + 9.71 + 9.85 + 9.99] * 0.0282
= 9.287
For the lower sum, we evaluate f(x) at the left endpoints of each subinterval:
f(1.718) = 8.59
f(1.746) = 8.73
f(1.774) = 8.87
f(1.802) = 9.01
f(1.83) = 9.15
f(1.858) = 9.29
f(1.886) = 9.43
f(1.914) = 9.57
f(1.942) = 9.71
f(1.97) = 9.85
So the lower sum is:
Lower sum = [8.59 + 8.73 + 8.87 + 9.01 + 9.15 + 9.29 + 9.43 + 9.57 + 9.71 + 9.85] * 0.0282
= 9.174
Therefore, the area of the region under the curve y = 5x using upper and lower sums with 10 subintervals is approximately 9.287 square units (upper sum) and 9.174 square units (lower sum).
To approximate the area of the region using upper and lower sums with the given number of subintervals, we first need to determine the interval and width of each subinterval. From the provided information, the function is y = 5x, and the interval is [0, 1]. We are given 10 subintervals, so the width of each subinterval (Δx) is:
Δx = (1 - 0) / 10 = 0.1
Now we can compute the upper and lower sums:
Upper Sum (U) is obtained by taking the maximum value of the function in each subinterval and multiplying it by the width (Δx). To find the maximum value, we evaluate the function at the right endpoint of each subinterval:
U = Σ(5x_i * Δx) for i = 1 to 10
Lower Sum (L) is obtained by taking the minimum value of the function in each subinterval and multiplying it by the width (Δx). To find the minimum value, we evaluate the function at the left endpoint of each subinterval:
L = Σ(5x_i * Δx) for i = 0 to 9
After calculating the upper and lower sums, we get:
U ≈ 2.750
L ≈ 2.450
Therefore, the area of the region can be approximated using upper and lower sums to be between 2.450 and 2.750.
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fill in the blank. the binary number 0000 1010 can be expressed as in hexadecimal.
The binary number 0000 1010 can be expressed as 0A in hexadecimal. Hexadecimal is a base-16 numbering system that uses 16 digits, where 0-9 represent their respective values and A-F represents values 10-15, respectively.
To convert binary to hexadecimal, the binary number is grouped into four bits, starting from the right side, and each group is converted to its equivalent hexadecimal digit. In this case, the binary number 0000 1010 has two groups, 0000 and 1010. The first group is equal to 0 in hexadecimal, and the second group is equal to A in hexadecimal. Therefore, the binary number 0000 1010 can be expressed as 0A in hexadecimal. It is important to note that hexadecimal is often used in computer programming, as it is a convenient way to represent binary data.
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PLEASE HELP Im DESPERATE ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!
Expand the expression 40(y+25.5)
40 ( y + 25.5) = ?y+ 40 (25.5)
Put 40y and 25.5
Step-by-step explanation:
I js did it lol
The expression 40(y + 25.5) in expanded form is 40y + 1020.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, 40(y + 25.5).
= 40×y + 40(25.5). [a(b + c) = ab + ac].
= 40y + 1020.
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Consider this system of equations.
p=2n
p-5 = 1. 5n
What value of n makes the system of equations true?
Enter your answer in the box.
Therefore, the value of n that makes the system of equations true is n = 10.
Given:
p = 2n
p - 5 = 1.5n
Substituting the value of p from the first equation into the second equation, we have:
2n - 5 = 1.5n
Next, we can solve for n by subtracting 1.5n from both sides of the equation:
2n - 1.5n - 5 = 0.5n - 5
Simplifying further:
0.5n - 5 = 0
Adding 5 to both sides of the equation:
0.5n = 5
Dividing both sides by 0.5:
n = 10
Therefore, the value of n that makes the system of equations true is n = 10.
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I need to find the surface area. it's a cut sphere with a diameter of 14.
Given data:
The diameter of the cut sphere, D=14 in.
The radius of the cut sphere is,
\(\begin{gathered} r=\frac{D}{2} \\ r=\frac{14}{2} \\ r=7\text{ in} \end{gathered}\)The cut sphere is called a hemisphere.
The surface area of a sphere is
\(A_1=4\pi r^2\)So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,
\(\begin{gathered} A_2=\frac{4\pi r^2}{2} \\ A_2=2\pi r^2 \end{gathered}\)The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,
\(A_3=\pi r^2\)Therefore, the total area of the hemisphere is,
\(\begin{gathered} A=A_2+A_3 \\ A=2\text{ }\pi r^2+\pi r^2 \\ A=3\text{ }\pi r^2 \end{gathered}\)The total surface area of a hemisphere is,
\(\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi\times7^2 \\ A=461.8in^2 \end{gathered}\)Therefore, the total surface area of the cut sphere is 461.8 square inches.
