The word count that can be accepted by the journalist's publication is 1,260.
Given,
A journalist is assigned to write a story that is 1,200 words long.
To fit in the publication's available space, the story's length can vary by no more than 75 words.
We need to find which word counts would be accepted by the journalist's publication.
1,100, 1,125, 1,290, 1,260, 1,300
Find the number of words the publication accepts.
We have,
1,200 words long.
The story's length can vary by no more than 75 words.
So,
1,200 + 75 = 1,275 words
The words can vary from 1,200 to 1,275 words.
Find the option which can be accepted.
1,100 - can not be accepted
1,125 - can not be accepted
1,290 - can not be accepted
1,260 - can be accepted
1,300 - can not be accepted
Thus the word count that can be accepted by the journalist's publication is 1,260.
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A number that is a multiple of 2 is also a multiple of 4.If a number is a multiple of 2, then it a multiple of 4. False If a number is a multiple of two, then it is a multiple of 4. True If a number is a multiple of 4 then it is a multiple of 2. True If a number is a multiple of 4, then it is a multiple of 2. False False
ITS WORTH 10 PTS
Answer:
If a number is a multiple of 2, it may NOT be a multiple of 4. An example would be the number 6.
\(6\div2=3\), but \(6\div4=1.5\).
However, if a number is multiple of 4, it is guaranteed to be a multiple of 2, since 4 itself is a multiple of 2.
Example:
\(8\div4=2\)
This is simply
\(8\div2\div2=2\).
It is a multiple of 2 twice.
Answer:
A store sells six-packs of soda for $3.00 a six pack. If this relationship is graphed with the number of cans of soda on the x-axis and the cost on the y-axis, what is the slope of the graph in dollars per can?
Step-by-step explanation:
Jenny has 45 tennis balls.
Sal had 20 tennis balls, but he gave 6 of them to Joe.
How many tennis balls do Jenny and Sal have now?
Answer:
45 and 14 are the correct answer
Write an equation of a line that would be parallel to y = 5x -9
Answer:
x/5+9/5=y or x+9/5=y
Step-by-step explanation:
y= 5x-9
x=5y-9
x+9=5y
x+9/5=y
Using f(x)=5x^2, identify the graph of f(x) and g(x)=2f(x)
The graph of g(x) is taller than the graph of f(x) by a factor of 2.
What is function?Function can be defined in which it relates an input to output.
The graph of f(x) = 5\(x^{2}\) is a parabola that opens upwards, with the vertex at the origin (0,0) and the axis of symmetry along the y-axis. The shape of the parabola is determined by the coefficient of \(x^{2}\), which is positive. (check attachment 1)
The graph of g(x) = 2f(x) is obtained by multiplying the output of f(x) by 2. This means that every point on the graph of f(x) is doubled in the y-direction to produce the corresponding point on the graph of g(x). (check attachment 2)
Since the shape of the parabola is not affected by the scaling factor of 2, the graph of g(x) is also a parabola that opens upwards, with the vertex at the origin (0,0) and the axis of symmetry along the y-axis. However, the y-coordinate of every point on the graph of g(x) is twice the y-coordinate of the corresponding point on the graph of f(x).
Therefore, the graph of g(x) is taller than the graph of f(x) by a factor of 2.
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the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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solve this asap
Given that <ABD= 42°, <EFD= 81° and <BCF= 60°, find the value of the unknown.
solve by using corresponding, alternate and interior angles method.
Step-by-step explanation:
angle G = 81°
angle CFG = 60°
total angle inside CFG = 180
a+81+60=180
a=39°
In DBCF
Total angle is 360
60+39+138+b=360
b=134°
hope its right :)
Two tow trucks are pulling on another truck that is stuck in the mud. Both tow trucks have 12 meter long towing straps attached to the hitch of the truck that is stuck. Tow truck #1 is pulling with a force of 2,850 Newtons of force while tow truck #2 is pulling with a force of 2,655 Newtons. The angle between the two tow trucks is 42. What is the magnitude resultant force?
The two tow trucks are exerting forces of 2,850 N and 2,655 N on a stuck truck via 12 m long towing straps attached to its hitch. The angle between the two trucks is 42. We have to determine the magnitude of the resultant force.
