The Maclaurin series of ln(1 − x) is f(x) = ∑xⁿ⁺¹/(n+1) + c
What is the Maclaurin series?A Maclaurin series is a Taylor series expansion of a function about 0,
f(x) = f(0) + xf'(0) + x²f''(0)/2! + x³f⁽³⁾(0)/3! +.... xⁿf⁽ⁿ⁾(0)/n! ...
We have been the given function
⇒ f(x) = ln(1 − x)
First, let us find the derivative of f(x) for the Maclaurin series,
f'(x) = 1/(1 − x) = 1/(1 − x)
⇒ 1/(1 − x) = 1 + x + x² + x³⋯ = ∑xⁿ if -1< x <1
f'(x) = ∑xⁿ if -1< x <1
By integrating using Power Rule,
⇒ f(x) = ∫∑xⁿ if -1< x <1 = ∑xⁿ⁺¹/(n+1) + c
Since f(0) = ln(1 − 0) = 0
So ln(1 − x) = ∑xⁿ⁺¹/(n+1) + c
Hence, the Maclaurin series of ln(1 − x) is f(x) = ∑xⁿ⁺¹/(n+1) + c
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A statewide poll for an upcoming gubernatorial election concluded that 52.8% of the voters will vote for candidate A and 47.1% will vote for candidate B. The margin of error is ±2.5%. The confidence level for this result is 95%. Explain the confidence interval.
Step-by-step explanation:
a) For a 95% confidence interval we use the formula
First we need to establish the sample proportion
The sample size is
n = 200
and the critical value of z for a 95% confidence interval is
z* = 1.960
This gives us
This gives us an upper confidence limit of
.525 + .069 = .594 or 59.4%
and a lower confidence limit of
.525 - .069 = .456 or 45.6%
b) At this point her supporters wonder what her chances of winning are. 45.6% is below 50%, so she might lose. To find her chances of losing, consider the bell shaped curve
top
Her probability of winning is the area to the right of 50%. We need to turn the 50% into a z score
= -.708
We look up a z-score of -.71 in Table A and get an area of .2389. This is the probability that she will lose. the probability that she will win is
.7611
c) The candidate's supporters would like to be more sure that she will win. They decide to increase the sample size until the 95% confidence interval is only plus or minus 3%. They want to know how large of a sample they will need to get that kind of accuracy. We use the formula for the margin of error.
top
To solve for n, first square both sides to get rid of the radical.
Multiply both sides by n and divide both sides by m2.
For a 95% confidence interval z* = 1.96. We put in our other numbers
= 1064.4433
so they would have to survey 1065 people in order to get a 95% confidence interval that would only stretch up and down 3%.
top
What is 7/8 + 8/45 =
Step-by-step explanation:
1.05277777778
hope it helps!
Answer:
1 19/360
Step-by-step explanation:
What we know:
The addends in this equation are 7/8 and 8/45.
First, find the LCM of 8 and 45. Since 8 and 45 don't have any common factors other than 1, just multiply the two numbers.
8 * 45 = 360
After that, find the equivalent fraction for both addends
7/8 * 45/45 = 315/360
8/45 * 8/8 = 64/360
Then, add the two new fractions together, and simplify if needed.
315/360 + 64/360 = 379/360 = 1 19/360
Please help its 50 points
Reflect on why you think the main character in "The White Umbrella" throws away her hard won prize.
Answer: The reason why the narrator throw the umbrella down the sewer after the car accident is that the umbrella symbolized the rejection of her mother The narrator feel ashamed about her working mother who cannot afford her the standard of living like she's seen in her friends. in the end, she feel ashamed of this and the umbrella remind her of her shameful thought about her mother
Step-by-step explanation:
Answer:
At first, she was upset. She had seen how Eugenie Roberts’s mother acted to her child and how she had treated them, with kindness and utmost interest. She was jealous because her mother had been working all of the time. After her mother came to pick them up, she told her mother she wanted her to quit her job, she didn't want her to work, she wanted to feel like every kid and have her mother there with her to let her know she loved her. And then she had gotten into an accident, in her anger, her mother tilted her head back and closed her eyes, waiting for the yelling people to approach her car. But she thought her mother was dead, she screamed at her mother to open her eyes, before her mother told her to be quiet because people were already going to yell at her and she couldn't take any more yelling. She threw her umbrella in the sewer. Deciding to never be that angry with her mother, for working again.