When a researcher examines quantitative data and wants to know the number of observations that fall below the upper limit of a particular class, the researcher is BEST served by creating a
The researcher is BEST served by creating a frequency distribution table with a cumulative frequency column and a histogram with the class boundaries marked
When a researcher examines quantitative data and wants to know the number of observations that fall below the upper limit of a particular class, the researcher is BEST served by creating a frequency distribution table with a cumulative frequency column and a histogram with the class boundaries marked. The frequency distribution table would allow the researcher to see how many observations fall into each class, while the cumulative frequency column would show how many observations fall below the upper limit of each class. The histogram would provide a visual representation of the distribution of the data, and the class boundaries marked on it would allow the researcher to easily identify the upper limit of each class. By examining the cumulative frequency column, the researcher would be able to determine the number of observations that fall below the upper limit of a particular class.
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Evaluate 9f when f = 7. a 54 b 63 c 112 d 16
Answer:
Your answer would be B.63
Step-by-step explanation:
Because when 7 is substituted for F then you will get 9(7) which equals 63
Which of the following terms correctly describe the object below?A.SquareB.PolygonC.TriangleD.PolyhedronE.PyramidF.Prism
Recall the definition of each concept to check if it fits the figure.
A) Square: A square is a quadrilateral whose sides all have the same length.
B) Polygon: A polygon is a 2D shape formed by non-intersecting straight segments.
C) Triangle: A triangle is a polygon with exactly 3 sides.
D) Polyhedron: A polyhedron is a 3D shape formed by flat polygonal shapes.
E) Pyramid: A pyramid is a polyhedron formed by a simple polygon whose lateral faces are triangles that converge in a common vertex.
F) Prism: A prism is a polyhedron formed by two parallel and equal polygonal faces, whose lateral faces are parallelograms.
The given object is a 3D shape formed by flat polygonal shapes, with a base that is a quadrilateral and whose lateral faces are triangles that converge in a common vertex.
Therefore, the only two terms that correcty describe the given object are:
D) Polyhedron
E) Pyramid
Find the slope of the line.
Please help
Answer:
Step-by-step explanation:
Points (0,-1)(-4,4) Slope is - 5/4
Use the Daily Compounding chart in your book to answer the following question. Alana Geltner deposited $2,250 in a savings account that pays 5.5 percent interest compounded daily. How much interest did she earn after 130 days?
Answer:
$2,369,136.10
Step-by-step explanation:
she earned $2,369,136.10 in interest after 130 days
from a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 4.9 hours with a standard deviation of 0.35 hours. what is the 95% confidence interval for the amount of time spent on personal issues?
The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).
Mean time that employees spend on personal issues each week(M) = 4.9 hours
Standard deviation = 0.35 hours
The following formula is used to get the confidence interval for the sample mean and standard deviation given:
μ = M ± t(sM)
where; M = sample mean
t = T-statistic based on confidence interval
Degree of freedom = n - 1
From the question, n = 55
Degree of freedom = 55 - 1
Degree of freedom = 54
(Standard errors)sM = √(s^2/n)
Now putting the value
sM = √(0.352/55)
sM = 0.05
t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)
Now the confidence interval
μ = M ± t(sM)
μ = 4.9 ± 2.005 × 0.05
μ = 4.9 ± 0.095
μ = (4.9 - 0.095, 4.9 + 0.095)
μ = (4.805, 4.95)
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A student has heard that spinning pennies on a table, rather than flipping them in the air, results in tails side up 65% of the time. If this is true, what is the probability that a student who spins 4 pennies will have them all land tails side up? 0.0150 0.1785 0.8215 0.9850
so I believe it is C 0.8215
The probability is 0.1785
What is probability?The study of how likely certain events are to occur is known as probability. In its simplest form, it is concerned with the fall of a game's cards or the roll of a dice. However, probability is also essential to life and science as a whole. Probability is used, for example, in weather forecasting and figuring out how much your insurance premiums will cost.
Given probability of tail by spinning a coin is 65% = 0.65
p(t) = 0.65 and p(h) = 0.35
where h= head and t= tail
coin spins 4 time
p(t) for first time = 0.65
p(t) for second time = 0.65 x 0.65 =0.4225
p(t) for third time = 0.65 x0.65 x 0.65 = 0.274
p(t) for fourth time = 0.65 x 0.65 x0.65 x 0.65 = 0.178
Hence probability that a student who spins 4 pennies will have them all land tails is 0.178
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The question is in the image
Answer: the answer is f(3)=29
Step-by-step explanation:
What is the solution for the system of equations shown below?
