The resulting two-dimensional shape is a square with an area of 72 square units.
The pyramid is a square right pyramid, the base is a square and the vertical height meets the base at its center. When the pyramid is sliced by a plane that passes vertically through the top vertex and is perpendicular to the base, the resulting two-dimensional shape is a square.
The plane section intersects the four triangular faces of the pyramid, creating four smaller triangles with the same shape and size. These four triangles can be rearranged to form a smaller square that is similar to the larger square base of the pyramid. The area of the plane section is equal to the area of the smaller square, which is proportional to the area of the larger square base. The proportionality constant is equal to the ratio of the height of the plane section to the height of the pyramid.
Let H be the height of the pyramid and h be the height of the plane section. Then, we have:
h/H = (side length of smaller square)/(side length of larger square)
= √(2)/2
Solving for h, we get:
h = (√(2)/2) * H
The area of the plane section is then:
A = (side length of smaller square)²
= (√2)/2 * side length of larger square)²
= (√(2)/2)² * (side length of larger square)²
= (1/2) * (side length of larger square)²
Since the side length of the larger square base is given, we can substitute it in and simplify to get:
A = (1/2) * (12)² = 72 square units
As a result, the resultant two-dimensional form is a square with 72 square units of area.
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Assume g and h are whole numbers, and g < h. Which expression has the least
value?
Answer:
[tex] \frac{ {g}^{4} {h}^{2} }{ g{h}^{6} } = \frac{ {g}^{3} }{ {h}^{4} } [/tex]
because other values are 1, and this one is less, because g<h
Tell whether a triangle can have the given angle measures. 115. 1∘, 47. 5∘, 93∘
No, a triangle cannot have the given angle measures, 115. 1∘, 47. 5∘, 93∘, as sum of these is greater than 180°.
The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well.
The sum of the angles in a triangle is always 180°, and 115.1° + 47.5° + 93° = 255.6°, which is greater than 180°.
Therefore, it is not possible for a triangle to have these angle measures.
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#14 Please Help!!!!!!!!
The measure of the angle m∠FGH is 83°.
How to find the measure of m∠FGH?
Since the measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the the difference of the intercepted arcs.
Thus, we can say:
m∠FGH = 1/2 * (∠FIH - 97°)
∠FIH = 360 - 97 = 263° (sum of angle in a circle)
m∠FGH = 1/2 * (263 - 97°)
m∠FGH = 1/2 * 166
m∠FGH = 83°
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PLEASE HELP ILL MARK U AS BRAINLIEST!!
Answer: 94 square inches 2
Step-by-step explanation:
2×(5×4 + 5×3 + 4×3) = 94 sq in 2
length x width x height
if you need more help with your ixl I am free to help!
have a good day!
Can someone help me asap? It’s due today
Answer: second one!
Step-by-step explanation:
we randomly select 100 pell grant recipients from two states. state a is a relatively small state with approximately 4,000 pell grant recipients. state b is a large state with approximately 200,000 pell grant recipients. suppose that the mean and standard deviation in individual pell grants is approximately the same for both states: and . for which state is the sample mean for our 100 pell grant recipients most likely to be within $80 of $2,600?
The sample mean for 100 pell grant recipients is more likely to be within $80 of $2,600 for State A, given the relatively smaller population size and the use of the t-distribution.
To compare the two states, we need to calculate the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 for each state.
For State A, with only 4,000 pell grant recipients, the sample size of 100 is relatively large, but not enough to use the normal distribution. Therefore, we need to use the t-distribution, which has fatter tails than the normal distribution, making it more likely to produce extreme values. This means that the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is higher for State A than for State B.
For State B, with a larger population of 200,000 pell grant recipients, the sample size of 100 is a small fraction of the population, allowing us to use the normal distribution. However, as the distribution is narrower than the t-distribution, the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is lower for State B than for State A.
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Mr. Frost worked 37 hours last week. He was paid $17 per hour. How much money did he make last week?
Answer:
$481
Step-by-step explanation:
37×$17=$481
he made $481
011.considering grade c or above as a pass grade, how many students from this data successfully passed the course?
If we consider grade "C" or above as a pass grade, then the number of students who successfully passed the course are 10 students.
The Number of students who got grade "A" = 8,
The Number of students who got "B" grade is 2,
The Number of students who got grade "C" = 0,
The Number of students who got grade "D" = 0,
The Number of students who got grade "F" = 1,
Since the question asks for the number of students who successfully passed the course (i.e., grade "C" or above is considered a pass grade),
We add the number of students who got grades "A" and "B".