I hope this helps! :)
Sam and his family go out to eat for his birthday. The total bill is $123.79. The tax on his meal is 8.25%. What is the total amount he will pay for the bill not including the tip for the waitress
please help
Answer:
It will come out to about $134 even.
Mark brainlyest if this helps
Step-by-step explanation:
f(x)=3x-9; horizontal stretch factor of 6
The Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .
The graph of the function y=f(x/a) represents a Horizontal Stretch by a factor of a of the graph y=f(x) , where a>0 and a≠1 .
To find the horizontal stretch we divide the input by a ,
In the given question
f(x)=3x-9 , is horizontally stretch by a factor of 6.
So we divide the inputs by 6 .
On dividing the inputs by 6 , we get
f(x/6)=3(x*1/6)-9 (...as 3/6=1/2)
Let g(x) represents the horizontal stretch of f(x) by factor 6 , So
g(x)=x/2-9
Therefore , the Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .
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An airplane flying at an altitude of 14,382 feet ascends another
9,372 feet. A little while later, it descends 10,345 feet.
What is the altitude of the airplane after it descends?
The altitude of the airplane after it descends is 13,409 feet.
What is altitude?The meaning of ALTITUDE is the vertical elevation of an object above a surface (such as sea level or land) of a planet or natural satellite.
Now it is given that,
Initial Altitude of airplane = 14,382 feet
Then plane ascends = 9,372 feet
So, Altitude of airplane = 14,382 feet + 9,372 feet = 23,754 feet
Again airplane descends = 10,345 feet
So, Altitude of airplane = 23,754 feet - 10,345 feet
⇒ Altitude of airplane = 13,409 feet
Thus, the altitude of the airplane after it descends is 13,409 feet.
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Which expression is equivalent to -6 (- 2/3+2x)?
Answer:
4-12x
Step-by-step explanation:
Answer:
4-12x so c
Step-by-step explanation:
Which fraction is the largest?
Answer:
17/30
Step-by-step explanation:
Which percent represents the diagram?
8.5%
0.85%
0.085%
85%
In an AP, the ratio of the 7th term to the 10th term is -1. If the 16th term is -15, what is the 3rd term?
Answer:
The 3rd term is 11
Step-by-step explanation:
The given parameters for the Arithmetic Progression, AP, are;
The ratio of the 7th term to the 10th term = (a + 6·d)/(a + 9·d) = -1
The 16th term = -15 = a + 15·d
The 3rd term= a + 2·d
From the 7th to the 10th term ratio, we have;
a + 6·d = -a - 9·d
2·a = -15·d
-2·a = 15·d...(1)
From the 16th term of the AP, we have;
-15 = a + 15·d = a + -2·a = -a
a = 15
From equation (1), -2·a = 15·d, we have;
-2·a = -2 × 15 = 15·d
15·d = -2 × 15
d = -2 × 15/15 = -2
d = -2
The 3rd term = a + 2·d = 15 + 2 × -2 = 11
∴ The 3rd term = 11
angle 4=x+30 and angle 2=2x+15. Find the measure of angle 4
9514 1404 393
Answer:
∠4 = 45°
Step-by-step explanation:
Angles 1, 2, and 4 are all congruent.
∠4 = ∠2
x +30 = 2x +15
15 = x . . . . . . . . . . . . . subtract x+15
x + 30 = 45 = ∠4
Which equation describes the line with a slope of 5 and a y-intercept of 4.
