Answer:
[tex]5x^5+5xyz+7xy+8x[/tex]
Step-by-step explanation:
When putting an equation in standard form, you always prioritize the term with the most variables - unless terms have a greater exponent.
The prioritization order is:
Exponents
Amount of variables
Value of coefficient
So, [tex]5x^5[/tex] is the only term with an exponent in this expression, so it will go first.
Next up, we have to choose between [tex]8x[/tex], [tex]5xyz[/tex], and [tex]7xy[/tex]. We know that [tex]5xyz[/tex] has more variables than the other ones, so it goes next.
Now we're left with [tex]7xy[/tex] and [tex]8x[/tex]. [tex]7xy[/tex] has more variables than [tex]8x[/tex], so it goes next.
This leaves [tex]8x[/tex] last.
So, the expression becomes [tex]5x^5+5xyz+7xy+8x[/tex].
Hope this helped!
Given the following estimated regression, please give the correct magnitude of the coefficients, and provide a one sentence interpretation of the relationship between Y and X as talked about in class Wage = 15.00 + 0.28-YrsEdu. Where Wage is currently in dollars, and YrsEdu. are in years. A) Suppose we want Wages to be in thousands of dollars instead of dollars. B) Suppose we want Yrsedu. to be in terms of weeks instead of years. C) Suppose we want Wages to be in hundreds of dollars AND YrsEdu. in days (given that a year of education is only 180 days).
Answer:
Following are the answer to the given choices:
Step-by-step explanation:
In potion A:
The model, that will be formed can be defined as follows:
[tex]\widehat{W age} = \hat b_{0} + \hat b_{1} x Y_{rs} \epsilon done \\\\ \hat B_1 = \frac{\sum_{i=1}^{n} (W_{age}i - \widehat{W age} \times (Y_{rs} Edui - \widehat{Y_{rs}\epsilon})}{\int S_{yrs}\epsilon dre}\\[/tex]
[tex]\ the \ new \ W_{age} = 10^{-3} \times W_{age} \\\\\hat {B_{1 new}} = 10^{-3} \hat {B}\\\\ \hat{B_{0}} = \widehat{W age} -\hat {B_1} \bar{Y_{rs}\epsilon dus} \\\\\hat{B_{0 \ new}} = \widehat{W age} \times 10^{-3} - 10^{-3} \hat {B_1} Y_{rs}\epsilon dus \\[/tex]
[tex]= 10^{-3} \hat {B_0}\\[/tex]
[tex]\hat B_{0 \ new} = 15 \times 10^{-3} \\\hat B_{1 \ new} = 0.28 \times 10^{-3} \\[/tex]
In potion B:
[tex]\ The \ new \ Y_{rs}\epsilon dus = \frac{Y_{rs} \epsilon dus}{7} \\\hat b_{1 \ new} = 7 \hat b_1\\\hat b_{ 0 \ new } = \widehat{W_{age}} - 7 \hat b_1 \times \frac{\bar Y_{rs}\epsilon dus}{7} \\\hat b_{0 \ new} = \hat B_{0}\\\hat b_{0} = 15.00 \\\hat b_{1} = 0.04 \\[/tex]
In potion C:
[tex]\ Y_{rs}\epsilon dus \ new = \frac{Y_{rs} \epsilon dus}{180} \\\\\widehat{W_{age} new} = \widehat{W_{age}} \times 10^{-2} \\\\\hat b_{1 \ new} = \hat b_{1} \times 10^{-2} \times 180 = \hat b_1 \times 1.8 \\\\\ hat b_{ 0 \ new } = 10^{-2} \widehat{W_{age}} - \hat b_1 \times 1.8 \times \frac{\bar Y_{rs}\epsilon dus}{180} \\\\[/tex]
[tex]= 10^{-2} \ \hat B_{0}\\[/tex]
[tex]\hat b_{0 \ new} = 0.15 \\\hat b_{1 \ new} = 0.504 \\[/tex]
given f(x) = 3x -1 & g(x)= -x + 6, find f(-2) + g(5)
Answer:
When added together, the sum of the given functions have a value of -6.