The formula to find the magnitude of the resultant force is given below:\(F = √(F₁² + F₂² + 2F₁F₂cosθ) where, F₁ = 2,850 NF₂ = 2,655 Nθ = 42 degrees F = √(2,850² + 2,655² + 2(2,850)(2,655)cos(42))F = 4,325 N (rounded off to th\)e nearest whole number) Hence, the magnitude of the resultant force is 4,325 N.
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solve this pls 6+8n+2n=4n+30
Answer:
\(\huge\boxed{\sf n = 4}\)
Step-by-step explanation:
Given equation:6 + 8n + 2n = 4n + 30
Combine like terms6 + 10n = 4n + 30
Subtract 4n from both sides6 + 10n - 4n = 30
6 + 6n = 30
Subtract 6 from both sides6n = 30 - 6
6n = 24
Divide both sides by 6n = 24 / 6
n = 4\(\rule[225]{225}{2}\)
irst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per A B unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case A O a. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms. O b. We need more information before we can know how to modify the Samuelson condition. O c. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. O d. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.
Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.
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practice using linear combinations to solve systems of equations. which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x 13y
The constants that have to multiply to eliminate one variable from the system are 12 and 5.
The equations are
5x+13y = 232
12x + 7y = 218
Elimination Method
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables
Both x term and y terms, choose x terms and apply the elimination method
The coefficient of x in the first equation is 5 and 12 in the second equation
Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.
To make it the same
Prime factorization
Prime factorization is a process of writing all numbers as a product of primes.
5 = 5×1
12 = 2×2×3
LCM (5, 12 ) = 2×2×3×5 = 60
Multiply the first equation by 12 and the second equation by 5
60x + 156y = 2784
60x + 35y = 1090
Subtract equation 2 from equation 1
121y = 1694
Eliminated x term
The constants that we have to multiply to eliminate one variable from the system are 12 and 5
The complete question is:
Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232
12x + 7y = 218
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2x + y = 5; (7,5)
I need to know if this is a Solution, or NOT a Solution by seeing if this ordered pair is a Solution of the equation Just substitute the x and y to see if the equation "works"... (I dont understand this, help!!)
Answer:
NOT a solution
Step-by-step explanation:
2x + y = 5; (7,5)
substitute the x and y
the value of x =7
the value of y=5
2*7 +5= 14+5 = 19
Answer:
give the guy above me brainliest plz
Step-by-step explanation:
the students of 3 sections of a class have to stand in rows each row has an equal number of students if there are 24 , 36 , and 60 students in 3 sections find the maximum number of students in each row
The maximum Number of scholars in each row is 12. This means that the scholars can be arranged in rows with an equal number of scholars, and each row can have a outside of 12 scholars.
To find the maximum number of scholars in each row, we need to determine the topmost common divisor( GCD) of the total number of scholars in each section. The GCD represents the largest number that divides all the given figures unevenly.
Given that there are 24, 36, and 60 scholars in the three sections, we can calculate the GCD as follows Step 1 List the high factors of each number 24 = 23 * 31 36 = 22 * 32 60 = 22 * 31 * 51
Step 2 Identify the common high factors among the three figures Common high factors 22 * 31 Step 3 Multiply the common high factors to find the GCD GCD = 22 * 31 = 4 * 3 = 12
thus, the maximum number of scholars in each row is 12. This means that the scholars can be arranged in rows with an equal number of scholars, and each row can have a outside of 12 scholars.
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If A is a 9x6 matrix, what is the largest possible dimension of the row space of A? If A is a 6x9 matrix, what is the largest possible dimension of the row space of A? Explain.
If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.
The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.
For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.
For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.
Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.
However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.
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Find the area of the prism 14 in. 4 in. 9in.
Answer:
504 in cubed
Step-by-step explanation:
I am assuming this is a rectangular prism, since you did not show a picture.
l x w x h
14 x 4 x 9
14 x 36
504
Can someone please help this is due soon and I don’t know how to do it I’ll give brainlest
Answer:
the explanation contains numbered sticky notes please follow them in order and i do encourage you to follow along somewhere.
merry christmas :)
x = 67,
y = 124
CAN YALL HELP ME WITH THIS ONEEE!!!!! PLZ
Answer:
b
Step-by-step explanation:
12x12
11x11
10x10
9x9
8x8
7x7
6x6
5x5
4x4
3x3
2x2
1x1
add em together equal 650
1. What are the dimensions of quality for a good and service? (6 marks)
When evaluating the quality of a good or service, there are several dimensions that are commonly considered. These dimensions provide a framework for assessing the overall quality and performance of a product or service. Here are six key dimensions of quality:
1. Performance: Performance refers to how well a product or service meets or exceeds the customer's expectations and requirements. It focuses on the primary function or purpose of the product or service and its ability to deliver the desired outcomes effectively.