So, total number of students who successfully passed course are :
⇒ 8 (students who got grade "A") + 2 (students who got grade "B")
⇒ 10
Therefore, 10 students successfully passed the course.
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The given question is incomplete, the complete question is
If 8 students of the class got grade "A", 2 student got grade "B", No student got grade "C" and "D", 1 student got grade "F".
Considering grade "C" or above as a pass grade, how many students from this data successfully passed the course?
Five balls, A, B, C, D, and E, weigh 30g, 50g, 50g, 50g, and 80g each. Which ball weighs 30g?
The only ball that weighs 30g is ball A. So the answer is: Ball A weighs 30g.
How to determine the ball that weighs 30gTo determine which ball weighs 30g, we need to compare the weights of each ball.
We know that there are five balls, and that their weights are 30g, 50g, 50g, 50g, and 80g.
Since we are looking for the ball that weighs 30g, we can eliminate the other weights one by one. We know that ball E weighs 80g, so it cannot be the one we're looking for. We can also eliminate balls B, C, and D since they all weigh 50g.
Therefore, the only ball that weighs 30g is ball A. So the answer is: Ball A weighs 30g.
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an lti system has the frequency response function h(ω)=1/(jω 3). compute the output if the input is
The output of the LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input[tex]x(t)[/tex], is:
[tex]y(t)[/tex]= inverse Fourier transform of [tex][1/(jw^3) X(w)][/tex]
To compute the output of an LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input x(t), we can use the Fourier transform:
[tex]H(w)[/tex] = Fourier transform of [tex]h(t)[/tex]
[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]
[tex]Y(w) = H(w) X(w)[/tex]
[tex]Y(w)[/tex] is the Fourier transform of the output [tex]y(t)[/tex].
Using the given frequency response function, we have:
[tex]H(w) = 1/(jw^3)[/tex]
Taking the Fourier transform of the input [tex]x(t)[/tex], we have:
[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]
And multiplying [tex]H(w)[/tex] and[tex]X(w)[/tex], we get:
[tex]Y(w) = H(w) X(w) = 1/(jw^3) X(w)[/tex]
Taking the inverse Fourier transform of [tex]Y(w)[/tex], we get the output [tex]y(t)[/tex]:
[tex]y(t)[/tex] = inverse Fourier transform of [tex]Y(w)[/tex]
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Find the length of each segment.
13. YW and WZ
The length of each segment is:
YW = 5 units
WZ = 8 units
How to find the length of each segment?The length of each segment can be found by using "bisector of an angle in a triangle theorem".
The theorem states that "the bisector of an angle in a triangle theorem divides the opposite sides in the ratio of the sides containing the angle".
Applying the theorem on the given triangle, we can say:
XY/XZ = YW/WZ
8/12.8 = (t/2)/(t-2)
8(t-2) = 12.8(t/2)
8t - 16 = 6.4t
8t - 6.4t = 16
1.6t = 16
t = 10
YW = t/2
YW = 10/2
YW = 5 units
WZ = t - 2
WZ = 10 - 2
WZ = 8 units
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select the correct answer. in a box containing 20 cans, 12 of the cans contain vegetables. in the box, 5 of the cans are dented, with 2 of the dented cans containing vegetables. what is the probability that a randomly selected can in the box is dented or contains vegetables?
The probability that a randomly selected can in the box is dented or contains vegetables is 19/20.
To solve the problem, we need to use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events.
In this case, we want to find the probability that a randomly selected can is dented or contains vegetables. Let's call these events D and V, respectively.
We are given that there are 20 cans in total, 12 of which contain vegetables, and 5 of which are dented, with 2 of the dented cans containing vegetables. This information allows us to calculate the probabilities of the individual events
P(D) = 5/20 = 1/4
P(V) = 12/20 = 3/5
P(D and V) = 2/20 = 1/10
To find the probability of the union of these events, we plug these values into the formula
P(D or V) = P(D) + P(V) - P(D and V)
= 1/4 + 3/5 - 1/10
= 19/20
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Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), what would be the coordinates of A'?
Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).
Describe Rotation?Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a transformation that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.
In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.
To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:
A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)
where (a,b) is the center of rotation and θ is the angle of rotation (90 degrees in this case).
Substituting the given values, we get:
a = 2, b = -1, x = 5, y = 4, θ = 90 degrees
x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1
y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2
Therefore, the coordinates of A' are (-1, 2).
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you want to obtain a sample to estimate a population mean. based on previous evidence, you believe the population standard deviation is approximately . you would like to be 90% confident that your estimate is within 2.5 of the true population mean. how large of a sample size is required? n
The required sample size of the given estimate is 1090.9809
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/2.5]²
Substitute values in the above equation,
n = [1.645×50.2/2.5]²
n = 1090.9809
Thus, the required sample size of the given estimate is 1090.9809.
