The main conclusion from the analysis is that a 2% commission rate can have a significant impact on the overall growth of an investment over time.
Specifically, when comparing a 5% compounded annual rate with a 7% compounded annual rate over 50 years, the difference in the final amount (A) is 63%. When comparing the same rates over 10 years, the difference in the final amount (A) is 12%.
To verify this, we can use the compound interest formula: A = P(1 + r)^t, where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
First, let's calculate the final amount (A) for a 5% compounded annual rate over 50 years:
A = $10,000(1 + 0.05)^50 = $10,000(1.05)^50 = $10,000(2.65892) = $26,589.20
Next, let's calculate the final amount (A) for a 7% compounded annual rate over 50 years:
A = $10,000(1 + 0.07)^50 = $10,000(1.07)^50 = $10,000(3.98107) = $39,810.70
To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:
$39,810.70 - $26,589.20 = $13,221.50
To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:
($13,221.50 / $26,589.20) * 100 = 49.86%
Now, let's calculate the final amount (A) for a 5% compounded annual rate over 10 years:
A = $10,000(1 + 0.05)^10 = $10,000(1.05)^10 = $10,000(1.63) = $16,300
Next, let's calculate the final amount (A) for a 7% compounded annual rate over 10 years:
A = $10,000(1 + 0.07)^10 = $10,000(1.07)^10 = $10,000(1.9079) = $19,079
To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:
$19,079 - $16,300 = $2,779
To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:
($2,779 / $16,300) * 100 = 17%
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what 20903 x 8748 because i do not understand and keep getting mixed up
Answer:
182859444
Step-by-step explanation:
You just have to times them together
for the following proof (of equivalence of 2 formulae) provide the justifications at each step, using the following equivalences. use the following key:
The two formulas X and Y will be known as equivalence if and only if X ↔ Y is a tautology.
Consider there to be X and Y as the two formulas. In the event that X Y is a tautology, these formulas are referred to as equivalence. If the two formulas X Y are tautologies, we can also write them as X Y and read this relation as X is equivalent to Y.
Using a truth table, We will build the truth tables for any two-statement formula using this technique, and then we will determine whether the assertions are equivalent.
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n the figure below, m∠AED=88∘, m∠AEC=61∘, and m∠BEC=24∘. If m∠BED=x∘, then what is x?
Please and thank you!!
Check the picture below.
now, if we just add that shaded part of (x-24)° to the 61°, we'll end up with the whole AED angle or 88°.
[tex](x-24)~~ + ~~61~~ = ~~88\implies x+37=88\implies x=51[/tex]
Distribute to create an equivalent expression with the fewest symbols possible.
\dfrac15(15+10k) =
5
1
(15+10k)=start fraction, 1, divided by, 5, end fraction, left parenthesis, 15, plus, 10, k, right parenthesis, equals
The expression when distributed is 3 + 2k
How to create an equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
1/5(15 + 10k)
The distribution property states that
a(b + c) = ab + ac
using the above as a guide, we have the following:
1/5(15 + 10k) = 1/5 * 15 + 1/5 * 10k
Evaluate the products
1/5(15 + 10k) = 3 + 2k
Hence, the equivalent expression is 3 + 2k
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Solve.
Morgan's school is 10 miles from his house on the same
street. If he walks down the street directly from his school
to his house he passes a park and a snack shack. The park
is 2.55 miles from the school to the and the snack shack is
3.45 miles from the park. How many miles is it from the
park to Morgan's house?
2021 Gifted on the Go
The distance between Morgan's house and the park is 7 miles.
How many miles is it from the park to Morgan's house?We know that the Morgan's house, the park, the snach shack, and the high school are on the same street.
We know that the distance between Morgan's house and the school is 10 miles.
