The area of the pigpen is approximately 725.5 square feet if each unit represents one foot.
To find the area of the polygon, we need to first identify its shape. From the given vertices, we can see that the polygon has four sides and is not a regular polygon.
To find the area of an irregular polygon with straight sides, we can divide it into simpler shapes such as triangles or rectangles and then calculate their individual areas before adding them up.
One way to do this for the given polygon is to divide it into two triangles and one rectangle:
Triangle WXY, with base WX = 14 - 7 = 7 feet and height YX = 12 - 7 = 5 feet: Area of triangle WXY = (1/2) * base * height = (1/2) * 7 * 5 = 17.5 square feet
Rectangle WZXY, with length WZ = XY = 71 - 12 = 59 feet and width WX = 7 feet: Area of rectangle WZXY = length * width = 59 * 7 = 413 square feet
Triangle XYZ, with base XY = 59 feet and height ZY = 17 - 7 = 10 feet (note that point 2 should be X(17,7)): Area of triangle XYZ = (1/2) * base * height = (1/2) * 59 * 10 = 295 square feet
Therefore, the total area of the polygon is the sum of the areas of these shapes:
Area of polygon WXYZ = Area of triangle WXY + Area of rectangle WZXY + Area of triangle XYZ
= 17.5 + 413 + 295
= 725.5 square feet
So the area of the pigpen is approximately 725.5 square feet if each unit represents one foot.
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2-2 additional practice
Answer:
0
Step-by-step explanation:
2-2=0
a new medical complex being built has a rectangular base. it is 400 ft long, 180 ft wide, and 40 ft tall. if the architect's scale model is 30 in. long, what are the width and height of the model?
The width and height of the model are;
Width of model = 13.5 inches
Height of model = 2.25 inches
How to Interpret the scale Model?A scale model is defined as a physical model that is geometrically similar to an object. Scale models are usually smaller than large prototypes such as vehicles, buildings, or people. However, these scale models may be larger than small prototypes such as anatomical structures or subatomic particles.
Now, we are given that the dimensions of the new medical complex are;
Length = 400 ft
Width = 180 ft
Height = 40 ft
Thus, for a scale model with length of 30 in(2.5 ft) long, the scale factor is; Scale factor = 2.5/400
Thus;
Width of model = 180 * (2.5/400)
= 1.125 ft = 13.5 inches
Height = 30 * (2.5/400)
= 0.1875 ft = 2.25 inches
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Calculate the average rate of change for the function
\(slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2(x-2)^2+1\qquad \begin{cases} x_1=-2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-2)}{4-(-2)} \\\\\\ \cfrac{[2(4-2)^2+1]~~ - ~~[2(-2-2)^2+1]}{4+2}\implies \cfrac{[9]~~ - ~~[33]}{6}\implies \cfrac{-24}{6}\implies -4\)
Sofia and Zara join a queue to get tickets for the school disco. There are 51 people in front of them. What are Sofia and Zara's positions in the queue?
The position of Zara and Sofia will be 52nd and 53rd.
According to the question, the persons standing in front of Sofia and Zara are 51. After 51 people, Sofia and Zara came and stood in line due to which they will be counted as the next persons.
The individual position of Zara and Sofia can't be determined as it is not given that between Zara and Sofia who came earlier.
This question is related to order and ranking. It means the process of knowing the position of a person, a thing, or a place in comparison to the position of other persons, or things.
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What is the rank ofa 4 x 5 matrix whose null space is three dimensional? Question 7: If the rank of a 7 x 6 matrix A is 2, what is the dimension of the solution space of A x = 0? Question &: Let A be an n X p matrix whose whose column space is p dimensional. Must the columns of A be linearly independent? Question 9: Suppose that H and K are subspaces of a vector space V_ Define: H+K= {wlw=h+kfor some h € Hand some ke K} Prove that H + K is a subspace of V'
The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns.
Thus, if the null space of a 4 x 5 matrix is three-dimensional, then the rank of the matrix is 5 - 3 = 2.
Answer to Question 2:
The dimension of the solution space of A x = 0 is 6 - 2 = 4, since the number of columns of A is 6 and its rank is 2. The solution space of A x = 0 is the null space of A, which has dimension 4 by the rank-nullity theorem.
