Page < > of 20 - ZOOM Problem 18. (Adapted from Lyryx Calculus) Let f(1) = 12 + 3x + 2. a) Approximate the area under f(x) from 1 = 0 to 2 = 2 using 4 subdivisions and the Left-Hand Rule. b) Approximate the area under f(x) from 1-0 to 1-2 using 4 subdivisions and the Right-lland Rule c) Given your answers to parts a) and b), what do you think the true area under f(x) from 0 to 4 is? Explain your reasoning,
Answers
Using the Left-Hand Rule with four subdivisions, the approximate area under f(x) from x=1 to x=2 is 3.1875. Using the Right-Hand Rule with four subdivisions, the approximate area under f(x) from x=1 to x=2 is 3.65625. Since the approximation is not very accurate, it's likely that the true area under f(x) from x=0 to x=4 is somewhere between the 6.84375 or two values obtained by the Left-Hand and Right-Hand Rules.
To approximate the area under f(x) from 1 to 2 using 4 subdivisions and the Left-Hand Rule, we first need to find the width of each subdivision
width = (2 - 1) / 4 = 0.25
Then we can use the Left-Hand Rule formula
∑f(x)Δx = width[f(1) + f(1.25) + f(1.5) + f(1.75)]
Plugging in the values, we get
∑f(x)Δx = 0.25[12 + 3(1.25) + 2 + 3(1.5) + 2 + 3(1.75) + 2]
∑f(x)Δx = 3.1875
Therefore, the approximate area under f(x) from 1 to 2 using 4 subdivisions and the Left-Hand Rule is 3.1875.
To approximate the area under f(x) from 1 to 2 using 4 subdivisions and the Right-Hand Rule, we use a similar approach
∑f(x)Δx = width[f(1.25) + f(1.5) + f(1.75) + f(2)]
Plugging in the values, we get
∑f(x)Δx = 0.25[3(1.25) + 2 + 3(1.5) + 2 + 3(1.75) + 2 + 3(2) + 2]
∑f(x)Δx = 3.65625
Therefore, the approximate area under f(x) from 1 to 2 using 4 subdivisions and the Right-Hand Rule is 3.65625.
To estimate the true area under f(x) from 0 to 4, we can add up the approximate areas under f(x) from 1 to 2 using the Left-Hand Rule and from 2 to 4 using the Right-Hand Rule
true area ≈ 3.1875 + 3.65625 = 6.84375
This is only an estimate, but we can be reasonably confident that the true area is close to 6.84375 because using more subdivisions and a different rule for approximation would likely give a similar result.
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Related Questions
In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is
Answers
Answer:
17
Step-by-step explanation:
Look at Triangle ABC, The rays meet at line BC and they are both from the interior point A. So this means that AB=AC. This makes ABC a isosceles triangle. Using the isosceles triangle theorem, Angle B and Angle C measure is equal to each other so
\(50 + x + x = 180\)
\(50 + 2x = 180\)
\(2x = 130\)
\(x = 65\)
This means angle b and C of the triangle ABC measure is 65.
External bisector bisect a figure that it makes the original angle split into half that they are equal to each other.
This means the angle below Angle B and angle C measure is 32.5. We can find the measure of Angle B and C in triangle BOC. This is a isosceles triangle as well so
\(32.5 + 65 + x = 180\)
\(98.5 + x = 180\)
\(x = 81.5\)
Angle C is 81.5 as well so
\(81.5 + 81.5 = 163\)
Find angle o
\(180 - 163 = 17\)
what is the value of x ?
Answers
Answer:
B). 55
Step-by-step explanation:
125 degree angle and angle x are supplementary.
the smith family has $4$ cats and $3$ dogs. in how many ways can these $7$ pets be placed in a row of $7$ chairs such that at least $2$ cats are next to each other?
Answers
There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.
Arrangement of entities can be done using permutation and combination in mathematics.
Consider the distributions where 2 cats are not next to each other as
C D C D C D C.
There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144
There are a total of 7!=5040 possible ways to seat both cats and dogs.
At least 2 cats seat together= All possible arrangements- None of the cat seat together.
Thus the number of seatings where at least 2 cats are adjacent is
5040-144 = 4896
So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.
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Which equation most likely describes the relation in the following table?
2 3 4 5
y 4 5 6 7
KA
X
O y = 2x
Oy--2-x
Oy=x+2
0y=x-2
Answers
Answer:
y = x + 2
Step-by-step explanation:
Each y value is 2 greater than the x value
Which of the green triangles is a reflection of the blue triangle? a Triangle D b Triangle B c Triangle C d Triangle A e None
Answers
Answer:
Triangle A
Step-by-step explanation:
Answer:
a
a
Step-by-step explanation:
a
What is the z score of 0.10?
Answers
Answer:
Z (0.10) = 1.282 (the Z-score which has 0.10 to the right, and 0.4000 between 0 and it). As a shorthand notation, the () are usually dropped, and the probability written as a subscript.
Step-by-step explanation:
hope this helped you if it did plz mark brainliest
In mrs.smiths class every time you turn in 10 assignments you earn 1 homework pass.Write 3 equivalent ratios if turned in assignments.