The distance between the park and the high school is 2.55mi, the the distance between Morgan's house and the park is:
10 mi - 2.55mi = 7.45mi
And the snack shack is at 3.45 miles from the park, then we will get that the distance between Morgan's house and the snack shack is:
7.45mi - 3.45mi = 4mi
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use the following sample data to calculate the measures of central tendency and dispersion: two decimal places. 10 12 15 22 22 34 42
The measures of central tendency are Mean: 22.14, Median: 22.00, Mode: 22.00, and dispersion are Range: 32, Variance: 183.14, Standard deviation: 13.53 Interquartile range: 12.00
According to the question
The mean, median, and mode values for this collection of data are 22, 14, and 22, respectively. The median is the midway value when the data are arranged, while the mode is the value that occurs the most frequently. The mean is the average of the data set. Range = 32, Variance = 183.14, Standard deviation = 13.53, and Interquartile Range = 12.00 are the metrics of dispersion for this data set. The variance measures the spread of the data, the standard deviation is the square root of the variance, and the interquartile range is the difference between the median of the upper half and the median of the lower half of the dataset. The range is the difference between the highest and lowest values.
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A firm is engaged in producing two products A and B each unit of product A require two kg of row material and 4 labour - hrs for procecing. wheras each unit of product B requres 3 kg of row material and 3 hrs labour. evrey unit of product A requires 4 hrs pakeging and whereas B needs 3.5 hrs. every week the firm has availablity of 60 kg of row material, labor 96 hrs and 105 hrs in pakeging department
1 unit of product A sold yields $40 profit and 1unit of B sold yildes $35 profit.
a.formulate this problame as a Lpp
b.find the optimal solution
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
a. Formulating this problem as a Linear Programming Problem (LPP):
Let x be the number of units of product A produced, and y be the number of units of product B produced.
The objective function is to maximize the total profit:
Maximize z = 40x + 35y
Subject to the following constraints:
The availability of raw material: 2x + 3y ≤ 60 (kg)
The availability of labor hours: 4x + 3y ≤ 96 (hrs)
The availability of packaging hours: 4x + 3.5y ≤ 105 (hrs)
Non-negativity constraints: x ≥ 0, y ≥ 0
b. To find the optimal solution, we can use a graphical method or simplex method.
We can use the simplex algorithm to find the optimal solution by iteratively moving from one feasible solution to another until we reach the optimal solution.
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
Note: The values and solution are obtained by solving the LPP problem and the availability of resources, hence the solution might be different for different values.
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not even sure where to start with this, all help is appreciated
[tex]\sqrt{tan^2y} + \sqrt{y^2}[/tex] for y ∈ ([tex]\frac{\pi }{2},\pi[/tex])
A function is what happens even if [tex]$f(-x)=f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] and A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] .
What do you mean parity?Parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}, \frac{\pi}{2} < y < \pi$[/tex] : Even .
Defining parity
A function is what happens even if. [tex]$f(-x)=f(x)$[/tex] [tex]for all $x \in \mathbb{R}$[/tex] A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex]
[tex]$$\begin{aligned}& f(-y): \quad \sqrt{y^2}+\sqrt{\tan ^2(y)} \\& -f(y): \quad-\sqrt{\tan ^2(y)}-\sqrt{y^2}\end{aligned}$$[/tex]
Check parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}$[/tex]
Equal or equivalentness, as a trait or state. Women have battled for equal pay to males in the workplace, or the equivalent of a commodity's price in one currency to that in another.
An integer's evenness or oddness is defined by its parity. In light of the fact that both 6 and 14 are even, it can be claimed that their parities are the same, but 7 and 12 have the opposite parity (since 7 is odd and 12 is even). the state of equality, particularly the state of equal pay or status Prison guards are want pay parity with the police. Women still lack balance in many occupations, especially at the top levels.
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Write an equation for a line perpendicular to y= -5x-1 and passing through the point of (10,3)
Answer: The slope of a line perpendicular to y = -5x - 1 is 5, as the slopes are negative reciprocals of each other. To find the equation of a line passing through the point (10, 3), we can use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope of the line, and y and x are the variables representing the coordinates of a point on the line.
Plugging in the given values:
y - 3 = 5(x - 10)
Simplifying, we get:
y = 5x - 25 + 3
y = 5x - 22
So the equation of the line is y = 5x - 22
Step-by-step explanation:
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The net surface area of rectangular prism is 242.2 meters square.
What is the net surface area?A rectangular prism is a three-dimensional shape with two top and bottom faces and four lateral faces. A rectangular prism seems to be a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism seems to be a cuboid, and a cuboid and a rectangular prism both have the same cross-section.
