Answer:
[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}][/tex]
when:
[tex]|x|<\frac{1}{2}[/tex]
Step-by-step explanation:
In order to solve this problem, we must begin by splitting the function into its partial fractions, so we must first factor the denominator.
[tex]\frac{x+6}{2x^2-9x+5}=\frac{x+6}{(2x+1)(x-5)}[/tex]
Next, we can build our partial fractions, like this:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]
we can then add the two fraction on the right to get:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A(x-5)+B(2x+1)}{(2x+1)(x-5)}[/tex]
Since we need this equation to be equivalent, we can get rid of the denominators and set the numerators equal to each other, so we get:
[tex]x+6=A(x-5)+B(2x+1)[/tex]
and expand:
[tex]x+6=Ax-5A+2Bx+B[/tex]
we can now group the terms so we get:
[tex]x+6=Ax+2Bx-5A+B[/tex]
[tex]x+6=(Ax+2Bx)+(-5A+B)[/tex]
and factor:
[tex]x+6=(A+2B)x+(-5A+B)[/tex]
so we can now build a system of equations:
A+2B=1
-5A+B=6
and solve simultaneously, this one can be solved by substitution, so we get>
A=1-2B
-5(1-2B)+B=6
-5+10B+B=6
11B=11
B=1
A=1-2(1)
A=-1
So we can use these values to build our partial fractions:
[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]
[tex]\frac{x+6}{(2x+1)(x-5)}=-\frac{1}{2x+1}+\frac{1}{x-5}[/tex]
and we can now use the partial fractions to build our series. Let's start with the first fraction:
[tex]-\frac{1}{2x+1}[/tex]
We can rewrite this fraction as:
[tex]-\frac{1}{1-(-2x)}[/tex]
We can now use the following rule to build our power fraction:
[tex]\sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}[/tex]
when |r|<1
in this case a=1 and r=-2x so:
[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2x)^n[/tex]
or
[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2)^{n} x^{n}[/tex]
for: |-2x|<1
or: [tex] |x|<\frac{1}{2} [/tex]
Next, we can work with the second fraction:
[tex]\frac{1}{x-5}[/tex]
On which we can factor a -5 out so we get:
[tex]-\frac{1}{5(1-\frac{x}{5})}[/tex]
In this case: a=-1/5 and r=x/5
so our series will look like this:
[tex]-\frac{1}{5(1-\frac{x}{5})}=-\frac{1}{5}\sum_{n=0}^{\infty} (\frac{x}{5})^n[/tex]
Which can be simplified to:
[tex]-\frac{1}{5(1-\frac{x}{5})}=-\sum_{n=0}^{\infty} \frac{x^n}{5^(n+1)}[/tex]
when:
[tex]|\frac{x}{5}|<1[/tex]
or
|x|<5
So we can now put all the series together to get:
[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}}[/tex]
when:
[tex]|x|<\frac{1}{2}[/tex]
We use the smallest interval of convergence for x since that's the one the whole series will be defined for.
The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given in as
x 01234
f(x) 0.41 0.37 0.16 0.05 0.01
Find the average number of imperfections per 10 meters of this fabric.
Answer:
0.88
Step-by-step explanation:
x 01234
f(x) 0.41 0.37 0.16 0.05 0.01
The mean or average is the expected value :
E(X) = Σ(x * p(x)) = (0 * 0.41) + (1 * 0.37) + (2 * 0.16) + (3 * 0.05) + (4 * 0.01)
E(X) = 0 + 0.37 + 0.32 + 0.15 + 0.04
E(X) = 0.88
Please help me i will give you brainlest
Answer:
Step-by-step explanation:
5 ) c
6) c
7) b
8) a
Suppose you have $1750 in your savings account at the end of a certain period of time. You invested $1500 at a 3.72% simple annual interest rate. How long, in years, was your money invested?
Answer:
4.48 years
Step-by-step explanation:
The formula for simple interest is
A = P(1+r*t), with A being the final amount, P being the initial amount, r being the interest rate, and t being the time. Plugging our values in, we get
1750 = 1500(1+0.0372 * t)
Note that 3.72 was translated into 0.0372 as changing percents to decimals requires dividing by 100
Expanding our equation, we get
1750 = 1500 + 55.8 * t
subtract 1500 from both sides to isolate the t and its coefficient
250 = 55.8 * t
divide both sides by 55.8 to get t
t = 4.48
Solve the system of linear equations below.
