The given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
What is the Taguchi loss function?The Japanese business statistician Genichi Taguchi created the Taguchi loss function, a graphical representation of loss, to describe a phenomenon that affects the value of a company's products.
It clarified the idea that quality does not suddenly decline when, for example, a machinist exceeds a strict plan tolerance, which was praised by Dr. W. Edwards Deming, the business guru of the e American quality movement in the 1980s.
Instead, the value of the "loss" grows over time as the deviation from the anticipated condition rises.
This was seen as a milestone in describing the quality and contributed to the growth of the continuous improvement movement.
According to the Taguchi loss function, as process variation drifts further and further from the mean, the loss to the organization grows.
Therefore, the given statement "A Taguchi loss function suggests that regardless of how much the output deviates from the process mean on either side, the loss to the company remains constant" is TRUE.
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In the diagram below determine the length of side b if cosθ=4/7.
Answer:
b = 8
Step-by-step explanation:
cosΘ = 4/7 = adjacent/hypotenuse
Therefore:
4/7 = b/14
7b = 56
b = 56/7 = 8
Find all x-intercepts and y-intercepts of the graph of the function.
f(x)=3x³-12x²-15x
Answer:
To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.
X-intercepts:
The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:
3x³-12x²-15x = 0
This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.
Y-intercepts:
The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:
f(0) = 3(0)³ - 12(0)² - 15(0) = 0
So the y-intercept of the graph is at the point (0,0)
In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)
Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.
Step-by-step explanation:
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 4), (2, 8), (3, 16), (4, 32)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
do not copy and paste from a different question because those aren't right.
Answer:
A) Exponential function
[tex]\textsf{B)} \quad y = 2(2)^x[/tex]
C) 12
Step-by-step explanation:
Given points:
(1, 4)(2, 8)(3, 16)(4, 32)Part AIn a linear function, the y-values have equal differences.
In an exponential function, the y-values have equal ratios.
From inspection of the given points, we can see that y doubles each time x increases by 1 unit, therefore the data models an exponential function.
Part B[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
As the function doubles, the base is 2.
Substitute one of the points (1, 4) and b = 2 into the formula and solve for a:
[tex]\implies 4=a \cdot 2^1[/tex]
[tex]\implies 4=2a[/tex]
[tex]\implies a = 2[/tex]
Substitute the found values of a and b into the formula to create the exponential function to represent the given data:
[tex]y=2(2)^x[/tex]
Part C[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]
Station 2: (2, 8)
Station 4: (4, 32)
To determine the average rate of change between station 2 and station 4 find the average rate of change over the interval 2 ≤ x ≤ 4.
Therefore, a = 2 and b = 4:
[tex]\implies \textsf{Rate of change}=\dfrac{f(4)-f(2)}{4-2}=\dfrac{32-8}{4-2}=\dfrac{24}{2}=12[/tex]
Math 5th grade
The rule for an input/output table is output = x + 2
Answer: add 2 to the input to have the output.
Step-by-step explanation: X=The Input and you have to mulitiply the input by the positive number then add it to the original number to get the output.
a Show that Δs ABC and ADC are congruent.
b What are the consequences of this congruence?
The triangles are congruent with SAS property.
What are congruent triangles?In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.
A triangle is a closed polygon with three line segments that intersect at each of its three angles.
When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.
Given question shows ΔABC and ΔADC
AD is parallel to AB,
AD = AB (equal sides)
∠DAC equal to ∠BAC
∠DAC = ∠BAC (angle equal)
and AC is common
AC =AC common side
so ΔABC ≅ ΔADC
by SAS (side angle side) property
B: since both triangles are congruent,
so BC = DC
∠BCA = ∠DCA
and ∠B = ∠D
because of congruency.
Hence, triangles are congruent by SAS property and and all remaining angles and sides are equal.
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A hotel packed breakfast for each of the three guests. Each breakfast should have consisted of threeTypes of rolls, one each of nut, cheese and fruit rolls. The preparer wrapped each of the nine rollsand once wrapped, the rolls were indistinguishable from one another. She then randomly put threerolls in a bag for each of the guests. If the probability that each guest got one roll of each type ism/n where m and n are relatively prime integers, find the value of (m+n).
The probability that each guest got one roll of each type is 3/1, which is a fraction with a numerator of 3 and a denominator of 1. Since the numerator and denominator are relatively prime integers, the value of m + n is 3
The equation for the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers.