Answer to Question 3:
No, the columns of A do not necessarily have to be linearly independent. The column space of A is the span of its columns, which has dimension p. However, the columns of A may be linearly dependent, which means that some columns can be expressed as linear combinations of the others.
Answer to Question 4:
To prove that H + K is a subspace of V, we need to show that it satisfies three conditions:
It contains the zero vector: 0 = 0 + 0 belongs to H + K, since it can be expressed as the sum of the zero vectors in H and K.
It is closed under vector addition: if w1 and w2 belong to H + K, then there exist h1 and k1 in H and K such that w1 = h1 + k1, and there exist h2 and k2 in H and K such that w2 = h2 + k2. Therefore, w1 + w2 = (h1 + h2) + (k1 + k2) belongs to H + K, since it can be expressed as the sum of vectors in H and K.
It is closed under scalar multiplication: if w belongs to H + K and c is a scalar, then there exist h and k in H and K such that w = h + k. Therefore, c w = c h + c k belongs to H + K, since it can be expressed as the sum of vectors in H and K.
Since H + K satisfies these three conditions, it is a subspace of V.
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pllzz help i'll give brainliest
Answer:
Triangle 20, 30, and 15 will create a triangle
Step-by-step explanation:
In order for side lengths to make a triangle, the sum of the two shortest sides must be greater than the longest side
5+3 < 9 so it does not work
15+20>30 so it does work
triangle qrs is similar to triangle xyz . the measure of ∠x is 75° and the measure of ∠q is equal to 5(n−3)° . which is the value of n
The two triangles n = (75 + 3) / 5 = 18. The measure of angle q is 18 degrees.
1. First, find the value of n by using the equation 5(n - 3) = 75 + 3
2. Next, add 75 and 3 together and divide by 5. This gives us a value of 18 for n.
3. Finally, use the equation 5(n - 3) to determine the measure of angle q in triangle qrs. This equals 5(18 - 3) = 5(15) = 75 degrees.
The two triangles qrs and xyz are similar, meaning they have the same angle measures. In order to find the measure of angle q in triangle qrs, we must first find the value of n. The measure of angle x in triangle xyz is 75 degrees and the measure of angle q in triangle qrs is equal to 5(n - 3) degrees. We can use this equation to solve for the value of n. To do this, we add 75 and 3, then divide by 5. This gives us a value of 18 for n. Therefore, the measure of angle q in triangle qrs is 18 degrees.
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What is the equation of the line that passes through the point (-6,-3) and has a slope of -1/6?
Answer:
y = (-1/6)x - 4
Step-by-step explanation:
Line equations are usually expressed in the following format:
y = mx + c
Where m is the gradient (slope), and c is the y-intercept.
We can fill in the value of m right away as we are given it in the question:
y = (-1/6)x + c
And we are given the point (-6,-3), so we can fill in the values for x and y, in order to find the value of c:
-3 = (-1/6)(-6) + c
Rearrange and simplify this:
-3 = 1 + c
c = -4
Finally, substitute the value of c back into the original equation to get the final equation of the line:
y = (-1/6)x - 4
jenny is five years older than chris little can be extracted from this. however we fud that a decade ago her age was twice his, therefore all we know is that get through this door a number made with digits four multaply jens age by ten to the two to finish it you must add chris's digits to the end of the number
answer:
2015
hope this helpsss
Bev has 1/3 cup of cereal. Her bowl holds 1/2 cup of cereal. How much of the bowl can she fill with cereal?
Answer:
2/3
Step-by-step explanation:
Given that :
Bev's cup capacity = 1/2
Fraction of cereal Bev has = 1/3
How much of the amount can be filled by the cup of cereal Bev has?
Fraction of cereal Bev has OF cup capacity
1/3 ÷ 1/2
1/3 * 2/1
(1*2) / (3*1)
= 2/3 of Bev's 1/2 capacity cup
Hence, 1/3 cup of cereal which Bev has will fill 2/3 of Bev's 1/2 capacity cup of cereal.