6x + 3y = 33
4x + y = 15
A.
x = 2, y = 7
B.
x = -13, y = 7
C.
x = - 2/3, y = 12 2/3
D.
x = 5, y = 1
Answer:
The answer for both linear equations is A. x = 2, y = 7
Step-by-step explanation:
First start by plugging in the variables with the given numbers (2,7). We'll start with 6x + 3y = 33.
6x + 3y = 33
6 (2) + 3 (7 )= 33 <--- This is the equation after the numbers are plugged in.
12 + 10 = 33
33 = 33 <---- This statement is true, therefore it is the correct pair.
Now we are not done, to confirm that this pair works with both equations we need to solve for 4x + y = 15 to see if it works. Linear Equations must have the variables work on both equations.
4x + y = 15 <----- We are going to do the exact same thing to this equation.
4(2) + 7 = 15
8 + 7 = 15
15 = 15 <-- 15=15 is a true statement therefore this pair works for this equation.
Therefore,
A. x = 2, y = 7 is the correct answer
Sorry this is a day late, I hope it helps.
(S
Sue can shovel snow from her driveway in 65 minutes. Tom can do the same job in 45 minutes How long would a
take Sue and Tom to shovel the driveway if they worked together?
Answer:
26.59 minutes
Step-by-step explanation:
Let's say the time needed to do the driveway combined is x. Sue does y parts of the driveway, and Tom does z parts of the driveway. Combined, y + z = 100% = 1, as they finish the whole driveway.
Next, Tom will take 45 * z minutes to do his part of the driveway. For example, if he did 50% = 0.5 of the driveway, he would take 45 * 0.5 = 22.5 minutes to do it. Similarly, Sue will take 65 *y minutes to do her part of the driveway. Since they will finish at the same time, we can say
45 * z = 65 * y
y + z = 1
Therefore, if we subtract y from both sides of the second equation, we have
z = 1-y
We can then plug 1-y in for z in the first equation to get
45 * (1-y) = 65 * y
45 - 45*y = 65*y
add both sides by 45 * y to separate the y values and their coefficients
45 = 110 * y
divide both sides by 110 to find y
y = 45/110 = 0.409
Use 1-y=z to get z = 1-0.409 = 0.59
Therefore, 45*z = 26.59 = 65*y
If 4x³+kx²+px +2 is divisible by x²+ α prove that kp=8.
Answer:
Attached images
It was just easier for me this way.
Let me know in comments if you have questions.
Step-by-step explanation:
While preparing for their comeback tour, The Flaming Rogers find that the average time it takes their sound tech to set up for a show is 56.1 minutes, with a standard deviation of 6.4 minutes. If the band manager decides to include only the fastest 23% of sound techs on the tour, what should the cutoff time be for concert setup? Assume the times are normally distributed.
Answer:
The cutoff time be for concert setup should be of 51.4 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Average time it takes their sound tech to set up for a show is 56.1 minutes, with a standard deviation of 6.4 minutes.
This means that [tex]\mu = 56.1, \sigma = 6.4[/tex]
If the band manager decides to include only the fastest 23% of sound techs on the tour, what should the cutoff time be for concert setup?
The cutoff time would be the 23rd percentile of times, which is X when Z has a p-value of 0.23, so X when Z = -0.74.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.74 = \frac{X - 56.1}{6.4}[/tex]
[tex]X - 56.1 = -0.74*6.4[/tex]
[tex]X = 51.4[/tex]
The cutoff time be for concert setup should be of 51.4 minutes.
Can someone do these for me and list the number because I’m struggling rn. And I’m having a breakdown lol.
Answer:
Step-by-step explanation:
First remove the parentheses.
As the sign outside the second parentheses is a + then the signs of the terms inside stay the same.
So the first one + (-3x +2) is just -3x + 2.
All the others on the left column are answered in the same way.
No. 4:
(-2x + 10 + (-8x - 1) Just remove the parentheses, we get:
-2x + 10 - 8x - 1 (we leave out the + before the second parentheses).
= -2x - 8x + 10 - 1
= -10x + 9
6. 8x + 8 + ( -6x - 1)
= 8x + 8 - 6x - 1
= 8x - 6x + 8 - 1
= 2x + 7.
- the other expressions on the right side column are solved in the same way.
