Use the remainder term to find the minimum order of the Taylor polynomial, centered at 0, that is required to approximate the following quantity with an absolute error no greater than 10^-2.
√1.06.
n>= __________
Answer:
n ≥ 3
Step-by-step explanation:
Applying the remainder term in evaluating the minimum order of the Taylor polynomial
absolute error ≤ 10^-2
[tex]\sqrt{1.06}[/tex]
∴ n ≥ ?
The remainder term is the leftover term after computation ( dividing one polynomial with another )
attached below is the detailed solution
The minimum order of the Taylor polynomial, n≥3
What is Taylor polynomial?Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.
[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]
Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0
[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]
f(x) = [tex]\sqrt{x+1}[/tex]
[tex]f'(x)=\frac{1}{2}[/tex]
[tex]f''(x)=3/8[/tex]
substituting in the Taylors series
T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......
T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]
T(0.06) =1.03
f(0.06) =
[tex]\sqrt{0.06+1}\\= 1.03[/tex]
Therefore, the minimum order of the Taylor polynomial, n≥3
Learn more about Taylor polynomial;
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for any Integer 'a',a ÷ 0 is _______
give me answer
Answer:
undefined, invalid
and for a limit expression like a/x, x->0 we also say this is infinite.
Write the additive inverse of each of the following rational numbers:
Answer:
(1)-3/4, (2) 5/21, (3)4/43
What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
-3
Step-by-step explanation:
Slope is equal to (-5-7)/(2-(-2)=-12/4=-3
2 hundreds equal how many tens?
Lets see if ya'll know the answer cause i do
Answer:
200 is equal to 20 tens I guess lol
Answer:
20 tens
Step-by-step explanation:
200÷10=20 groups of ten
Find inverse of f(x)=(x+4)^2
Answer:
f⁻¹(x) = -4 + √x
Step-by-step explanation:
Switch the positions of x and y then solve for x.
[tex]f(x)=(x+4)^2\\x=(y+4)^2\\\sqrt{x} =y+4\\\sqrt{x} -4=y[/tex]
Express the decimal 0.7 as a percentage.
Answer:
70% IS THE ANSWER
Step-by-step explanation:
Hope I helped.
Answer:
70%
Step-by-step explanation
0.7×100=70
The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounce. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
Answer:
The right solution is:
(a) 0.8849
(b) 12.28%
(c) 4.9935
(d) 28004
Step-by-step explanation:
Given:
Mean,
= 4.5
Standard deviation,
= 0.3
(a)
P(x > 4.14)
As we know,
⇒ [tex]z = \frac{4.14-4.5}{0.3}[/tex]
[tex]=-1.20[/tex]
then,
⇒ [tex]P(z>-1.20) = P(z<1.20)[/tex]
[tex]=0.8849[/tex]
(b)
P(4.8 < x < 5.04)
= [tex]P(\frac{4.8-4.5}{0.3} < \frac{x-\mu}{\sigma} < \frac{5.04-4.5}{0.3} )[/tex]
= [tex]P(1<z<1.80)[/tex]
= [tex]P(z<1.80)-P(z<1)[/tex]
= [tex]0.9641 -0.8413[/tex]
= [tex]0.1228[/tex]
or,
= [tex]12.28[/tex] (%)
(c)
P(x > x) = 0.05
z value will be,
= 1.645
⇒ [tex]1.645 = \frac{x - 4.5}{0.3}[/tex]
[tex]x = 4.9935[/tex]
(d)
P(x < 5.01)
⇒ [tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]=\frac{5.01-4.5}{0.3}[/tex]
[tex]=1.7[/tex]
P(z < 1.70) = 0.9554
⇒ [tex]n = \frac{27875}{0.9954}[/tex]
[tex]=28004[/tex]
Solve the equation. If there is no solution, select no solution.
Answer:
no solution to the question
Answer:
4 2/3
Step-by-step explanation:
The two-step equation is solved regularly. The answer is 4 2/3.
Ba sinh viên A, B, C cùng làm bài thi một cách độc lập. Xác suất làm được bài thi của sinh viên A, B, C tương ứng là 0,6; 0,7 và 0,9. Tính xác suất để có ít nhất 1 sinh viên làm được bài.
Answer:
2 sinh viên sẽ làm đc 0,452
The lines shown below are parallel. If the green line has a slope of -2, what is
the slope of the red line?
Answer:
Hi! There's no picture, but we don't need that to find the answer. Parallel lines always have the same slope. I suppose you're saying that the green and red line are parallel -- so, the red line's slope is also -2.
-2 <--
Hope this helps!! Have a nice day & please mark brainliest if you don't mind!
If a runner jogs 3 miles west and then jogs 8 miles
north, how far is the runner from her starting point
if she plans to run straight back? Remember to
simplify your answer.
If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.
A^2+B^=C^2
3^2+8^3=C^2
9+64=C^2
Square root 73=C or 8.54=C (Miles)
The runner is 8.54 miles from her starting point if she plans to run straight back.
From the question, a runner jogs 3 miles west and then jogs 8 miles north.
An illustrative diagram for the journey is shown in the attachment below.
In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.
The cardinal points (North, East, West and South) are indicated beside the diagram.
Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.
The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.
The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.
In the diagram, hypotenuse = /ES/
∴ /ES/² = /SR/² + /RE/²
/SR/ = 3 miles
/RE/ =8 miles
/ES/² = 3² + 8²
/ES/² = 9 + 64
/ES/² = 73
/ES/ = [tex]\sqrt{73}[/tex]
/ES/ = 8.54 miles
Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.
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what value of x is in the solution set of 8x-6>12+2x
Answer:
x>3
Step-by-step explanation:
8x - 2x > 12+ 6
-> 6x > 18
-> x > 3
[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]
➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]
PLEASE HELPPPPPPPPPPPPPP
Answer:
False
Step-by-step explanation:
To find the inverse of a function, switch the variables and solve for y.
The inverse of f(n)=-(n+1)^3:
[tex]y=-(n+1)^3[/tex]
[tex]n=-(y+1)^3[/tex]
[tex]\sqrt[3]{n} =-(y+1)[/tex]
[tex]\sqrt[3]{n} =-y-1[/tex]
[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]
[tex]-\sqrt[3]{n} -1=y[/tex]
Answer:
False
Step-by-step explanation:
The stem-and-leaf plot lists the ages of customers in a bookstore.
How many customers are 19 or younger?
Enter your answer in the box.
Answer:
Step-by-step explanation:
find the value of the trigonometric ratio
Answer:
15/17
Step-by-step explanation:
sinA = CB/CA =15/17
Answer:
15/17Step-by-step explanation:
sine = opposite / hypotenusesin A = BC/ACsin A = 15/17help what it is please help
9514 1404 393
Answer:
A. the mean
Step-by-step explanation:
The Greek letter μ is customarily used to represent the mean of a distribution or data set. Its location in this figure at the highest point and the line of symmetry is consistent with μ identifying the mean of this normal distribution.
A stick 1 meter long casts a shadow 1.3 meters long. A building casts a shadow 25 meters long. How tall is the building (to 2 decimal places)
Answer: 19.23 meters
Step-by-step explanation:
1/1.3 = x/25
(1) (25) / 1.3
= 19.23 meters
Keith may need some help from his manager. A customer is on the phone and she is really angry. She is threatening to post nasty comments on her blog. What should Keith say to his manager? O a) "She's angry. You deal with it." b) "So she's really angry. Her product never arrived. I think we should offer to send her a replacement product free of charge, but wanted your input." "So l'll tell her to calm down. I think she's overreacting. I doubt she'll post c) anything online." "She's really angry; she ordered the product last Wednesday, Don in customer d) service said it would arrive a week later. It was a dollhouse for her niece, Can you take it from here?"
Answer:
"She's really angry; she ordered the product last Wednesday, Don in customer service said it would arrive a week later. It was a dollhouse for her niece, Can you take it from here?" is the best option
Step-by-step explanation:
20 students were asked “How many pets do you have in your household?” and the following data was collected:
2 1 0 3 1 2 1 3 4 0
0 2 2 0 1 1 0 1 0 1
Select the type of the data ?
CHOOSE ONE PLEASE HELP
Discrete
Continuous
Categorical
Qualitative
Answer:
Discrete
Discrete data represent items that can be counted; they take on possible values that can be listed out. The list of possible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity (making it countably infinite).
P over 8 4
The solution is ___.