Step-by-step explanation:
When we see f(-2), it means that our value of x for the f(x) function is -2. When we see g(5), it means that our value of x for the g(x) function is 5. So, let's use this information and plug it into our equation.
f(-2) + f(5) = (3(-2) - 1) + (-(5) + 6)
Multiply 3 by -2 and distribute the negative to 5.
f(-2) + f(5) = (-6 - 1) + (-5 + 6)
Subtract 1 from -6 and add 6 to -5.
f(-2) + f(5) = (-7) + (1)
Add 1 to -7.
f(-2) + f(5) = -6
So, when added, the sum of the functions is -6.
-5m-2 (1-7m) show work please
Answer:
9m - 2
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
-5m - 2(1 - 7m)
Step 2: Distribute -2
-5m - 2 + 14m
Step 3: Combine like terms
9m - 2
Simplify the expression(2x²y)^3
Answer:
8x^6y^3
Step-by-step explanation:
(2x2y)3
=8x6y3
Point J is on line segment I K ‾ IK . Given J K = x + 6 , JK=x+6, I J = 9 , IJ=9, and I K = 2 x , IK=2x, determine the numerical length of J K ‾ . JK .
Answer:21
Step-by-step explanation:
A community sports league is raising money by making custom shirts to sell at league games. They plan to sell the shirts for $14. Each shirt costs $7 to make. They spent $55 for advertising. Use n to represent the number of shirts they sell. Multiply this by the money they make for each shirt, then subtract the advertising cost. Which expression represents the money that the league raises?
O A. (14 – 7)n – 55
B. 55 – (14 – 7) n
O C. 14 – 7n – 55
O D. 14n – 7 – 55
Answer:
A. (14 – 7)n – 55
Step-by-step explanation:
it cost $14 to make so $14 - $7 to make then you have to advertise it AFTER and it takes more money to advertise so, -55 so the answer would be:
(14 – 7)n – 55
Could you simplify this question? 4xy-6xy+5y-9x
The solution of expression is,
⇒ - 2xy + 5y - 9x
We have to given that,
An expression to solve,
⇒ 4xy - 6xy + 5y - 9x
Now, We can simplify the expression by combining like terms as,
⇒ 4xy - 6xy + 5y - 9x
⇒ - 2xy + 5y - 9x
Therefore, The solution of expression is,
⇒ - 2xy + 5y - 9x
Learn more about the mathematical expression visit:
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name all the values of x if
7|x|=63
(seven times the absolute value of x equals sixty-three)
Answer:
I think they are
|9|
|-9|
Compute the critical value z Subscript alpha divided by 2 that corresponds to a 96% level of confidence.
Complete Question
Compute the critical value [tex]Z_{\frac{\alpha }{2} }[/tex] that corresponds to a 96% level of confidence.
Answer:
The value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
Step-by-step explanation:
From the question we are told that
The confidence level [tex]C = 96\%[/tex]
Generally the level of significance is mathematically represented as
[tex]\alpha = (100 -96)\%[/tex]
[tex]\alpha = 0.04[/tex]
Now from the normal distribution table the critical value for [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.04}{2} }= 2.326[/tex]
Can you think of a situation where it would make the most sense to express your birth year in binary numbers?
Answer:
Yeah I've thought of it and have an example with the year 2000 as the birth year
So 2000 In binary= 11111010000
Step-by-step explanation:
Binary numbers consist of only 0 and 1
So to convert a number to binary we divide by 2
Let's assume a birth year of 2000
Now let's convert it to binary
2000/2= 1000 R 0
1000/2= 500 R 0
500/2= 250. R 0
250/2= 125. R 0
125/2 = 62. R 1
62/2= 31. R 0
31/2= 15. R 1
15/2 = 7. R. 1
7/2= 3. R 1
3/2 = 1. R 1
1/2 = 0. R 1
Where R signifies the remainder
So we'd pick the remainder from the bottom and that becomes our binary number
So 2000 In binary= 11111010000
A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a discrete quantitative variable that might be included in the brochure? A. number of seats B. type of transmission C. presence of a sunroof D. fuel efficiency (in mpg)
Answer:
Option A:
Number of seats
Step-by-step explanation:
A discrete quantitative variable is a variable that can be enumerated. This means that they are in units in which numbers can be assigned to and can be counted.