2. Reliability: Reliability relates to the consistency and dependability of a product or service to perform as intended over a specified period of time. It involves the absence of failures, defects, or breakdowns, and the ability to maintain consistent performance over the product's or service's lifespan.
3. Durability: Durability is the measure of a product's expected lifespan or the ability of a service to withstand repeated use or wear without significant deterioration. It indicates the product's ability to withstand normal operating conditions and the expected frequency and intensity of use.
4. Features: Features refer to the additional characteristics or functionalities provided by a product or service beyond its basic performance. These may include extra capabilities, options, customization, or innovative elements that enhance the value and utility of the offering.
5. Aesthetics: Aesthetics encompasses the visual appeal, design, and sensory aspects of a product or service. It considers factors such as appearance, style, packaging, colors, and overall sensory experience, which can influence the customer's perception of quality.
6. Serviceability: Serviceability is the ease with which a product can be repaired, maintained, or supported. It includes aspects such as accessibility of spare parts, the availability of technical support, the speed and efficiency of repairs, and the overall customer service experience.
These six dimensions of quality provide a comprehensive framework for evaluating the quality of both goods and services, taking into account various aspects that contribute to customer satisfaction and value.
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The sun is at a focus of Earth's elliptical orbit.
a. Find the distance from the sun to the other focus.
The distance from the sun to the other focus is 5.01 × 10⁹ m.
What is the distance from the sun?
(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;
2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.
(b) To express this in terms of solar radii, we set up a ratio;
(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2
Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.
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Complete question is;
The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.
At 98°F, a certain insect chirps at a rate of 88 times per minute, and at 107°F, they chirp 151 times per minute. Write an equation in slope-intercept form that represents the situation.
The equation in slope-intercept form that represents the situation is y = 7x - 598
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
The ordered pair are ( 98, 88) and (107, 151)
Equation of line in slope-intercept form is y = mx + c
at x = 98, y =88
so that by substituting we have,
88 = 98m + c -------------------1
at x = 107, y = 151 and by substituting we have
151 = 107m + c -----------------2
subtract equation 1 from 2
63 = 9m
m = 63/9
m = 7
substitute m = 7 in equation 1
88 = 98(7) + c
c = 88 - 686c
c = -598
substitute m and c for their values equation becomes
y = 7x - 598
In conclusion, the equation in slope-intercept form is y = 7x - 598
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Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for 10 years) and has a utility function U = V1/2 (where V is the number of healthy vacation days they experience). Suppose they are not a particularly healthy family and the probability that someone will have a vacation-ruining illness (V = 0) is 20%. What is the expected value of V?
Select one:
a. 10
b. 8
c. 2
d. 0
Answer: The expected value of V can be calculated as the sum of the products of the possible values of V and their corresponding probabilities. Let's consider the three possible scenarios:
V = 0 (with probability 0.2, as given in the problem)
V > 0 but V < 10 (with probability 0.8 * (9/10), because if nobody gets sick, they will have at least 1 healthy vacation day, and if they have 1 healthy day, they can still have 9 more days of vacation)
V = 10 (with probability 0.8 * (1/10), because if nobody gets sick, they can have all 10 days of vacation)
Using the utility function, we can see that the expected value of V is:
E[V] = 0 * 0.2 + (1/2) * (0.8 * 9/10) + 10 * (0.8 * 1/10)
E[V] = 0 + 0.36 + 0.8
E[V] = 1.16
Therefore, the expected value of V is 1.16. However, since V represents the number of healthy vacation days, it must be a non-negative integer. So, the closest integer to 1.16 is 1. Therefore, the answer is c. 2.