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Which number line represents the solution to the inequality
Answer:
B
Step-by-step explanation:
Andy has 3.2 x 10³ dollars in his bank account. His brother Dan has 4.7 times that amount in his account. How much does Dan have in his account? Write the amount in scientific notation.
Answer:
1.504 x 10^4
Step-by-step explanation:
A 150 pound crate is used to hold the boxes on the forklift. What is the maximum number of boxes that the forklift can carry in the crate.
Answer: To determine the maximum number of boxes that the forklift can carry in the crate, we need to know the weight of each box and the weight capacity of the forklift. Let's assume that each box weighs 20 pounds and the weight capacity of the forklift is 2000 pounds.
To find the maximum number of boxes, we need to subtract the weight of the crate from the weight capacity of the forklift and then divide by the weight of each box:
Maximum number of boxes = (Weight capacity of forklift - Weight of crate) / Weight of each box
Maximum number of boxes = (2000 - 150) / 20
Maximum number of boxes = 1850 / 20
Maximum number of boxes = 92.5
Since we cannot have a fraction of a box, we need to round down to the nearest whole number. Therefore, the forklift can carry a maximum of 92 boxes in the crate.
Step-by-step explanation:
Round to the nearest 10th a cylinder is 22 inches and 12.5 inches what is the surface area 
you are constructing a box from a piece of cardboard with dimensions 5 by 7 meters. you cut equal-size squares from each corner of the cardboard so you may fold the edges to construct the open top box. what are the dimensions of the box with the largest volume?
3.1634 m , w = 1.1634 , h = 1.91834 m are the dimensions of the box with the largest volume.
What is a simple volume definition?
Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The basic formula for the area of a rectangle is length x width, but the basic formula for volume is length x width x height.
Length of cardboard = 7 m
width of a cardboard = 5 m
let x be the side of square of piece cut from each corner
length of box = (7 -2x) m
width of box = (5 - 2x) m
height of box = x
volume V = (7 -2x) * (5 - 2x) * X
= (35 - 14X - 10X + 4X²) * X
= 4X³ - 24X² + 35X
If v is max v' = 0 and v'' < 0
v' = 12x² - 48x + 35
x = 6.0816 or 1.91834
if x = 6.0816 , box will not be follow.
x = 1.91834
v''(x) = 24x - 48
= 46.04 - 48 = -1.95 < 0
V is max.
length = 7 - 3.8366 = 3.1634 m
width = 5 - 3.8366 = 1.1634 m
height = 1.91834 m
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Carla looks from a height of 1515 yards at the top of her apartment building. She lines up the top of a flagpole with the curb of a street 2020 yards away. If the flagpole is 1212 yards from the apartment building, how tall is the flagpole?
Answer: 4545 yards
Step-by-step explanation:
We can use similar triangles to solve this problem. Let's represent the height of the flagpole with the variable "x".
Using the triangle formed by Carla's line of sight, the height of the apartment building, and the top of the flagpole, we can set up the following proportion:
x / (x + 1515) = 15 / 20
Simplifying this proportion, we get:
4x = 3(x + 1515)
4x = 3x + 4545
x = 4545
Therefore, the height of the flagpole is 4545 yards.
How to perform bootstrapped likelihood ratio test?
To perform a bootstrapped likelihood ratio test, you need to fit the two nested models to your data, calculate the likelihood ratio test statistic, generate bootstrap samples, fit the two models to each bootstrap sample, calculate the p-value, and interpret the results.
The bootstrapped likelihood ratio test is a statistical method used to compare the goodness-of-fit of two nested models. Here's how you can perform a bootstrapped likelihood ratio test
Fit the two nested models: Start by fitting the two nested models to your data. One model is a restricted model, and the other is an unrestricted model that contains additional parameters.
Calculate the likelihood ratio test statistic: Calculate the likelihood ratio test statistic by subtracting the log-likelihood of the restricted model from the log-likelihood of the unrestricted model. This gives you the test statistic (often denoted as "LR").
Generate bootstrap samples: Generate a large number of bootstrap samples from the original dataset. Each bootstrap sample should be the same size as the original dataset and drawn with replacement.
Fit the two models to each bootstrap sample: For each bootstrap sample, fit the two nested models and calculate the likelihood ratio test statistic as described in steps 1 and 2.
Calculate the p-value: Calculate the p-value as the proportion of bootstrap samples for which the likelihood ratio test statistic is greater than or equal to the test statistic calculated from the original dataset.