We can expand this equation to
m/n
= 3/1.
Since the numerator and denominator are relatively prime integers, we can solve for m + n by multiplying both sides of the equation by 1.
Multiplying both sides of the equation by 1 gives us
m + n = 3.
Therefore, the value of
m + n is 3.
Let m = numerator and n = denominator in the probability of m/n.
Given that each guest got one roll of each type, the probability is m/n.
The numerator and denominator are relatively prime integers, so m and n have no common factors.
Therefore,
m + n = 3.
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Simplify:
2√20-2√5
A.)√5-√5
B.)2
C.)2√5
D.)4√4-√5
Answer:
To simplify the expression 2√20 - 2√5, you can start by applying the rule that the square root of a product is the product of the square roots of the factors. This means that you can rewrite √(20) as √(4*5) = 2√(5).
Applying this rule, the expression simplifies to:
2√(5) - 2√(5) = 2√(5) - 2√(5) = 0
Therefore, the simplified expression is equal to 2√(5).
Step-by-step explanation:
Cool Down: Rewrite This Expression
A quadratic function is defined by the expression x² - 20x + 19.
Rewrite the expression in vertex form and give the coordinates of the vertex. Show your
reasoning.
Answer: Write properties of function:
vertex form:
vertex form:
vertex:
vertex:
Please help asap! will give 25 points. Need help with all of these questions below the graph.
We may conclude from the stated answer that: (here on the graph, we have on solving equation =[tex]x^2 + 3y^2 = > 7[/tex]
Equation: What is it?A mathematical equation is a formula that connects two assertions using the equal sign (=) to signify equivalence. A mathematical statement demonstrating the equivalence of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two sentences on each side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.
here-
Graph shows that x=2.
y = 1
[tex]x^2 + 3y^2\\7[/tex]
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
The volume of 3 cones = The volume of one cylinder.
The volume of 2 cones = The volume of one sphere.
The volume of 1 sphere = 2/3 the volume of one cylinder.
The volume of one cone = 1/3 the volume of one cylinder.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is 1/3πr²h.
We have,
Volume of a cylinder = πr²h
Volume of a cone = 1/3 πr²h
Volume of a sphere = 4/3 πr³
Now,
The radius is the same.
Height of cone and cylinder = 2r
The new volume:
Volume of a cylinder = 2πr³
Volume of a cone = 2/3 πr³
Volume of a sphere = 4/3 πr³
Thus,
Volume of 3 cones = 2πr³ = volume of one cylinder
Volume of 2 cones = 4/3 πr³ = volume of one sphere
Volume of 1 sphere = 4/3 πr³ = 2/3 x volume of a cylinder
Volume of one cone = 2/3 πr³ = 1/3 x volume of cylinder
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A journalist writes n articles and gets 200(n + 7) for each article. If he gets N52000 altogether, how many articles did he write?
Since this journalist writes n articles and gets 200(n + 7) for each article. If he gets N52000 altogether, the number of articles which he wrote is equal to 253 articles.
How to determine the number of articles?In order to determine the number of articles that was written by this journalist, we would simplify the expression and then determine the value of n as follows;
52,000 = 200(n + 7)
Opening the bracket through expansion, we have the following:
52,000 = 200n + 1,400
Subtracting 1,400 from both sides of the expression, we have the following:
52,000 - 1,400 = 200n + 1,400 - 1,400
Rearranging the expression, we have the following:
200n = 52,000 - 1,400
200n = 50,600
Dividing both sides of the expression by 200, we have the following:
n = 50,600/200
n = 253 articles.
In this context, we can reasonably infer and logically deduce that the total number of articles that was written by this journalist is equal to 253 articles.
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Use the segment to complete the
statements.
The value of x is ___
The length of in inches is ___
The length of ec in inches is ___
On solving the provided question, we can say that in the line, The value of x is 5; the length of in inches is 5; the length of ec in inches is 15
what is a line?A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line.
here,
The value of x is 5
The length of in inches is 5
The length of ec in inches is 15
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Find a 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1
A 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1, is:
f(x) = x³ + 4x² + 6x - 36
What is polynomial function?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.
we have to find third degree polynomial, so, n = 3
Since 2 is its zero ,so, x - 2 is its factor
As complex zeros occur in conjugate pairs .
So,other factors are (x + (3 + 3i)) and (x + (3 - 3i)) ,
Firstly, we find the product of these two factors:
= x² + 6x + 9 - 9i²
= x² +6x +9 - 9(-1)
= (x² +6x + 18)
Now multiply (x² +6x + 18) with (x - 2) we get f(x):
= (x² +6x + 18) (x - 2)
= x³ - 2x² + 6x² - 12x + 18x - 36
= x³ + 4x² + 6x - 36
Correct option: b
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Graph the equation below by plotting the
y-intercept and a second point on the
line. When you click Done, your line will
appear.
y = 3x - 5
Answer:
See the graph below
Step-by-step explanation:
yesterday the price of a loaf of bread at five supermarkets was 1.54, 1.69, 1.79, 1.57, and 1.71, but today each supermarket raised its price by 0.05. What is todays mean price of a loaf of bread at five supermarket?
The mean price of a loaf of bread at five supermarket is 1.71.
How to calculate the mean?From the information, yesterday the price of a loaf of bread at five supermarkets was 1.54, 1.69, 1.79, 1.57, and 1.71, but today each supermarket raised its price by 0.05.
The mean price of a loaf of bread at five supermarket will be:
(1.54 + 1.69 + 1.79 + 1.57 + 1.71) + (0.05 × 5) / 5
= 8.55 / 5
= 1.71
The mean price is 1.71.
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Chung read 5/8 of a book one day and 1/4 of the book less than this the next day. What fraction of the book did Chung read on the second day? Did he finish the book in two days?
Answer:
Yes he did finish the book on the second day as 1/4=2/8 so 5/8-2/8=3/8 so he read 5/8 on the first day and 3/8 on the second day and 5/8+3/8=8/8=1
Step-by-step explanation:
1/4=2/8 so 5/8-2/8=3/8 so he read 5/8 on the first day and 3/8 on the second day and 5/8+3/8=8/8=1
A person deposits Rs 10,000/- in a bank which offers an annual compounded interest of 9%. What is the amount he can receive after 3 years?
The amount received after 3 years is ₹12950.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Given that, principal = ₹10,000, rate of interest =9% and time period = 3 years.
Now, amount =10000(1+9/100)³
= 10000(1.09)³
= 10000×1.295
= ₹12950
Therefore, the amount is ₹12950.
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Find the smallest positive integer k such that, for every positive integer n, 6n+k is relatively prime to each of 6n+3, 6n+2, and 6n+1.
Answer:
Use Mathpapa to find your answer.
Step-by-step explanation:
It's a good, and powerful program.
(3x2-14x-5)/(x-5) long divided
Answer:
3x + 1
Step-by-step explanation:
1/5/2023
7:25PM
answer........................
3x +1
Imagine you have a whole
a) how many holes are there in a whole?____
b) how many fifths are there in a whole?____
in four wholes?____
c)how many fourths are there in a two whole?____
in five wholes?___
this is fractions btw
Answer:
a) There is only one hole in a whole.
b) There are five fifths in a whole. In four wholes, there would be 5 x 4 = 20 fifths.
c) There are eight fourths in two wholes. In five wholes, there would be 8 x 5 = 40 fourths.
Give me a harder one lol
Step-by-step explanation:
Need help with finding answer
Answer:D
Step-by-step explanation:i think
Y=-3 Y=Ax2+4x-4 In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A) -4
B) -2
C) 2
D) 4
For constant A to be -4 (option 1) the system of equations have exactly one real solution.
NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?
We have given, y=-3
y= Ax^2+4x-4
Therefore, -3= Ax^2+4x-4
or, Ax^2+4x-1=0
For second order equation of ax^2+bx+c=0 have a solution for
x= [-b± (√b^2-4ac)]/2a] [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]
For single solution b^2-4ac=0
here, Ax^2+4x-1=0
4^2 - 4a(-1)=0
16+4a=0
a= -(16)/4
a= -4
option A is correct .
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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.
B) -2
The given system of equations can be written as:
Y = A*x^2 + 4*x - 4
We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:
x = [-b +/- sqrt(b^2-4ac)]/2a
where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.
Substituting these values into the equation, we get:
x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A
Simplifying this, we get:
x = [-4 +/- sqrt(16 + 16A)]/2A
For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.
This is only true when A is equal to -2. Therefore, the correct answer is B) -2.
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The graph of an exponential function is given. Which of the following is the correct equation of the function?
a.
b.
D
-10
y-24
y = 3.5"
-5
10-
-10
5
10
C. y = 0.65*
d.
y=0.32*
The equation of an exponential function is y = a * b^x, where a and b are constants, and x is the independent variable.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. It is used to make a program easier to read, debug, and maintain. Functions are key to programming languages as they allow code to be broken into smaller, more manageable parts that can be easily reused, updated, and modified. Functions can also be used to pass data between different parts of a program.
From the graph, the equation of the function can be determined by finding the values of a and b. To do this, we need to identify two points on the graph and then calculate a and b using those points. For example, if we choose the points (0,2) and (2,8),
we can calculate a and b using the equation y = a * b^x, such that 2 = a * b^0 and 8 = a * b^2.
Using these equations, we can solve for a and b, yielding a = 2 and b = 2.
Therefore, the equation of the exponential function in the graph is y = 2 * 2^x.
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At the market, almonds cost $0.51 per ounce. How much does a bag of almonds cost if it weighs 1.6 ounces?
Answer:
A bag of almonds that weighs 1.6 ounces will cost $0.51 x 1.6 = $<<0.51*1.6=0.816>>0.816.
Step-by-step explanation:
528 students at James Madison Middle School play a sport. This is 48 % of the students in the school. How many students are in the school?
The total number of students in the school is 1100
How to determine the number of students in the schoolFrom the question, we have the following parameters that can be used in our computation:
Number of students that play a sport = 528
Proportion of students that play a sport = 48%
Using the above as a guide, we have the following:
Number of students that play a sport = Proportion of students that play a sport * number of students in the school
Substitute the known values in the above equation, so, we have the following representation
48% * number of students in the school = 528
Express as decimal
This gives
0.48 * number of students in the school = 528
Divide both sides by 0.48
number of students in the school = 528/0.48
Evaluate
number of students in the school = 1100
Hence, the students are 1100
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There are 16 city buses. There are 806 people waiting to get on a bus. How many people will not fit on a bus?
A
12 people
B
10 people
C
6 people
D
3 people
the cost price of a refrigerator is $280. find:
a). the percentage loss if it sells for $224.
b). the selling price if the profit is 15% of the cost price.
c). the new price of the refrigerator if it gives a discount if 43%.
Answer:
Read below
Step-by-step explanation:
) To find the percentage loss on the sale of the refrigerator, we need to subtract the selling price from the cost price and divide that number by the cost price. Then, multiply the result by 100% to express the answer as a percentage.
(280 - 224) / 280 * 100% = 57.14% loss
b) To find the selling price if the profit is 15% of the cost price, we need to add 15% of the cost price to the cost price.
280 + (15% * 280) = 280 + 42 = $322
c) To find the new price of the refrigerator after a 43% discount, we need to subtract 43% of the cost price from the cost price.
280 - (43% * 280) = 280 - 120.4 = $159.60
Spencer's average weekly net pay is $305.18. If he has $1,084.41 in monthly expenses, what percent of his average monthly net pay is left over for savings? (4 points)
Itiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length of the line segment shown.
On solving the provided question, we can say that -the given graph is a starlight lined .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here,
in the graphs we have been given a straight line,
so its a straight line graphs
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Which of the following did you include in your response? Check all of the boxes that apply. Use the distributive property to multiply the factors on the right side of the equation. Simplify the product by combining like terms. Show that the right side of the equation can be written exactly the same as the left side. Show that the right side of the equation simplifies to a cubed minus b cubed.
You can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²) based on the following responses:
A. Use the distributive property to multiply the factors on the right side of the equation.
B. Simplify the product by combining like terms.
C. Show that the right side of the equation can be written exactly the same as the left side.
D. Show that the right side of the equation simplifies to a cubed minus b cubed.
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
a³ – b³ = (a - b)(a² + ab + b²)
a³ – b³ = a(a² + ab + b²) - b(a² + ab + b²)
Next, we would combine like terms:
a³ – b³ = a³ + a²b + ab² - a²b - ab² - b³
a³ - b³ = a³ - b³.
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Complete Question:
Explain how you can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²)
Which of the following did you include in your response? Check all of the boxes that apply.
Use the distributive property to multiply the factors on the right side of the equation.
Simplify the product by combining like terms.
Show that the right side of the equation can be written exactly the same as the left side.
Show that the right side of the equation simplifies to a cubed minus b cubed.