Thanks!
Answers
Answer:
Step-by-step explanation:
For every 10 assignments you get 1 homework pass. So you would multiply them by two and up more.
So here's some of your answers:
10:1
20:2
30:3
40:4
50:5
60:6
70:7
80:8
90:9
100:10
You would just continue this pattern.
if line M is parallel to line and, in the slope of M is -5/7, what is the slope of line end? Your denominator must be positive
(easy question, easy points)
Answers
Answer:
7/5
Step-by-step explanation:
Everything is positive as I explained,
the answer of the reverse reciprocal is 7/5 because 7/5 is parallel to -5/7 so they are perpendicular to each other.
Graph the line 2y-6x+4=0 on Tell me the slope and y-intercept
sloper
y intercept=
Blank 1:
Blank 2:
Answers
Answer:
Slope: 3
Y-intercept: (0, -2)
Step-by-step explanation:
Concept 9.5: Find x Assume that segments that appear to be tangent are tangent.
Answers
Answer:
x = 2
Step-by-step explanation:
Here's your solution
=> we know that tangents from a point to a common circle are equal
=> so, ST = SU
=> 7x - 3 = 5x + 1
=> 7x - 5x = 1 + 3
=> 2x = 4
=> x = 4/2
=> x = 2
hope it helps
Answer:
X will be 2
Step-by-step explanation:
ST=SU
7x-3=5x+1
2x=3+1
2x=4
x=4/2
x=2
hope it helps....
have a great day!!!
a. A = {men with good set of teeth} empty or non empty?
Answers
Answer:
de choices i see are matcheing up to A not sure tho could be C
Step-by-step explanation:
codeine
(›)
Which is more, 1 tablespoon or 2 teaspoons?
Answers
Answer: 1 tablespoon
Step-by-step explanation:
A forecasting method has produced the following over the past five months. What is the mean absolute deviation? 3. 6 3.8 3.2. \( 3.4 \) \( 3.0 \)
Answers
The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.
The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:
1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.
2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.
3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.
So, the mean absolute deviation for the given dataset is approximately 0.996.
The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.
The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.
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The circumference of a circle is 6.28 meters. What is the circle's radius?
C = 6.28 m
Answers
Using the scale factor, what is the value of x?
X=
Answers
X= 9
Answer:
9
Step-by-step explanation:
QR- 2(9-3)=
2(6)=12
MP- 9+5=14
QRS=MNP
12/8, 15/10, 21/14= 3/1
Scale Factor is 3:1 or 3 to 1
Which statement best explains the relationship between
lines AB and CD?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative
reciprocals.
They are not parallel because their slopes are not
equal.
They are not parallel because their slopes are
negative reciprocals.
Answers
A- they are parallel because they have equal slopes.
PLEASE NO LINKS AND NO NEGATIVITY
Answers
Explanation: The order of operations is distributive property so think of it as
(1/2 • 8) - (1/2 • 4g) Also just think of dodging 8 and 4 by two since 1/2 in a number format is .5 and 8 mutuales by .5 is 4 and 4 is 2.
Hope this helps!
A jet goes 119 miles at a speed of 240 mph.
Answers
Answer:
0.495 hours
Step-by-step explanation:
assuming asking for how long it takes the jet
240mi/hr = 119mi / time
119mi/(240mi/hr) = 0.495 hours
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n 16) with the following results:
Regression Statistics
Multiple R 0.802
R Square 0.643
Adjusted R Square 0.618
Standard Error SYX 0.9224
Observations 16
Answers
There is a moderately strong positive correlation between the company's sales and industry sales.
The statistical results from the regression analysis indicate that there is a multiple R value of 0.802. This value represents the correlation coefficient, which measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient suggests a moderately strong positive correlation between the company's sales and industry sales. Additionally, the R-squared value is 0.643, which indicates that approximately 64.3% of the variability in the company's sales can be explained by the variability in industry sales. This suggests that industry sales have a significant influence on the company's sales performance. Furthermore, the adjusted R-squared value is 0.618, which takes into account the number of variables and observations in the regression analysis. It provides a more accurate measure of the model's goodness of fit. Finally, the standard error SYX is 0.9224, which represents the average distance between the actual company sales data and the predicted values based on the regression model. A lower standard error indicates a better fit of the model to the data. Overall, based on the given statistics, it can be concluded that there is a moderately strong positive correlation between the company's sales and industry sales, and industry sales significantly influence the company's sales performance.
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The mean test score of 28 students is 72.
A student joins the class and the mean becomes 71.
Find the test score of the student who joined the class.
Test score =
Answers
Answer:
test score of new student = 43
Step-by-step explanation:
28 x 72 = 2016 (total points class scored)
29 x 71 = 2059 (total points class scored after student joined)
2059 - 2016 = 43
The test score of the student who joined the class is 43.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The mean test score of 28 students is 72.
A student joins the class and the mean becomes 71.
We have to find the test score of the student who joined the class.
