cos^2(x) - cos^4(x)
sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).
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The attorney does not accept legal cases involving litigation that would result in less than a $45,000 fee. The attorney has the opportunity to represent a client who will pay him $175 per hour plus 25% of the settlement. What is the minimum acceptable settlement on a case on which the attorney spent 110 hours?
In linear equation, 103000 is the minimum acceptable settlement on a case on which the attorney spent 110 hours.
What in mathematics is a 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.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let x be the amount settlement.
amount he earn from client = 175 * 110
= 19250
amount he earn from settlement = x * 25/100 = x/4
according to given condition
19250 + x/4 ≥ 45000
x/4 ≥ 45000 - 19250
x/4 ≥ 25750
x ≥ 25750 * 4
x ≥ 103000
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Gauss Jordan elimination method step by step 0. 99x-0. 04y-0. 2z=4
-0. 1x+0. 97y=6
-0. 2x-0. 01y+0. 96z=3
[ 1 -0.0004 -0.00202 | 0.0404 ] [ 0 1 -0.00020828 | 6] this is the Gauss Jordan elimination method step by step of the given linear equation.
The Gauss Jordan elimination method is a systematic way of solving a system of linear equations by performing elementary row operations on an augmented matrix. The augmented matrix is formed by combining the coefficients and constants of the linear equations.
The given system of linear equations can be written in matrix form as:
[ 99 -0.04 -0.2 | 4 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
The goal of the Gauss Jordan elimination method is to transform the augmented matrix into reduced row echelon form, which is a unique form that represents the solution of the system of linear equations.
The following steps outline the Gauss Jordan elimination method to solve the given system of linear equations:
Step 1: Begin with the first column and eliminate the coefficients below the first row by using row operations.
Divide the first row by 99 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ -0.1 0.97 0 | 6 ]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.1 times the first row to the second row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ -0.2 -0.01 0.96 | 3 ]
Add 0.2 times the first row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 0.9704 -0.000202 | 6.00404]
[ 0 -0.00018 0.960396 | 3.00808]
Step 2: Continue with the second column and eliminate the coefficients below the second row by using row operations.
Divide the second row by 0.9704 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 -0.00018 0.960396 | 3.00808]
Add 0.00018 times the second row to the third row:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6.18377]
[ 0 0.0000324 0.96052174| 3.01998]
Step 3: Continue with the third column and eliminate the coefficients above the third row by using row operations.
Divide the third row by 0.96052174 to make the leading coefficient equal to 1:
[ 1 -0.0004 -0.00202 | 0.0404 ]
[ 0 1 -0.00020828 | 6]
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The graph of f (x)=√x is transformed to create the
graph of g (x)= -2√x+6. Which of these describes a
transformation used to create the graph of g?
The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).
The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.
Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.
lines AB and CD are perpendicular to each other. If 3 measures (4x + 3)°, and 4 measures 43°, what is the value of x?
Step-by-step explanation:
4x+3+43=180
46+4x=180
4x=180-46
4x/4=134/4
X=33,5
Simplify the expression \( \sqrt{y^{2}-81} \) as much as possible after substituting \( 9 \sec x \) for \( y \).
The expression√{y²-81} can be simplifies to trigonometry as 9|tanx|.
If an algebraic expression has no like terms and no parenthesis, it is said to be in its simplest form. Use the Distributive Property to add or subtract the coefficients to combine like terms with variables. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
We start by substituting 9 sec x for y:
√{y²-81} = √{(9 sec x)²-81}
= √{81(sec²x) - 81}
= √{81(sec²x-1)}
= 9√{sec²x-1}
Using the trigonometric identity sec²x - 1 = tan²x, we can simplify further:
9√{sec²x-1} = 9√{tan²x}
= 9|tanx|
Therefore, the simplified expression is 9|tanx|.
