Answers
Answer:
Answer is Option B.
That is the nth term of the sequence.
1/8 + 1/16 + 1/32....
You notice that all the numerators are the same. Which is (1).
so we have to both about getting the nth term of the denominator
Since all the denominator are divisible by 2... and Your intuition should tell you that they'd multiples of 2
So Lets go with 2^n
2^n
let n be all Integers
let take 1,2,3
2¹ = 2
2² = 4
2³ = 8
Now Observe that
If you multiply all these by 4... We will have all the values of the denominator
which are 4,16,32
So thats our nth term
1/4(2^n)
as n approaches positive Infinity.
The expression is [tex]\lim_{n \to \infty} \frac{1}{4(2^{n}) }[/tex] , so option (B) is the correct expression.
What is series expansion?"A series expansion is an expansion of a function into a series or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication, and division)".
For the given situation,
The series is given as [tex]\frac{1}{8} +\frac{1}{16}+ \frac{1}{32}+ \frac{1}{64}+ \frac{1}{128}+......[/tex]
In the series, all the numerators are 1 and the denominators are even numbers so multiples of 2.
Now, we examine the denominators alone.
[tex]8,16,32,64,128[/tex]
⇒ Multiples of 2. So we get [tex]2^{n}[/tex] multiplied by some integers.
Put [tex]n=1,[/tex]
⇒ [tex]2^{1}[/tex] × [tex]4=8[/tex]
Put [tex]n=2,[/tex]
⇒ [tex]2^{2}[/tex] × [tex]4=8[/tex]
Put [tex]n=3,[/tex]
⇒ [tex]2^{3}[/tex] × [tex]4=32[/tex]
Put [tex]n=4,\\[/tex]
⇒ [tex]2^{4}[/tex] × [tex]4=64[/tex]
Put [tex]n=5[/tex],
⇒ [tex]2^{5}[/tex] × [tex]4=128[/tex]
Thus [tex]2^{n}[/tex] expression becomes [tex]2^{n}(4)[/tex] .
Hence we can conclude that the expression is [tex]\lim_{n \to \infty} \frac{1}{4(2^{n}) }[/tex] . So option (B) is the correct expression.
Learn more about the series expansion here
https://brainly.com/question/14874506
#SPJ2
Related Questions
WILL
GIVE BRAINLISTTT
.
.
.
..
.
.
.
.
..
.
Answers
Answer:
c
Step-by-step explanation:
explanation needed
A = {prime numbers between 4 and 25}
B = {odd numbers less than 16}
List the outcomes of A U B
List the outcomes of A n B
Please Show your work
Answers
Which could be the graph of y - 3*?
A)
B)
D)
Answers
Answer:
Option D is correct
Step-by-step explanation:
Hope it is helpful....
Rewrite the function by completing the square. f(x)=x^{2}+8x+4
Answers
Answer:
[tex]\implies f(x) = ( x + 2)^2[/tex]
Step-by-step explanation:
Given :-
f(x) = x² + 8x + 4 .And we need to rewrite the function by completing the square. The function is ,
[tex]\implies f(x) = x^2+8x + 4[/tex]
We can rewrite the function in the form of ,[tex]\implies ( a + b)^2= a^2+b^2+2ab [/tex]
Rewriting the function :-
[tex]\implies f(x) = x^2+8x + 4\\\\\implies f(x) = x^2 + 2.2.2x + 2^2[/tex]
This is similar to the whole square form stated above . So ,[tex]\implies f(x) = ( x + 2)^2[/tex]
Hence the function in whole square form is (x + 2)² .
Solve the value of w
Answers
Answer: 13
Step-by-step explanation:
This is a right angle, since there is a box
So, 33° + (4w + 5)° = 90°
33° + 4w + 5 = 90°
38° + 4w = 90°
Subtract 38° on both sides
4w = 90° - 38°
4w = 52°
Divide 4 on both sides
w = 13
How many people were surveyed for the frequency table below?
6
25
63
8
Answers
Answer:
25 people were surveyed.
Step-by-step explanation:
Add up the frequency.
help with no link please
Answers
Answer:
1. 156 2. 84 3. 74
Step-by-step explanation:
1. b x h. 8 x 8 is every side on the square so one side is 64 and the one behind it is 64 also which is 128 and since that is the case with the other sides its 128 + 128 = 156
2. 1/2 x b x h = 1/2 x 4 x 3 = 6 x 2 because of the side behind it that is the same = 12. 6 x 5 = 30; 6 x 4 = 24; 6 x 3 = 18. 12 + 30 + 24 + 18 = 84
3. b x h. 2.5 x 2 = 5 x 2 because of the other side = 10; 7 x 2.5 = 17.5 x 2 = 35; 7 x 2 = 14 x 2 = 28. 10 + 35 + 28 = 76
Which is the slope of the line that passes through the points (12, -6) and (12, 3)?
a -8
b -1/8
c 0
d undefined
Answers
Step-by-step explanation:
Its Undefined.
Reason
Slope (m) = y2 - y1/(x2-x1)
= 3-(-6)/(12-12)
=9/0
Undefined
You can clearly see this from the points. The x value has 2 different values for y... Which Makes the points not that of a function.
Helppppppppppp !!!!!!!!!!!!!!!!!!!!!!
Answers
Explanation
Answer:
The line equation is Y=(1/2)x+2
Step-by-step explanation: Start with the standard from: y=mx+b
Find the slope, or change in the y value divided by change in the x value.
For this graph the slope is 1/2 meaning the y value goes up once every time the x value goes up two. this is represented by the m value
Now we need to find the y intercept, or where the graph passes through the y intercept, this is represented by b
We find the intercept by inserting a point n the line into our equation and solving for b:
Point: (2,3) Equation: y=(1/2)x+b
3=(1/2)2+b
3=1+b
-1 -1
2=b
The table shows all possible outcomes when Juan tosses a penny, a nickel, and a quarter at the same time.
Answers
Answer:
A
Step-by-step explanation:
HELP ASAP!
Identify the type of graph, label appropriate vertices, intercepts and asymptotes.
a) x2−4y2=16
b) 4x2+y2=4
c) x=y2−2y−3
Answers
Answer:
They are all linear equations/functions, I graphed them here:
Step-by-step explanation:
The scores on a test are normally distributed, with a mean of 82 and standard deviation of 8. What percent of scores are greater than 90? Explain your answer.
Answers
Answer:
14.64%
Step-by-step explanation:
P(90<X<100) = normalcdf(90,100,82,8) = 0.1464308262 ≈ 0.1464 ≈ 14.64%
Therefore, about 14.64% of the scores are greater than 90.
By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.
What is CDF function of normal distribution?The CDF function of a Normal distribution is calculated by translating the random variable to the Standard Normal, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the standard normal. The Standard Normal, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).
Let x1, x2, .... be the scores on the test.
X ~ N (82, 64)
[tex]= P(90 < X < 100) \\\\= P(\frac{90 -82 }{8} < \frac{X - 82}{8} < \frac{100-82}{8} ) \\\\= P(1 < \frac{X - 82}{8} < \frac{18}{8}) \\\\P(1 < Z < \frac{18}{8})\\ \\[/tex]
P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)
Learn more about CDF function of normal distribution here
https://brainly.com/question/14936604
#SPJ2
Can someone answer this please
Answers
Answer:
3x+94+x+18+2x-4=180(being straight line)
6x+108=180
6x=180-108
x=72/6
x=12
Step-by-step explanation:
The management of a relatively new social networking website named BooglePlus is conducting a pilot study comparing use of its own site with use of a longer established social networking site named FaceList. Some articles published on the Internet give the reader the opportunity to register votes (called "likes") for the article on social networking sites to which the reader belongs. A BooglePlus employee selects from the Internet a random sample of 28 articles where the opportunity is given for registering votes for the article on both BooglePlus and Face List. Letting x be the number of votes on FaceList and y be the number of votes on the BooglePlus, the slope of the least squares regression line of y on x is found to be 0.0623, with a standard error of 0.0224.
Required:
What could be used to compute a 95% confidence interval for the slope of the population regression line of y on x?
Answers
Answer:
0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x
Step-by-step explanation:
Given the data in the question;
sample size n = 28
slope of the least squares regression line of y on x or sample estimate = 0.0623
standard error = 0.0224
95% confidence interval
level of significance ∝ = 1 - 95% = 1 - 0.95 = 0.05
degree of freedom df = n - 2 = 28 - 2 = 26
∴ the equation will be;
⇒ sample estimate ± ( t-test) ( standard error )
⇒ sample estimate ± ( [tex]t_{\alpha /2, df[/tex]) ( standard error )
⇒ sample estimate ± ( [tex]t_{0.05 /2, 26[/tex]) ( standard error )
⇒ sample estimate ± ( [tex]t_{0.025, 26[/tex]) ( standard error )
{ from t table; ( [tex]t_{0.025, 26[/tex]) = 2.055529 = 2.056
so we substitute
⇒ 0.0623 ± ( 2.056 )( 0.0224 )
Therefore, 0.0623 ± ( 2.056 )( 0.0224 ) can be used to compute a 95% confidence interval for the slope of the population regression line of y on x
Jamie is working on simplifying a problem with negative exponets and got the answer 1/4³. What might Jamie's original expression have been? In other words, work backwards and rewrite this expression with a negative exponet
Answers
Answer:
Your answer would be 4^-3.
Step-by-step explanation:
So, a negative exponent by definition, is writing out 1/x^y. Where x is the number and y is the negative exponent.
In this case, 4 would be the number and -3 would be the negative exponent.
So we're going from 1/x^y to x^-y in order to solve this. Therefore, this is something where the numbers can just be plugged in.
1/x^y ---> x^-y
1/4^3 ---> 4^-3
Your answer would be 4^-3.
PLS HELPPPP ! I need itttt
Answers
Answer:
x = 10
Step-by-step explanation:
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If
the trip takes 6 hours at 900 km/h, what would be the speed if the trip took 10 hours?
Answers
Answer: speed is 540 km/h
Step-by-step explanation: Lets mark speed as v.
Because distenace is same, you can mark 6 h · 900 km/h = 10 h · v
and v = 5400 km / 10 h = 540 km/h.
Or using inverse proportions : 10 h / 6 h = v / 900 km/h .
Before multiplying you turn lastproportion around :
10 h / 6 h = 600 km/ h / v ,which gives 10 v = 6 · 900 km/h
and result is same
The length of a rectangle is twice the width. The area is 50 square inches. Find the
dimensions of the rectangle.
Answers
Answer:
The dimensions are 5 and 10 inches
Step-by-step explanation:
The area is 50 square inches and the length is twice the width. 10 is the length, which is two times 5. 10 times 5 is 50.
The length is 10 and the width is 5.
I’ll give brainliest for the right answer!
Answers
Answer:
[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]
Step-by-step explanation:
Radius of the circle [tex] r = \sqrt {37}\: units [/tex]
Center of the circle (h, k) = (1.3, - 3.5)
Equation of the circle in center radius form is given as:
[tex] (x-h) ^2 + (y-k) ^2= r^2 [/tex]
Plugging the values of h, k and r in the above equation, we find:
[tex] (x-1.3) ^2 + (y+3.5) ^2= (\sqrt {37})^2 [/tex]
[tex] (x-1.3) ^2 + (y+3.5) ^2= 37 [/tex]
This is the required equation of the circle.
Select the correct answer. What is the domain of the function represented by this graph? the graph of a quadratic function y = x^2 – 4 with a minimum value at the point (0,-4) A. x ≤ 0 B. -2 ≤ x ≤ 2 C. x ≥ 4 D. all real numbers
WILL GIVE BRAINLIEST
Answers
Answer:
For a general function f(x), the domain is the set of the possible values of x that we can input in the function.
The trick to find the domain is first to assume that the domain is the set of all real numbers, and then let's try to find the values of x that cause a problem in the function. (If the graph is cut in some value of x, such that it ends with an open or a closed point, then these values define the domain).
Such that one of these problems can be like x = 1 in the function:
g(x) = 1/(x - 1)
Because that value causes the denominator to be equal to zero, then the domain of that function will be the set of all real numbers except the value x = 1.
In this case, we have:
f(x) = x^2 - 4
There is no value of x that causes a problem for this function, then the domain is the sett of all real numbers.
Correct option D.
The cost of purchasing a bag of rice is partly constant and partly varies inversely as the square root of the number of people demanding the bag. when the cost was 100 naira the number of people were 36 when the cost was 150 naira the number of people were 144. Find
1. The cost when the number of people were 225.
The number of people when the cost was 200 naira
Answers
Answer:
(a) 160 Naira
(b) Undefined
Step-by-step explanation:
Given
Let:
[tex]y \to[/tex] cost of bag of rice
[tex]x \to[/tex] people demanding the bag
So, we have:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex] ---- The variation
[tex]y = 100; x = 36[/tex]
[tex]y = 150; x = 144[/tex]
We have:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex]
When: [tex]y = 100; x = 36[/tex]
[tex]100 = \frac{k}{\sqrt {36}} + c[/tex]
[tex]100 = \frac{k}{6} + c[/tex] -- (1)
When: [tex]y = 150; x = 144[/tex]
[tex]150 = \frac{k}{\sqrt {144}} + c[/tex]
[tex]150 = \frac{k}{12} + c[/tex]--- (2)
Subtract (1) from (2)
[tex]150 - 100 = \frac{k}{12} - \frac{k}{6} + c - c[/tex]
[tex]50 = \frac{k}{12} - \frac{k}{6}[/tex]
Multiply through by 12
[tex]600 = k - 2k[/tex]
[tex]600 = -k[/tex]
[tex]k = -600[/tex]
To solve for x, we have:
[tex]100 = \frac{k}{6} + c[/tex] -- (1)
This gives:
[tex]100 = \frac{-600}{6} + c[/tex]
[tex]100 = -100 + c[/tex]
[tex]c = 100 + 100[/tex]
[tex]c = 200[/tex]
So, the equation is:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex]
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
Solving (1): y; when x = 225
We have:
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
[tex]y = -\frac{600}{\sqrt {225}} + 200[/tex]
[tex]y = -\frac{600}{15} + 200[/tex]
[tex]y = -40 + 200[/tex]
[tex]y = 160[/tex]
Solving (2): x; when x = 200
We have:
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
[tex]200 = -\frac{600}{\sqrt x} + 200[/tex]
Collect like terms
[tex]\frac{600}{\sqrt x} = 200 - 200[/tex]
[tex]\frac{600}{\sqrt x} =0[/tex]
Cross multiply
[tex]600 =0 * \sqrt x[/tex]
[tex]600 =0[/tex]
x is undefined
Could someone leave an explanation? I don’t understand how to solve properties of exponents. Thanks
Answers
Algebraic expression for six times 4 Less Than 3 times x
Answers
Answer:
6(3x - 4)
Step-by-step explanation:
From the question, we can deduce the following points;
- 6 is multiplied by 3x minus 4
Translating the word problem into an algebraic expression, we have;
6 * (3x - 4)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
Answer:
From Pythagoras Rule
c=√1²+2²
c=√5 cm
c= 2.2cm
To the Nearest tenth..
La ecuación de la recta que pasa por el punto P(1,3) y es paralela a la recta
Answers
Answer: No puedo responder a esto sin que me muestres el problema.
please help me with this
Answers
9514 1404 393
Answer:
C = 40°c ≈ 5.79a ≈ 6.89Step-by-step explanation:
The acute angles in a right triangle are complementary, so ...
C = 90° -50°
C = 40°
__
SOH CAH TOA reminds you of the relations ...
Cos = Adjacent/Hypotensue
Sin = Opposite/Hypotenuse
Then ...
cos(50°) = c/9
c = 9·cos(50°) ≈ 5.79
sin(50°) = a/9
a = 9·sin(50°) ≈ 6.89
ecosystem biodiversity is often used a measure of its overall
a shape
b size
c health
d income
Answers
Answer:
c... health
Step-by-step explanation:
Answer:
ecosystem biodiversity is often used a measure of its overall health.
Step-by-step explanation:
I 13. Angeles is 5yrs younger
Than her husband Joseph
The sum of their ages is 63yrs.
How old world Angeles be in
5yrs Time
Answers
Answer:
x - 5 = 63
x = 63 - 5
x = 58 years
Answer:
she will be 34
Step-by-step explanation:
x - Joseph age
(x-5)+x=63
2x=68
x=34
34- 5 =29 Angeles age
in 5 years she will be 29+5=34
Find the area of the figure
area: units2
Answers
Answer:
24
Step-by-step explanation:
Answer: 25 units^2
Step-by-step explanation:
This is the correct answer
Is x = 13 a solution to the equation x - 9 = 4? please answer ASAP
Answers
Answer:
yea
Step-by-step explanation:
x=13 so 13-9=4