The number of seats present in the car can be counted. This feature can also be evaluated based on its numeral value, rather than its quality. In a simple form, the buyers feel that the more the number of seats present in the car, the more people it can carry. Hence, the family would love to buy a car with a good number of seats in it.
The other features in the options are rather continuous, qualitative, or boolean. Some of them are continuous because they cannot be counted e.g fuel efficiency. The others such as the presence of a sunroof can be seen as a boolean variable. (it can either be true or false)
Type of the transmission is a qualitative variable
Answer: fuel efficiency
Step-by-step explanation:
took the exam review on edg
Automobile repairs and maintenance cost
Jana Padgett $900 last year. She drove 15,900
miles. To the nearest cent, what was her cost
per mile?
Answer:
17.67
Step-by-step explanation:
You find the unit rate. So, 15,900 divided by 900 gives you 17.666666 (repeating). Then round to the nearest cent to get 17.67
Decide which of the two given prices is the better deal and explain why.
You can fill a 12 gallon tank of gas for $43.75 or buy gas for $3.30/gallon.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The better deal is to because the price to fill a 12 gallon tank of gas for $43.75 is $ ____ per gallon.
B. The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $____per gallon.
Answer:
B; $3.30
Step-by-step explanation:
Since $43.75 is the cost of 12 gallon tanks, you want to multiply $3.30 by 12 to compare them when they each have the same amount of gallon tanks. This gets us to $39.60 which makes B the better deal.
However, the question asks for the unit price of one gallon tank, so you would want to put $3.30.
The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $ 39.60 per gallon.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is given that You can fill a 12 gallon tank of gas for $43.75 or buy gas for $3.30/gallon.
Since $43.75 is the cost of 12 gallon tanks, we need to multiply $3.30 by 12 to compare them when they each have the same amount of gallon tanks.
$3.30 x 12 = 39.60
Thus, $39.60 which makes B the better deal.
However, the question asks for the unit price of one gallon tank, so we would want to put $3.30.
The better deal is to buy gas $3.30/gallon because the price to fill a 12-gallon tank of gas for $43.75 is $ 39.60 per gallon.
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Solve the equation below, and check the solution. 0.3x = 9 The solution set is { }
I know the answer is x = 30, but I do not know how to give my answer in the form of a solution set??
Answer:
{30}
Step-by-step explanation:
The solution set can be written a couple of ways:
Roster: lists the elements of the set:
x = {30}
Set builder notation: defines the elements of the set according to some rule or rules
{x : x = 30}
The latter form can have variations that define the domain of x on the left, such as
[tex]\{x\in\mathbb{Z}:x=30\}[/tex]
This is pronounced, "x is an element of the set of integers such that x is equal to 30." This sort of notation is more commonly used when the set is specified by an inequality or a functional relationship. You may see the colon (:) replaced by a vertical bar (|).
_____
Comment on the above notations
I don't like the notation x = {30} because the solution to the equation is a value, not a set of values. I prefer to write it as x ∈ {30}. "x is an element of the set containing 30." The "is an element of" symbol (∈) is not always available, so the equal sign is often used instead.
Simplify completely x^2+4x-45 / x^2+10x+9
Answer: x - 5/x + 1
Step-by-step explanation:
This algebraic fraction
The task to be performed here is factorisation and simplification. Now going by the question,
x² + 4x - 45/x² + 10x + 9, the factorisation of
x² + 4x - 45 = x² + 9x - 5x - 45
= x(x + 9 ) - 5(x + 9 )
= ( x + 9 )(x - 5 ), don't forget this is the algebraic fraction's Numerator
The second part
x² + 10x + 9 = x² + x + 9x + 9
= x(x + 1) + 9( x + 1 )
= ( x + 9 )( x + 1 ), this is the algebraic denominator.
Now place the second expression which is the denominator under the first expression which is the numerator.
( x + 9 )( x - 5 )/( x + 9 )( x + 1 ).
You can see that, ( x + 9 )/( x + 9 ) divide each other , therefore therr then cancelled and left with
x - 5/x + 1
I'm trying to solve a equation of 3x-2=1 In the book, it says that 3 -2=-1 turns into 3x=3. I don't get it?! Shouldn't it be 3x=-1?
Answer: The book is right, it would break down to 3x = 3.
3x - 2 = 1 so add the 2 to the other side.
3x = 3 and then you can divide both sides by 3 to get x = 1.
Sorry if I misread what you were asking
Answer: The answer should be 3x = 3.
Step-by-step explanation:
Here's why:
3x -2 = 1
First one must isolate the 3x in order to solve the problem. So, then one must add 2 to both sides, since the 2 is negative. (So if it is a -2, add it to the other side because remember, you are doing it on both sides and you have to get it to the other side).
So doing that, you get:
3x = +2 +1
3x = 3
If you want to simplify further:
3x = 3
x = 1
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2
This question is incomplete, the complete question is;
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis
Answer:
V = π (512/15)
Step-by-step explanation:
Given that;
region of rotation
y² = 2x, x = 2y
Region is rotated about y-axis as shown in the image
for the point of intersection,
y²/2 = 2y
y² - 4y = 0
y(y-4) = 0
∴ y = 0, y = 4
so the region lies in 0 ≤ y ≤ 4
Now cross section area of washer is
A(y) = π(outer radius)² = π(inner radius)²
A(y) = π(2y)² - π(y²/2)²
A(y) = π(4y²) - π(y⁴/4)
A(y) = π(4y² - (y⁴/4))
now volume of the solid of revolution is
V = ⁴∫₀ A(y) dy
V = ⁴∫₀ π(4y² - (y⁴/4))dy
V = π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }
V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }
V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }
V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }
V = π { 256/3 - 1024/20 }
V = π { (5120 - 3072) / 60 }
V = π (512/15)
which of the binomials below is a factor of this trinomial
x^2-13+42
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{(x - 7)(x - 6)}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ {x}^{2} - 13x + 42 }[/tex]
Here, we have to find the two numbers that adds to 13 and multiplies to 42.
The numbers are 7 and 6
[tex] \sf{ {x}^{2} - (7 + 6)x + 42}[/tex]
⇒[tex] \sf{ {x}^{2} - 7x - 6x + 42}[/tex]
Factor out x from the expression
⇒[tex] \sf{x(x - 7) - 6x + 42}[/tex]
Factor out 6 from the expression
⇒[tex] \sf{x(x - 7) - 6(x - 7)}[/tex]
Factor out x - 7 from the expression
⇒[tex] \sf{(x - 7)(x - 6)}[/tex]
Hope I helped!
Best regards!!
Answer:
x-7 For AP EX peeps
Step-by-step explanation:
If M is the midpoint of XY, find the coordinates of X if M(-3, -1) and Y(-8, 6) A. (2.5, -5.5) B. (-5.5, 2.5) C. (0, 0) D. (2, -8)
Answer:
(2, -8)
Step-by-step explanation:
(x, y)=(-3, -1)
(x1+x2)/2=-3,
(y2+y2)/2=-1,
-------------------
(x1+x2)/2=-3
(y1+y2)/2=-1
---------------------
x1-8=-6
x1=2
----------
y1+6=-2
y1=-8
(2, -8)
You decide to get a new job as a furniture salesman. Each day you work you get $180 plus an additional $27 for each couch , chair , table you sell. Write a linear equation for the pay p for x piece of furniture sold on a shift.
Answer:
180+27x=p
Step-by-step explanation:
help please I don't understand
Answer:
x = 8AM = 64 cmBM = 64 cmM is the midpointStep-by-step explanation:
Part A. The total length of a line segment is the sum of the lengths of its parts.
AM +MB = AB
Substituting the given information, this equation becomes ...