Bella i baking 34 cookie for the holiday party tonight. She baked 18 before leaving for chool and will bake the ret when he return home. Which equation how how many cookie Bella will bake when he return home?
The equation based on the information is:
34 = x - 18
In mathematics, an equation is an expression that states that two expressions are equal by joining them with the equal sign =. Equations and their cousins in other languages may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation. To solve an equation involving variables, it is necessary to determine which values of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values of the variable. A constraint expression applies only to specific values of a variable.
Given that :
Bella is baking 34 cookie for the holiday party tonight. She baked 18 before leaving for school and will bake the ret when he return home.
Therefore, the equation is:
34 = x - 18
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11. Jackie ate of a bag of popcorn. She
shared the rest with Enrique. List three
ways they could have shared the
remaining popcorn
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 130 square feet is 5,200 pounds when the plane is going at 150 miles per hour. Find the lifting force if the speed is 220 miles per hour. Round your answer to the nearest integer if necessary.
The lifting force if the speed is 220 miles per hour is F' = 708.53 N.
The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.
The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.
We have,
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,
\(F=kAv^{2}\)
Where
k is constant
If, A = 190 Ft², v = 220 mph, F = 950 pounds
Now, find k first from the above data. So,
\(k=\frac{F}{Av^{2} }\)
⇒ \(k=\frac{950}{190* (220)^2}\)
⇒ k = 0.0001033
It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.
Let F' is a new force. So,
F' = 0.0001033 × 190 × (190)²
⇒ F' = 708.53 pounds.
So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.
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Traci is collecting donations for a dance marathon. One group of sponsors will donate $36 for each hour she dances. Another group of sponsors plans to donate $75 no matter how long she dances. Traci plans to dance until she has raised at least $1,200. Let h represent the number of hours that Traci dances. Write and solve an inequality to determine the minimum number of hours that Traci needs to dance in order to raise $1,200.
Answer:
36h + 75 < 1200
solve:
36h + 75 = 1200
36h = 1125
h = 1125 divided by 36 = 31.25.
Therefore, Traci has to dance a minimum of 31.25 hours to raise $1200
Black Diamond Company produces snowboards. Each snowboard requires 2 pounds of carbon fiber. Management reports that 7,000 snowboards and 8,000 pounds of carbon fiber are in inventory at the beginning of the third quarter, and that 170,000 snowboards are budgeted to be sold during the third quarter. Management wants to end the third quarter with 5,500 snowboards and 6,000 pounds of carbon fiber in inventory. Carbon fiber costs $19 per pound. Each snowboard requires 0.5 hour of direct labor at $24 per hour. Variable overhead is budgeted at the rate of $14 per direct labor hour. The company budgets fixed overhead of $1,802,000 for the quarter. Required: 1. Prepare the production budget for the third quarter. Hint: Desired ending inventory units are given. BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter Budgeted sales units Add: Desired ending inventory units Total required units Less: Beginning inventory units Units to produce 170,000 5,500 175,500 7,000 168,500 2. Prepare the direct materials budget for the third quarter. BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter Units to produce Materials needed for production (pounds) Total materials required (pounds) Materials to purchase (pounds) + Cost of direct materials purchases 3. Prepare the direct labor budget for the third quarter. BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter Units to produce Direct labor hours needed Cost of direct labor 4. Prepare the factory overhead budget for the third quarter. BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter Direct labor hours needed Budgeted variable overhead Budgeted total factory overhead
Production: 168,500 units.
Direct materials: 337,000 pounds.
Direct labor: Calculated based on units produced.
Factory overhead: Calculated based on direct labor hours.
1. Production Budget for the Third Quarter:
BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter
Budgeted sales units: 170,000
Add: Desired ending inventory units: 5,500
Total required units: 175,500
Less: Beginning inventory units: 7,000
Units to produce: 168,500
2. Direct Materials Budget for the Third Quarter:
BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter
Units to produce: 168,500
Materials needed for production (pounds): 2 pounds per snowboard
Total materials required (pounds): 337,000 pounds
Materials to purchase (pounds): Total materials required - Beginning inventory pounds - Desired ending inventory pounds
3. Direct Labor Budget for the Third Quarter:
BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter
Units to produce: 168,500
Direct labor hours needed: 0.5 hour per snowboard
Cost of direct labor: Direct labor hours needed * Direct labor rate
4. Factory Overhead Budget for the Third Quarter:
BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter
Direct labor hours needed: Calculated from the direct labor budget
Budgeted variable overhead: Direct labor hours needed * Variable overhead rate
Budgeted total factory overhead: Budgeted fixed overhead + Budgeted variable overhead
Note: The specific rates for direct materials, direct labor, and variable overhead were not provided in the given information and would need to be included in the calculations based on the company's specific cost structure.
