The power series is
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence
The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.
Its radius of convergence is 0.5
Let,
f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....
The power series expansion (geometric series),
valid for I2xI < 1 , IxI < 0.5
so, radius of convergence = 0.5
The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5
Now, g(x) = ln(1-2x)
= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]
=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
is the power series expansion for g(x).
radius of convergence =0.5
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if y=mx+b, find m and use the formula for the previous question to find m when the coordinates are (4,7) and b=12
Answer:
m = -5/4
Step-by-step explanation:
In the slope-intercept form formula, y = mx + b, substitute 4 for x, 7 for y, and b for 12 to solve for m.
y = mx + b
7 = 4m + 12
-5 = 4m
m = -5/4
Defective electronics: A team of designers was given the task of reducing the defect rate in the manufacture of a certain printed ole circuit board. The team decided to reconfigure the cooling system. A total of 985 boards were produced the week before the reconfiguration was implemented, and 260 of these were defective. A total of 842 boards were produced the week after reconfiguration, and 194 of these were defective. Part: 0/2 Part 1 of 2 (a) Construct a 99% confidence interval for the decrease in the defective rate after the reconfiguration. Use the TI-84 Plus calculator and round the answers to three decimal places. A 99% confidence interval for the decrease in the defective rate after the reconfiguration is <21-22<0.
The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
How to find Confidence Intervals?Let the random variable & parameters be;
x1 : Number of successes from group 1
x2 : Number of successes from group 2
p1: Proportion of successes in group 1
p2: Proportion of successes in group 2
n1 : number of trial in group 1
n2: number of trial in group 2
We are given;
x1 = 260
n1 =985
x2 = 194
n2 = 842
Thus;
p1 = 260/985
p1 =0.2640
p2 = 194/842
p2 = 0.2304
Constructing a (1 - α)100% confidence interval for proportion from the formula;
(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]
plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;
(-0.0184631, 0.0855743)
Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
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In your own words, define the unit rate in an equation of proportional relationship y= kx.
Answer:
hdchyf
Step-by-step explanation:
fhyrb ufgfyg hchybgvtct ugh
How many ways can a 2 person subcommittee be selected from a comittee of 6 people?
Answer: 15 ways
Step-by-step explanation: 5+4+3+2 + 1 = 15
Answer:
15.
Step-by-step explanation:
That would be the number of combinations of 2 from 6.
6C2
= 6! /4!2!
= 6*5/2*1
= 15.
PLEASE HELP ME PLEASE
WHICH EQUATION DOES THE GRAPH REPRESENT
Answer:
Step-by-step explanation:
B is the best answer
the selling price of a mobile after discount is 10000.if the discount is 10% find the mp
Answer:
Rs.11,111.11 (2 d.p.)
Step-by-step explanation:
The original price of the mobile is 100% of the price.
Therefore, the price of the mobile after a discount of 10% is 90% of the original price.
Let x be the original price.
If the price of the mobile after the discount is Rs.10000 then:
⇒ 90% of x = Rs.10000
⇒ 0.9x = 10000
⇒ x = 10000 ÷ 0.9
⇒ x = 11111.11 (2 d.p.)
M.P. =Rs 11111.1111
Answer:
Solution Given:
Selling price (S.P.) = Rs 10,000.
Discount =10%
Marked Price (M.P.)=?
we have
M.P. = S.P. + discount% of M.P.
keeping M.P. on same side
M.P. - discount% of M.P=S.P.
substituting value
M.P. - 10% of M.P.= Rs 10,000
taking common M.P.
M.P.(1-10%)=Rs. 10,000
we know that %=1/100
M.P.(1-10/100)=Rs 10,000
(9/10)M.P.= Rs 10,000
M.P.= Rs 10,000*10/9
M.P.=Rs11111.1111
Write 304.9% as a decimal.
Answer:
3.049
Step-by-step explanation:
Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.
Brainliest, please :) Hope this helps!
I need help on how to solve for Z
Answer:
[tex]z=\frac{t^{2}(m-3) }{4}[/tex] or [tex]z=\frac{1}{4}t^{2} (m-3)[/tex]
Step-by-step explanation:
[tex]t=\sqrt{\frac{4z}{m-3} }[/tex]
[tex]t^{2} =\frac{4z}{m-3}[/tex]
[tex]4z=t^{2} (m-3)[/tex]
[tex]z=\frac{t^{2}(m-3) }{4}[/tex]
Hope this helps
A contractor is excavating a ramp into a trench for a construction project. How much dirt will the crew have to remove? To answer, find the volume of the triangular prism in the figure shown. Opening 4 x 6, ramp 8'deep
Which of the following linear equations corresponds to the table above?