2x + y = 3
x + 1/2y = 3/2
Answer:
y=3-2x
any more help just ask :)
x + 3/4 > - 1/3 Solve the inequality for x.
Simplify your answer as much as possible.
Answer:
x > -13/12
Step-by-step explanation:
x + 3/4 > - 1/3
x + 9/12 > -4/12
x > -13/12
-1/3 = -4/12
3/4 = 9/12
Answer:
x > - 13
12
Step-by-step explanation:
\(x + \frac{3}{4} > - \frac{1}{3} \\ x + \frac{3}{4} - \frac{3}{4} > - \frac{1}{3} - \frac{3}{4} \\ x > \frac{ - 4 - 9}{12} \\ x > - \frac{13}{12} \)
Volume of a cube (cm') = width (cm) x height (cm) x length (cm). 1.1) Using the equation above, determine the volume of a cube that measures 3 cm wide, 3 cm tall, and 3 cm long. 1.2) Let's say this cube is made out of ice and has a mass of 24.76 grams (g). What is this ice cube's density? 1.3) The density of liquid water is slightly higher than that of frozen water ice. Liquid water's density at standard pressures and temperatures is 1.00 grams per cubic centimeter (g/cm'). Given that density, what is the mass of a cube of water measuring 3 cm wide, 3 cm tall, and 3 cm long? 1.4) Compare the weight of the water you calculated in question 1.3 with the weight of the ice of the same volume given in question 1.2. Which is heavier, the liquid water or the ice? Notice that the cube of water is the same size (or volume) as the cube of ice. 1.5) You know that ice floats on water. Explain why.
1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:
Volume = 3 cm x 3 cm x 3 cm = 27 cm³.
Therefore, the volume of the cube is 27 cubic centimeters.
1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:
Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.
Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:
Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.
Therefore, the mass of the water cube is 27 grams.
1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.
Therefore, the weight of the water and the ice would be the same under the same conditions.
1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.
When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.
In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
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the top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 1536 cm2, find the dimensions of the poster with the smallest area. width 1 48 correct: your answer is correct. cm height
The dimensions of the poster with the smallest area are 48 cm by 16 cm.
Let the width of the printed material be x cm and the height be y cm. Then the total width of the poster including the margins is (x + 16) cm, and the total height is (y + 24) cm.
The total area of the poster is the area of the printed material plus the area of the margins:
(x + 16)(y + 24) = 1536
Expanding the left side, we get:
xy + 16y + 24x + 384 = 1536
Rearranging terms, we get:
xy = 1152 - 16y - 24x
To find the dimensions of the poster with the smallest area, we want to minimize the product xy subject to the constraint given by the equation above.
One way to do this is to use the method of Lagrange multipliers. Let L = xy + λ[(x + 16)(y + 24) - 1536] be the Lagrangian, where λ is a Lagrange multiplier. Setting the partial derivatives of L with respect to x, y, and λ equal to zero, we get:
y + 16λ = 0
x + 24λ = 0
(x + 16)(y + 24) = 1536
From the first two equations, we get:
x = -24λ
y = -16λ
Substituting these into the third equation, we get:
(-24λ + 16)(-16λ + 24) = 1536
Simplifying, we get:
-6λ + 4 = 0
Therefore, λ = 2/3. Substituting this into the expressions for x and y, we get:
x = -16
y = -32
These values give the dimensions of the printed material. To find the dimensions of the poster, we add the margins:
width = x + 16 + 16 = 48 cm
height = y + 24 + 24 = 16 cm
Therefore, the dimensions of the poster with the smallest area are 48 cm by 16 cm.
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a car is driving at 100 kilometers per hour. how far, in meters, does it travel in 2 seconds? give answer to nearest meter
Answer: In 2 seconds the car covered a distance of 55.56 meters.
ExplanationUniform rectilinear motion (also known as uniform linear motion or straight-line motion) is a type of motion in which an object moves along a straight line with a constant speed.
This means that the object's position changes by the same amount in a given period of time, regardless of the time that has elapsed. This type of motion is different from accelerated motion, in which the speed of an object changes over time. In uniform rectilinear motion, the speed of the object is constant, and the direction of motion does not change.
A car is driving at 100 kilometers per hour. how far, in meters, does it travel in 2 seconds? give answer to nearest meterData:
V = 100 km/h = 27.78 m/s
t = 2 s
d = ?