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Answer:
1680
Step-by-step explanation:
nPk = n!/(n-k)!
8P4 = 8!/(8-4)! = 8·7·6·5 = 1680
An automobile went 84 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 126 miles
Answer:
10 gallons
Step-by-step explanation:
84 ÷ 6.5 =12.9(The unit rate.)
Seeing as one gallon can get you 12.9 miles;
126÷12.9=9.7
So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.
Answer:
9.75
Step-by-step explanation:
We can write a ratio to solve
84 miles 126 miles
-------------- = -------------------
6.5 gallons x gallons
Using cross products
84 x = 6.5 * 126
84x=819
84x/84 = 819/84
x = 9.75
State the counting number in the periodic table of elements of the element considered to be the heaviest gas. (the answer should consist of numbers only)
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Answer:
118
Step-by-step explanation:
Oganesson is the heaviest element ever created. It is a "super-heavy" noble gas with a half-life less than 1 millisecond. Its atomic number is 118.
Please if anyone can help me
Kendall wants to estimate the percentage of vegetarians who are also vegan. She surveys 150 vegetarians and finds that 45 are vegan. Find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
Answer:
0.0733364
Step-by-step explanation:
Given :
Number of vegans = x ;
Sample size, n = 150
Zα/2 ; Zcritical at 95% = 1.96
p = x / n = 45 / 150 = 0.3
Margin of Error :
Zcritical * √(p(1 - p) / n)
1.96 * √(0.3(1 - 0.3) / 150)
Margin of Error :
1.96 * √(0.3 * 0.7) / 150)
1.96 * √0.0014
Margin of Error = 0.0733364
PLZ HELP ASAP
A student poll on campus wanted to analyze the correlation of the Number of calories consumed per day to the weight of a student. in the form of a paragraph describe which visual display is most appropriate to represent the data. explain your reasons for choosing this type of visual display.
Answer:
Each kids weight in a chart
Step-by-step explanation:
I chose this because its the most organized way of doing that
Draw a graph of direct proportion, expressed by the formula: y=3x
Answer.
ANSWER
.......
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden. She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
What is the sample mean of the heights of the plants in Susan's garden?
Answer:
3.5 inches
Step-by-step explanation:
Sample mean basically means that we need to find the average of the samples.
So the formula for finding average is
Number of observations/ Number of Occurrences
So when we add the values together we get
42.
So there are 12 numbers
So, 42/12 =
3.5 inches
The sample mean of the heights of the plants in Susan's garden is
3.5 inches.
Here,
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.
She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
We have to find the sample mean of the heights of the plants in Susan's garden.
What is Average?
Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.
Now,
The recorded data is;
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.
Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]
Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]
Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.
Learn more about the average visit:
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The picture shows the graph of the movement of a pedestrian (B) and a bicyclist (A). Using the graph, answer the following questions: How many times is the distance covered by the bicyclist for 1 hour greater than the distance covered by the pedestrian for the same amount of time
Answer:
15km
Step-by-step explanation:
hope it is well understood
Drag each label to the correct location on the table. Each label can be used more than once. Match the attributes to the quadratic functions. x-intercept (-2,0) 1 y-intercept: 0,-8) minimum value: -1 axis of symmetry: 1 x-intercept: 2,0) y-intercept: (0,8) f(x) = x2 - 2x - 8 g(x) = x2 + 6x + 8 h(x) = -x2 + 2x
9514 1404 393
Answer:
f: x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1g: x-intercept (-2, 0), y-intercept (0, 8), minimum value -1h: axis of symmetry x = 1Step-by-step explanation:
The equations can be written in factored form and vertex form to see the x-intercepts, axis of symmetry, and extreme value.
The y-intercept is the constant in the equation in standard form.
The axis of symmetry is the vertical line through the vertex.
__
f(x)f(x) = x² -2x -8 = (x -4)(x +2) = (x -1)² -9
x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1
__
g(x)g(x) = x² +6x +8 = (x +2)(x +4) = (x +3)² -1
x-intercept (-2, 0), y-intercept (0, 8), minimum value -1
__
h(x)h(x) = -x² +2x = -(x)(x -2) = -(x -1)² +1
axis of symmetry x = 1
_____
Additional comment
We have only listed the intercepts, axis, and extreme where the values match a label.