Interpret the results: If the p-value is less than your chosen significance level (e.g., 0.05), you can reject the null hypothesis that the restricted model is better than the unrestricted model in favor of the alternative hypothesis that the unrestricted model is better.
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Dylan bought 3 identical shirts online for a total cost of $71.83 including a flat rate of $7.99 for shipping. Complete an equation to find the cost of each shirt, s, using the numbers below.
Answer:
$21.28
Step-by-step explanation:
We Know
Dylan bought 3 identical shirts online for a total cost of $71.83
$7.99 for shipping
We have the equation:
71.83 = 3s + 7.99
63.84 = 3s
s = $21.28
So, each shirt cost $21.28
the mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.90 degree of confidence. for a small pilot study, the mean was 150 days and the standard deviation was 16 days. if the population mean is estimated within two days, how many salespeople should be sampled
Estimate the mean number of travel days per year for salespeople employed by three hardware distributors with a 0.90 degree of confidence and an error margin of 2 days, a sample size of at least 179 salespeople should be selected.
The sample size needed to estimate the population mean with a 0.90 degree of confidence:
[tex]n = (Z\times\sigma / E)^2[/tex]
where:
Z = the Z-score for the desired level of confidence (0.90 corresponds to a Z-score of 1.645)
σ = the population standard deviation (unknown)
E = the maximum error of the estimate, which is given as 2 days
We can estimate the population standard deviation using the sample standard deviation from the pilot study, which is given as 16 days.
Therefore, plugging in the values, we get:
[tex]n = (1.645 \times 16 / 2)^2 = 178.26[/tex]
Rounding up to the nearest whole number, we get a minimum sample size of 179 salespeople.
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Find the value of the indicated trigonometry ratio cos in right tringle with side of 6,6*squort 2, 6*squort 3
Answer:√2/2
Step-by-step explanation:
Let's label the sides of the right triangle as follows:
The side adjacent to the angle θ (cosine is adjacent/hypotenuse): 6
The hypotenuse (the longest side): 6√2
The side opposite to the angle θ (sine is opposite/hypotenuse): 6√3
Using the Pythagorean theorem, we can find the length of the missing side:
a² + b² = c²
6² + (6√3)² = (6√2)²
36 + 108 = 72
144 = 72
√144 = √72
12 = 6√2
Now that we know the length of all three sides, we can use the cosine ratio to find the value of cos(θ):
cos(θ) = adjacent/hypotenuse = 6/6√2 = √2/2
Therefore, the value of cos(θ) in the right triangle with sides of 6, 6√2, and 6√3 is √2/2.
solving systems by eliminations; finding the coeficients
please write all the problems down, 5 points for each problem, and Brainliest
The solution to the given system of equations is x = -3 and y = 4 or (-3,4)
How does the elimination approach work to solve an equation?Pick one of the variables (x or y) and remove it by adding or subtracting the equations in such a manner that one of the variables is cancelled out.Solve the resultant equation with only one variable for that variable.To solve for the other variable, plug the discovered variable value into one of the original equations.Now, for given problem
2x + 5y = 14 ................(1)
4x + 2y = -4 ................(2)
Multiply equation (1) by '2' and equation (2) by '-1' :
4x + 10y = 28 ................(3)
-4x - 2y = 4 ..................(4)
Adding equations (3) and (4) to eliminate 'x':
4x + 10y + (-4x) - 2y = 28 + (4)
8y = 32
y = 32 / 8
y = 4
on substituting the value (y = 4) into equation (1), we get :
2x + 5(4) = 14
2x + 20 = 14
2x = 14 - 20
2x = -6
x = (-3)
Hence, solution for the given system of equations is (-3,4).
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Simplify these expressions
5×x
6×x×y
2×x×3×y
Answer:
5x
6xy
2x3y
hope it's helpful
the cylinder with the height of 4 M has a volume of 2,827.43 cubic meters find the length of the diameter
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=2827.43\\ h=4 \end{cases}\implies 2827.43=\pi r^2(4)\implies \cfrac{2827.43}{4\pi }=r^2 \\\\\\ \sqrt{\cfrac{2827.43}{4\pi }}=r\hspace{5em}\stackrel{\textit{twice that is the \underline{diameter}}}{2\sqrt{\cfrac{2827.43}{4\pi }}} ~~ \approx ~~ \text{\LARGE 30}[/tex]
I NEED HELP ON THIS ASAP!
f(x) = N * 4^x is an exponential function that represents the number of new participants of the challenge as a function of the day number, x.