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Find the area of the entire figure.
the area of the figure will be 15cm²
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
We are given that rajiv wishes to make a cube without lid with cardboard.
the area will be = area of square+area of rhombus
area of square = 3² = 9 cm²
area of rhombus = 2cm * 3cm =6cm²
The total area will be 15cm²
Hence the area of the figure will be 15cm²
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Answer:
watch sean delete this LOL IMAGINE HAVING TO DO THAT BC YOU SUK
the area of the figure will be 15cm²
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
We are given that rajiv wishes to make a cube without lid with cardboard.
the area will be = area of square+area of rhombus
area of square = 3² = 9 cm²
area of rhombus = 2cm * 3cm =6cm²
The total area will be 15cm²
Hence the area of the figure will be 15cm²
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Step-by-step explanation:
A kite is graphed on a coordinate grid and then dilated by a scale factor of 4/3 with the center of dilation at (1, 1). Vertex A of the original kite is located at (6, 15) Write the ordered pair that represents the location of vertex A after the dilation.
The ordered pair that represents the location of vertex A after the dilation is (8, 20).
What is vertex?Vertex is a point in geometry that describes the location of a object in a two-dimensional or three-dimensional space. In two-dimensional space, it is a point where two lines, curves, or surfaces intersect. In three-dimensional space, it is the point where three planes intersect. In a graph, it is the point where two lines intersect.
Vertex A of the original kite is located at (6, 15).
The center of dilation is at (1, 1). To dilate the kite by a scale factor of 4/3, each point (x,y) of the kite must be multiplied by the scale factor, 4/3. In this case, vertex A will transform to (8, 20) after the dilation.
Therefore, the ordered pair that represents the location of vertex A after the dilation is (8, 20).
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100 points please help
Answer:
I really want to help you!
Factored completely:
2x2(−x−2)(x−7)
Step-by-step explanation:
A brick of mass 6 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 5 cm. The spring is then stretched an additional 3 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g = 980 cm/s^2.
Set up a differential equation with initial conditions describing the motion and solve it for the displacement s(t) of the mass from its equilibrium position (with the spring stretched 5 cm).
The differential equation with initial conditions describing the motion is F = -k * (s(t) + 5) - 6g and the displacement of the mass from its equilibrium position as a function of time s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
The differential equation for the motion of the mass is given by Newton's Second Law, F = ma:
F = -k * (s(t) + 5) - 6g
where k is the spring constant, s(t) is the displacement from the equilibrium position, and g is the acceleration due to gravity. The initial conditions are s(0) = 3 and s'(0) = 0, since the spring is initially stretched an additional 3 cm and released from rest.
We can rearrange the equation to get:
s''(t) + (k/6) * s(t) = -5k/6 - g
This is a second-order linear homogeneous differential equation with constant coefficients. The general solution is:
s(t) = C1 * e^(r1*t) + C2 * e^(r2*t)
where r1 and r2 are the roots of the characteristic equation:
r^2 + (k/6) * r = -5k/6 - g
Using the quadratic formula, we get:
r1,2 = -(k/12) ± √((k/12)^2 + 5k/6 + g)
We can find the values of C1 and C2 by applying the initial conditions:
s(0) = C1 + C2 = 3
s'(0) = C1 * r1 + C2 * r2 = 0
Solving for C1 and C2, we get:
C1 = (3 * r2) / (r2 - r1)
C2 = (3 * r1) / (r1 - r2)
Substituting back into the general solution, we get:
s(t) = (3 * r2 * e^(r1*t)) / (r2 - r1) + (3 * r1 * e^(r2*t)) / (r1 - r2)
This is the displacement of the mass from its equilibrium position as a function of time.
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The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute.
Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Answer:
Step-by-step explanation:
The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.
(Open Ended) Describe a general method for adding a decimal with two decimal places to a decimal with three decimal places. Give an example.
How would I answer this?
Answer:
I think you could just add a zero onto the end of the two digit decimal, assuming it's not a decimal that continuously repeats, but is just like 2.25 or something like that. So to add 3.184 to 2.25, you would ads a 0 to the 2.25, making it 2.250.
a cable company earned 125 million in one year. the next year they earned 312.5 million dollars. estimate how many times bigger their profit was the second year compared to the first year.
Answer: The difference between 125 million dollars and 312.5 million dollars is, 187.5 Million Dollars.
Fill in the blanks to make the equations true. (x ....)(x ....)=x^2-4x-32
3. The ends of a thermometer on an aquarium are 3
4
inch above the water and 31
2 inches below
the water. What is the length of the thermometer
The length οf the thermοmeter is 16 1/4 inches.
What is thermοmeter ?Any instrument that measures temperature οr a thermal diffusivity is called a thermοmeter (the degree οf hοtness οr cοldness οf an οbject). Twο crucial cοmpοnents make up a thermοmeter:
(1) a temperature sensοr that changes in respοnse tο changes in temperature (fοr example, the mercury-in-glass thermοmeter's bulb οr an infrared thermοmeter's pyrοmetric sensοr);
(2) a way tο translate this change intο a specific number (e.g. the visible scale that is marked οn a mercury-in-glass thermοmeter οr the digital readοut οn an infrared mοdel). In technοlοgy, business, meteοrοlοgy, medicine, and scientific research, thermοmeters are frequently used tο track prοcesses.
Tο find the length οf the thermοmeter, we need tο add the distance abοve the water tο the distance belοw the water.
Distance abοve water: 3/4 inch
Distance belοw water: 31/2 inches
The tοtal length οf the thermοmeter:
3/4 + 31/2 = 6/8 + 124/8 = 130/8 = 16 1/4 inches
Therefοre, the length οf the thermοmeter is 16 1/4 inches.
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I think of a number, treble it and take 6 from my answer. If the result is 18, find the number. My teacher says its 4 I say its eight whats the answer?
Answer: Let's work through the problem step by step:
"Treble it": If we call the unknown number "x", then "trebling" it means multiplying it by 3, so we have 3x.
"Take 6 from my answer": We subtract 6 from 3x, giving us 3x - 6.
"If the result is 18": We set 3x - 6 equal to 18 and solve for x.
So, we have:
3x - 6 = 18
Adding 6 to both sides:
3x = 24
Dividing both sides by 3:
x = 8
Therefore, the answer is 8.
Step-by-step explanation:
i need a friend what is 234x 7364
Answer:
1,723,176
Step-by-step explanation:
By plugging this into a calculator, you will receive 1,723,176.
Answer: 234 x 7364 = 1,723,176
Please only help me if your going to give me the answer thanks
The area of the rectangular prism from the net is 209.8 square meters
Two B's = 30.4Two C's = 87.4How to determine the area of the rectangular prism from the netFrom the question, we have the following parameters that can be used in our computation:
The net of a rectangular prism
Start by calculating the areas of each labelled rectangle by multiplying tthe dimensions
So, we have
A = 2 * 11.5 * 4 = 92
Two B's
B = 2 * 3.8 * 4 = 30.4
Two C's
C = 2 * 3.8 * 11.5 = 87.4
Add the individual areas to get the net area
Area = 92 + 30.4 + 87.4
Evaluate the sum
Area = 209.8
Hence, the total area is 209.8 square meters
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A popcorn container is in the shape of a square pyramid the container meausers 9 inches high and each side measures 6 inches how many cubic inches does the popcorn container hold?
NEED HELP SO LOST AND CONFUSED PLS HELPP IM NOT A VERY SMART PERSON SO HELPPPP IM LOSIN ME MIND
The popcorn container can hold 432 cubic inches of popcorn.First, we need to find the volume of the popcorn container. The formula for the volume of a square pyramid is:
Volume = (1/3) * base area * height
To find the base area, we need to first find the area of one of the square sides. Since each side measures 6 inches, the area of one square side is:
Area = side length^2 = 6^2 = 36 square inches
Since the popcorn container is a square pyramid, it has four identical square sides, so the total base area is:
Base area = 4 * 36 square inches = 144 square inches
Now we can plug in the values for the base area and height into the formula for volume:
Volume = (1/3) * 144 square inches * 9 inches
Volume = 432 cubic inches
So the popcorn container can hold 432 cubic inches of popcorn.
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According to the 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino. A political party wants to know how much impact the Hispanic and Latino vote will have, so they wonder if that percentage has changed since then. They take a random sample of 853 adults in Oregon and ask, among other things, their race. 113 of the people surveyed were Hispanic or Latino. Can the political party conclude that the Hispanic proportion of the population has changed since 2010?
Do not provide links, improper answers, etc or I will report the answer!
Yes, the political party can conclude that the Hispanic proportion of the population has changed since 2010
Now, let's look at the given information. In 2010, the percentage of Hispanic or Latino people in Oregon was 11.7%. This means that out of every 100 people in Oregon, approximately 12 were Hispanic or Latino.
The political party conducted a survey of 853 adults in Oregon and found that 113 of them were Hispanic or Latino. To determine if the percentage of Hispanic or Latino people in Oregon has changed since 2010, we need to compare the survey results to the 2010 percentage.
To do this, we can calculate the percentage of Hispanic or Latino people in the survey by dividing the number of Hispanic or Latino people in the survey (113) by the total number of people surveyed (853), and then multiplying by 100. This gives us a percentage of approximately 13.2%.
Using this formula, we can estimate the margin of error for this survey to be approximately +/- 2.8%.
This means that the true percentage of Hispanic or Latino people in Oregon could be as low as 10.4% or as high as 15.6%, based on the survey results.
Since the margin of error includes the 2010 percentage of 11.7%, we cannot conclude that the Hispanic proportion of the population has definitively changed based on this survey alone.
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Work out the area of the rectangle using a calculator and giving your anwser in as a mixed number
The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.
To find the area of the rectangle, we need to multiply its length by its width.
First, we need to convert the mixed numbers to improper fractions:
Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm
Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm
Now, we can multiply the two fractions to get the area of the rectangle:
Area = length × width
= (31/6 cm) × (16/7 cm)
= (31 × 16) / (6 × 7) cm²
= 496/42 cm²
= 248/21 cm²
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:
248/21 cm² = (8 × 31)/ (8 × 3) cm²
= 31/3 cm²
= 10 1/3 cm²
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3x-2=7-6x
help pls???
Answer:
x=1
Step-by-step explanation:
3x-2=7-6x
3x-2 +2=7-6x +2
3x+6x=9-6x +6x
9x=9
x=1
Answer:
x = 1
Step-by-step explanation:
3x -2 = 7 -6x
9x - 2 = 7
9x = 9
x = 1
Let's check
3(1) -2 = 7 - 6(1)
3 - 2 = 7 - 6
1 = 1
So, x = 1 is the correct answer.
After how many years will the battery life of a cell phone be 2 hours? Rounds to the nearest tenth if necessary
To round to the nearest tenth, we can say that a cell phone's battery life is typically 2 hours after two years.
Generally speaking, the battery life of a cell phone will depend on the type of phone and usage habits. Most cell phones will last about 18-24 months before needing to be replaced.
The battery life of a cell phone is determined by a variety of factors, including battery capacity, phone usage habits, and battery age. We can, however, make certain assumptions and calculate how long it would take for a common mobile phone battery to decline to 2 hours of battery life.
Considering that a typical lithium-ion battery, which is often used in mobile phones, has a capacity of approximately 3,000 mAh when new and that its capacity drops by roughly 20% after 2-3 years of usage, we may estimate that the battery capacity would be around 2,400 mAh after 2-3 years.
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If you start as 2,10 and move 2 units to the left. Where will you end
HELP ME PLEASE THIS IS DUE TOMORROW
Answer:∠A = 9
Step-by-step explanation:In a Parallelogram opposite angles are always equal thus, 14x - 4 = 15x - 13.
Start by isolating the variable on one side of the equation. You can do this by subtracting 14x from both sides:
14x - 4 - 14x = 15x - 13 - 14x
Simplifying the left side gives:
-4 = x - 13
Now, isolate x by adding 13 to both sides:
-4 + 13 = x - 13 + 13
Simplifying the left side gives:
9 = x
Therefore, the solution to the equation 14x - 4 = 15x - 13 is x = 9
How did the ticket sales for the spring play change? Complete the statement
Answer:
"The sales for the spring play (Increased) by (30) tickets"
Step-by-step explanation:
The opening night sales were 200, to 230 by closing night so it increased by 30.
susan is making a blanket. she bought 1/3 pf a yard of material to use for the border for the blanket.susant cut the material into 4 same-size strips. what part of a whole yard is each strip
The fraction of the material that each strip represents is 1/12 of a yard.