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The question is in the image
1. A state is considering adding another character to their vehicle license plates in order to increase the number of license plates available. Currently, a license plate must have exactly six character spaces. Each character space may be filled with any capital letter other than I or O or any number between, and including, 0 to 9. Letters and numbers may repeat on the plates.
(a) How many different license plate numbers are available under the current structure of exactly six characters per plate? Show your work.
(b) If the state required all license plates to have exactly seven characters instead of six, how many different license plate numbers would be available with the additional character requirement? Show your work.
(c) How many times bigger is the set of license plate numbers with exactly seven characters than that with the set of six characters? Show your work.
Answer:
9514 1404 393
Answer:
a) 1,544,804,416
b) 52,523,350,144
c) 34
Step-by-step explanation:
(a) Each character position can be any of 24 letters or 10 digits, so any of 34 characters. The number of possible characters sets increases by a factor of 34 for each added character. A six-character plate will have ...
34^6 = 1,544,804,416 . . . possibilities
__
(b) 34^7 = 52,523,350,144 . . . possibilities
__
(c) 34^7/34^6 = 34 . . . times as many
HELP ASAP PLS, matching sequence to its recursive formula
Vince bought six boxes of worms to use as bait while fishing what his friends if each person uses exactly 3 over three, and eight of a box of worms, how many people can share dorms?
Vince bought six boxes of worms to use as bait while fishing what his friends if each person uses exactly 3/8 of a box of worms, the number of people who can share the boxes of worms is 16.
The number of people who exactly share the boxes is determined through division of total number of boxes by fraction of box used by each person exactly.
The given information to compute the required information is:
The total number of boxes = 6
Box used by each person = 3/8
Therefore,
Number of people = Number of Boxes/Part of Box Used by One Person = 6÷ 3/8 = 6 x 8/3 = 16
Hence, the number of people who can share the six boxes exactly are 16 people.
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What is the type? f(x)=-1/5x³-5+10x²
URGENT i need to check my answer
A recipe calls for 150 grams of cheddar cheese. Dylan has 4.0 ounces of cheddar cheese. How many more ounces will he need for the recipe? Give your answer to the nearest tenth. Complete the explanation of how you solved this problem. Use 1 kilogram ≈ 2.2 pounds.
Dylan will need another _____ ounces of cheese.
Convert (a.150 grams to ounces b. 4.0 ounces to grams). Subtract the number of ounces Dylan has to find out how much more he needs.
Using conversion of units, it is found that Dylan needs another 1.29 ounces of cheese.
----------------------------
The conversion of units are applied using a rule of three.Each gram has 0.035274 ounces. How many ounces are there in 150 grams?1 gram - 0.035274 ounces
150 grams - x ounces
Applying cross multiplication:
\(x = 150 \times 0.035274 = 5.29\)
----------------------------
Dylan has 4 ounces of cheddar cheese.He needs 5.29 ounces.Thus, he needs another 5.29 - 4 = 1.29 ounces.A similar problem is given at https://brainly.com/question/13251881
PLEASE HELP!!
(04.03)
Given the function g(x) = 5(2)^x, compare the average rate of change from x = 1 to x = 2 and from x = 3 to x = 4.
How many times greater is the average rate of change from x=3 to x=4 than from x=1 to x=2?
О 4 times
O 5 times
O 2 times
O The average rate of change of Section B is not greater than the average rate of change of Section A.
Answer: Choice A. 4 times
========================================================
Explanation:
We'll be using this formula
\(m = \frac{f(b)-f(a)}{b-a}\)
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
\(m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\\)
Do the same for the AROC from x = 3 to x = 4.