O A. y = 4x - 3
O B. y=¹/4 x-3
OC. y=1/4x+3
OD. y = 4x + 3
The linear equations that corresponds to the table is y = 4x + 3
How to determine the linear equation?The missing table of values in the complete question is given as:
x y
0 3
3 15
7 31
10 43
Start by calculating the slope of the equation using
m = (y2 - y1)(x2 - x1)
Substitute the values on the table in the above equation
m = (15 - 3)/(3 - 0)
Evaluate the difference
m = 12/3
Evaluate the quotient
m = 4
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 4(x - 0) + 3
Evaluate the expression
y = 4x + 3
Hence, the linear equations that corresponds to the table is y = 4x + 3
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What is the independent variable in the following function?
The independent variable of f(c) = -3c + 9 is c
What are variables?Variables in an equation are the unknown parameters of the equation that change in values
There are two types of variables
Dependent variableIndependent variableHow to determine the independent variable?The equation of the function is given as
f(c) = -3c + 9
The dependent variable is the output of the function, while the independent variable is the input of the function
For the function, f(c) = -3c + 9
The input variable is c
Hence, the independent variable of f(c) = -3c + 9 is c
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There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.
The length of the railing needed is 31.4 feet
Calculating the length of an arcFrom the question, we are to determine the length of railing needed
To determine the length of railing needed, we will determine the length of the arc formed by the balcony
Using the formula,
l = θ/360° × 2πr
Where l is the length of the arc
θ is the angle subtended by the arc
and r is the radius
From the given information,
θ = 45°
r = 40 feet
Putting the parameters into the equation, we get
l = 45°/360° × 2 × 3.14 × 40
l = 1/8 × 2 × 3.14 × 40
l = 2 × 3.14 × 5
l = 31.4 feet
Hence, the length of the railing needed is 31.4 feet
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The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of
the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches
Answer:
15
Step-by-step explanation:
12 / 2 = 6
5 / 2 = 2.5
6 x 2.5 = 15
15 inches²
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 10 child bikes and 12 adult bikes in a week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
The answer is C- Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Solve the equation in the image (yr 8 maths, 50pts)
Answer: x = 4
Step-by-step explanation:
Given equation
4x - 20 = -x
Add x on both sides
4x - 20 + x = -x + x
5x - 20 = 0
Add 20 on both sides
5x - 20 + 20 = 0 + 20
5x = 20
Divide 5 on both sides
5x / 5 = 20 / 5
[tex]\Large\boxed{x=4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which of the following is a monomial? O A. 11x-9 OB. 20x9 OC. 20x⁹ - 7x O D.9/x
Answer:
B. 20x⁹
Step-by-step explanation:
A monomial is a polynomial with just one term.
Example: 3x²
A. 11x - 9
INCORRECT, this has two terms 11x and 9
B. 20x⁹
CORRECT, this only has one term!
C. 20x⁹ - 7x
INCORRECT, this has two terms 20x⁹ and 7x
D.9/x
INCORRECT, this is not a polynomial
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Please help!!!!! Please explain too, I want to understand it!
Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?
Answer:
Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?
The Answer Is X = 20 or x = 4
Select the correct answer. which of these organizations provides help to the friends and families of an alcoholic? a. national clearing house for alcohol and drug information b. american council on alcoholism c. alateen
Answer: C
Step-by-step explanation:
For 17-20, Find the value of each variable.
The unknown angles are as follows;
x = 180 degrees
r = 90 degrees.
How to find the angles of each value in a circle?The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.
Therefore,
x = 2(90)
x = 180
Therefore, the sum of angle in a circle is 360 degrees.
Hence, the 2 angles of the arc are the same.
Therefore,
360 - 180 = 2r
2r = 180
divide both sides by 2
2r / 2 = 180 / 2
r = 90 degrees.
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can someone please help mee ( will give brainliest 20 points!!!)
The piecewise function graphed below is given as follows:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex][tex]f(x) = x + 2, -2 < x \leq 3[/tex][tex]f(x) = -1, 3 < x \leq 5[/tex]What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:
[tex]f(x) = 3, -4 \leq x \leq -2[/tex]
For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:
[tex]f(x) = x + 2, -2 < x \leq 3[/tex]
For x greater than 3 until 5, the function is constant at -1, hence the definition is:
[tex]f(x) = -1, 3 < x \leq 5[/tex]
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Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
The total number of integral solutions of x + y + z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3 is; 59 integer solutions
How to find the number of Integral Solutions?We are given the condition that;
−3 ≤ x ≤ 4
Thus, we will use x values of -3, -2, -1, 0, 1, 2, 3, 4
When;
x = -3 and y = 2, in x + y + z = 12, solving for z gives z = 13
x = -3 and y = 3, in x + y + z = 12, solving for z gives z = 12
x = -3 and y = 4, in x + y + z = 12, solving for z gives z =11
x = -3 and y = 5, in x + y + z = 12, solving for z gives z = 10
x = -3 and y = 6, in x + y + z = 12, solving for z gives z = 9
x = -3 and y = 7, in x + y + z = 12, solving for z gives z = 8
x = -3 and y = 8, in x + y + z = 12, solving for z gives z = 7
x = -3 and y = 9, in x + y + z = 12, solving for z gives z = 6
x = -3 and y = 10, in x + y + z = 12, solving for z gives z = 5
x = -3 and y = 11, in x + y + z = 12, solving for z gives z = 4
Thus, there are 10 solutions with x =-3
Repeating the above with x = -2, we will have 10 solutions
Similarly, with x = -1, we will have 9 more solutions
Similarly, with x = 0, we will have 8 more solutions.