28 x 72 = 2016
29 x 71 = 2059 (total points class scored after student joined)
The difference between 2016 and 2059 is the test score of new student.
2059 - 2016 = 43
Hence, the test score of the student who joined the class is 43.
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answer?.......................
Answers
When we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.
The given function is \(y=2-\sqrt{x}\).
We need to find which is the graph of the given function from the options.
What are coordinates?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Take, x=0, 1, 4, 9, 16, 25, 36,....
Now, when x=0, y=2.
When x=1, y=1.
When x=4, y=0.
When x=9, y=-1
So, when we mark the coordinates (0, 2), (1, 1), (x, 0), (9, -1) on graph we obtain option C.
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Find (13x−3)+(−34x−5)
Answers
Answer: -21x-8
Step-by-step explanation:
Combine the like terms
Sketch the line 4x+3y=11
Answers
sketch of the line 4x + 3y = 11, slope (-4/3), y-intercept of the line y = 11/3
Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:
3y = -4x + 11
y = (-4/3)x + 11/3
Step 2: Identify the slope and y-intercept:
From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.
Step 3: Plot the y-intercept:
On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.
Step 4: Use the slope to find additional points:
Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.
Step 5: Connect the points:
Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.
The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.
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=
The line y = 4x + 3 crosses the y-axis at A.
1) What is the coordinates of point A?
Answers
Answer:
A(0,3)
Step-by-step explanation:
the line crosses y-axis so its x-coordinates must be zero,
so we subistitute by x=0 in the equation of the line, from this we get y=3
then the coordinates of point A will be (0,3)
can i get the answer?
Answers
Area is the inside, for rectangles that’s found by multiplying the length and width, which is 12 x 16, which is 192. For triangles that’s found by multiplying one half times the base times the height, which is 1/2 x 18 x 3, which is 27.
The population proportion for a certain characteristic is 0.48. In a sample of
100 people, 45 had that characteristic.
Which equation correctly describes the point estimate?
Answers
Answer:
the answer is ^p=0.45 I just took the test
you play a game 5 times. the results of the plays are probabilistically independent, and on each play, your probability of winning, p(w), is 0.4, and your probability of losing, p(l), is 0.6. what is the probability of the sequence w, w, l, l, w?
Answers
The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².
Given data;
Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.
To get the probability of the sequence W, W, L, L, W.
Now,
As the results are probabilistically independent,
The probability of the sequence is;
→ [(P(W)]³ + [(P(L)]²
→ (0.4)³ + (0.6)²
Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².
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I need help asap!
add steps pleasee
Answers
a. The numbers are 23 and -6.
b. The numbers are 22 /3 and - 20 / 3.
How to find the numbers described?The sum of two numbers is 17 and there difference is 29. Therefore, let's find the two numbers as follows:
let the two numbers be x and y
Therefore,
x + y = 17
x - y = 29
add the equations
2x = 46
x = 46 / 2
x = 23
Therefore, let's find y
y = 17 - 23
y = -6
Therefore, the numbers are 23 and -6
b.
The sum of a number and twice a greater number is 8. The sum of the greater number and twice the lesser number is -6.
Therefore, let's find the numbers as follows:
x + 2y = 8
y + 2x = -6
Hence,
x + 2y = 8
2x + y = -6
multiply equation(ii) by 2
2x + 4y = 16
2x + y = -6
subtract the equations
3y = 22
y = 22 / 3
Let's find x
x = 8 - 2(22 / 3)
x = 8 - 44 / 3
x = 24 - 44/ 3
x = - 20 / 3
Therefore, the numbers are 22 / 3 and - 20 / 3
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Last Tuesday was silly hat day at Aaron's school. 64 students wore a silly hat and 36 students did not. What percentage of the students wore a silly hat?
Answers
The percentage of the students who wore a silly hat is 64 %.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Last Tuesday was a silly hat day at Aaron's school. 64 students wore a silly hats and 36 students did not.
We have to determine the percentage of the students who wore a silly hat
The total number of students = 64 students wore silly hats and 36 students did not.
The total number of students = 64 + 36 = 100
We have to determine the percentage of the students who wore a silly hat
The percentage of the students wore a silly hat = (64/ 100) × 100
The percentage of the students wore a silly hat = 0.64 × 100
The percentage of the students wore a silly hat = 64 %
Thus, the percentage of students who wore silly hats is 64 %.
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suppose a is a set with m elements and b is a set with n elements. a. how many relations are there from a to b? explain. b. how many functions are there from a to b? explain. c. what fraction of the relations from a to b are functions?
Answers
a)There are \(2^m^n\) possible relation
b)Similarly \(n^m\)
c)\(\frac{n^m}{2^m^n}\)
a)Set A has m elements and set B has n elements
Firstly determine the number of elements A*B by using the multiplication rule
Number of elements\(=A*B=m*n=mn\)
For each element, \(A*B\) we have two option
First element 2 ways
Second element 2 ways
mn element 2 ways
By using the multiplication rule
\(2*2*2......=2^m^n }\)
Then there are \(2^m^n\) possible relation
b)Similarly \(n^m\)
c)\(\frac{n^m}{2^m^n}\)
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