If h(x) is the parent function, which equation describes the function song shifted 3 units left and 5 units down?
Answer:
h(x + 3) - 5Step-by-step explanation:
Given function h(x).
Shift left:
h(x) → h(x + 3)Shift down:
h(x + 3) → h(x + 3) - 5Given function is,
→ h(x)
As we shift left,
→ h(x) = h(x + 3)
As we shift down,
→ h(x + 3) = h(x+3)-5
Then the equation is,
→ h(x+3)-5
It is correct answer.
Diana adds either 2 or 5 to every whole number from 1 to 9. She wants to achieve as few different sums as
possible. What is the minimum number of different values she obtains?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
the inner diameter of the top of am ornamental cup is 7,5cm and the diameter of the inner bottom is 3,0cm.the depth of the cup is 10cm.calculate the capacity of the cup
Answer:
Frustum Volume =
[PI * height * (small radius^2 + (small radius * large radius) * + large radius^2)] / 3
Frustum Volume = PI * 10 * ( 1.5^2 + 1.5*3.75 + 3.75^2 ) / 3
Frustum Volume = 31.41592654 * (2.25 +5.625 +14.0625) / 3
Frustum Volume = (31.41592654 * 21.9375) / 3
Frustum Volume = 689.1868884713 / 3
Frustum Volume = 229.72896282 cubic cm
Source: http://www.1728.org/volcone.htm
Step-by-step explanation:
One urn contains 6 blue balls and 14 white balls, and a second urn contains 12 blue balls and 7 white balls. An urn is selected at random, and a ball is chosen from the urn. a. What is the probability that the chosen ball is blue? b. If the chosen ball is blue, what is the probability that it came from the first urn?
Answer:
a) 0.4658 = 46.58% probability that the chosen ball is blue
b) 0.322 = 32.2% probability that it came from the first urn
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What is the probability that the chosen ball is blue?
6/20 = 0.3 of 0.5(first urn)
12/19 = 0.6316 out of 0.5(second urn).
So
[tex]P(A) = 0.3*0.5 + 0.6316*0.5 = 0.4658[/tex]
0.4658 = 46.58% probability that the chosen ball is blue.
b. If the chosen ball is blue, what is the probability that it came from the first urn?
Event A: Blue Ball
Event B: From first urn
From item a., [tex]P(A) = 0.4658[/tex]
Probability of blue ball from first urn:
0.3 of 0.5. So
[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.4658} = 0.322[/tex]
0.322 = 32.2% probability that it came from the first urn
Identify the sampling technique used for the following study.
A statistics student interviews the last fifteen attendees to arrive.
A) Census
B) Stratified Sample
C) Systematic Sampling
D) Simple Random Sampling
E) Cluster Sampling
F) Convenience Sampling
Answer:
F) Convenience Sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
A statistics student interviews the last fifteen attendees to arrive.
Conveniently available, so convenience, and the correct answer is given by option F.
Consider the function f(x)=x^3-4x^2+2. Calculate the limit of the difference quotient at x0=3 for f(x).
The limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex] such that [tex]f(x)=x^{3} - 4x^{2} + 2[/tex].
Difference of quotientThe difference quotient of a function [tex]f(x)[/tex] is [tex]\frac{f(x+h)-f(x)}{h}[/tex].
How to evaluate the limit of the function?The given equation is, [tex]f(x)=x^{3} -4x^{2} +2[/tex]
So, [tex]f(x+h)=(x+h)^{3} -4(x+h)^{2} +2= x^{3} +h^{3}+3x^{2} h+3xh^{2} -4x^{2} -4h^{2} -8xh+2[/tex]
Now, [tex]f(x+h)-f(x)[/tex]
[tex]=x^{3}+h^{3}+3x^{2}h+3xh^{2}-4x^{2}-4h^{2}-8xh+2-x^{3}+4x^{2}-2[/tex]
[tex]=h^{3}+3x^{2}h+3xh^{2}-4h^{2}-8xh[/tex]
So, [tex]\frac{f(x+h)-f(x)}{h} =\frac{h^{3}+3x^{2}h+3xh^{2} -4h^{2}-8xh }{h}[/tex]
[tex]=h^{2}+3x^{2}+3xh-4h-8x[/tex]
Now, at [tex]x=3[/tex],
[tex]h^{2}+3x^{2}+3xh-4h-8x=h^{2}+27+9h-4h-24=h^{2}+5h+3[/tex]
If [tex]h[/tex]→[tex]0[/tex], the value of [tex]h^{2}+5h+3=3[/tex]
Thus, the limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex].