Similarly, with x = 1, we will have 7 more solutions.
Similarly with x = 2, we will have 6 more solutions.
Similarly with x = 3, we will have 5 more solutions.
Similarly with x = 4, we will have 4 more solutions.
Thus,
Total number of solutions = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 10
= 59 integer solutions
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The price of a jacket is $500 and the price of a pair of jeans is $250.
(a) The price if the jacket is ____% if the pair of jeans.
(b) The price of the pair of jeans is ___% or the price of the jacket.
Answer:(a) 50% (b)5%
Step-by-step explanation:
For a, it's not really difficult because the price of a jacket is 1/2 more than jeans. So it's 50%.
For b, it's similar to no. (a) because the price of the jean is 1/2 less than a jacket. So u need to divide 250 by 500 and u will get 0.5 so if u want to put in % u need to multiply with 10, so u will get 5%.
Use the discrete probability distribution to find the probability that x exceeds 5. (note that it is not required to find the missing probability. )
The discrete probability distribution that finds the probability that x exceeds 5 is 0.38
Opportunity provides records approximately the likelihood that something will manifest. Meteorologists, for instance, use weather patterns to are expecting the chance of rain. In epidemiology, the probability idea is used to recognize the connection between exposures and the risk of fitness consequences.
Finding the possibility of a simple event happening is fairly straightforward: upload the changes collectively. For example, if you have a 10% chance of triumphing $10 and a 25% threat of triumphing $20 then your normal odds of prevailing something is 10% + 25% = 35%.
If there is no ambiguity within the occurrence of an occasion, then the chance of such an occasion is equal to 1. In other phrases, the chance of a sure occasion is 1. If an occasion has no probability of taking place, then its chance is zero.
We want to find the probability for x exceeding 5 means for x>5
Consider,
P(X>5)=P(x=6)+P(X=8)
=0.18+0.2
=0.38
Hence, the probability is 0.38
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Write an expression containing x2-terms, x-terms and constants. The
x2-terms should combine to −2x2 the x-terms should sum to 3x,
and the constants should sum to 3.
[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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What are the solutions to this quadratic equation x2+6x-5=0
Answer:
See Below.
Explanation:
Quadratic Form:
[tex]a {x}^{2} + bx + c[/tex]
Quadratic Formula:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Based on the information given from the question, we can deduce:
a = 1
b = 6
c = -5
Now we can substitute all these values into the formula to find x.
[tex]x = \frac{ - 6 + - \sqrt{ {6}^{2} - 4(1)( - 5)} }{2(1)} \\ = - 3 + \sqrt{14} \: or \: - 3 - \sqrt{14} [/tex]
I really don't know what to do for this question! :( help?
The amount of money she should deposit is 6131.14 dollars.
How to find the compound interest ?The amount she should deposit can be found as follows:
[tex]p = \frac{A}{(1+\frac{r}{n} )^{nt} }[/tex]
where
A = amount to depositr = raten = number of timest = timep = principalTherefore,
p = [tex]\frac{20000}{(1+\frac{0.12}{4}{} )^{40} }[/tex]
[tex]p=\frac{20000}{(1+0.03)^{40} }[/tex]
[tex]p = \frac{20000}{1.03^{40} }[/tex]
[tex]p=\frac{20000}{3.262037792}[/tex]
Hence,
p = $6,131.14
Therefore, she should deposit 6131.14 dollars.
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Area=
Help Me asap pleaseee thanks
The area of the shaded region shown in the image is 14π unit²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Area of semicircle = π*diameter² / 4
The area of the shaded region is the sum of the area of the individual semi circles shown in the diagram.
Area of shaded region = area of SR + area of QR + area of PQ
Area of shaded region = (1/2) * π(4²/4) + (1/2) * π(2*4²/4) + (1/2) * π(2 * 2 * 4²/4) = 14π
The area of the shaded region shown in the image is 14π unit²
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In need of help for answers
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
From the diagram using the point (-6, 0.5) and (-1, 5):
y - 0.5 = [(5 - 0.5)/(-1 - (-6))](x - (-6))
y = (9/10)x + 5.9
Also, using the point (2, 1) and (4, -4):
y - 1 = [(-4 - 1)/(4 - 2)](x - 2)
y = -(5/2)x + 6
The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]
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number 7 please and don t care abt others lol
Answer:
The question does not make a lot of sense to me but I think this is how its supposed to be done
so there are 15 shirts
2 are sold at 3.90, 2 x 3.90 = 7.8
15-2= 13 t shirts
13 sold at 4.70, 13 x 4.70 = 61.1
amount of money made is = 7.8 + 61.1
= 68.9