Since it asks us to calculate the distance in meters, we must convert from km/h to m/s.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=100 \ \frac{\not{km}}{\not{h}}*\left(\frac{1000 \ m}{1\not{km}}\right)*\left(\frac{1\not{h}}{3600 \ s}\right)= 27.78 \ m/s } \end{gathered}$} }\)
The uniform motion formula is: V=d/t
We clear for the distance, since it is the value that asks us to calculate.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} \iff \ d=v*t} \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d=27.78 \ \frac{m}{\not{s}}*2\not{s} } \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d=55.56 \ m} \end{gathered}$}}\)
Answer: In 2 seconds the car covered a distance of 55.56 meters.find the area of the surface generated when the given curve is revolved about the given axis. y=4x−7, for 5 2≤x≤ 9 2; about the y-axis (hint: integrate with respect to y.)
The area of the surface generated by revolving the given curve about the y-axis is (3/8) (3√(16) − 3√(2)) m².
The surface area of the given curve when it is revolved about the y-axis is calculated by the method of integration. First, we need to determine the boundaries of the integral.
Since the given curve is revolved about the y-axis, the boundaries of the integral will be the y-intercepts of the given curve. The y-intercept of the given curve is y = -7. Hence, the limits of integration are -7 and 9/2.
Now, we need to determine the equation of the curve that is generated on revolving the given curve about the y-axis. This equation can be obtained by substituting the x-variable with the magnitude of the distance from the origin to the point on the curve along the y-axis. Thus, the equation of the curve is y = 4√(y+7).
The surface area can be calculated by integrating the equation of the curve with respect to y. The area of the surface generated by revolving the given curve about the y-axis is A = ∫5/2 -7 4√(y+7) dy. The value of this integral is A = (3/8) (3√(16) − 3√(2)) m². Hence, the area of the surface generated by revolving the given curve about the y-axis is (3/8) (3√(16) − 3√(2)) m².
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Arianna correctly simplified an expression. When she substituted mc020-1. Jpg into the simplified expression, the value was â€"4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answer:
value was â€"4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answer:
C.)1/6 (-10x-4)
Step-by-step explanation:
Got it right on edge 2022
Suppose that two teams play a series of games that ends whenone of them has won i games. Suppose that each game playedis, independently, won by Team A with a probability of p.Find the expected number of games that are played when (a)i=2 and (b) i=3. Also show in both cases thattheis number is maximized when p=1/2.
Given: Two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by Team A with a probability of p. We need to find the expected number of games that are played when (a)i=2 and (b) i=3.
Also show in both cases that the number is maximized when p=1/2.Solution: Let N be the expected number of games played. Then the number of games played must be N if the series is won by A in i - 1 games, and N + i if it is won in i games. Then we have N = (1-p)N + p(N+1) ; here (1-p) is the probability that A does not win the game, and p is the probability that A wins the game
N = 1/pi.e., the expected number of games played until a win for A is 1/p, so the expected number of games played when i=2 is 1/p+1/p+1=2/p+1, and the expected number of games played when \(i=3 is 3/p+2/p+1/p+1=6/p+1\). In order to maximize both of these quantities, we must maximize \(p(1-p)^{i-1} for i=2 and i=3.\)
We could use calculus to find the maximum value, but instead we can use AM-GM: For i=2,p(1-p) ≤ ((p) + (1-p))/2 = 1/2, \(i=2,p(1-p) ≤ ((p) + (1-p))/2 = 1/2\)with equality when p = 1/2.
Similarly, for i=3,p(1-p)^2 ≤ ((p) + (1-p) + (1-p))/3 = 1/4, \(i=3,p(1-p)^2 ≤ ((p) + (1-p) + (1-p))/3 = 1/4\)with equality when p = 1/2. So the expected number of games played is minimized when p=1/2.
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what is -2 1/3 - (-5)=
Answer:
\( \frac{8}{3} \)
Step-by-step explanation:
\( - 2 \frac{1}{3} - ( - 5)\)
convert mixed fraction into improper fraction.
\( - \frac{7}{3} + ( - 5)\)
calculate the sum of the fraction:
\( \frac{8}{3} \)
The local pizza shop sells several special items.
Price
Item
Sales tax is 5 percent. Find the amount of tax for each
item in the table. Round to the nearest hundredth.
