consider an infinite geometric series of positive terms that converges to s. what fractional part of s is the sum of the odd-numbered terms?
Answers
The fractional part of s that is the sum of the odd-numbered terms is \[\frac{1-r}{1+r}\]
Let us consider an infinite geometric series of positive terms that converges to s.
Therefore, we know that the sum of the series is given by \[s=\frac{{{a}_{1}}}{1-r}\]
where a1 is the first term of the series and r is the common ratio of the series.
Now, we need to find the fractional part of s, which is the sum of the odd-numbered terms.
Let's say the sum of odd-numbered terms is t.
Then, we have:\[\begin{aligned}t&={{a}_{1}}+{{a}_{3}}+{{a}_{5}}+{{a}_{7}}+...\\&={{a}_{1}}+{{a}_{1}}{{r}^{2}}+{{a}_{1}}{{r}^{4}}+{{a}_{1}}{{r}^{6}}+...\end{aligned}\]
We can observe that t is an infinite geometric series with the first term a1 and common ratio r2.
Therefore, we know that the sum of t is given by \[t=\frac{{{a}_{1}}}{1-{{r}^{2}}}\]Now, we need to find the fraction of s, which is given by \[\frac{t}{s}=\frac{\frac{{{a}_{1}}}{1-{{r}^{2}}}}{\frac{{{a}_{1}}}{1-r}}=\frac{1-r}{1+r}\]
Hence, the fractional part of s that is the sum of the odd-numbered terms is \[\frac{1-r}{1+r}\]
Know more about fractional part here:
https://brainly.com/question/30154928
#SPJ11
Related Questions
the standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known true false
Answers
True, The normalized normal distribution is used to calculate population percent confidence intervals regardless of whether the population standard deviation is known.
The mean-bell-shaped curve is one of the most frequent continuous random variables.
A normal distribution's mean is fully symmetrical. The sampling rate is used to calculate the percentage population confidence interval.
The z-distribution, often known as the standard normal distribution, is a form of normally distributed with mean 0 and variance 1.
A transform can be used to normalize the values of a normal distribution. It is subsequently transformed into a z value.
The amount of standard variations between each result and the mean is represented by the Z-score.
Normalized distributions are used to construct confidence intervals for population percentages when the sample size is big enough.
Learn more about the normal distribution at
https://brainly.com/question/25270058?referrer=searchResults
#SPJ4
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 2 42% compounded monthly. The annual percentage yield is
Answers
The Annual Percentage Yield (APY) in this situation is approximately 2.454%.
To find the Annual Percentage Yield (APY) in this situation, use the formula:
\(APY = (1 + r/n)^n - 1\)
where:
- r is the annual interest rate (APR) expressed as a decimal,
- n is the number of compounding periods per year.
In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).
Substituting these values into the formula,
\(APY = (1 + 0.0242/12)^{12} - 1\)
Calculating this expression:
\(APY = (1 + 0.002017)^{12} - 1\)
\(= (1.002017)^{12} - 1\)
≈ 0.02454 or 2.454%
Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.
To learn more about Annual Percentage Yield
https://brainly.com/question/27997520
#SPJ11
let f(x) = 4 - xf(x)=4−x and g(x) = 5 - x^2g(x)=5−x 2 . find g(f(x))g(f(x)) and simplify completely.
Answers
The answer to the question is g(f(x)) = 21 - 8x + x^2.
Substitute f(x) into g(x) wherever there is an x. So we get g(f(x)) = 5 - (4 - x)^2.
Expanding this gives g(f(x)) = 5 - (16 - 8x + x^2).
Simplifying further, we get g(f(x)) = 21 - 8x + x^2.
Therefore, the long answer is g(f(x)) = 21 - 8x + x^2, which is the simplified expression obtained by substituting f(x) into g(x) and expanding and simplifying.
The answer is g(f(x)) = -11 + 8x - x^2.
To know more about expression visit :-
https://brainly.com/question/14083225
#SPJ11
2x+2=4+1x
and we are solving for X
Answers
Answer:
the answer is x = 2
Step-by-step explanation:
2x+2=4+1x
(2x-1x)+2= 4 +(1x-1x)
1x+2=4
1x(2-2)=(4-2
1x=2
2/1=x
x=2
Answer: X=2
I might be wrong
Show the process also please...
Answers
Answer: 5
Step-by-step explanation:
The point B(2,2) is translated 7 units left.
Answers
Answer: (2,-5)
Step-by-step explanation:
since moving left is considered negative/ decreasing on a graph, u would use the equation 2-7 to get 5. also since it’s moving to the left, Y (x,y) would be the coordinate changing. hope this helped
NEED HELP
Which ordered pair is a solution to the following system of inequalities?
y24x+3
ys-5x+4
O A. (-1,-6)
OB. (-3, 4)
O C. (1,-6)
OD. (4, 5)
Answers
The ordered pair which is a solution to the given system of inequalities is: B. (-3, 4).
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Next, we would test the ordered pair with the given system of inequalities as follows:
For ordered pair (-1, -6), we have:
y ≥ 4x + 3
-6 ≥ 4(-1) + 3
-6 ≥ -4 + 3
-6 ≥ -1 (False).
For ordered pair (-3, 4), we have:
y ≥ 4x + 3
4 ≥ 4(-3) + 3
4 ≥ -12 + 3
4 ≥ -9 (True).
y ≤ -5x + 4
4 ≤ -5(-3) + 4
4 ≤ 15 + 4
4 ≤ 19 (True).
For ordered pair (1, -6), we have:
y ≥ 4x + 3
-6 ≥ 4(1) + 3
-6 ≥ 4 + 3
-6 ≥ 7 (False).
For ordered pair (4, 5), we have:
y ≥ 4x + 3
5 ≥ 4(4) + 3
5 ≥ 16 + 3
5 ≥ 19 (False).
Read more on inequality here: https://brainly.com/question/27166555
#SPJ1
due last weeeekk help!!!!
Answers
A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:
Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).
In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;
(x, y) → (y, -x)
Ordered pair B' (-2, 1) → E (1, 2)
Read more on dilation and scale factor here: brainly.com/question/4421026
#SPJ1
which equations would you use the subtraction property of equality to solve? check all that apply. 5 y
Answers
answer 5y - 12 = 8.
In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.
Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27
The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.
You can read more about equations at https://brainly.com/question/22688504
#SPJ11
The point plotted on the number line is What is the approximate value of x? 04 O 9 O 17 O 20
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\( \sqrt{17} ≈4.1\)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is Option Three .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
C
Step-by-step explanation:
Please help! Reporting all irrelevant answers.. Thank you.
Answers
3x=12
x=4
2(4)+12=A
A=20 degrees
Find the area of a triangle with legs that are: 6 mm, 4 mm, and 8 mm.
A. 16.4 mm
B. 11.6 mm
C. 14.5 mm?
D. 5.8 mm?
Answers
How do I solve this?
Answers
Answer:
Given:A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x
To find :The value of angle 7x+6
Solution:we know that ,
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.
so,
\(7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10\)
so ,the measure of green angle would be
\(7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76\)
Verification:To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)
so,
\(7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified\)
Solution:
Note that:
Green angle = 7x + 64x + 7x + 6 + (180 - 116) = 180Simplify the equation to find x.
4x + 7x + 6 + (180 - 116) = 180=> 11x + 6 + (64) = 180=> 11x + 70 = 180=> 11x = 180 - 70=> 11x = 110=> x = 110/11 = 10Substitute the value of x into the measure of the green angle.
7x + 6=> 7(10) + 6=> 76°The measure of the green angle is 76°.
For what value of x is the figure a rectangle? Please help
Answers
Answer:
x = 8
Hope this helps!
Step-by-step explanation:
( 2x + 42 )° + ( 4x )° = 90° ( right angle )
6x + 42 = 90
6x = 90 - 42
6x = 48
x = 8
(2x + 42) + 4x = 90 degrees
Add 4x + 2x to get 6x + 42 = 90
Then, subtract 42 from both sides to get, 6x = 48
Lastly, divide both sides by 6 to get your final answer of X = 8.
Which of the following figures has reflected over the y-axis? 40 POINTS! PLEASE ANSWER!
Answers
Answer:
the third one
Step-by-step explanation:
Answer:
its a
Step-by-step explanation:
What is the value of n in the equation 3n 2(n 2) = 9n 12? −4 −2 2 4.
Answers
Equation is formed when two equal expressions are equated together with the help of an equal sign '='. The value of n is -4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
As the equation is given to us, therefore, the value of the n can be found as,
\(3n+2(n+2)=9n+12\\\\3n+4n+4=9n+12\\\\7n-9n=12-4\\\\-2n = 8\\\\n =\dfrac{8}{-2}\\\\n=-4\)
Hence, the value of n is -4.
Learn more about Equation:
https://brainly.com/question/2263981
can someone please help me with this?
Answers
Answer:
3=3x+3
4=2x+8
Step-by-step explanation:
1. for function f (x) =3x2-5x +7
a. whether it turns up ward or down ward
b.the vertex
c.the axis of symmetry
Answers
For function f (x) =3 x²- 5 x +7 a) It turns upward b) The vertex is (5/6, 59/12) c) The axis of symmetry is 5/6.
a) The graph formed in the function is turns upward please refer to image.
b) vertex = (-b/2a , -D/4a)
f (x) =3 x²- 5 x +7
on comparing equation by general equation of parabola ax² + bx +c
a = 3 , b = - 5 , c = 7
D = b² - 4ac
D = (-5)² - 4(3)(7)
D = 25 - 84
D = -59
vertex = (5/6 , 59/12)
c) The axis of symmetry is -b/2a
b = -5 , a = 3
The axis of symmetry = 5/6
To know more about axis of symmetry:
https://brainly.com/question/22495480
#SPJ4
What is the difference between -3 and five a number line
Answers
A rectangular bathroom mirror is 4
feet tall and 7 feet wide. What is its
area?
square feet
Answers
Given -
A rectangular bathroom mirror is 4 feet tall and 7 feet wide.ie, length of the mirror, L = 4 feet and breadth of the mirror, B = 7 feet .
To find -
the area of the mirrorSolution -
As we know to find the area of rectangle we use the formula, Area = L × B
Hence, we will be doing the same.
Area = 4 × 7
Area = 28 square feet
Answer:
28 sq. feet
Step-by-step explanation:
Given:-
The length of bathroom mirror :- 4 feetWidth :- 7 feetTo find:-
The area of the rectangular bathroom mirrorSolution:-
Area of rectangular bathroom mirror:- L × B
putting the values ,
Area :- 4 × 7 sq. feet
Area:- 28 sq. feet
A circular patio has a diameter of 12 feet. Holly is stringing lights around the edge of the patio. Approximately how many feet of stringed lights does Holly need? Use 3. 14 for π. Enter your answer as a decimal in the box.
Answers
The Holly is stringing lights around the edge of the patio is 37.68 feet.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
A circular patio has a diameter of 12 feet.
Then the radius (r) will be
\(\rm r = \dfrac{diameter}{2}\\\\r = \dfrac{12}{2}\\\\r = 6\)
Holly is stringing lights around the edge of the patio will be
\(\rm Circumference = 2 \pi r\\\\Circumference = 2*3.14 *6\\\\Circumference = 37.68 \ \ ft\)
Thus, the Holly is stringing lights around the edge of the patio is 37.68 feet.
More about the circle link is given below.
https://brainly.com/question/11833983
Answer: The answer is 37.68 ft
Step-by-step explanation: I took the test and it was right
A train travels 200 miles in 5 hours. How far does the train travel in 3 hours
Answers
Answer:
120 miles
Step-by-step explanation:
200/5 = 40 miles per hour
3 hours = 40*3 = 120 miles
PLS GIVE BRAINLIEST
1.) 7x-3=18
2.) 9x-4=32
3.) 5x-1=64
4.)12x-9=39
5.) 2x-1=2
6.) 4x-8=10
7.) 15x-2=3
Answers
2.) x=4
3.) x=13
4.) x=4
5.) x=3/2
6.) 9/2
7.) 1/2
let f, g, and h be functions n → n. that is, both the input and the output is a natural number. suppose further, that f(n)
Answers
In this scenario, we are given three functions: f, g, and h, where the input and output for each function are natural numbers. Additionally, we are given the condition that f(n) < g(n) < h(n) for all natural numbers n.
The objective is to determine the relationship between the three functions based on this condition.Based on the given condition, we can conclude that the output of function g is greater than the output of function f for all natural numbers. Similarly, the output of function h is greater than the output of function g for all natural numbers. This implies that the functions f, g, and h are ordered in increasing order.
In other words, for any input value n, the value of f(n) is the smallest, followed by g(n), and then h(n) is the largest. This order is maintained consistently for all natural numbers. This information allows us to establish the relative magnitudes of the outputs of the three functions and the overall ordering of the functions themselves.
To learn more about natural numbers click here : brainly.com/question/17273836
#SPJ11
What is the volume of a hemisphere with a radius of 3.6cm, rounded to the nearest tenth of a cubic centimeter?
Answers
Answer:
V(sphere) =
\( \frac{4 }{3} \pi \:{r}^{3} = 195.43 \\ \)
V(hemisphere) = V(sphere)/2 = 97.715 = 97.7
Give an example and describe why there exists a function between
the groups Z6 and Z8 that is NOT a homorphism.
Answers
There exists a function between Z6 and Z8 that is NOT a homomorphism because the function does not preserve the group operation.
In what way can a function between Z6 and Z8 fail to be a homomorphism?When we talk about a function between two groups, Z6 and Z8 in this case, a homomorphism is a function that preserves the group operation. In other words, if we have two elements a and b in Z6, their image under the function should satisfy the equation f(a⋅b) = f(a)⋅f(b), where ⋅ denotes the group operation.
However, we can find a function that does not satisfy this condition. Let's consider the function f: Z6 → Z8 defined by f(x) = 2x. This function maps every element in Z6 to its double in Z8. While it is a valid function, it is not a homomorphism because it fails to preserve the group operation.
For example, let's take a = 2 and b = 3 in Z6. The product of a and b is 2⋅3 = 6, which is congruent to 0 modulo 6. Applying the function f to both sides, we have f(6) = f(0) = 0. However, f(2)⋅f(3) = 4⋅6 = 24 ≡ 0 (mod 8), which is not equal to f(0).
Learn more about homomorphism
brainly.com/question/6111672
#SPJ11
Please help me with this please and thank you
Answers
Answer:
L bozo
Step-by-step explanation:
ur whole life is an L
What are the 4 properties of a rhombus?
Answers
- Opposite angles are equal in a rhombus.
- The diagonals bisect each other at 90 degrees.
- Adjacent angles add up to 180 degrees.
The 4 properties of the rhombus are:
All sides of the rhombus are equalThe opposite sides of a rhombus are parallelOpposite angles of a rhombus are equaldiagonals bisect each other at right angles.What is a rhombus?A quadrilateral in Euclidean geometry is a rhombus. It's a parallelogram with all sides equal and diagonals intersecting at 90 degrees. In addition, opposing sides are parallel, and opposing angles are equal. This is a fundamental property of the rhombus. A rhombus is shaped like a diamond. As a result, it's also known as a diamond.
Some of the important properties of the rhombus are as follows:The rhombus's sides are all equal. A rhombus' opposite sides are parallel. A rhombus' opposite angles are equal. Diagonals in a rhombus bisect each other at right angles. Diagonals cut the angles of a rhombus in half. 180 degrees is the sum of two adjacent angles. When you connect the midpoints of the sides, you will get a rectangle. When you join the midpoints of half the diagonal sides as the axis of rotation, you will get another rhombus.To know more about Rhombus visit the link
https://brainly.com/question/27870968
#SPJ4
The wholesale price of a sweater is $ 35 . The retail price of the sweater is 10 % more than the wholesale price. What is the retail price of the sweater?
Answers
Answer:
$38.5Step-by-step explanation:
In this problem we are going to first solve for 10% of $35 an add it to the wholesale price to get the retail price
10% of $35
\(\frac{10}{100}*35= 0.1*35= 3.5\)
The retail price is 3.5+35= $38.5
Answer:
$38.50
Step-by-step explanation:
( 1,-2), gradient = -3
Answers
Answer:
if you are required to find the equation of a straight line use the formula y-y1= m (x-x1)
y+2=-3(x-1)
y+2=-3x+3
y= -3x+3-2
y -3x+1
hope this helps
Answer:
y = -3x + 1
Step-by-step explanation:
(y -(-2)) = -3(x-1)
y+ 2 = -3x+ 3
y = -3x + 1