Please help me with my classwork
Answer:(b)7m^4
Step-by-step explanation:
56m^8/8m^4
is can be said as
(7m^4 )(8m^4)/8m^4
8m^4 from both numerator and as well as denominator cancels so the final answer is 7m^4(7 m to the power 4)
the amount of sugar in billy's kitchen is directly proportional to the number of cookies he can bake. the number of cookies that billy bakes is inversely proportional to a score of his physical health (since he eats all the cookies). by what percent will billy's health score go down if his sugar resources are quadrupled?
Billy's health score go down by 75% if his sugar resources are quadrupled
Let the amount of sugar in Billy's kitchen be denoted by S and the number of cookies he can bake be denoted by C. Let his health score be denoted by H. Then we have the following relationships:
C ∝ S (directly proportional)
C ∝ 1/H (inversely proportional)
Combining these two relationships, we get:
C ∝ S/H
If S is quadrupled, then C will also quadruple according to the first relationship. However, H will decrease by some percentage x according to the second relationship. To find x, we can use the fact that C is proportional to S/H:
C = k*S/H
where k is a constant of proportionality. If S is quadrupled, then C will also quadruple, so we have:
4C = k4S/H
C = kS/(H/4)
This tells us that if S is quadrupled, then C will be divided by H/4. In other words, C/H will be divided by 4. So, the percentage decrease in H can be found as follows:
C/H → (C/H)/4 = (S/H)/(4/k) → x = 100%*(1 - 1/4) = 75%
Therefore, if Billy's sugar resources are quadrupled, his health score will go down by 75%.
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a 39 3939-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at 10 1010 meters per minute. at a certain instant, the bottom of the ladder is 36 3636 meters from the wall. what is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?
The distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.
Let's call the distance between the bottom of the ladder and the wall as "x".
At a certain instant, x = 3636 meters
The rate of change of x with respect to time is 10 meters per minute, so dx/dt = 10 m/min.
At that same instant, the height of the ladder above the ground can be expressed as
h = (3939 - x)
since the ladder is 3939 meters long
The rate of change of h with respect to time can be found using the chain rule of differentiation.
dh/dt = dh/dx * dx/dt = -10 m/min
So, at the instant when the bottom of the ladder is 3636 meters from the wall, the rate of change of the distance between the top of the ladder and the ground is -10 meters per minute. This means that the distance between the top of the ladder and the ground is decreasing at a rate of 10 meters per minute.
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Each year, a magazine compiles a list of the 400 richest Americans. As of September 19, 2012, 8 of the top 10 are as shown in the following table. Complete parts (a) through (c) below. Person Wealth ($ billions) Christy Walton and family 27.9 Warren Buffett 46.0 Charles Koch 31.0 David Koch 31.0 S. Robson Walton 26.1 Bill Gates 66.0 Jim Walton 26.8 Alice Walton 26.3 a. Find the mean. The mean is (Type an integer or decimal rounded to two decimal places as needed.) b. Find the median. The median is (Type an integer or decimal rounded to two decimal places as needed.) c. Find the mode(s). Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The mode(s) is(are) (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) OB. There is no mode.
On solving the provided question we can say that - the answer of the quadratic equation is S(x) = ( 2 ) + ( 1 ) =3 \(P(x) = ( 2 ) * ( 1 ) =2\)
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. A quadratic equation is referred to as an equation of degree two in mathematics. As a result, this function's highest exponent is 2. Y = ax2 + bx + c, where a, b, and c are integers and a must be 0, gives the typical form of a square. These are all examples of quadratic equations: y = x2 + x3 + x + 1.
S(x) = ( ) + ( ) =3
\(P(x) = ( ) * ( ) =2\)
S(x) = ( 2 ) + ( 1 ) =3
\(P(x) = ( 2 ) * ( 1 ) =2\)
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Evaluate the function f(x) = 5x2 - 7x + 3 a. f(-4) = ___________________ b. f(4) =_____________________ c. f(0)= ______________________ d. f(12)= _____________________ e. f(-12)= ___________________ f. f(-5) =____________________ g. f(-3) = ____________________ h. f(6) = _____________________ i. f(-6) = ___________________ j. f(-3) = __________________
Answer:
say what
Step-by-step explanation:you + your = answer ( ask your teacher )
The diameter of a circle is 17 ft. Find its area to the nearest whole number.