Answer:
The line should look like: y=5x+4
Step-by-step explanation:
The equation for slope-intercept form is y=mx+b, where m is your slope and b is your y-intercept.
Therefore, if we plug in the given values, our equation should look like the following:
y=5x+4
Answer:
y=5x+4
y=mx+b
.A gym charges an enrollment fee of $85 plus $25 per month, where x
is the number of months and y is the total amount of money spent in
dollars. Which equation matches this situation
Answer:
85+25x=y
Step-by-step explanation:
if you plug in the number of months for x, and multiply that number by 25, you will get the total amount.
two standard $6$-sided dice are rolled. what is the probability that the sum rolled is a perfect square?
Two standards $6$-sided dice are rolled. The probability that the sum rolled is a perfect square 7/36.
What is probability?Likelihood is the part of math concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a suggestion is valid. Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a recommendation is valid. Likelihood and measurements, the parts of science worried about the regulations administering arbitrary occasions, including the assortment, investigation, understanding, and show of mathematical information. While calculation and variable based math were concentrated on by old Greek mathematicians over long time back, the ideas of likelihood just arose in the seventeenth and eighteenth 100 years.
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At a pizza eating competition, Davonne at two more than twice as many slices as the runner-up. If Davonne at 11 slices, then how many slices did the runner-up eat?
HELPPP ITS AN EMERGENCY!!!!!!
Answer:
The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]
Step-by-step explanation:
We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line [tex]y=-\frac{1}{3}x+4[/tex]
The general form of point-slope is; [tex]y-y_1=m(x-x_1)[/tex]
where m is slope and [tex](x_1,y_1)[/tex] is the point
We need to calculate slope.
We are given equation of line [tex]y=-\frac{1}{3}x+4[/tex] that is perpendicular to the required line.
The equation is given in slope-intercept form [tex]y=mx+b[/tex] where m is slope.
Comparing both equations we get m= -1/3
But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e [tex]m=-\frac{1}{m}[/tex]
So, slope of required line is m = 3 (opposite reciprocal of -1/3)
Now, the equation in point-slope form having slope m=3 and point (6,-5) is
[tex]y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)[/tex]
So, The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]
A total of 250 people were surveyed about whether or not each person carries a cell phone.
Total
Carries
Cell
Phone
0.42
Does Not
Carry Cell
Phone
0.16
Female
0.58
Male
0.12
0.42
0.30
0.72
Total
0.28
1.00
Which statement is correct?
The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant
digits.
2 x 10^2
2 x 10^3
0.7 x 10^1
6.67 x 10^2
The number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1
How many times smaller is the bacterial cell than the amoeba cell?The given parameters are:
Bacteria cell = 3 x 10^-6 m
Amoeba cell = 4.5 x 10^-4 m
The number of times (n) is calculated as
n = Amoeba cell/Bacteria cell
This gives
n = (3 x 10^-6 m)/(4.5 x 10^-4 m)
This gives
n = 0.7 * 10^-2
Rewrite as
n = 7 * 10^-1
Hence, the number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1
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y=2x+5y=2x+5y, equals, 2, x, plus, 5
Complete the missing value in the solution to the equation.
(2,(2,left parenthesis, 2, comma
))
Answer:
y=2x+5y
x=−2
y=.5
Answer: 9
Step-by-step explanation:
Khan Academy
A local fabric store advertises three and one-half yards of fabric for $4.50. If their everyday price per year is $1.15, is it less expensive to buy the fabric while it is on sale?
Answer:
one spool of thread costs $1.89
Step-by-step explanation:
$8.99x3=$26.97
$32.64-$26.97=$5.76
$5.76 divided by 3=$1.89
can someone please help? i will mark brainliest please explain your answer too, thank you
Answer: B. ZX is parallel to CA
Step-by-step explanation:
B is the correct answer because ZX and CA form parallel lines which shows they are parallel to each other.
