Answer:
i think it is 10
Step-by-step explanation:
Graph the given data set and describe what kind of model best describes the data. Then write a function that models
the data..
X y
-2,-1
-1,-2
0,-1
1,2
2,7
The linear equation that models the data based on the information is y = 2.2x + 0.6.
What is an equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
In conclusion, the linear equation that models the data based on the information is y = 2.2x + 0.6.
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Use ®P to find the length of the arc. Round to the nearest hundredth.
RTS,if P Q=3 meters
To find the length of the arc RTS, we need the measure of angle ®P. Without that information, we cannot calculate the length of the arc. Additional information is needed to proceed with the calculation.
To find the length of the arc RTS using the angle ®P and the radius PQ, we need to know the value of angle ®P. However, in the given information, only the length of PQ is provided as 3 meters.
To calculate the length of the arc RTS, we need to know the measure of angle ®P in either degrees or radians. Without that information, we cannot determine the length of the arc.
Please provide the measure of angle ®P in degrees or radians so that I can assist you in finding the length of the arc RTS.
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Kindly someone tell me the area of circumference
Answer:
The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle. If a circle has a diameter of 4, its circumference is 3.14*4=12.56. If you know the radius, the diameter is twice as large.
Step-by-step explanation:
^^^
hoping it was helpful
Riley bought 4 and 2/3 apple pies. She decides she wants to serve each of her guests 1/3 of a
pie. How many guests can she serve?
guests
Answer:
14
Step-by-step explanation:
4 pies with a third each is 4 times
+
2 thirds with is 2 so 4 times 3 is 12 plus 2 is
In a class of 34 students, 19 of them are girls.
What percentage of the class are girls?
Give your answer to 1 decimal place
Step-by-step explanation:
Since we have given that
Total no. if students= 34
no. of girls = 19
so, percentage of the class are girls is given by
\( \frac{number \: of \: girls}{total \: number \: of \: students} = \frac{19}{34} \times 100 \\ = 55.88 \: percentage\)
You are given the following statements comparing k-fold cross validation (with k < n) and leave-one-out cross validation (LOOCV), used on a generalized linear model with log link and gamma error. [[Hint: You only need to know this is not a linear regression model fit by least squares.]] I. k-fold cross-validation has a computational advantage over LOOCV. II. k-fold cross-validation has an advantage over LOOCV in bias reduction. III. k-fold cross-validation has an advantage over LOOCV in variance reduction. Determine which of the above statements are true. No explanation needed.
(A) None are true.
(B) I and II only
(C) I and III only
(D) II and III only
(E) The correct answer is not given by (A), (B), (C), or (D)
Only options I and III are (C)'s correct responses.
I. k-fold cross-validation requires fitting the model k times, whereas LOOCV requires fitting the model n times. Since k > n, k-fold cross-validation is more efficient computationally than LOOCV.
II. k-fold cross-validation has an advantage over LOOCV in bias reduction since each training set is a random sample of the data and tends to reduce bias.
III. LOOCV has an advantage over k-fold cross-validation in variance reduction since LOOCV uses almost all the data to fit the model for each test observation, resulting in lower variance in the test error estimate. In contrast, k-fold cross-validation uses only a subset of the data for each training set, which can lead to higher variance in the test error estimate.
In conclusion, assertions I and III are valid, and the proper response is (C) I and III alone.
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calculate the surface area of the square pyramid below. SA= blank in^2
please help me!!
Answer:
Step-by-step explanation:
ILL HELP
Answer:
gib points
Step-by-step explanation:
I need help on this problem
-10.7 + (-19.26)
(I have to show my work btw)
Answer:
-29.96
Step-by-step explanation:
You add both numbers, as both are negative, and you get the answer.
Which ratio represents the value of pi
Answer:
The answer is circumference and diameter
Step-by-step explanation:
C= πd
Which figure is described below?
The points in a plane 4 units
from pq.
A. 2 lines
B. ray
C. sphere
D. line
Answer:
A. 2 lines
Step-by-step explanation:
Just did it on Acellus
Figure constitute 2 lines.
What is a Line?A line is a part of line that is bounded by two distinct end point, and contains every point on the line is between its endpoint.
option d) 2 lines will be described in the figure
PQ is already a line . Since , a point let say R is 4 unit away from that line , then this will constitute another line which is 4unit away from PQ.
Hence , figure constitute 2 lines.
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Write 1/3 x 1/3 x 1/3 as a exponent
Answer:
1/3^3
Step-by-step explanation:
1/3 to the power of three, since you are multiplying 1/3 by itself 3 times consider 3 as your exponent
What is the angle in both radians and degrees determined by an arc of length 4π meters on a circle of radius 16 meters? NOTE: Enter the exact answers. Do not include symbols in the answer boxes. The angle, in radians, is The angle, in degrees, is
The formula to determine the angle subtended by an arc is:θ = (L/r), where θ is the angle in radians, L is the length of the arc, and r is the radius of the circle.
We are given a circle with a radius of 16 meters and an arc length of 4π meters. Therefore, we can plug in the values of L and r to obtain the angle in radians:
θ = (L/r) = (4π/16) = π/4 radians
We can convert radians to degrees using the formula:
π radians = 180 degrees
Therefore, we can convert the angle in radians to degrees as follows:
θ (in degrees) = (θ in radians) × (180/π) = (π/4) × (180/π) = 45 degrees
Hence, the angle subtended by an arc of length 4π meters on a circle of radius 16 meters is π/4 radians or 45 degrees.Conclusion:Thus, the angle, in radians, is π/4 and the angle, in degrees, is 45 degrees.
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the scores on a standardized test are normally distributed with a mean of 90 and standard deviation of 15. what test score is 0.1 standard deviations above the mean?
The test score is 91.5.
z-score:
A z-score is the number of standard deviations from the mean value of the reference population.
Here we have to find the test score.
Mean(μ) = 90
Standard deviation(б) = 15
z-score = 0.1
Formula for z-score:
z = X - μ / б
Now putting the values in the equation:
0.1 = X - 90 / 15
1.5 = X - 90
X = 91.5
Therefore the test score is 91.5.
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At the movie theatre, child admission is $5.90 and adult admission is $9.00. On Tuesday, four times as many adult tickets as child tickets were sold, for a total sales of $879.90. How many child tickets were sold that day
21 child tickets were sold that day.
Let x be the number of child tickets sold and y be the number of adult tickets sold.
The total revenue generated from the child tickets is 5.9x dollars and the total revenue generated from the adult tickets is 9y dollars,
so the total revenue generated is 5.9x + 9y dollars.
The number of adult tickets sold is four times the number of child tickets sold,
so y = 4x.
Substituting this into the previous equation gives
5.9x + 9(4x) = 879.9.
Simplifying the equation,
5.9x + 36x = 879.9,
so 41.9x = 879.9.
Solving for x,
we get x = 21.
Therefore, 21 child tickets were sold that day.
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A cone is a solid with base that is a___ A point not in the same plane as the base and all the points between them
Answer:
the base should be a circle
Step-by-step explanation:
the moon's orbit about the earth is an ellipse with the earth at one focus. if the major and minor axes of the ellipse have lengths of 474000 miles and 473000 miles respectively, what are the greatest and least distances from the earth to the moon?
The foot print on the picture are congruent . what transformation we have to use to map one of them to the other one
A- reflection and dilation
B- translation and rotation
C- reflection and translation
D- translation and dilation
The transformation we need to use to map one congruent footprint to another congruent footprint is a combination of reflection and translation so the correct answer is (C) reflection and translation.
What is the combination of transformations?To map one congruent footprint to another congruent footprint, we need to use a combination of transformations that preserve shape and size. The only transformations that do this are translations, rotations, and reflections.
Since the footprints are the same shape and size, we can rule out dilation as a possible transformation.
Additionally, the footprints are not in the same position, so we can rule out translation as the only transformation.
Therefore, the transformation we need to use to map one congruent footprint to another congruent footprint is a combination of reflection and translation. This means that the correct answer is (C) reflection and translation.
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Please help! Correct answer only!
