The first three taylor polynomials of the function f(x) = e⁻ˣ at x = 0 is 1, 1 - x and 1 - x + x²/ 2.
Taylor polynomial of degree n for a function f(x) which is infinitely differentiable at a is
f(a) + f'(a)×(x - a)/ 1! + f''(a)×(x - a)²/ 2! + ... + (f⁽ⁿ⁾(a)×(x - a)ⁿ/ n! = ∑(i = 1 to n)(f⁽i⁾(a)×(x - a)^{i}/ i!)
where f⁽i⁾(a) denotes the ith derivative of f(x) at a
The first, second and nth derivative of the function f(x) = e⁻ˣ is
f'(x) = -e⁻ˣ
f''(x) = e⁻ˣ
f⁽ⁿ⁾x = (-1)ⁿe⁻ˣ
First Taylor polynomial, n = 1, here f(x) = e⁻ˣ and a = 0.
P₁(x) = f(0) = e⁻⁰ = 1
Similarly
P₂(x) = f(0) + f'(0)(x - 0)/ 1!
P₂(x) = 1 + -1×e⁻⁰×(x - 0)
P₂(x) = 1 - x
P₃(x) = f(0) + f'(0)(x - 0)/ 1! + f''(0)(x - 0)²/ 2!
P₃(x) = 1 - x + e⁻⁰×(x - 0)²/ 2
P₃(x) = 1 - x + x²/ 2
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Plot the data points into the calculator. resize the window to fit the data and use the power regression function. what is the power regression equation for these data points? round to the nearest hundredth. y = 71.59x0.49 y = 72.49x0.50 y = 73.48x0.51 y = 72.34x0.50
Answer: B
Step-by-step explanation:
y = 72.49x0.50
Answer:
B
Step-by-step explanation:
edge2023 and because i said so ;)
Which of the following choices correctly names <1 and <8?
alternate interior angles corresponding angles
alternate exterior angles
vertical angles
Answer:B
Step-by-step explanation:
I want to know how to work out this question (question 20)
The value of c that satisfies the Mean Value Theorem for this problem are given as follows:
A. [tex]4\sqrt{3}[/tex]
How to obtain the value or values of c?The function for this problem is given as follows:
f(x) = x + 48/x.
The bounds of the interval are given as follows:
a = 3, b = 16.
The derivative of the function is given as follows:
f'(x) = 1 - 48/x².
The numeric value of the derivative at x = c is given as follows:
f'(c) = 1 - 48/c²
The numeric values of the functions at the bounds are given as follows:
f(b) = f(16) = 16 + 48/16 = 19.f(a) = f(3) = 3 + 48/3 = 19.Then the value of c is obtained as follows:
1 - 48/c² = 0/16
1 - 48/c² = 0
48/c² = 1
c² = 48
c = square root of 48.
[tex]c = \sqrt{16 \times 3}[/tex]
c = [tex]4\sqrt{3}[/tex]
Option A, as we have to be reminded that the interval is [3,16], hence the negative root is not considered.
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Please help me get this correct :(
Answer: ≈0.71
Step-by-step explanation: The real decimal would be 0.70710678118655. Yes, I know it is a big number. So, after doing some calculations, I got 0.5, remember we need to find the square root of 0.5. So, after finding that, I got 0.70710678118655. Which, your answer wants it to be rounded, so it would be D: ≈0.71
The Buffett Rule: Wealthy individuals often hire good accountants who find loopholes to lower their taxes. In addition, income from investments (e.g. Warren Buffett's fortune) is taxed differently than normal income. In 2011, Warren Buffett wrote an op-ed in the New York Times entitled, "Stop Coddling the Super-Rich." In it, he proposed what became known as the Buffett Rule: Tax codes must guarantee that the wealthy pay a higher dollar amount and a higher percent of their income in taxes. To do this, he suggested closing tax loopholes and raising taxes on investments. Discussion: Do you agree with Buffett that the wealthy should pay not only a higher dollar amount in taxes, but also a higher percent of their income in taxes? Why or why not?
Answer:
No, I do not agree with Buffett as the wealthy barely have any struggles, and them only paying less than a dollar in taxes will make the government add to the less fortunate. Meaning: If a large number of people aren't paying taxes, the government would not be getting a certain amount of money p/m&yr (per month and year), and that's a huge problem because hundreds of thousands of dollars are being spent every day. And where does the government get that income? We, the givers. And so if they aren't reaching that expectation, where will they get it from? And it's likely that they will add to the less fortunate. Which is terrible. That can lead to putting thousands of people in debt leaving them miserable with nothing
Step-by-step explanation:
What is the equation, in slope-intercept form, for a line that passes through the point (9,2) and (3, -2)
A: y = 2/3 x - 4
B: y = - 2/3 x - 4
C: y = 3/2 x + 4
D: y = - 3/2 x + 4
Answer: The answer is therefore (B) y = - 2/3 x - 4.
Step-by-step explanation: To find the equation of the line in slope-intercept form, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, we are given the points (9,2) and (3,-2). We can use either point as (x1, y1), but let's use (9,2) as the point. The slope of the line is the difference in y-values divided by the difference in x-values:
m = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4/6 = -2/3
Substituting this value for m and the coordinates of (9,2) for (x1, y1) into the point-slope form of a line, we get:
y - 2 = -2/3(x - 9)
Distributing the -2/3 on the right side, we get:
y - 2 = -2/3x + 6
Adding 2 to both sides, we get:
y = -2/3x + 8
This is the equation of the line in slope-intercept form. The answer is therefore (B) y = - 2/3 x - 4.
Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
a = 12, b = 12, C =
cans of soda are samples to ensure proper weight. the overall average for the sample is 10 ounces. each sample contains 25 cans. the standard deviation is estimated to be 3 ounces. what are the 99.73% control limits? group of answer choices 0.000 to 7.824 5.200 to 14.800 8.602 to 11.398 none of the above 0.000 to 10.176
The 99.73% control limits are 8.602 to 11.398
The correct answer is an option (c)
In this question we have been given:
sample size = 25
mean = 10
Standard deviation = 3
We need to determine the 99.73% control limits.
We know that Confidence interval = sample mean ± margin of error
Margin of error = z* x population of standard deviation/√n
The value of z* for 99.73% confidence interval is 3.00
Margin of error = 3 × (3/√25)
Margin of error = 9/5
Margin of error = 1.8
So, the control limits would be,
upper limit = 10 + 1.8
= 11.8
And the lower limit = 10 - 1.8
= 8.2
Therefore, from given choices the control limits are 8.602 to 11.398
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Let the graph of g be a translation 2 units right followed by a horizontal shrink by a factor oft of
the graph of f(x) = x^2 + x. Write a rule g.
Answer:vertical
Step-by-step explanation:
A plane takes 30 seconds to fly a distance of 8 kilometres.
Work out the average speed of the plane, in miles per hour
Answer: 4.97 / 0.00833 = 597.77 miles per hour.
Step-by-step explanation:
To find the average speed of the plane in miles per hour, we first need to convert the distance the plane travels from kilometers to miles. One mile is equal to 1.609 kilometers, so 8 kilometers is equal to 8 / 1.609 = 4.97 miles.
Next, we need to convert the time the plane takes to travel this distance from seconds to hours. There are 3600 seconds in an hour, so 30 seconds is equal to 30 / 3600 = 0.00833 hours.
To find the average speed of the plane in miles per hour, we can now divide the distance the plane travels by the time it takes to travel that distance. This gives us 4.97 / 0.00833 = 597.77 miles per hour.
Pls. Help find these answers?!
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
Karen runs 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
Answer:
2.8 miles
Step-by-step explanation:
in 60 minutes = 7 miles
in 1 minute = 7/60 miles
In 24 minutes = 7/60 × 24
Hope this helps.
Answer: She would run 2.8 miles in 24 minutes.
Step-by-step explanation:
[tex]\frac{x}{24minues} =\frac{7miles}{60minues}[/tex]. we cross multiply it, then we got:
60x = 7(24)
60x = 168
x = 2.8 miles
can anybody explain this or tell me the answer?
The required probability of P(Girls/Sophomore) is 0.9.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Data are shown in the table, P(Girls/Sophomore) is to be determined.
In order to determine the probability of the girls over Sophommer,
From,
P(A|B) = P(A ∩ B) / P(B)
P(Girl | Sophomore ) = P(Girl ∩ Sophomore ) / P(Sophomore)
Substitute the value in the above equation,
P(Girls/Sophomore) = 9 / 10
Thus, the required probability of P(Girls/Sophomore) is 0.9.
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y is directly proportional to x².
Given that y = 87.5 when x = 5, work out the value of y when x = 6.
If your answer is a decimal, then round it to 1 d.p.
Answer:
y = 126
Step-by-step explanation:
which shows how the distributive property can be used to evaluate 7 times 8 and four-fifths? 56 startfraction 28 over 5 endfraction
56 * (28/5) shows how the distributive property can be used to evaluate 7 times 8 and four-fifths.
7 times 8 = 56
4/5 = 28/5
Using the distributive property:
7 * 8 * (4/5) = (7 * 8) * (4/5) = 56 * (4/5) = 56 * (28/5) = 56 startfraction 28 over 5 endfraction
The distributive property states that for any numbers a, b, and c, a * (b + c) = a * b + a * c. To evaluate 7 times 8 and four-fifths, we can use the distributive property to separate the two factors. First, we calculate 7 times 8, which is equal to 56. Then, we calculate four-fifths, which is equal to 28/5. We then use the distributive property to multiply the two factors together, which is (7 * 8) * (4/5). This simplifies to 56 * (4/5) which is equal to 56 startfraction 28 over 5 endfraction.
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the length of a rectangle is 7 inches more than the width. the perimeter is 38 inches. find the length and the width of the rectangle.
A rectangle's length is 7 inches longer than its width. the perimeter is 38 inches. the length is 13 inches and the width of the rectangle is 12 inches
width = (38 - 14) / 2 = 12 inches
length = (38 - 12) / 2 = 13 inches
to find the length and width of the rectangle given that the length is 7 inches more than the width, and the perimeter is 38 inches, we can use the formula for perimeter (2 x length + 2 x width = perimeter). Plugging in the values given, we get 2 x length + 2 x width = 38. Solving for width, we get width = (38 - 14) / 2 = 12 inches. Plugging this value into the original equation, we get length = (38 - 12) / 2 = 13 inches. Therefore, the length and width of the rectangle are 13 inches and 12 inches, respectively.
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What is the Lcd of 11/12 and 1/2
LCD = 12
Equivalent Fractions with the LCD
11/12 = 11/12
1/2 = 6/12
Solution:
Rewriting input as fractions if necessary:
11/12, 1/2
For the denominators (12, 2) the least common multiple (LCM) is 12.
LCM(12, 2)
Therefore, the least common denominator (LCD) is 12.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
11/12 = 11/12 × 1/1 = 11/12
1/2 = 1/2 × 6/6 = 6/12
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There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?
The gold, silver, and bronze medals can be awarded in ????
ways.
The gold, silver, and bronze medals can be awarded in 720 ways.
What is Permutation?
The permutation is the number of ways to arrange the specified number of things out of the total available number of things, it is calculated by using excel function(=PERMUT(r, n)).
Given data,
n=10, r=3
Number of ways gold, silver, bronze can be awarded to 10 finalists is = nPr =10P3
=720
720 ways gold ,silver and bronze can be arranged.
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Tanner wants to cover a hallway in his house with carpet it cost about four dollars to cover a square foot with carpet
hope this helps
Step-by-step explanation:
a high school student applies to seven colleges, each of which makes an admission decision by rolling a fair six-sided die and admitting the student if a 1 is rolled. what is the expected number of colleges to which the student is admitted?
The expected number of colleges to which the student is admitted .2344
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Write examples of permutation in real life.Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colours. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.
Let X= college to which student is admitted
We are given with n=7 and p=1/6
P(X=2)=⁷P₂[tex]\frac{1}{6^{2} }(1-\frac{1}{6}) ^{7-2}[/tex]
=.2344
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HELPPP WILL MARK BRAINLIEST
Dimitri wrote the equations y = 3x and y = x + 3.
Use the drop-down menus to make true statements about the equations and the graph.
Graph of a diagonal line on a coordinate plane going up and to the left with x-axis and y-axis. Co-ordinates are (0,0) (1,3) and (2,6).
The equation
represents the graph. The point
is a point on the line that is NOT shown on the graph.
Answer:
Step-by-step explanation:
The coordinate point of intersection on the graph will be at (1.5, 4.5)
Given the equations Dimitri wrote expressd as:
y = 3x
y = x + 3
Since they are both y-values, we can equate the right hand side to have:
3x = x + 3
3x - x = 3
2x = 3
x = 3/2
x = 1.5
Get the value of y:
y = 3x
y = 3(1.5
y = 4.5
Answer:
I don't know this problem or the answer
a class has 11 students who are to be randomly assigned seating. what is the probability that the students will be arranged in order from shortest to tallest? (assume that no two students are the same height.)
The Probability that the student will arranged in order from shortest to tallest is 2.505210.
Probability is a branch of math which deals with the numerical description of certain events is to occur. It is the ratio of the numbers of favorable outcomes to the total number of outcomes. When solving probability problems we need to consider series of random experiments or experiments that involve several different aspects, such as drawing two cards from a deck or rolling several dice. the ability to calculate relative frequencies requires counting the number of possible outcomes of the experiment
If a class has 11 students who are to be randomly assigned seating in the order of shortest to tallest.
The total outcomes= 11! = 39916800
here the total favorable outcome is 1.so,
Probability = 1 / 39916800
= 2.505210
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The
is a natural 'reservoir'
for dissolved carbon dioxide. What one word completes the sentence?
Answer:
The oceans – the largest CO2-reservoir
Step-by-step explanation:
The oceans absorb substantial amounts of carbon dioxide, and thereby consume a large portion of this greenhouse gas, which is released by human activity.
The ocean is a natural 'reservoir' for dissolved carbon dioxide.
We have,
The _____________ is a natural 'reservoir' for dissolved carbon dioxide.
Oceans absorb large amounts of carbon dioxide consuming a large portion of greenhouse gas such as carbon dioxide which is released by human activity.
Oceans are the largest carbon dioxide reservoir.
Thus,
The ocean is the answer.
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You know the slope and one point on a line that is not the y‑intercept. Why might you write the equation in point-slope form instead of slope-intercept form?
Answer:
I think either way is correct.
For a point (a, b), and slope m:
point-slope form: y - b = m(x - a)
slope-intercept form: b = ma + c, where c is the y-intercept.
Please help me answer this is question
Answer:
no. Only Lin is right.
Step-by-step explanation:
As you can see, 2.5 and d are multiplied with each other. To get rid of the 2.5, though, you’d have to do the inverse operation, which is division.
Rewrite tan 0 x csc 0 in terms of sine and cosine.
tan 0. csc 0 = ?
(Simplify your answer.)
pls help asap i can’t pass this class without passing this test
To rewrite the expression tan 0 x csc 0 in terms of sine and cosine, we can use the following trigonometric identities:
The reciprocal identity: csc 0 = 1/sin 0
The tangent identity: tan 0 = sin 0/cos 0
The Pythagorean identity: sin^2 0 + cos^2 0 = 1
Substituting these identities into the given expression, we get:
tan 0. csc 0 = (sin 0/cos 0) * (1/sin 0)
Using the reciprocal identity and the Pythagorean identity, we can simplify this expression further to get:
tan 0. csc 0 = (sin 0 * 1)/(cos 0 * sin 0)
Next, we can cancel out the sin 0 term on the numerator and denominator to get:
tan 0. csc 0 = 1/cos 0
Finally, we can use the Pythagorean identity again to rewrite the denominator as:
tan 0. csc 0 = 1/sqrt(1 - sin^2 0)
Therefore, the final simplified expression is:
tan 0. csc 0 = 1/sqrt(1 - sin^2 0)
This is the final answer.
a force of 10 pounds compresses a 21-inch spring 8 inches. how much work is done in compressing the spring from a length of 15 inches to a length of 13 inches?
The work is done in compressing the spring from a length of 15 inches to a length of 13 inches are the 0.897ftlb.
Work Done:According to the paintings-power theorem, the internet paintings performed on an item equals the alternate withinside the power of the item . If the simplest alternate withinside the power located is withinside the capability power (say U) of the item, then the internet paintings performed W=△U.
Answer and Explanation:When a spring is compressed x in with the aid of using a pressure F,
F=kx, where k is the spring constant.
Since it's miles for the reason that the spring is compressed to 8in from 21in, that is, a compression of (21−eight)=13in, we obtain
F=kx⇒k=Fx=10lb1312ft=12013lbft−1.
Using the theorem, the internet paintings performed on an item equals the alternate withinside the power of the item. In this situation the simplest alternate in power is withinside the capability power of the spring while it's miles compressed with the aid of using x gadgets of duration, which is 12kx2. (k is the spring constant.)
The capability power of the spring while it's miles compressed to 15cm=0.5k(21−1512)2
The capability power of the spring while it's miles compressed to 13cm=0.5k(21−1312)2
Work Done equals the alternate withinside the capability power while it's miles compressed from 15in to 13in
=0.5k[(21−1312)2−(21−1512)2]=0.512013[(21−1312)2−(21−1512)2]≈ 0.897ftlb
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Quadrilateral ABCD is rotated 90° clockwise to produce A'B'C'D' Is each statement true?
AB=A'B'
If AC BD, then A'C' B'D'.
m2ABC
Yes No
000
Answer:
all yes
Step-by-step explanation:
AB = A'B' → yes
If AC // BD, then A'C' // B'D' → yes
m∠ABC < m∠A'B'C → No
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Quadrilateral ABCD.
After rotation of 90 degrees, Quadrilateral A'B'C'D'.
We see that,
The side length of the quadrilateral remains the same after rotation.
The parallel sides of the quadrilateral remain the same after rotation.
The angle of the quadrilateral remains the same after rotation.
Thus,
AB = A'B'.
If AC // BD, then A'C' // B'D'.
m∠ABC = m∠A'B'C.
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Maddox is trying to figure out which of two websites he should recommend to a friend. He wants to compare them based on customer ratings in order to make an educated recommendation. He creates a boxplot for each website with the same number of ratings.
What can Maddox conclude?
Select one:
a. Website B has a lower median rating.
b. Website A has a larger interquartile range.
c. Website B has a larger range.
d. Both websites have the same median rating.
e. Both websites have the same interquartile range.
The correct option that Maddox can conclude with is
e. Both websites have the same interquartile range.What is box plot?Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot.
The graph's appearance as a rectangle with lines extending from the top and bottom gave rise to the phrase "box plot."
How to read a box plot:Read the minimum value at the bottom of the first line.
Read the maximum value after the final line.
Read the bottom quartile, which is at the box's beginning.
Read the top quartile, which is towards the box's edge.
Read the median that coincides with the box's inside line.
The interquartile range is
= top quartile - bottom quartile
for website A
= 65 - 10
= 55
for website B
= 75 - 20
= 55
hence the both websites has same interquartile range
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The world’s largest freestanding escalator, which is located inside the CNN Center in Atlanta, Georgia, is 196 feet tall. Before visiting the escalator, Mary and Kenneth are discussing how fast they would like th escalator to rise.Mary wants the escalator to rise at 4 feet per second, and Kenneth wants the escalator to rise at 10 feet per second. Based on each persons desire, how long would it take the escalator to reach the top? Whose rate is safer? Explain
Answer:
Step-by-step explanation:
The world's largest freestanding escalator is 196 feet tall. If the escalator were to rise at 4 feet per second, it would take 49 seconds to reach the top. If it were to rise at 10 feet per second, it would take 19.6 seconds to reach the top.