(7x +8) cm + (9x -8) cm = 128 cm
16x = 128 . . . . . . . . . collect terms, divide by cm
x = 128/16 . . . . . divide by the coefficient of x
x = 8
__
Part B. Then the length of AM is ...
AM = (7x +8) cm = (7(8) +8) cm = (56 +8) cm
AM = 64 cm
__
Part C. The length of BM is ...
BM = (9x -8) cm = (9(8) -8) cm = (72 -8) cm
BM = 64 cm
__
Part D. AM = BM = 64 cm, so point M is the midpoint of AB. Point M divides the segment into two equal parts.
write each statement as a decimal to two decimal places. $6.00 to 95 cents 3 hours to 35 minutes 42 inches to 2 feet
Answer:
1. $6.00 to 95 cents = 6.32
2. 3 hours to 35 minutes = 5.14
3. 42 inches to 2 feet = 1.75
Step-by-step explanation:
Given
$6.00 to 95 cents
3 hours to 35 minutes
42 inches to 2 feet
Required
Express in 2 decimal places
1. $6.00 to 95 cents
Express as ratio
[tex]\$6.00 : 95\ cents[/tex]
Convert dollars to cents
[tex]6.00 * 100\ cents: 95\ cents[/tex]
[tex]600\ cents: 95\ cents[/tex]
Convert ratio to division
[tex]\frac{600\ cents}{95\ cents}[/tex]
[tex]6.31578947368[/tex]
Approximate
[tex]6.32[/tex]
2. 3 hours to 35 minutes
Express as ratio
[tex]3\ hours : 35\ minutes[/tex]
Convert hours to minutes
[tex]3 * 60\ minutes: 35\ minutes[/tex]
[tex]180\ minutes: 35\ minutes[/tex]
Convert ratio to division
[tex]\frac{180\ minutes}{35\ minutes}[/tex]
[tex]5.14285714286[/tex]
Approximate
[tex]5.14[/tex]
3. 42 inches to 2 feet
Express as ratio
[tex]42\ inches: 2\ feet[/tex]
Convert feet to inches
[tex]42\ inches:2 * 12\ inches[/tex]
[tex]42\ inches : 24\ inches[/tex]
Convert ratio to division
[tex]\frac{42\ inches}{24\ inches}[/tex]
[tex]1.75[/tex]
A pitcher throws a baseball 90 miles per hour. Convert this speed into feet per second.
3 folders cost $2.91 dollar sign . Which equation would help determine the cost of 2 folders? WRITE THE LETTER IN THE SPACE BELOW. see the file plz
Answer:
none of the above
Step-by-step explanation:
the equation is supposed to be 3=2.91, 2=x, I hope you get it.
Mr smith and mr stein were driving to a buisness meeting 250 miles from their office. Mr Smith drove the first x miles, then Mr Stein drove the rest of the way. Write an algebric expression for how many miles mr stein drove
Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges?
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
Help ASAP! MATH!!! Important
Answer:
x=3
Step-by-step explanation:
BC= 5 ~ EC=25
And we can see that BC times 5 equals the EC value. This means that BA times 5 will equal ED.
So we can set 5 * (BC) = (ED)
5x=18-x
Then solve for x:
6x=18
x=3
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
So we are given that ΔABC and ΔDEC are similar.
In other words, AB and DE are similar. And CA and CD are also similar.
When the sides are similar, it means that their proportions are equal to the each other. Therefore:
[tex]\frac{AB}{DE}=\frac{CA}{CD}[/tex]
Substitute 30 for AB, 18 for DE, 2x-1 for CA and x+1 for CD. So:
[tex]\frac{30}{18}=\frac{2x-1}{x+1}[/tex]
Reduce the left by dividing both layers by 6. Thus:
[tex]\frac{5}{3}=\frac{2x-1}{x+1}[/tex]
Cross multiply:
[tex]3(2x-1)=5(x+1)[/tex]
Distribute:
[tex]6x-3=5x+5[/tex]
Add 3 to both sides:
[tex]6x=5x+8[/tex]
Subtract 5x from both sides:
[tex]x=8[/tex]
So, the value of x is 8.