This rectangular prism's surface area = l x b
We have provided
4 rectangular areas
A₁ = 4.3m x 10m
= 43 m²
2 rectangular areas
A₂ = 6.75m x 5.2m
= 35.1 m²
As a result, the rectangular prism's surface area is:
S.A. = 4A₁ + 2A₂
S.A. = 4(43) + 2(35.1)
= 172+ 70.2
= 242.2 meter square
As a result, the net surface area of the rectangular prism is 242.2 meters square.
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PLEASE HELP I NEED TO FINISH MY HW TODAY SO I WONT HAVE TO DO IT ON MY BDAY TOMORROW!!!
Michael took out a loan at an annual
compound interest rate of 30%.
After 2 years, he owes a total of £9126.
What was the original amount that Michael
borrowed?
Give your answer to the nearest £1.
Answer:
Start: 400
After 1 Year: 7020
Step-by-step explanation:
You will have a good b-day tmrw
HAPPY EARLY BIRTHDAY!!!!
What number gives a result of −4
when 8
is subtracted from the quotient of the number and 4
?
The number that gives a result of −4 when 8 is subtracted from the quotient of the number and 4 is: 16.
What is the Quotient of Two Numbers?The quotient of two numbers is the result obtained when one number is divided by the other. It is the number of times one number can be divided into the other. For example, if you divide 20 by 4, the quotient is 5, meaning that 4 can be divided into 20 five times. It is represented mathematically as: quotient = numerator/denominator.
Let x represent the number. Therefore, you can find this number by solving the equation:
(x/4) - 8 = -4
(x/4) = -4 + 8
x/4 = 4
x = 4 * 4 = 16
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the sum of 8 and 11 times a number
The sum of 8 and 11 times a number will be (8+11x).
What does a math sum mean?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms. The result or conclusion of adding two or more numbers or sentences is known as the sum.
Let x be the number.
The result is 11 times the number, or 11x.
The result of adding the number's multiples of 8 and 11 is 8+11x.
What is sum, for instance?The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of addends 14 and 6.
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Over what interval is the function increasing? x (x, y) −4 −8 (−4, −8) −2 −2 (−2, −2) 0 0 (0, 0) 2 −2 (2, −2) 4 −8 (4, −8)
The increasing and decreasing function is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the function f(x).
Increasing and decreasing functions are functions in calculus for which the value of f(x) increases and decreases respectively with the increase in the value of x. We can write -
Increasing Function - A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).Decreasing Function - A function f(x) is said to be decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≥ f(y).Strictly Increasing Function - A function f(x) is said to be strictly increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) < f(y).Strictly Decreasing Function - A function f(x) is said to be strictly decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) > f(y).Properties of increasing or decreasing functions If the functions f and g are increasing functions on an open interval I, then the sum of the functions f + g is also increasing on this interval.If the functions f and g are decreasing functions on an open interval I, then the sum of the functions f + g is also decreasing on this interval.If the function f is an increasing function on an open interval I, then the opposite function -f is decreasing on this interval.If the function f is a decreasing function on an open interval I, then the opposite function -f is increasing on this interval.If the function f is an increasing function on an open interval I, then the inverse function 1/f is decreasing on this interval.If the function f is a decreasing function on an open interval I, then the inverse function 1/f is increasing on this interval.If the functions f and g are increasing functions on an open interval I and f, g ≥ 0 on I, then the product of the functions fg is also increasing on this interval.If the functions f and g are decreasing functions on an open interval I and f, g ≥ 0 on I, then the product of the functions fg is also decreasing on this interval.Therefore, the increasing and decreasing function is discussed above.
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The graph of h is a translation 4 units right and 1 unit down of the graph of f(x) = x^2. Write function h in vertex form
After translation of the graph 4 unit right and 1 unit down the graph of the function h(x) = (x +4)² -1
What is translation?The translation is defined as the displacement of the geometrical shape as per the given condition in the coordinate plane.
According to the question, The graph of h is a translation of 4 units right and 1 unit down of the graph of f(x) = x^2.
Given function,
f(x) = x^2.
As per the given condition,
Graph of h is a translation of 4 units right and 1 unit down of the graph of f(x).
x translated by 4 unit right = (x +4)²
f(x) translated 1 unit down = f(x) -1
Vertex form of function h(x) = (x +4)² -1
Therefore, h(x) = (x +4)² -1 is the function After translation of the graph 4 unit right and 1 unit down
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Sarah is cycling at a speed of -8 mph. If she starts at the zero point what will her position be after 45 minutes?
Answer:
-8mph
It is not possible for Sarah to have a speed of -8 mph, as speed is a scalar quantity and cannot be negative. Speed is defined as the magnitude of velocity, which is a vector quantity that has both magnitude and direction. A negative speed would indicate that the direction of Sarah's motion is opposite to what is stated. It is likely that you meant to ask about Sarah's velocity, which could be -8 mph. But since the question does not specify her direction, it is impossible to give an accurate answer.
Step-by-step explanation:
help me will mark BRAINLIEST
The measure of angle Y is given as follows:
m < Y = 90º.
How to obtain the measure of angle y?The sum of the measures of the internal angles of a triangle is of 180º.
For the larger triangle, the measures are given as follows:
2 x 25 = 50º.x = z.Hence the measures of angles x and z are given as follows:
x + z + 50 = 180º
2x = 130
x = 130/2
x = z = 65º.
Then for the smaller triangle, the measures are:
y.25.65.Meaning that the measure of angle y is given as follows:
y + 25 + 65 = 180
y + 90 = 180
y = 90º.
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please help don't ignore :(
Answer:
Its either .5 or 5
Step-by-step explanation:
im not sure which one though lol
:)
A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold? show it in a graphhhhhh!!! THANK YOU!!!!
Answer: We can use a system of equations to solve this problem. Let x be the number of oranges sold and y be the number of apples sold. Then we know that:
x + y = 15 (the total number of fruits sold)
1x + 2y = 25 (the total cost of the fruits sold)
We can use the first equation to solve for one variable in terms of the other.
For example, we can solve for x:
x = 15 - y
Now we can substitute this expression into the second equation:
1(15 - y) + 2y = 25
15 - y + 2y = 25
3y = 10
y = 10/3 = 3.333
We can round it to 3 apples sold
So we have 3 apples and 12 oranges sold.
This can be represented in a graph with a point (12,3)
Alternatively, we can solve for y:
y = 15 - x
Now we can substitute this expression into the second equation:
1x + 2(15 - x) = 25
1x + 30 - 2x = 25
-x = -5
x = 5
So we have 5 oranges and 10 apples sold.
This can be represented in a graph with a point (5,10)
Both solutions represent the same values, the number of oranges and apples sold, but represented in a different way.
Step-by-step explanation:
The variables y and x have a proportional relationship, and y = 9 when X = 2.
What is the value of y when X = 3?
Enter
your answer as a decimal in the box.
y=
Answer:
13.5
Step-by-step explanation:
y=kx
k=y/x
k=9/2
k=4.5
y=kx
y=4.5*3
y=13.5
Área de la base
Segundo de secundaria
Los datos faltantes de los prismas rectos (áreas de base, longitudes)
A = 45 mm² A = 81 m², V = 729 m³ A = 21 cm² b = 8.696 m, A = 78.264 m²¿Cómo determinar los datos faltantes en prismas rectos?
El volumen de los prismas rectos (V), en unidades de longitud al cubo, es igual al producto de la área de la base (A), en unidades de longitud al cuadrado, y la altura (h), en unidades de longitud:
V = A · h
A continuación, determinamos los datos faltantes asociados a cada casa:
Caso 1 - Prisma recto de base hexagonal
A = V / h
A = 450 mm³ / 10 mm
A = 45 mm²
Caso 2 - Prisma recto de base cuadrada
A = l²
A = (9 m)²
A = 81 m²
V = A · l
V = (81 m²) · (9 m)
V = 729 m³
Caso 3 - Prisma recto de base trapezoidal
A = V / h
A = 147 cm³ / 7 cm
A = 21 cm²
Case 4 - Prisma recto de base rectangular
b = V / (h · a)
b = 900 m³ / [(11.5 m) · (9 m)]
b = 8.696 m
A = (9 m) · (8.696 m)
A = 78.264 m²
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Solve this right triangle. C = 90. (Round off the answer to the nearest whole number or degree.) a = 2, b = 3, A =
The triangle ΔABC is the right-angle triangle. Then the measure of angle ∠A is 33.7°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The triangle ΔABC is the right-angle triangle in which angle ∠C is the right angle.
Then the measure of the angle ∠A is given as,
tan ∠A = 2/3
∠A = tan⁻¹ (2/3)
∠A = 33.7°
Thus, the measure of angle ∠A is 33.7°.
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What expression is equivalent to 4/9(2n -3)
8n/9-4/3 is the equivalent expression of 4/9(2n -3)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 4/9(2n -3)
Four by nine times the 2n minus three.
n is the variable in the given expression and minus is the operator.
Apply distributive property
4/9(2n)-4/9(3)
8n/9-12/9
8n/9-4/3
Hence, 8n/9-4/3 is the equivalent expression of 4/9(2n -3)
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Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Answer:
Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Step-by-step explanation:
You're welcome
What type of transformation is shown?
Answer:
the third one.
Step-by-step explanation:
clockwise rotation of 90*
Answer:
clockwise rotation of 90 degrees
Step-by-step explanation:
Please put me as brainliest answer :)
Situation:
An archaelogist in Turkey discovers a
spear head that contains 32% of its
original amount of C-14.
N = Noe
-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Find the age of the spear head to the nearest year
Answer:
13,093 years
Step-by-step explanation:
N = N0 e -kt . Here, N = 27 % of N0 = 27/100(N0 ) , k = 0.0001, then 27/100N0 = N0 e-0.001t .
Therefore, 0.27 = e-0.001t .On taking natural logarithms of both the sides, we get - 0.001t ln e = ln 0.27 ( log ab = b log a), or, - 0.001t = -1.30933332 ( as ln e = 1).
Therefore, t = 1.30933332/ 0.0001 = 13093.33 years = 13093 years on rounding off to the nearest year.
Which of the following measures of dispersion can attain a negative value?
Mean deviation
Range
Standard deviation
None of the above
Answer: Option D is correct (None of the above)
Step-by-step explanation:
None of the above.
A measure of dispersion is a statistical technique for extracting a particular value from a dispersed series in which the amount to which different values of the series tend to deviate from one another or from the average is quantified. All dispersion measurements, from range to standard deviation, are positive.
the si (metric) unit of length, the meter, is defined as the distance between two marks on a standard metal bar
The SI unit of length is meter and it defines the length between two end points.
The term length in math is defined as the measurement or extent of something from end to end.
Here we need to find the SI unit of length.
As we all know that the SI unit of length is The meter ad the symbol m and it is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s⁻¹ where the second is defined in terms of ΔνCs.
Here the value of length is required to be measured ad it can convert a meter into various units like milliliters (mm), kilometer (km), centimeter (cm).
Complete Question:
What is the SI unit of length and elaborate the details about it.
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Find the equation of the line that passes through (-3,1) and is parallel to y=4-3x
The equation of the line that passes through (-3,1) and is parallel to y=4-3x is y = -3x -8.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
An equation y = 4 - 3x
The slope of a line that is parallel to y = 4 - 3x is,
= -3
The equation of the line that passes through (-3,1) and is parallel to y=4-3x,
y - 1 = -3(x + 3)
y - 1 = -3x -9
y = -3x -8
Therefore, y = -3x -8 is the required equation.
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The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H_0:p=0.08H0:p=0.08 versus H_a:p\ne0.08Ha:p=0.08 at the significance level of \alpha=0.08α=0.08 .The p-value of the test was 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion?
The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
Given information:
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.
The director tested the hypotheses H.
p=0.08
[tex]\alpha =\\[/tex]0.05
p-value of of the test is found to be 0.03 which is smaller than the significance level of [tex]\alpha =0.05\\[/tex]
Now, for smaller value of p-value, the null hypothesis is ignored.
Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
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The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
Given information:
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.
The director tested the hypotheses H.
p=0.08
α =0.05
p-value of of the test is found to be 0.03 which is smaller than the significance level of α =0.05
Now, for smaller value of p-value, the null hypothesis is ignored.
Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.
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