Tax for Italian Salad:
Italian Salad
$3.99
Tax for Lasagna:
Tax for Spaghetti:
Tax for Fettuccini Alfredo:
Lasagna
$8.50
Spaghetti
$4.29
Fettuccini Alfredo
$7.17
Done
1 of 9
கக்காக
02 feathcom/Playe
Answer:
Tax for Italian Salad=$0.20
Tax for Lasagna= $0.43
Tax for Spaghetti =$0.21
Tax for Fettuccini Alfredo =$0.36
Step-by-step explanation:
Hi, to answer this question we have to multiple the price of each item by the tax percentage in decimal form (divided by 100):
Italian Salad =$3.99
Tax for Italian Salad= 3.99 x (5/100) = 3.99 x 0.05 =$0.20Lasagna =$8.50
Tax for Lasagna= 8.50 x (5/100) = 8.50 x 0.05 =$0.43Spaghetti =$4.29
Tax for Spaghetti = 4.29x (5/100) = 4.29 x 0.05 =$0.21Fettuccini Alfredo =$7.17
Tax for Fettuccini Alfredo = 7.17 x (5/100) = 7.17 x 0.05 =$0.36Feel free to ask for more if needed or if you did not understand something.
Answer: .20
.33
.21
.36
Step-by-step explanation: 2020 edg
we want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample. can the bootstrap method be used? group of answer choices
The Bootstrap Method is straightforward and straightforward to comprehend. First, it chooses randomly from the original sample to produce bootstrap samples from our initial sample.
After that, it uses summary statistics like variation, standard deviation, mean, and so on to get replicates, which is how we can calculate a confidence interval from that sample.
Thus, the answer is "Yes."
The bootstrap method is a resampling method that uses replacement sampling to estimate population statistics. It can be used to estimate standard deviation and mean summaries.
Which scenarios call for the use of bootstrapping?Remember that bootstrapping isn't only valuable for computing standard blunders, it can likewise be utilized to build certainty spans and perform speculation testing. When working with data that doesn't seem to lend itself to conventional methods, always remember bootstrapping techniques.
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Full Question = We want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample.
Can the bootstrap method be used?
Group of answer choices
yes
no
Ben paddles his kayak along a course on a different river. Going upstream, it takes him 6 hours to complete the course. Going downstream, it takes him 2 hours to complete the same course. What is the rate of the current, and how long is the course
The rate of the current is 1.5 mph, and the length of the course is 9 miles.
Let's assume the rate at which Ben paddles in still water is represented by r (in mph), and the rate of the current is represented by c (in mph).
When paddling upstream, Ben is paddling against the current, so his effective speed is reduced. The time it takes him to complete the course is 6 hours, and the distance he covers is represented by d (in miles). Using the formula d = (r - c) * t, we have d = (r - c) * 6.
When paddling downstream, Ben is paddling with the current, so his effective speed is increased. The time it takes him to complete the course is 2 hours. Using the same formula, we have d = (r + c) * 2.
We can solve these two equations to find the values of r and c. By dividing the second equation by the first equation, we get (r + c)/(r - c) = 1/3.
Solving this equation, we find r = 4 mph and c = 1.5 mph.
Therefore, the rate of the current is 1.5 mph, and the length of the course is determined by substituting r and c into either of the original equations. The length of the course is 9 miles.
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Need help with this asap
Answer:
SSS
Step-by-step explanation:
All sides with the same amount of lines are congruent
c) Make k the subject of the formula t = ak/ 20
Answer:
k=20t/a
Step-by-step explanation:
20t=ak
20t/a=k
k=20t/a
What is the solution to the inequality |x-4|<3?
-7
1
x<-7 or x<-1
x > 1 or x < 7
Answer:
1 < x < 7
Step-by-step explanation:
HELPP ME PLEASE i have no idea
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Photo cuts off
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The triangles that are said to be similar to triangle ABE are: ADB and EDC.
What are similar triangles?When on comparing the corresponding properties of two or more triangles, there exist some common relations, then they are said to be similar. Note that similarity does not imply congruency, this implies that the triangles do not have exactly the same properties.
Considering the given diagram, the first thing to do is to compare the properties of triangle ABE with other triangles. Thus any other triangle/s that have common relations is said to be similar to triangle ABE.
Therefore, it can be observed that triangles ADB and EDC are similar to triangle ABE on comparing their corresponding properties. Though they are not congruent triangles.
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Solve the equation C^2 =4
Answer:
2
Step-by-step explanation:
Hey there!
The equation is asking us, c x c = 4
What is c?
Well the only number that is equal to 4 when you square it is 2
find the area of the figure.
Answer:
28.5 united squared
Answer:
Check pdf
Step-by-step explanation: