The Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = e^x, a = 1 is
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]
In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.
The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
In the scenario above, we are given the function f(x) = e and a = 1.
The first derivative of e^x is e^x,
the second derivative is e^x,
and the third derivative is also eˣ.
We then evaluate these derivatives at a = 1, we get:
f(1) = e¹ = e
f'(1) = e¹ = e
f''(1) = e¹ = e
f'''(1) = e¹ = e
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]
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Help please
Expand the logarithm as much as possible
logy^10
Answer: 2.303
Explanation: In image
WILL GIVE BRAINLIEST IF CORRECT
Will report is answer is a guess. Include reasoning behind answer
The image of point R by rotation is equal to R'(x, y) = (- 4, 7).
How to find the image of a point by rotation
The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:
(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.θ - Angle of rotation, in degrees.If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:
R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)
R'(x, y) = (- 4, 7)
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
Therefore, the volume of the composite solid is approximately 1357.28 cubic feet, rounded to the nearest hundredth.
What is volume?Volume is a measure of the amount of space occupied by an object or a substance. In other words, it is the three-dimensional space that an object or substance occupies. The SI unit for volume is cubic meters (m³), although other units such as cubic centimeters (cm³) and liters (L) are also commonly used.
Here,
The composite solid is made up of a hemisphere and a cone with the same base radius and height. The volume of the hemisphere is given by (2/3)πr³, and the volume of the cone is given by (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 6 feet and the height is 12 feet, we can find the volumes of the hemisphere and the cone as follows:
Volume of hemisphere = (2/3)π(6³)
= 288π cubic feet
Volume of cone = (1/3)π(6²)(12)
= 144π cubic feet
The total volume of the composite solid is the sum of the volumes of the hemisphere and the cone, which is:
Total volume = Volume of hemisphere + Volume of cone
= 288π + 144π
= 432π
To find the numerical value of this volume, we can use the approximation π ≈ 3.14 and round the result to the nearest hundredth:
Total volume ≈ 432(3.14)
= 1357.28 cubic feet
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blank g = blank kg =3/10kg
It should be noted that 3/10 kg to grams will be 300 grams.
How to convert the valueTo convert 3/10 kg to grams (g), we can use the following conversion factor:
1 kg = 1000 g
Therefore:
3/10 kg = (3/10) x 1000 g = 300 g
Hence, 3/10 kg is equal to 300 grams (g).
In conclusion, it should be noted that 3/10 kg to grams will be 300 grams.
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how do i use change of base formula with logorothims
To use the change of base formula, we first identify the base of the original logarithm and the desired base of the new logarithm.
The change of base formula is a useful tool in logarithmic functions that allows us to rewrite a logarithm with one base as an equivalent logarithm with a different base. The formula is as follows:
logᵦ a = logᵦ(x) / logₐ(x)
where a is the value being logged, β is the base of the original logarithm, and x is any positive number other than 1.
We then apply the formula by taking the logarithm of the value being logged with the desired base, and dividing it by the logarithm of the same value with the original base.
For example, let's say we want to rewrite the logarithm log₂ 8 in base 10. Using the change of base formula, we have:
log₂ 8 = log₁₀ 8 / log₁₀ 2
The value of log₁₀ 8 is simply 0.9031, and the value of log₁₀ 2 is 0.3010, so we have:
log₂ 8 = 0.9031 / 0.3010 ≈ 3
Therefore, log₂ 8 is equivalent to log₁₀ 8 ≈ 3. By using the change of base formula, we can simplify logarithmic expressions and evaluate them using common logarithms or natural logarithms.
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A spherical balloon has a 20-in. diameter when it is fully inflated. Half of the air is let out of the balloon. What is the volume of the fully-inflated balloon?
The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.
What is a sphere?
The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.
We are given diameter as 20 inches.
So, the radius is half of the diameter which comes out to be 10 inches.
From this, we get the volume as
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]
⇒ Volume = [tex]\frac{4000}{3}[/tex] π
⇒ Volume = 4186.67 cubic inches
Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.
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If the prism on top of the figure was 4 inches tall instead of 3 inches tall, what would be
the difference between the volume of the original prism on top and the new prism on
top?