Answer:
\(\boxed{\mathtt{Area \approx 227ft^{2}}}\)
Step-by-step explanation:
\(\textsf{We are asked to find the area of a circle.}\)
\(\textsf{First, we should identify the formula for the area of a circle.}\)
\(\large\underline{\textsf{Formula:}}\)
\(\mathtt{Area = \pi (radius)^{2}}\)
\(\textsf{The radius is \underline{half} of the diameter.}\)
\(\mathtt{\frac{17}{2} = 8.5ft.}\)
\(\textsf{Let's begin solving for the area.}\)
\(\large\underline{\textsf{Substitute:}}\)
\(\mathtt{Area = \pi (8.5)^{2}}\)
\(\mathtt{Area = 72.25 \pi}\)
\(\boxed{\mathtt{Area \approx 227ft^{2}}}\)
How many fluid ounces in a tablespoon
By rewriting a relation we will see that there are 0.5 fluid ounces in a tablespoon.
How many fluid ounces are in a tablespoon?We know the relation between the different units:
1 fluid ounce = 2 tablespoons.
To see how many fluid ounces are in a tablespoon, we just need to work with the relation above and write "1 tablespoon" on the right side.
So if we take our relation:
1 fluid ounce = 2 tablespoons.
And we divide both sides by 2 then we will get:
1/2 fluid ounce = 2/2 tablespoons.
0.5 fluid ounces = 1 tablespoon.
then we can conclude that there is 0.5 fluid ounces in a tablespoon.
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A store in Wildgrove purchased an antique pull toy at a cost of $890 and marked it up 200%. Later on, Jeffrey bought the antique pull toy. If the sales tax in Wildgrove is 10%, how much did he pay in all?
Answer: Jeffery paid $ 2937 in all.
Step-by-step explanation:
Given: The cost of antique pull = $890
Mark up percentage = 200%
New price = (cost) + (Mark up percentage) x (cost)
\(=\$( 890+\dfrac{200}{100}\times890)\\\\=\$( 890+2(890))\\\\=\$2670\)
After a tax of 10% , the amount needs to be paid = New price + 10% of New price
\(=\$(2670+\dfrac{10}{100}\times2670)=\$(2670+267)\\\\=\$2937\)
Hence, Jeffery paid $ 2937 in all.
A chi-square test of independence is a one-tailed test. The reason is that Multiple Choice we are testing whether the frequencies exceed their expected values. we square the deviations, so the test statistic lies at or above zero. hypothesis tests are one-tailed tests when dealing with sample data. the chi-square distribution is positively skewed.
A chi-square test of independence is indeed a one-tailed test. The reason for this is that we are testing whether the observed frequencies of two categorical variables are significantly different from the expected frequencies.
We square the deviations between the observed and expected frequencies, and since deviations can only be positive, the test statistic always lies at or above zero. Hypothesis tests are one-tailed when dealing with sample data because we have a specific direction for our research question. In the case of a chi-square test of independence, we are interested in whether one variable is dependent on the other variable, so we have a directional hypothesis. Furthermore, the chi-square distribution is positively skewed, meaning that the majority of the distribution is on the right-hand side. This is important to consider when interpreting the results of a chi-square test.
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Rectangle PQRS is dilated about the origin to form P'Q'R'S'.
• Point P has coordinates (2, 0.5).
• Point P' has coordinates (8,2).
.
• The perimeter of PQRS is 16.
What is the perimeter of P'Q'R'S'?
A. 16
B. 24
C. 32
D. 64
The perimeter of the rectangle P'Q'R'S' is 64
What is the perimeter of P'Q'R'S'?If we let k be the dilation factor, then for any point (x, y) in PQRS and its corresponding point (x', y') in P'Q'R'S', we have:
k = distance from (0, 0) to (x', y') / distance from (0, 0) to (x, y)
To find the dilation factor, we can use the given points P and P':
k = distance from (0, 0) to (8, 2) / distance from (0, 0) to (2, 0.5)
k = √(8^2 + 2^2) / √(2^2 + 0.5^2)
k = √(68) / √(4.25)
k = 4
Given that
The perimeter of PQRS is 16.
So, we have
Perimeter of (PQRS)' = 16 * 4
Evaluate
Perimeter of (PQRS)' = 64
Hence, the perimeter of (PQRS)' is 64
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