\(m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\\)
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
What is the name of the equation for the regression line?
The name of the equation for the regression line is the Regression Equation.
Regression Line:
Regression is a statistical technique used in finance, investing, and other fields that attempts to determine the strength and nature of the relationship between one dependent variable (usually denoted Y) and several other variables (called independent variables).
Simple linear regression:
Y = a + bX+ u
Multiple linear regression:
Y = a + b₁ X₁ + b₂ X₂ + b₃ X₃ +..... + bₙ Xₙ +u
where:
Y = The dependent variable that can be predicted.
X =The independent variables that are used to predict
a = The y-intercept
b (beta coefficient) = is the slope of the independent variable(s)
u = The error term
Regression equation:
Regression equations are used in statistics to determine if there is any relationship between data sets. For example, if you measure a child's height every year, you'll find that they grow about 3 inches each year. This trend (growth of 3 inches per year) can be modeled using a regression equation. In fact, most things in the real world (from oil prices to hurricanes) can be modeled with a few equations. You can predict future events.
There are several types of regression equations. Some of the more common ones include exponential and simple linear regression (to fit data to an exponential or linear equation). The regression equation most likely to be encountered in elementary statistics takes the form of a linear one.
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At least three scoutmasters must accompany every
20 scouts on a camping trip. If 80 scouts are going
on the next camping trip, what is the minimum
number of scoutmasters needed?
a.) 12
b.) 14
c.) 15
d.) 20
Henry sang 12 songs every song was 3/8 minutes long. For how much time did he sing in total?
Answer:
4.5 minutes or 36/8 minutes or 9/2 minutes
Step-by-step explanation:
So we simply find 3/8 of 12 by multiplying:
\(\frac{3}8} \times 12\)
This gives us 36/ 8
Now, depending on how you want your answer formulated, we just reduce it to either 9/2 minutes, or 4.5 minutes.
Hope this helpss!!!
a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
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for a normal distribution, find the z-score for which a total probability of 0.71 falls more than z standard deviations (in either direction) from the mean.(round to two decimal places as needed.)
The z-score for which a total probability of 0.71 falls more than z standard deviations (in either direction) from the mean is -1.04 (rounded to two decimal places).
How to find the probabilityWe need to find the z-score for which a total probability of 0.71 falls more than z standard deviations (in either direction) from the mean.
The given information can be represented as:
P(Z > z) + P(Z < -z) = 0.71
We know that the total probability for the standard normal distribution is equal to 1.
Therefore, we can rewrite the equation above as:
P(Z > z) + P(Z > z) = 0.71 ⇒ 2P(Z > z) = 0.71 ⇒ P(Z > z) = 0.355
Now, we need to find the z-score that corresponds to P(Z > z) = 0.355.
Using a standard normal distribution table, we can find the z-score that corresponds to this probability as follows:
z = -1.04 (rounded to two decimal places)
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Please help me !! would appreciate
The answers that describe the quadrilateral DEFG area rectangle and parallelogram.
The correct answer choice is option A and B.
What is a quadrilateral?A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.
Quadrilateral DEFG
if line DE || FG,
line EF // GD,
DF = EG and
diagonals DF and EG are perpendicular,
then, the quadrilateral is a parallelogram
Hence, the quadrilateral DEFG is a rectangle and parallelogram.
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test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2)against the alternative that it is not (and assume equal variances). find the t-stat to 3 decimal places.
To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))
where:
x1 and x2 are the sample means of the two sheets,
s_p is the pooled standard deviation,
n1 and n2 are the sample sizes.
The pooled standard deviation (s_p) can be calculated using the following formula:
s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
where:
s1 and s2 are the sample standard deviations.
To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.
Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.
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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.
The t-statistic for a paired t-test is calculated as follows:
t = (X1 - X2) / (s / √n)
where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.
Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.
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Harry made 22 pans of fudge bars for an event at the University of Central Florida. Only of each pan was eaten. 10 How many total fudge bar pans were eaten at the event? А 198 220 B 211 10 99 C D 220 9 E I don't know yet
Answer:
Answer is 235/45
Step-by-step explanation: