let and be two integers with 0≤<≤100 . suppose you approximate (≤100≤) by ∑=−11! . what is the largest possible error you could make?

Answers

Answer 1

The largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex]

To approximate the value of [tex]e^x[/tex] using the series expansion, we can use the formula:

[tex]e^x[/tex] ≈ ∑ [tex](x^n)/n![/tex]

In this case, we have:

x = -1/10

To find the largest possible error in the approximation, we can consider the next term in the series that we are neglecting:

1 / (10^11 * 11!) = [tex]|x^(n+1) / (n+1)!|[/tex]

For the given approximation, n = 10 (since we are using terms up to n = 10).

Substituting the values, we have:

[tex]|Error|[/tex] = [tex]|(-1/10)^(10+1) / (10+1)!|[/tex]

|Error| =[tex]|(-1/10)^11 / 11!|[/tex]

|Error| =[tex]1 / (10^11 * 11!)[/tex]

Since the value of n is fixed at 10, the largest possible error occurs when x is at its maximum value within the given range (0 ≤ x ≤ 100).

In this case, the maximum value of |Error| would be obtained by using the maximum value of x = 100 in the formula.

|Error| = [tex]1 / (10^11 * 11!)[/tex]

Therefore, the largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex].

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Related Questions

Data Mining. Data Mining cannot automatically find beneficial patterns for a business. True False

Answers

False. Data mining can automatically find beneficial patterns for a business by utilizing various techniques and algorithms to extract valuable insights and uncover hidden patterns from large datasets.

Data mining refers to the process of discovering patterns, relationships, and insights from large datasets. It involves using various techniques and algorithms to extract valuable information and knowledge from data. One of the primary goals of data mining is to uncover patterns that can be beneficial for businesses, such as identifying customer preferences, market trends, or predicting future outcomes.

Through automated analysis and pattern recognition, data mining can uncover hidden patterns and relationships that may not be apparent through traditional manual analysis. Therefore, data mining has the potential to automatically find beneficial patterns for businesses, making the statement "Data Mining cannot automatically find beneficial patterns for a business" false.

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Carissa’s gerbil has a tail that is the same length as its body length. Its tail is 102 millimeters. How long is her gerbil in centimeters?

Answers

Answer:

10.2 cm

Step-by-step explanation:

Divide the tail length by 10

HoPe ThIs HeLpEd youuu! lol :)

Answer: 10.2 cm

Hope this helped! :D

Find the missing side. Round to the nearest tenth. (a2+b2=c2)

Answers

Answer: 5.4

Step-by-step explanation:

Pretty Simple 5 squared plus 2 squared is 29.Just find the square root of that and it is the third side.:)

Answer:

5^2 + 2^2 = 29

sqr root of 29 is 5.385

Step-by-step explanation:

7.13 hm³ = _____m³
Convert this!
Options
713 x 10^4
71.3 x 10²
71.3 x10³
713 x 10²

Answers

Answer:

71.3 * 10² that's the answer to your question

Step-by-step explanation:

The answer is 713 X 10^4

I hope it helps

The mean number of years of marriage preceding divorce is 7. The median mber of years is 6. Most divorces occur, however, either at 3 years of marriage 22 years. Which measure of central tendency best describes these data, and y?

Answers

The measure of central tendency that best describes the given data is the Mode.

The mode is the value that occurs most frequently in a data set. According to the given data, most divorces occur either at 3 years of marriage or 22 years. Hence, the mode best describes these data.

The mean is the average value of a data set, which is calculated by adding all the values and dividing by the number of values.

The median is the middle value of a data set when arranged in numerical order. In the given data, the mean number of years of marriage preceding divorce is 7, and the median number of years is 6. Since most divorces occur at either 3 years or 22 years, the mode best describes the given data.

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consider the following function. (if an answer does not exist, enter dne.) f(x) = e−x2

Answers

The function f(x) = e⁻ˣ² has critical points at x = 0 and inflection points at x = √(1/2) and x = -√(1/2). function does not have any local maximum or minimum points

The given function is f(x) = e⁻ˣ².

a) The derivative of the function f(x) can be found using the chain rule. Let's calculate it:

f'(x) = d/dx(e⁻ˣ²)

f'(x) = -2x × e⁻ˣ²)

b) The second derivative of the function f(x) can be found by differentiating f'(x) with respect to x:

f''(x) = d/dx(-2x × e⁻ˣ²)

= -2 × e⁻ˣ² + (-2x) × (-2x) × e⁻ˣ²)

= -2 × e⁻ˣ² + 4x² × e⁻ˣ²)

= e⁻ˣ²(-2 + 4x²)

c) To find the critical points of the function f(x), we need to solve the equation f'(x) = 0

-2x × e⁻ˣ² = 0

Setting -2x = 0, we get x = 0.

d) To determine the intervals where the function is increasing or decreasing, we can analyze the sign of the first derivative. Recall that

f'(x) = -2x × e⁻ˣ².

When x < 0, e⁻ˣ² is positive, and -2x is negative. Therefore, f'(x) < 0 for x < 0, indicating that the function is decreasing in this interval.

When x > 0, e⁻ˣ² is positive, and -2x is positive. Therefore, f'(x) > 0 for x > 0, indicating that the function is increasing in this interval.

e) To find the inflection points of the function, we need to solve the equation f''(x) = 0

e⁻ˣ²(-2 + 4x²) = 0

Setting -2 + 4x² = 0, we get x² = 1/2, which leads to

x = ±√(1/2)

x = ±(1/√2)

x = ±(√2/2).

Therefore, the function f(x) = e⁻ˣ² has critical points at x = 0 and inflection points at x = √(1/2) and x = -√(1/2). function does not have any local maximum or minimum points

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x^2-8x+15
expresión racional ​

Answers

Answer:

x = 3, 5

Step-by-step explanation:

(x - 3)(x - 5) = 0

2+x5-3=(2+)x(5-3) is the equation true or not show work why

Answers

This equation has some nested grouping symbols on the left-hand side. As usual, I'll simplify from the inside out. I'll start by inserting the "understood" 1 in front of that innermost set of parentheses:

3 + 2[4x – (4 + 3x)] = –1

3 + 2[4x – 1(4 + 3x)] = –1

3 + 2[4x – 1(4) – 1(3x)] = –1

3 + 2[4x – 4 – 3x] = –1

3 + 2[1x – 4] = –1

3 + 2[1x] + 2[–4] = –1

3 + 2x – 8 = –1

2x + 3 – 8 = –1

2x – 5 = –1

2x – 5 + 5 = –1 + 5

2x = 4

x = 2
It is not required that you write out this many steps; once you get comfortable with the process, you'll probably do a lot of this in your head. But until you reach that comfort zone, you should write things out at least this clearly and completely.

Always remember, by the way, that you can check your answers in "solving" problems by plugging the numerical answer back in to the original equation. In this case, the variable is only in terms on the left-hand side (LHS) of the equation; my "check" (that is, my evaluation at the solution value) looks like this:

LHS: 3 + 2[4x – (4 + 3x)]:

3 + 2[4(2) – (4 + 3(2))]

3 + 2[8 – (4 + 6)]

3 + 2[8 – (10)]

3 + 2[–2]

3 – 4

–1
Since this is what I was supposed to get for the right-hand side (that is, I've shown that the LHS is equal to the RHS), my solution value was correct.

Poosjsjdiwjqjsnsjjdd

Answers

Answer:

poosjsjdwjqisnsjjdd

Step-by-step explanation:

Answer:

what's the question?

look at photo for the question and answer choices... NO LINKS OR BLANK ANSWERS

Answers

Answer:

B and E

Step-by-step explanation:

Let T: R3 → R3 be the linear transformation that projects u onto v = (a) Find the rank and nullity of T (b) Find a basis for the kernel of T.

Answers

The linear transformation T: R³ → R³ that projects u onto v has Rank(T) = 1 and the basis for the kernel of T is {a}.

To find the rank and nullity of the linear transformation T: R³→ R³, we need to determine the dimensions of the image space (range) and the kernel (null space) of T.

(a) Rank of T:

The rank of T is equal to the dimension of the image space. Since T projects u onto v, the image of T is the span of the vector v. Therefore, the rank of T is 1.

Rank(T) = 1

(b) Basis for the kernel of T:

The kernel of T consists of all vectors u in R³ that are mapped to the zero vector in R³. In other words, it consists of all vectors u perpendicular to the vector v.

To find a basis for the kernel, we need to solve the equation T(u) = 0. Since T projects u onto v, we can express this as u - proj_v(u) = 0.

For any vector u in R³, the projection of u onto v can be computed as:

proj_v(u) = (u · v) / (||v||²) * v

where u · v represents the dot product of u and v, and ||v|| is the norm (length) of v.

In this case, v = (a), so we can rewrite the projection formula as:

proj_v(u) = (u · (a)) / (||a||²) * (a)

Since T(u) = u - proj_v(u) = 0, we have:

u - (u · (a)) / (||a||²) * (a) = 0

This equation can be rearranged as:

u = (u · (a)) / (||a||²) * (a)

Now we can find a basis for the kernel by setting u to be a free variable and expressing it in terms of (a).

Let's denote the scalar (u · (a)) / (||a||²) as k:

u = k * a

Therefore, any vector in the kernel of T can be written as k * a, where k is a scalar.

A basis for the kernel of T is {a}.

So, the basis for the kernel of T is {a}.

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Jennifer is buying party supplies. She is planning on buying twice as many balloons as noisemakers. The number of napkins Jennifer is planning on buying is one-quarter of the number of noisemakers. If Jennifer buys 65 items, how many noisemakers does Jennifer buy? Write and solve an equation using a variable for this problem. <3

Answers

Couldnt find the link but answer is in a pic online

You spin the spinner and flip a coin. Find the probability of the compound event. The probability of spinning a number less than 3 and flipping tails is

Answers

Answer:

1/5

Step-by-step explanation

The spinner has the numbers 1-5 and they want the numbers less than 3 there a 2/5 then multiply the denominator by 1/2 thin divide it by 2

2/10 divided by 2 = 1/5

.

A secret agent wants to break a 6-digit code. He knows that the sum of the digits in even positions is equal to the sum of the digits in odd positions. Which of the following numbers could be the code?

A)12*9*8. B)181*2

Answers

The code could be the number "181*2" since the sum of the digits in even positions (8+2) is equal to the sum of the digits in odd positions (1+1).(option A)

To determine if a number could be the code, we need to check if the sum of the digits in even positions is equal to the sum of the digits in odd positions.

Let's analyze the options:

A) 12*9*8: The sum of the digits in even positions is 1+9 = 10, while the sum of the digits in odd positions is 2+8 = 10. Therefore, this number could be the code.

B) 181*2: The sum of the digits in even positions is 8+2 = 10, and the sum of the digits in odd positions is 1+1 = 2. These sums are not equal, so this number cannot be the code.

Based on the given information, only option A (1298) satisfies the condition where the sums of the digits in even and odd positions are equal.

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When light arrives and leaves a reflecting surface the angle with the line perpendicular to the surface is what?

Answers

Answer:

the angle of reflection is the angle between the reflected wave and the "normal" (the perpendicular line to the reflecting surface).

Step-by-step explanation:

Answer:

The angle which the light leaves or bounces off a surface is angle of reflection.

Step-by-step explanation:

has two types of light rays. The incoming ray and the outgoing, or reflected, ray. The angle between the incident ray and an imaginary perpendicular line drawn to the surface of the mirror is called the angle of incidence.

Is PXY PXZ? Choose...

Answers

Answer:

i just did this one it is YES

Step-by-step explanation:

Help fastttt someone pls and no files will block you

Answers

I believe h is the answer

verify x+(y+z) =(x+y) +z, when x=-4/15, y=-4/5and z =17/8​

Answers

Answer:

The equality is true

Step-by-step explanation:

x+(y+z)=(x+y)+z

x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for y

x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get

x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/8

x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/817/24=17/24

x+(y+z)=(x+y)+zwhen we plug in -4/15 for x,-4/5 for yand 17/8 for z,we get-4/15+(-4/5+17/8)=(-4/15+-4/5)+17/817/24=17/24so this equality is true

triangle abc with vertices at a(−1, −1), b(1, 1), c(0, 1) is dilated to create triangle a′b′c′ with vertices at a′(−3, −3), b′(3, 3), c′(0, 3). determine the scale factor used.

Answers

1] The scale factor used to dilate triangle ABC to create triangle A'B'C' is

2] To determine the scale factor used, we can compare the corresponding side lengths of the original triangle ABC and the dilated triangle A'B'C'.

Using the distance formula, we can calculate the lengths of the sides:

Side AB:

For triangle ABC: AB = √[(1 - (-1))^2 + (1 - (-1))^2] = √8 = 2√2

For triangle A'B'C': A'B' = √[(3 - (-3))^2 + (3 - (-3))^2] = √72 = 6√2

Side AC:

For triangle ABC: AC = √[(0 - (-1))^2 + (1 - (-1))^2] = √5

For triangle A'B'C': A'C' = √[(0 - (-3))^2 + (3 - (-3))^2] = √72 = 6√2

Side BC:

For triangle ABC: BC = √[(1 - 0)^2 + (1 - 1)^2] = 1

For triangle A'B'C': B'C' = √[(3 - 0)^2 + (3 - 3)^2] = 3

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What is the fraction for 0.85?, what is the percent for 0.85?. What is the ratio for 0.85

Answers

Answer:

Fraction: 17/20

Percent: 85%

Ratio: 85 out of 100

Step-by-step explanation:

Step-by-step explanation:

Fraction = 85/100 = 17 / 20

Percent = 17 / 20 × 100 = 85%

Ratio = 17 : 20

The area of the following parallelogram is 77m2. What is the length it’s base?

Answers

Answer:

11 maybe???

Step-by-step explanation:

Find the surface area.

Answers

The surface are is 29

Answer:

600ft^2

Step-by-step explanation:

Step One: There are two identical faces of each, which means we can multiply each face times two to make it faster. The first face will be 2(4*12)=96. I muliplied by two, because, once again, there are two faces of each.

Step Two: The next is 2(18*12)=432 and lastly, 2(4*18)= 72

Step Three: We just have to add it all up: 72+96+432= 600ft^2

If the point (-4,-8) is on the graph of the function L(x) and the slope of the line is 15, what is the equation for the function L(x).

Answers

The equation of the function L(x) is given by y = 15x + 52.

To find the equation of the function L(x), given that the point (-4, -8) is on the graph of the function L(x) and the slope of the line is 15, we use the point-slope form of the equation of a line.

Let's assume that the equation of the function L(x) is of the form y = L(x).

The slope of the line, m = 15

The point (-4, -8) is on the line, which means that it satisfies the equation of the line: y - y1 = m(x - x1),

where (x1, y1) = (-4, -8)

Substituting m, x1 and y1 in the equation of the line, we get:

y - (-8) = 15(x - (-4))y + 8

= 15(x + 4)y + 8

= 15x + 60y

= 15x + 52

The equation of the function L(x) is y = 15x + 52.

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The velocity vector of a particle moving in the XY plane has components given by dx/dt= sin(t^2) and dy/dt= e^(cost). At time t=4 the position of the particle is (2,1). What is the y-coordinate of the position vector at time t=3.

Answers

The y-coordinate of the position vector at time t=3 is approximately 1.446.

For the y-coordinate of the position vector at time t=3, we first need to integrate the given velocity components with respect to time to obtain the position components:

x(t) = ∫(dx/dt) dt = ∫sin(t²) dt

= (1/2)∫sin(u)/√(u) du

(where u = t²)

y(t) = ∫(dy/dt) dt

= ∫[tex]e^{cos t}[/tex] dt = [tex]e^{cos t}[/tex] + C

We can then use the given initial condition at time t=4 to determine the constant value C for the y-component:

x(4) = 2, y(4) = 1

Plugging in t=4 to the position equations, we get:

x(4) = (1/2)∫sin(u)/√(u) du = 2

y(4) = [tex]e^{cos 4}[/tex] + C = 1

Solving for C, we get:

C = 1 -  [tex]e^{cos 4}[/tex]

Now we can plug in t=3 to find the y-coordinate of the position vector:

y(3) =  [tex]e^{cos 3}[/tex] + C

y(3) =  [tex]e^{cos 3}[/tex] + 1 -  [tex]e^{cos 4}[/tex]

y(3) ≈ 1.446 (rounded to three decimal places)

Therefore, the y-coordinate of the position vector at time t=3 is , 1.446.

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Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 20. Find P15, which is the IQ score separating the bottom 15% from the top 85%.

Answers

Taking the given data into consideration we reach the conclusion that the IQ score ranging the bottom 15% from the top 85% is approximately 79.2, under the standard deviation 20.

Let us assume that adults have IQ scores that are normally expressed  with a mean of 100 and a standard deviation of 20, we need to calculate the IQ score ranging the bottom 15% from the top 85%, which is denoted as [tex]P_{15}[/tex]
To find the answer for this problem, we need to evaluate the z-score that corresponds to the 15th percentile. We can utilise a standard normal distribution table to  evaluate this value.
Implementing a standard normal distribution table, we could evaluate that the z-score corresponding to the 15th percentile is approximately -1.04.
[tex]z = (P_{15} - mean) /standard deviation[/tex]
[tex]-1.04 =( P_{15} - 100) /20[/tex]
[tex]- 20.8 = P_{15} - 100[/tex]
[tex]P_{15} = 79.2[/tex]
Hence, the IQ score separating the bottom 15% from the top 85% is approximately 79.2.
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The height of a cone is twice the radius of its base.

What expression represents the volume of the cone, in

cubic units?

23x3

49X3

Answers

Answer:

2/3πx³

Step-by-step explanation:

Volume of a cone is expressed as;

V = 1/3πx²h ... 1

x is the radius

h is the height of the cone

If the height of a cone is twice the radius of its base, then;

h = 2x ... 2

Substitute equation 2 into 1

Recall that V =  1/3πx²h

V = 1/3πx²(2x)

V = 2/3πx³

Hence the expression that represents the volume of the cone is 2/3πx³ cubic units

What is the constant in y=−3x+7

dont say the answer in a file i have to download

Answers

Answer:

7

Step-by-step explanation:

The constant is a number without the variable. So the answer is 7

Which of these is an example of a continuous random variable?
O A. Number of breaths in a minute
O B. Number of employees at a company
O C. Scores in a bowling tournament
D. Length of a fish

Answers

Answer:

D Length of  F I S H

Step-by-step explanation:

I chose the bowling one and got it wrong, but you can have the right answer

Answer: length of a fish

Step-by-step explanation: quizzzz

Let f be a given function. A graphical interpretation of the 2-point backward difference formula for approximating f'(x) is the slope of the line joining the points of abscissas xo - h and X, with h > 0. False True

Answers

A graphical interpretation of the 2-point backward difference formula for approximating f'(x) is the slope of the line joining the points of abscissas xo - h and X, with h > 0 is False

The 2-point backward difference formula for approximating f'(x) is given by:

f'(x) ≈ (f(x) - f(x - h)) / h

In this formula, the slope is calculated using the values of f(x) and f(x - h) at two points: x and x - h. The graphical interpretation of this formula involves finding the slope of the line passing through these two points.

However, the given statement states that the line is joining the points of abscissas xo - h and X, with h > 0. This implies that the line is connecting a fixed point xo - h to a variable point X. This interpretation does not align with the 2-point backward difference formula.

Therefore, the statement is false.

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Theater tickets are marked down 15%. How much are the tickets if they originally cost $55?​

Answers

The answer is 46.75 mark me brianliest if right!!
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Explain why or why not using the following sentence stem:Joining these two sentences with a semicolon would be a __________ (good or bad) idea because... The structural formulas of amino acids are the same EXCEPT for the A) amino group. B) side chain or R group. C) hydrogen bonding D) carboxyl group. E) alpha carbon how many grams is 4.2 moles HCL A Scooter travelling at 10m/s speed up to 20m/s in 4 sec.find the acceleration of scooter HELP ASAP PLEASE!!! :) The roots of 3x2 + x = 14 are 1. imaginary2. real,rational,equal3.real,rational,unequal4.real,irrational,unequal Allocation to accomplish smoothing LO 12-1, 12-2, 12-3 Thornton Corporation estimated its overhead costs would be $23,700 per month except for January when it pays the $163,440 annual insurance premium on the manufacturing facility. Accordingly, the January overhead costs were expected to be $187,140 ($163,440 + $23,700). The company expected to use 7,100 direct labor hours per month except during July, August, and September when the company expected 9,800 hours of direct labor each month to build inventories for high demand that normally occurs during the Christmas season. The company's actual direct labor hours were the same as the estimated hours. The company made 3,550 units of product in each month except July, August, and September, in which it produced 4,900 units each month. Direct labor costs were $24.50 per unit, and direct materials costs were $11.60 per unit. Required a. Calculate a predetermined overhead rate based on direct labor hours. b. Determine the total allocated overhead cost for January, March, and August. c. Determine the cost per unit of product for January, March, and August. d. Determine the selling price for the product, assuming that the company desires to earn a gross margin of $20.60 per unit. Activity 09Fill in the blanks using the words given in the box. (The first one is don(a) I'll give you aottle ..... of water.(b) He has brought a ......of fruits.(c) Please light the ......(d) This is very interesting ...(e) The ......is leaning against the table.(f) Oh! The ....... ........ of this bag is broken.basket, book, broom, bottle, handle, candl Which of the following is true concerning the substitution effect of a decrease in price?a. It will lead to an increase in consumption only for a normal good.b. It always will lead to an increase in consumption.c. It will lead to an increase in consumption only for an inferior good.d. It will lead to an increase in consumption only for a Giffen good. Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill. How many kits did she buy?