Learn more about the limit of the difference quotient here- https://brainly.com/question/17008881
#SPJ2
please show me step by step how to simplify this equation
Answer:
1-x^2/x^3 - 1 = 1/x
Step-by-step explanation:
First rewrite x^3 as x^2 * x cancel x^2 in both numerator and denominator.
Write below
1 - 1/x - 1
Subtract
1 - 1 = 0
now simplify
1 -1 /x - 1 = 1/x
1/x = Answer
Can you Understand
Notación científica de 0,567
Answer:
0,00567×10¹
Step-by-step explanation:
Para convertir a notación decimal:
0.00567×10¹
Complete the sentences below:
The value of________ is negative because 240 is in quadrant III. The reference angle is___________. and the exact value of 240 degrees is_________.
Answer Deleted
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need help now!!! Please and thanks
Answer:
the answer of r is 8 i hope it will help
A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for $25, 15% for $50, and 10% for $500. What are the odds of a player winning $5 or $25
Answer: 75%
Step-by-step explanation:
Which graph represents the function?
Answer:
D
Step-by-step explanation:
I have attached the explanation above. hopefully this will help
Evaluate the expression when c = 3 and x= -5,
-C+5x
Answer:
-28
Step-by-step explanation:
if c = 3 and x = -5 than,
-c + 5x = -3 + 5 * (-5) = -3 + (-25) = - 28
Find the domain.
p(x) = x^2+ 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( − ∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
Step-by-step explanation:
hope that helps bigger terms
Find the probability of selecting 3 cards from a standard deck without
replacing them and all 3 are hearts.
Answer:
B
Step-by-step explanation:
THere are 52/4= 13 hearts we can draw
The number of ways to draw 3 hearts from 13 is
13C3= 286
The number of ways to draw 3 cards from 52 is
52C3= 22100
divide these
286/22100= 11/850
This is answer B
pls help
With a coupon you can buy up to 4 medium pizzas at $6 each. What is the
domain of this graph?
Answer:
Domain: {1, 2, 3, 4}
Step-by-step explanation:
The domain of the graph (input values) is the number of pizzas which are plotted on the x-axis while the range (output values) is the cost of pizza, plotted on the y-axis (vertical axis)
The domain therefore would consists of each x-coordinate that represent each point on the graph, which are {1, 2, 3, 4}
help me guys, I really need your help
Answer:
The answer should be like this;
a) A-B
b) BUC
c) C-A
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
Which statements below represent the situation? Select three options.
Answer:
where is the statement
Step-by-step explanation:
its incomplete po
When P(x) is divided by (x - 1) and (x + 3), the remainders are 4 and 104 respectively. When P(x) is divided by x² - x + 1 the quotient is x² + x + 3 and the remainder is of the form ax + b. Find the remainder.
Answer:
The remainder is 3x - 4
Step-by-step explanation:
[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]
So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]
In this case our dividend is always P(x).
Part 1
When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]
When [tex]x = 1[/tex],
[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]
--------------------------------------------------------------------------------------------------------------
Part 2
When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]
In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]
When solving for [tex]x[/tex], we get
[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]
When [tex]x = -3[/tex],
[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]
--------------------------------------------------------------------------------------------------------------
Part 3
When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]
We will call [tex]a + b = -1[/tex] equation 1
From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]
When we do, we get:
[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]
We will call [tex]3a - b = 13[/tex] equation 2
Now we can create a system of equations using equation 1 and equation 2
[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]
By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]
So equation 1 + equation 2:
[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]
Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.
So substituting [tex]a = 3[/tex] into equation 1:
[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]
Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.
So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:
[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]
Therefore, the remainder is [tex]3x - 4[/tex].
For a population with µ = 40 and σ = 8, what is the z-score corresponding to X = 34?
Answer:
Step-by-step explanation:
[tex]\frac{34-40}{8}= -.75[/tex]
Would you rather?
buy 2 lollypops for $2
buy 30 lollypops for $40
Answer:
Buy 2 lollipops for $2.
Step-by-step explanation:
If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.
Find the value of X in each case:
Answer:
hi, see mate the third angle is not in the photo, please upload another one