Show your work.
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What is the difference in what you have as a balance in your check register versus your online statement by 11/18?
your answer goes here
Answered
What is the combined total of the two translation they have in common
The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.
The combined total of the 2 transactions they have in common is $206.99.
How to calculate the valueUse the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.
Check Register:
Total = 397.45 - 50.32 - 16.32 + 190.67
Total = 521.48
Online Statement:
Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67
Total = 556.26
Difference = online - check register
Difference = 34.78
On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99
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Tamika is seeking a loan with a simple
The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.
What is simple interest?Simple interest is the interest system that computes interest only on the principal for each period.
Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.
The principal loan amount borrowed by Tamika = $5,000
The interest rate per year = 8%
The loan period = 24 months = 2 years (24/12)
Simple Interest = Principal x Rate x Period
= $800 ($5,000 x 8% x 2)
Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.
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Complete Question:Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?
which has the greatest rate? y = -x , y = 3/4x +1, y = 1/2x +2, y = x
The function that has the greatest rate of change is y = x
Which function has the greatest rate of change?From the question, we have the following parameters that can be used in our computation:
y = -x ,
y = 3/4x +1,
y = 1/2x +2,
y = x
A linear function is represented as
y = mx + c
Where
rate of change = m
So, we have
y = -x , rate = -1
y = 3/4x +1, rate = 3/4
y = 1/2x +2, rate = 1/2
y = x, rate = 1
This means that the function with the highest rate is y = x
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what is the area of a circle with the diameter of 22 in
Answer:380.1 square inches
Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)
What number of hours corresponds to making $41
Can yall help me with this pls
Answer:
x=6.4
Step-by-step explanation:
2/3.2 = 4/x
2x=4(3.2)
2x=12.8
x=6.4
What is the p value of a right tailed one-mean hypothesis test with a test statistic of z0-1.74
Answer:
The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.
Factor Completely
n^4 − 4n^3 − 17n^2 − 36n + 108
Answer:
It can't be factor
Step-by-step explanation:
n^4 − 4n^3 − 17n^2 − 36n + 108
The GCF of this is 1, so the equation can't be factor.
Out of 300 applicants for a job, 134 are male and 40 are male and have a graduate degree. You were asked to find the probability that a randomly chosen applicant has a graduate degree, given that they are male.
Answer: We can use Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male. Bayes' theorem states:
P(A|B) = P(B|A) * P(A) / P(B)
where A and B are events, P(A|B) is the conditional probability of event A given that event B has occurred, P(B|A) is the conditional probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this case, we want to find P(grad degree | male), which is the probability that an applicant has a graduate degree given that they are male. Using Bayes' theorem, we have:
P(grad degree | male) = P(male | grad degree) * P(grad degree) / P(male)
We are given that 134 applicants are male, and 40 of those males have a graduate degree. Therefore:
P(male | grad degree) = 40 / total number of applicants with a graduate degree
We are not given the total number of applicants with a graduate degree, but we can find it using the fact that 40 applicants are male and have a graduate degree, and that there are 134 male applicants in total. Therefore:
total number of applicants with a graduate degree = 40 / (40/134) = 118.33 (rounded to the nearest whole number)
Next, we need to find the prior probability of having a graduate degree, P(grad degree). We can use the total number of applicants and the number of applicants with a graduate degree to calculate this probability:
P(grad degree) = number of applicants with a graduate degree / total number of applicants = 118 / 300 = 0.3933 (rounded to four decimal places)
Finally, we need to find the prior probability of being male, P(male). This probability can be calculated similarly:
P(male) = number of male applicants / total number of applicants = 134 / 300 = 0.4467 (rounded to four decimal places)
Now, we can substitute these values into Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male:
P(grad degree | male) = (40 / 118) * 0.3933 / 0.4467 = 0.332 (rounded to three decimal places)
Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they are male, is approximately 0.332 or 33.2%.
Step-by-step explanation:
Need the right answer for problem 12
The distance of the point from the line is d =
Given data ,
Let the point be P ( 1 , 1 )
Let the equation of line be represented as e
where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line
So , slope m = ( 0 + 2 ) / ( -5 - 1 )
m = 2/-6
m = -1/3
So , the equation of line is
y - 0 = ( -1/3 ) ( x + 5 )
y = ( -1/3 ) ( x + 5 )
( 1/3 )x + y + 5/3 = 0
Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
On simplifying , we get
D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]
D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]
D = 3 / ( 10 ) / 9
D = 27/10
D = 2.7 units
Hence , the distance is 2.7 units
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Directions - Answer the questions based on the following scenario and graph.
Jim and Cassie are both saving money each week in order to buy an awesome Bulls snapback hat (and leave the price stickers on it, of course). The hat costs $27.
Jim's rate of savings (slope): 3
Cassie's rate of savings (slope): 3
Jim's y intercept: 3
Cassie's y intercept: 12
Jim's Savings Equation: y = 3x + 3
Cassie's Savings Equation: y = 3x + 12
Number of weeks it will take to Cassie to save $27: 5
Number of weeks it will take to Jim to save $27: 8
Yes, Jim and Cassie's rates parallel.
Cassie will be able to buy the hat first.
We know that the slope intercept form of a straight line is,
y = mx + c, where m is the slope of the line and c is the y intercept.
For the straight line for Cassie:
The line passing through the points (0, 12) and (1, 15).
So the slope = (15 - 12)/(1 - 0) = 3
The y intercept is = 12.
Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.
For the straight line for Jim:
The line passing through the points (0, 3) and (1, 6).
So the slope = (6 - 3)/(1 - 0) = 3
The y intercept is = 3
Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.
Since the slope of both are equal so the rates of both are parallel.
Substituting the value y = 27 in equation (i) and (ii) we get,
equation (i): 3x + 12 =27
3x = 27 - 12
3x = 15
x = 15/3
x = 5
So Cassie needs 5 weeks to save $27.
Equation (ii): 3x + 3 = 27
3x = 27 - 3
3x = 24
x = 24/3
x = 8
So Jim needs 8 weeks to save $27.
Hence Cassie will be able to buy the hat first.
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The question is incomplete. The complete question will be -
22 randomly picked people were asked if they rented or owned their own home, 9 said they rented. Obtain a point estimate of the proportion of home owners. Use a 95% level of confidence.
point
Answer:
True proportion of homeowners in the population lies between 0.333 and 0.847
Step-by-step explanation:
If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:
Point estimate = Number of homeowners / Total number of people surveyed
Point estimate = 13 / 22
Point estimate = 0.59 (rounded to two decimal places)
To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:
Confidence interval = Point estimate ± (Z-value x Standard error)
where the Z-value corresponds to the desired level of confidence and the standard error is given by:
Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]
For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:
Standard error = sqrt [ (0.59 x 0.41) / 22 ]
Standard error = 0.131 (rounded to three decimal places)
Substituting these values into the formula, we get:
Confidence interval = 0.59 ± (1.96 x 0.131)
Confidence interval = 0.59 ± 0.257
Confidence interval = (0.333, 0.847)
Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.
Angles in parallelograms maze
The values of angles x in the parallelogram maze are calculated below
Calculating the angles x in the parallelogram mazeThe question is solved by taking the shapes from left to right on each row
So, we have
x + 65 = 180 --- adjacent angles
x = 115
x + 103 = 180 --- adjacent angles
x = 77
9x = 90 --- angles in a rectangle
x = 10
x + 85 = 180 --- adjacent angles
x = 95
x + 60 = 180 --- adjacent angles
x = 120
2x = 90 --- angles in a rectangle
x = 45
x = 98 -- opposite angles in a parallelogram
3x = 81 -- opposite angles in a parallelogram
x = 27
4x + 76 = 180 --- adjacent angles
x = 26
3x = 78 -- opposite angles in a parallelogram
x = 26
8x + 68 = 180 --- adjacent angles
x = 14
4x = 72 -- opposite angles in a parallelogram
x = 18
x + 126 = 180 --- adjacent angles
x = 54
x = 90 -- opposite angles in a parallelogram
6x = 90 -- opposite angles in a parallelogram
x = 15
2x + 62 = 180 --- adjacent angles
x = 59
6x = 106 --- opposite angles in a parallelogram
x = 17.6
5x = 90 --- angles in a rectangle
x = 18
5x + 80 = 180 --- adjacent angles
x = 20
10x = 90 --- angles in a rectangle
x = 9
2x = 100 --- opposite angles in a parallelogram
x = 50
6x = 96 --- opposite angles in a parallelogram
x = 16
x + 105 = 180 --- adjacent angles
x = 75
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Drag the tiles to the correct boxes to complete the pairs.