And we're done :)
Use a power series to approximate the value of the integral with an error of less than 0.0001. (Round your answer to four decimal places.)
integral^1_0 sin(x)/x dx
integral^1_0 sin(x)/x dx approximately equal to summation^2_n=0 (-1)^n x^2n+1 (-1)^n (x-1)^n/(2n + 1)!
Answer:
The answer is "0.9461"
Step-by-step explanation:
Given:
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex]
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]\sum^2_{n=0}\frac{(-1)^n x^{2n+1} (-1)^n (x-1)^n}{(2n + 1)!}[/tex]
[tex]\therefore[/tex]
[tex]\to \sin x = \sum^{\infty}_{n=0} (-1)^n\frac{x^{(2n+1)}}{(2n + 1)!}[/tex]
[tex]\because \\\\ \to \frac{\sin x}{x} =\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n+1-1}}{(2n+1)!}\\[/tex]
[tex]=\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n}}{(2n+1)!}[/tex]
The value is in between 0 and 1 then:
[tex]\to \int^1_0 \frac{sin(x)}{x} = =\sum^{2}_{n=0} \frac{(-1)^n}{ (2n+1) (2n+1)!}[/tex]
The above-given series is an alternative series, and it will give an error, when the nth term is bounded by its absolute value, that can be described as follows:
[tex]\to \frac{1}{(2n+3) (2n+3)!}< 0.0001\\\\\to (2n+3) (2n+3)!> 0.0001\\\\\to n\geq 2 \\[/tex]
So,
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]1 - \frac{1}{3 \cdot 3!}+\frac{1}{5 \cdot 5!}\\\\[/tex]
[tex]\approx 1 - \frac{1}{3 \cdot 6}+\frac{1}{5 \cdot 120}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx \frac{18-1}{18}+\frac{1}{600}\\\\\approx \frac{17}{18}+\frac{1}{600}\\\\\approx \frac{1700+3}{1800}\\\\ \approx \frac{1703}{1800}\\\\\approx 0.9461[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then the approximation summation is equal to 0.9461.
What is a power series?The finite series can be used as a polynomial with an infinite number of the term.
[tex]\int_{0}^{1} \dfrac{\sin x}{x} dx = \sum_{n=0}^{2} \dfrac{(-1)^{n}x^{2n+1}(-1)^{n}x^{n}}{(2n+1)!}[/tex]
Then we have
[tex]\Rightarrow \sin x = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1}}{(2n+1)!} \\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1-1}}{(2n+1)!}\\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n}}{(2n+1)!}[/tex]
Then the value is between 0 and 1, will be
[tex]\Rightarrow \int_0^1 \dfrac{\sin x}{x} = \sum_{n=0}^{2} \dfrac{(-1)^{n} }{(2n+1)(2n+1)!}[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then which can be described as
[tex]\Rightarrow \dfrac{1}{(2n+3)(2n+3)!} < 0.0001\\\\\\\Rightarrow (2n+3)(2n+3)! = > 0.0001\\\\\\\Rightarrow n > 2[/tex]
So,
[tex]\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 3!} + \dfrac{1}{5\times 5!}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 6} + \dfrac{1}{5\times 120}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{18} + \dfrac{1}{600}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 0.9461[/tex]
More about the power series link is given below.
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please help me with this question i’ll mark you as brainliest
Answer:
11^3/5
Step-by-step explanation:
Fractional exponents work like so:
[tex]x^{\frac{a}{b}} = \sqrt[b]{x^a}[/tex]
Essentially, the numerator (a) of the fraction is the power and the denominator (b) of the fraction is the root.
[tex]x^\frac{power}{root}[/tex]
We are given:
[tex]\sqrt[5]{11^3}[/tex]
The power is 3 and the root is 5. Let's substitute the values in.
[tex]x^\frac{power}{root}[/tex]
[tex]power=3\\root=5[/tex]
[tex]x^\frac{3}{5}[/tex]
x is the base. In this case, the base is 11.
[tex]11^\frac{3}{5}[/tex]
Therefore, 11^3/5 is the correct answer.
I need help again....