The first astronaut on mars tossed a rock straight up.the height h measured in feet after tt seconds is given by function h(t)=-6t²+24t+6
After how many seconds will the rock be 30 ft above the surface of Mars?
After how many seconds will the rock be 10 ft above the surfaces of Mars? (Round to nearest hundredth)
Answer:
h'(t)= -12
Step-by-step explanation:
h'(t)=d/dt (-6t x 2 + 24 + 6)
h'(t)=d/dt (-12t + 24 + 6)
h'(t)=d/dt (-12t + 30)
h'(t)=d/dt (-12t) + d/dt (30)
h'(t)= -12+0
a) After 2 seconds the rock will be 30 feet above the surface.
b) After 3.83, 0.17 seconds the rock will be 10 feet above the surface.
a) Given that the height = h(t) =30
Plug it in the equation and find t.
[tex]30=-6t^2+24t+6\\6t^2-24t+24=0\\6(t^2-4t+4)=0\\6(t-2)^2=0\\t=2[/tex]
b) Given that the height = h(t) =10
Plug it in the equation and find t.
[tex]10=-6t^2+24t+6\\6t^2-24t+4=0\\2(3t^2-12t+2)=0\\3t^2-12t+2=0[/tex]
Then use the quadratic formula.
[tex]t=\frac{12 \pm \sqrt{(-12)^2-4(3)(2)} }{2(3)}\\ t=\frac{12 \pm \sqrt{120} }{6}\\\\t=3.83, 0.17[/tex]
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Please answer Quickly! I'LL GIVE 20 POINTS !!!
There are two questions I need help with:
1.) What is the distance between -11 and 3? Writean expression and then solve.
2.) A bird has built a nest on a branch 15 feet from the ground. A groundhog has dug a burrow 2 feet below the ground. What is the distance from the nest to the burrow?
1. There is a distance of 14
2. There is a distance of 17
Given f(x)= x-3 and g(x)= 2x+1
Find (fºg) (-10)
Answer:
- 66
Step-by-step explanation:
Evaluate g(- 4) then substitute the value obtained into f(x) , that is
g(- 4) = - 2(- 4)² = - 2 × 16 = - 32, then
f(- 32) = 2(- 32 - 1) = 2 × - 33 = - 66
What is the perimeter?
Answer:
26
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
6 +6=12
12+3=15
15+2=17
17+4=21
Anyone know how to solve this?
Answer:
ya we have to tell its initial value after 11 years it too simple
Answer:
The value after 11 years would be: 2880 us dollars
Step-by-step explanation:
Given the function
[tex]v\left(t\right)=32,000\left(0.80\right)^t[/tex]
The initial value is basically the first output value when the input value = 0.
Here,
The initial value can be obtained by putting t=0 in the function
[tex]v\left(0\right)=32,\:000\left(0.80\right)^0[/tex]
[tex]\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0[/tex]
[tex]0.8^0=1[/tex]
Thus,
[tex]v\left(0\right)=32000\cdot \:\:1[/tex]
[tex]=32000[/tex]
Thus, initial value = v(0) = 32000
Value after 11 years can be obtained by putting t=11 in the function
[tex]v\left(11\right)=32,\:000\left(0.80\right)^{11}[/tex]
as
[tex]0.8^{11}=0.09[/tex]
so the expression becomes
[tex]v(11)=32000\cdot \:\:0.09[/tex]
[tex]=2880[/tex] us dollars
Thus, the value after 11 years would be: 2880 us dollars
what is 14 radical 2 divided by radical 2
Answer: either 14
Step-by-step explanation:
I need help with this
Answer:
1: yes
2:no
3:yes
Step-by-step explanation:
that's what i know
can anyone help? I’ll give brainlest ❤️
Answer:
C
Step-by-step explanation:
I inserted 5 for a and c is the correct answer
will list you brainlest please hurry
Answer:
0- -3 1/4+1 3/4
Step-by-step explanation:
i belive this is the answer, but im not 100% sure sry if im wrong