In a raffle, one ticket out of 200 will win a $980 prize, one ticket will win a $950 prize, one ticket will win a $270 prize, and one ticket will win a $260 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " - $ 12.30
Step-by-step explanation:
Consider the steps below;
\(Total Number of Tickets - 200 Tickets,\\Tickets Entered - 1 Ticket,\\\\Proportion - 1 / 200\\\\Amount Won ( First ) = 980 Dollars,\\Amount Won ( Second ) = 950 Dollars,\\Amount Won ( Third ) = 270 Dollars,\\Amount Won ( Fourth ) = 260 Dollars\\\\Proportionality ( First ) - 1 / 200 = x / 980,\\Proportionality ( Second ) - 1 / 200 = x / 950,\\Proportionality ( Third ) - 1 / 200 = x / 270,\\Proportionality ( Fourth ) - 1 / 200 = x / 260,\\\\1 / 200 = x / 980,\\200 * x = 980,\\x = 4.90,\\\\\)
\(1 / 200 = x / 950,\\200 * x = 950,\\x = 4.75,\\\\1 / 200 = x / 270,\\200 * x = 270,\\x = 1.35,\\\\1 / 200 = x / 260,\\200 * x = 260,\\x = 1.3\)
\(Conclusion ; " Expected Payoff " = 4.90 + 4.75 + 1.35 + 1.3 = 12.30\)
is the point below which a specified percentage of the observations fall.
In mathematics, the point below which a specified percentage of the observations fall is commonly referred to as the percentile.
A percentile is a measure that indicates the relative position of a particular value within a dataset.
For example, if a value is at the 80th percentile, it means that 80% of the observations in the dataset are below that value, and only 20% of the observations are above it.
Percentiles are often used to analyze and understand the distribution of data, especially in fields such as statistics, probability, and data analysis. They provide insights into how individual data points compare to the overall dataset and help identify outliers or extreme values.
A percentile is a statistical measure that indicates the relative standing of a particular value within a dataset. It represents the point below which a specified percentage of the observations or data points fall. Percentiles are primarily used to understand the distribution of data and analyze how individual values compare to the overall dataset.
To calculate a percentile, the dataset is arranged in ascending order, from the smallest value to the largest value. The position of a specific percentile is then determined based on the percentage of data points below it. For example, the 75th percentile represents the value below which 75% of the data points fall.
Percentiles are commonly used in various fields, including statistics, probability, and data analysis. They provide valuable insights into the spread, variability, and distribution of data. Here are a few key points to consider:
1. Median: The median is the 50th percentile, representing the value that divides the dataset into two equal halves. It is a measure of central tendency and provides information about the middle point of the distribution.
2. Quartiles: Quartiles divide the dataset into four equal parts. The first quartile, or the 25th percentile (Q1), represents the value below which 25% of the data points fall. The third quartile, or the 75th percentile (Q3), represents the value below which 75% of the data points fall. The difference between Q3 and Q1 is known as the interquartile range (IQR) and provides insights into the spread of the middle 50% of the data.
3. Percentile Ranks: Percentile ranks indicate the percentage of data points that are below a specific value. For example, if a student scores in the 80th percentile on a standardized test, it means they performed better than 80% of the test-takers.
4. Outliers: Percentiles can be useful in identifying outliers, which are data points that significantly deviate from the rest of the dataset. Extremely high or low percentiles may indicate unusual or extreme values that warrant further investigation.
5. Normal Distribution: In a normal distribution, the 50th percentile (median) coincides with the mean and mode, and specific percentiles have known standard deviations from the mean (e.g., the 68-95-99.7 rule).
Percentiles are versatile tools for summarizing and analyzing data, providing valuable insights into the distribution and relative positions of individual values. They enable comparisons and help make informed decisions based on the characteristics of a dataset.
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PLEASE PLEASE HELP REALLY QUICK❤️❤️
Answer:
Sorry
Step-by-step explanation:
Sorry I don't know the answer because I haven't learned this yet. Hope you get your answer!
2) Answer the following optimization problems systematically: d. Find the radius and height of the right circular cylinder of largest volume that can be inscribed in a right circular cone with radius 4 cm and height 3 cm.
The radius and height of the right circular cylinder of largest volume inscribed in a right circular cone with radius 4 cm and height 3 cm are approximately 2.667 cm and 1.333 cm, respectively.
1. Let r and h be the radius and height of the cylinder.
2. Use similar triangles: r/R = h/H, where R and H are the radius and height of the cone (4 cm and 3 cm).
3. Obtain the expression for the volume of the cylinder: V = πr²h.
4. Substitute the ratio from step 2: V = π(r³/3).
5. Differentiate the volume function with respect to r: dV/dr = πr².
6. Set dV/dr to 0 and solve for r: r = 2.667 cm.
7. Substitute r back into the ratio from step 2: h = 1.333 cm.
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SOLVE FOR X ANSWER IN FRACTION FORM I DONT NEED TO SHOW WORK
Answer:
\(x=\frac{27}{2}\:\text{or}\:13.5\)
Step-by-step explanation:
Both triangles are shown are similar. Therefore, the ratio of their sides will be maintained. We can then set up the following proportion:
\(\frac{2}{11}=\frac{3}{3+x},\\2(3+x)=33,\\(3+x)=16.5,\\x=\boxed{13.5\text{ or }\frac{27}{2}}\)
You have a rectangular space where you plan to create an obstacle course for an animal. The area of the rectangular space is represented by the expression 10x2 − 6x. The width of the rectangular space is represented by the expression 2x.