Match the accounting terms to their relevant action by the company or the investors.
high free cash flow
low free cash flow
capital expenditure
company buying assets like machinery or a plant
investors think about selling the shares of the company
investors will hold on to their shares as the company is sure to pay dividends
comoany try to reduce this to increase profits.
Reset
Next
operating activities
The accounting terms when matched with their relevant actions would be;
high free cash flow - investors will hold on to their shares as the company is sure to pay dividendslow free cash flow - investors think about selling the shares of the companycapital expenditure - company buying assets like machinery or a plantoperating activities - company trying to reduce capital expenditure to increase profits What do some accounting terms lead to ?A company's free cash flow is an indicator of its ability to cover expenses and invest in future growth opportunities. A high level of free cash flow suggests that the business is doing well financially, while a low amount indicates that the opposite is true.
In order to generate income or save money over time, companies will make capital expenditures. However, if investors deem a company to be underperforming or unlikely to provide returns on investment, they may choose to sell their shares as a preventative measure against further financial losses.
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sum of 213341 & 444233 base 5
Answer:
1213124
To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.
Here's how to do it:
2 1 3 3 4 1
+ 4 4 4 2 3 3
-----------------------
1 2 1 3 1 2 4
Therefore, the sum of 213341 and 444233 in base 5 is 1213124.
Evaluate this limit without using L'Hopital's Rules
The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1
Evaluate this limit without using L'Hopital's RulesFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]
By substitution, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]
So, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]
Evaluate the exponents
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]
Evaluate the sum
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]
Hence, the solution is 1
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Use the given feasible region to find the maximum possible value of the objective function f=5x+6y
The calculated value of the maximum possible value of the objective function is 46
Finding the maximum possible value of the objective functionFrom the question, we have the following parameters that can be used in our computation:
Objective function, F = 5x + 6y
The coordinates of the feasible region are
(0, 6), (1, 6.5) and (2, 6)
Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation
F(0, 6) = 5(0) + 6(6) = 36
F(1, 6.5) = 5(1) + 6(6.5) = 44
F(2, 6) = 5(2) + 6(6) = 46
The maximum value above is 46 at (2, 6)
Hence, the maximum possible value of the objective function is 46
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A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?
The Regular polygon has the following measures.
a=7√3cm
s=14 cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
what is the area of the polygon?
Round to the nearest tenth and include correct units
The vocabulary for a is called the apothem
The area of the regular polygon is [tex]2419.68 cm^2.[/tex]
How to solve for areaa = 7√3 cm
s = 14 cm
The perimeter of the polygon is:
P = ns
where n is the number of sides of the polygon. We can find n using the formula:
[tex]n = 360 / (180 - (360 / 2n))[/tex]
where n is the number of sides. Substituting the given value for s, we get:
[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]
Therefore, the polygon has 14 sides.
a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])
= 24.615 cm
A = (1/2) * apothem * perimeter
[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]
Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]
In summary,
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pls help me on algebra here is screenshot
Answer:
The answer to the question provided is option 2.
Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
74
%, Worksheets =
76
%, and Quizzes =
77
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
‼️‼️‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️‼️‼️
If g(x) = 3x -2 and (gof)(x) = 15x + 10, find f(x).
Answer:
the function f(x) is f(x) = 5x + 4.
Step-by-step explanation:
To find f(x), we need to use the formula:
(gof)(x) = g(f(x)) = 3f(x) - 2
We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:
3f(x) - 2 = 15x + 10
Simplifying this equation, we get:
3f(x) = 15x + 12
Dividing both sides by 3, we get:
f(x) = 5x + 4
Therefore, the function f(x) is f(x) = 5x + 4.