Susan bought 1/3 of a yard of material to use for the border for the blanket. She cut the material into 4 same-size strips. The problem is asking for the part of a whole yard that each strip represents.
Since Susan has 1/3 of a yard of material and she cut it into 4 same-size strips, we can use division to find the fraction of the material that each strip represents.
Therefore, the fraction of the material that each strip represents is 1/3 ÷ 4.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 4 is 1/4, so we can rewrite the expression as:
1/3 ÷ 4 = 1/3 × 1/4
Now we can multiply the fractions:
1/3 × 1/4 = 1/12
Therefore, each strip represents 1/12 of the whole yard of material.
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A cylinder has a height of 11 millimeters and a radius of 15 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of this cylinder is equal to 7,771.5 cubic millimeter
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Since the radius of the base is 15 mm and the height of this cylinder is 11 mm, the volume of the cylinder in cubic millimeter can be calculated as follows;
Volume of a cylinder, V = 3.14 × 15² × 11
Volume of a cylinder, V = 3.14 × 2,475
Volume of a cylinder, V = 7,771.5 cubic millimeters.
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can I get help with this question?
The coordinate of points of the image are:
A' = (-1, 1), B' = (1, 1) and C' = (1, -1)
How to dilate the preimage about the origin?To dilate the preimage about the origin using a scale factor of 1/3, we can use the following formula:
image coordinate = scale factor * preimage coordinate
Substituting the values, we get:
A' = 1/3 * (-3, 3)
A' = (-1, 1)
B' = 1/3 * (3, 3)
B' = (1, 1)
C' = 1/3 * (3, -3)
C' = (1, -1)
Thus, the coordinate of points of the image are A' = (-1, 1), B' = (1, 1) and C' = (1, -1)
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Sketch a graph that could represent each scenario below. Be sure to label the axes appropriately and then write a description of the graph. a. The height of a baseball thrown from centerfield to home plate in relation to the distance from the centerfield. b. The number of shoppers at the mall each hour during business hours on a given day. c. The temperature of a cup of coffee x minutes after being poured.
The function graph for each of the cases with the description of the graph is plotted.
Explain about the graphing of functions?You must choose x-values and insert those into the equation in order to graph a function. You will obtain a y-value if you enter those values in into equation. Your coordinates for such a single point are made up of your x-values and your y-values.a. The ratio of the height of such a baseball thrown across outfield to home plate to the distance from centerfield.
This, will a parabolic graph as shown.
b. The volume of people who visit the mall per hour during regular business hours on such a particular day.
Thus, this graph will be step wise function as the value of people visiting the mall varies with the time.
c. A cup of coffee's temperature x minutes after it has been poured.
This, will be decreasing graph as the temperature of the coffee will keep on decreasing.
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3. repeated-measures and matched-subjects experiments repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? check all that apply. they both use the same t statistic. the researcher computes difference scores to compute a t statistic. the researcher must compute an estimated standard error for the mean difference score to compute a t statistic. the researcher must compute a pooled variance to compute a t statistic. for a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. how many subjects participated in this study? 64 32 62 31 a matched-subjects experiment produced a t statistic with a df of 17. how many subjects participated in this study? 34 36 18 17
A repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. 32 subjects participated in this study.
A matched-subjects experiment produced a t statistic with a df of 17.
34 subjects participated in this study.
Both a repeated-measures experiment and a matched-subjects experiment share the following characteristics when used to compare two treatment conditions:
1. They both use the same t statistic.
2. The researcher computes difference scores to compute a t statistic.
3. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31.
The number of subjects that participated in this study is 32 because the degrees of freedom (df) for a repeated measures experiment is calculated as (number of subjects - 1),
so 31 + 1 = 32.
A matched-subjects experiment produced a t statistic with a df of 17.
In this case,
the number of subjects that participated in the study is 34 because the degrees of freedom (df) for a matched-subjects experiment is calculated as (number of pairs - 1),
since there are two subjects in each pair, 17 + 1 = 18 pairs, which means 18 * 2 = 34 subjects.
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