Part A: Write an expression to represent the length of the rectangular space. Then simplify your expression. Show all your work. (6 points)
Part B: Prove that your answer in part A is correct by multiplying the length and the width of the rectangle. Show all your work. (4 points)
The required expression for part A ⇒ 2x(3x-8)
The required expression for part B ⇒2x(3x-8)
Part A:
The area of the rectangular space is given by the expression 6x²-16x, which is equal to the length times the width. We are given that the width of the rectangular space is 2x.
Therefore, we can write:
length x width = area
length x (2x) = 6x²-16x
length = (6x²-16x) / (2x)
Simplify the expression for length by factoring out 2x from the numerator:
length = 2x(3x-8)
So the expression for the length of the rectangular space is 2x(3x-8).
Part B:
To prove that our expression for the length is correct, we can multiply it by the width and show that we get the original expression for the area:
length x width = 2x(3x-8) x (2x)
= 4x²(3x-8)
= 12x³ - 32x²
Now we can compare this result with the original expression for the area, which is 6x²-16x.
We can simplify the original expression by factoring out 2x:
6x²-16x = 2x(3x-8)
We can see that the expression we obtained by multiplying the length and the width is equivalent to the original expression for the area, so our expression for the length is correct.
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if the sum of a number and two is doubled, the result is nine less than the number. find the number
I need help with a equation
The solution of the expression (√13)² is 13.
How to solve expression?The law of square root and exponentials can be used to solve the expression as follows:
(√13)²
Therefore,
\(\sqrt{x} = x^{\frac{1}{2} }\)
Therefore,
(√13)² = \((13^{\frac{1}{2} } )^{2}\)
Using the law of indices, we have to multiply the exponentials.
Therefore,
\((13^{\frac{1}{2} } )^{2} = 13^{\frac{1}{2}(2) }\)
Finally,
\((13^{\frac{1}{2} } )^{2} = 13^{\frac{1}{2}(2) } = 13\)
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Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $85,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 9%, whereas the Blue Chip fund has a projected annual return of 8%. The investment advisor requires that at most $55,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be
6(10) + 4(10) = 100.
Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 410.
(a)
Formulate a linear programming model to find the best investment strategy for this client. (Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.)
Max _______________ s.t.
Available investment funds
Maximum investment in the internet fund
Maximum risk for a moderate investor
N, B ≥ 0
(b)
Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio (in dollars) for this client?
internet fund$
blue chip fund$
What is the annual return (in dollars) for the portfolio?
$
(b)
Suppose that a second client with $85,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 450. What is the recommended investment portfolio (in dollars) for this aggressive investor?
internet fund$
blue chip fund$
(d)
Suppose that a third client with $85,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 320. Develop the recommended investment portfolio (in dollars) for the conservative investor.
internet fund$
blue chip fund$
A. N, B ≥ 0 (non-negativity constraint)
B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
C. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(a)
The linear programming model to find the best investment strategy for this client can be formulated as follows:
Maximize: 0.09N + 0.08B
Subject to:
N + B ≤ 85 (maximum investment of $85,000)
N ≤ 55 (maximum investment of $55,000 in the internet fund)
6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)
N, B ≥ 0 (non-negativity constraint)
(b)
To solve the problem using Excel Solver, you can set up the following spreadsheet model:
Cell A1: N (amount invested in the internet fund)
Cell B1: B (amount invested in the Blue Chip fund)
Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)
Constraints:
Cell A2: ≤ 85
Cell B2: ≤ 85
Cell C2: ≤ 55
Cell D2: ≤ 410
The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.
Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.
The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
(b)
For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 450
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(d)
For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 320
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
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For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to indicate the given bundle, and accurately draw the indifference curve that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis.
b) The consumers utility function is given by U(X,Y) = X1/2*Y1/2, and the given bundle is X = 1 and Y = 16.
i) MRS = __________________________________________________
ii) For this graph, scale each axis up to 16. Do not go above 16 on either axis. Draw your graph in this space:
MRS =\(\frac{\partial U/\partial X}{\partial U/\partial Y} = \frac{2}{1/4} = 8\) It is a rectangular hyperbola whose slope becomes steep as we move down the curve.
Utility function is
\(U(X,Y) = X1/2Y1/2.\) The given bundle is X=1 and Y=16.
i) Marginal Rate of Substitution (MRS) is:
\(\frac{\partial U/\partial X}{\partial U/\partial Y} Substitute the given bundle X = 1 and Y = 16 into\)
\(U(X,Y) = X1/2Y1/2:U(X,Y) = (1)1/2(16)1/2U(X,Y) = 4\)
Taking partial derivatives,
\(\frac{\partial U}{\partial X} = \frac{1}{2}X^{-1/2}Y^{1/2}\frac{\partial U}{\partial Y} = \frac{1}{2}X^{1/2}Y^{-1/2}\)
Substitute the given bundle X = 1 and Y = 16 into the partial derivatives above,
\(\frac{\partial U}{\partial X} = \frac{1}{2}(1)^{-1/2}(16)^{1/2} = 2\frac{\partial U}{\partial Y} = \frac{1}{2}(1)^{1/2}(16)^{-1/2} = \frac{1}{4}\)
Now, the MRS at (1, 16) is,
\(MRS = \frac{\partial U/\partial X}{\partial U/\partial Y} = \frac{2}{1/4} = 8\)
ii) The given bundle is (1, 16).
For the given utility function, the indifference curve passing through (1,16) can be calculated as below:
\(U(X,Y) = X^{1/2}Y^{1/2}lug in U(X,Y) = 4, and solve for Y,4 = X^{1/2}Y^{1/2}16 = Y\\)
therefore\(U(X, 16) = X^{1/2}(16)^{1/2}\)
Indifference curve passing through (1, 16) is\(X^(1/2)(16)^(1/2) = 16.\)
It is a rectangular hyperbola whose slope becomes steep as we move down the curve.
To draw the graph, the scale of each axis is up to 16. The graph is:
The given bundle (1,16) is marked on the graph with a point. The IC curve is the rectangular hyperbola
\(X^(1/2)(16)^(1/2) = 16.\) The axis of good X and good Y are also marked. The scale of each axis is up to 16.
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11 Finding a difference quotient for a linear or quadratic function V Find the difference quotient f(x)=-3x²-2x+5 Simplify your answer as much as possible. f(x +h)-f(x) h f(x+h)-f(x) h = ( where h#0,
The difference quotient for the given function is 9 -2/h.
The difference quotient for the given function can be calculated as:
[f(x+h) - f(x)]/h
= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h
= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h
= (6xh + 3h² - 2h)/h
= (6x + 3h -2)/h
Simplifying the expression further, we get:
(6x + 3h -2)/h = 6 + 3h/h -2/h
= 6 + 3 -2/h
= 9-2/h
Therefore, the difference quotient for the given function is 9 -2/h.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.
f(x)=3x² -2x+5. Simplify your answer as much as possible.
Un concensario de coches rebaja a 16000 un vehiculo que valia 18300 en que porcentaje lo han rebajado?
As a car dealer lowers a vehicle that was worth 18300 to 16000 by applying the formula of change in percentage we get that by 12.569 percentage (approximately) the price gets lowered .
The initial price of the car is set at P = 18300 (units)
The price after lowering drom P becomes A= 16000 (units)
Hence the change in price (or value) of the car, that is the price of the car is lowered by, C = (initial price - lowered price) = (P - A) = (18300 - 16000) units = 2300 units.
The formula for calculating percentage change is given as follows,
Change in percentage = [(Change in value)/ ( Initial value) ]*100
⇒Change in percentage = (C/ P)*100
⇒ Change in percentage =( 2300/ 18300)*100 = 12.569% (approximately)
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question 1.7 construct a histogram and compare to above estimates, are they consistent? what is your best estimate of the random modiifer based on the above, without examining the value?
To construct a histogram of the estimates and compare it to the above estimates, follow these steps:
1. Compile the data and organize it into groups or bins.
2. Assign each group a height or frequency, usually the number of occurrences in the group.
3. Represent each group by drawing a bar with the corresponding height.
4. Connect the tops of the bars to form a histogram.
Comparing the histogram to the above estimates, if the histogram is similar in shape and spread, then the estimates are consistent.
The best estimate of the random modifier without examining the value is the mode of the data, which is the value that occurs most often.
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