How do we calculate?We define our variables:
N: the total number of participants on Day 1 (including Aliyah, Kim, and Reese)
r: the constant ratio by which the number of participants grows each day
x: the number of days since Day 1
r = 4.
There are N participants on Day 1. Each of the N participants contacts 4 new participants on Day 2, resulting in a total of 4N participants.
Each of the 4N participants makes contact with 4 new participants on Day 3, resulting in a total of 4(4N) = 16N people. Since we can see that there are more participants every day, we can write:
f(x) = N * 4^x as an exponential function that represents the number of new participants of the challenge as a function of the day number, x.
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A radioactive substance decays exponentially. A scientist begins with 200 milligrams of a radioactive substance. After 22 hours, 100 mg of the substance remains. How many milligrams will remain after 32 hours?A radioactive substance decays exponentially. A scientist begins with 200 milligrams of a radioactive substance. After 22 hours, 100 mg of the substance remains. How many milligrams will remain after 32 hours?
76.74 milligrams will remain after 32 hours.
What is a radioactive substance?N(t) = N₀e^(-kt)
where:
N(t) is the amount of substance remaining after time t
N₀ is the initial amount of substance
k is the decay constant
To solve for the decay constant, use the information given in the problem:
100 = 200e^(-22k)
Dividing both sides by 200, we get:
0.5 = e^(-22k)
Taking the natural logarithm of both sides, we get:
ln(0.5) = -22k
Solving for k, we get:
k = ln(0.5)/(-22) = 0.0316
Use this value of k to find the amount of substance remaining after 32 hours:
N(32) = 200e^(-0.0316*32) = 76.74 mg
Therefore, approximately 76.74 milligrams of the substance will remain after 32 hours.
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76.4 milligrams will remain after 32 hours.
Define the term exponential?Exponential refers to a mathematical function in which a constant base is raised to a variable exponent. The value of the function increases or decreases rapidly as the exponent increases, depending on whether the base is greater than 1 or between 0 and 1. Exponential functions are commonly used to model situations where a quantity grows or decays at a constant percentage rate over time.
What is decay?Decay is the natural process of deterioration or rotting of a substance over time. It can occur in both organic and inorganic materials and is often caused by the activity of microorganisms, exposure to oxygen or other environmental factors.
To determine the amount of radioactive substance that remains after 32 hours, we can use the formula A = A₀ ×[tex]e^{-kt}[/tex], where A is the amount remaining, A₀ is the initial amount, k is the decay constant, and t is the time elapsed.
we can use the same formula for exponential decay to find the value of k:
100 = 200 × [tex]e^{(-k*22)}[/tex]
0.5 = [tex]e^{(-k*22)}[/tex]
ln(0.5) = -k×22
k = ln(2)/(22)
Now we can use this value of k to find the amount of substance remaining after 32 hours:
N(32) = 200 [tex]e^{(-k*32)}[/tex]
N(32) = 200 [tex]e^{(-(ln(2)/(22))32)}[/tex]
N(32) ≈ 76.4 mg
Therefore, approximately 76.4 milligrams of the substance will remain after 32 hours.
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Evaluation researchers encounter more logistical problems than other researchers because evaluation researchA. occurs in the context of real life.B. takes longer.C. is more costly.D. has more measurement problems.E. examines more variables.
The answer is A. Evaluation researchers encounter more logistical problems than other researchers because evaluation research occurs in the context of real life.
Evaluation research often takes place in real-world settings, which can present logistical challenges such as accessing participants, coordinating schedules, and dealing with unexpected events. Additionally, evaluation research often involves multiple stakeholders and requires collaboration and communication among various groups, which can further complicate logistical issues. While evaluation research may also involve longer timelines, higher costs, measurement problems, and examination of multiple variables, these factors do not necessarily contribute to greater logistical challenges.
This means that evaluation researchers have to navigate complex, real-world situations, adapt to unforeseen challenges, and work with various stakeholders, making the research process more logistically challenging compared to controlled laboratory settings or theoretical research.
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Evaluation research is a type of research that focuses on assessing the effectiveness, efficiency, and impact of programs, policies, or interventions in real-life settings.
The correct answer is A. occurs in the context of real life.
This often involves evaluating the outcomes and impacts of interventions in complex and dynamic environments, such as organizations, communities, or systems. As a result, evaluation researchers may encounter more logistical problems compared to other types of researchers because they need to navigate real-life contexts, deal with multiple stakeholders, collect data from diverse sources, and address issues such as ethics, confidentiality, and validity in the evaluation process. Logistical problems may include challenges related to data collection, measurement, sample selection, data quality, and managing time and resources.
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