Answer:
(-\infty,-1/2) U (1/2,+\infty)
Step-by-step explanation:
You have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex]
You calculate the radius of convergence by using the formula:
[tex]R= \lim_{n \to \infty} |\frac{a(x)_n}{a(x)_{n+1}}|= \lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^{n+1}}{n+1}}|\\\\=\lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^n(2x)}{n+1}}|=\lim_{n \to \infty}|\frac{n+1}{2xn}|=|\frac{1}{2x}|\lim_{n \to \infty}|1+\frac{1}{n}|=|\frac{1}{2x}|[/tex]
The radius of convergence is R=1/2x.
Hence, the interval of convergence is
|2x| < 1
|x| < 1/2
By evaluating in the extrems of the interval:
[tex]\sum_{n=1}^{\infty} \frac{(2 (\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(1)^n}{n}=0\\\\\sum_{n=1}^{\infty} \frac{(2 (-\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
for x=-1/2 we obtain an Alternating Harmonic Series, for x=1/2 we obtain the divergent harmonic series. Thus the interval is:
(-\infty,-1/2) U [1/2,+\infty)
Answer:
Step-by-step explanation:
Recall the ratio test. Given a series [tex]\sum_{n=1}^{\infty}a_n[/tex] if
[tex] \lim_{n\to \infty} \left|\frac{a_{n+1}}{a_n}\right|<1[/tex]
Then, the series is absolutely convergent.
We will use this to the given series [tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex], where [tex] a_n = \frac{(2 x)^n}{n}[/tex]. Then, we want to find the values for which the series converges.
So
[tex] \lim_{n\to \infty} \left|\frac{(2x)^{n+1}}{n+1}\cdot \frac{n}{(2x)^n}\right|<1[/tex], which gives us that
[tex] |2x|\cdot\lim_{n\to \infty} \frac{n}{n+1}<1[/tex]
We have that [tex]\lim_{n\to \infty} \frac{n}{n+1}=1[/tex]. Then, we have that
[tex]|2x|<1[/tex],
which implies that |x|<1/2. So for [tex]x \in (-1/2,1/2)[/tex] the series converges absolutely.
We will replace x by the endpoints to check convergence.
Case 1, x=1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{1}{n}[/tex] which is the harmonic series, which is know to diverge.
Case 2, x=-1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
This is an alternating series with [tex]b_n = \frac{1}{n}[/tex]. Recall the alternating series test. If we have the following
[tex]\sum_{n=1}^\infty (-1)^nb_n [/tex] and[tex] b_n[/tex] meets the following criteria : bn is positive, bn is a decreasing sequence and it tends to zero as n tends to infinity, then the series converge.
Note that in this case, [tex]b_n = \frac{1}{n}[/tex] si always positive, its' limit is zero as n tends to infinity and it is decreasing, hence the series converge.
So, the final interval of convergence is
[tex] [\frac{-1}{2}, \frac{1}{2})[/tex]
I NEED HELP ON THIS SO BAD I WILL GIVE CROWN FOR ANSWER
Edwin fills 15 test tubes with a solution. Each test tube contains 150 milliliters of solution.
How many liters of solution in all is there in the test tubes?
2.25 L
22.5 L
225 L
2,250 L
The number of liters of solution in all is there in the test tubes is 2.25L, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Edwin fills 15 test tubes with a solution.
Each test tube contains 150 milliliters of solution.
Now,
The solution in all the tubes=150ml x 15
=2250ml
To convert it in liters
=2250/1000
=2.250L
Therefore, by algebra the answer will be 2.250L.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ6
£399 is shared between Ann, Bill, Chloe and Dave.
The ratio of the amount Ann gets to the amount Bill gets 2 : 9
Chloe and Dave get 2.5 times the amount Ann gets.
Work out the amount of money that Bill gets.
Show your working out.
Answer:
Ann=£38
Bill=£171
Chloe=£95
Dave=£95
Step-by-step explanation:
By the information provided we can create an equation:
[tex]2x+9x+2*5x=399\\11x+10x=399\\21x=399\\x=19[/tex]
Now that we know x, we multiply it correspondingly.
For Ann -> 2*19=38
Bill -> 9*19= 171
Chloe and Dave have the exact same amount each (because they both have 2.5 times the amount Ann's money)
Chloe/ Dave -> 5*19=95 each.
What is the first quartile of the box-and-whisker plot
Answer:
Between 36 and 38
Answer:
girl, is that USA Test Prep???
im doing that also!!
i think its between 36 and 38 basically.
Step-by-step explanation:
hope it helps i guess!! <33
Which is the best estimate for (6.3 times 10 Superscript negative 2 Baseline) (9.9 times 10 Superscript negative 3 Baseline) written in scientific notation?
Final answer:
The best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) in scientific notation is approximately 6.237 x 10⁻⁵.
Explanation:
To find the best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) written in scientific notation, you need to multiply the coefficients and add the exponents.
The product of 6.3x 10⁻² and 9.9 x 10⁻³ can be calculated as (6.3 x 9.9) x (10⁻² x 10⁻³). The coefficients multiply to give 62.37 (approximately), and the exponents add to give -5.
Therefore, the best estimate for (6.3 x 10⁻²) (9.9 x 10⁻³) in scientific notation is approximately 6.237 x 10⁻⁵.
find the inner product for (3,5) x (4,-2) and state whether the vectors are perpendicular. a.1; no b.1;yes c.2; no d.2; yes
Answer:
c. 2; no
Step-by-step explanation:
The inner product is the sum of the products of corresponding vector components. It is a scalar value, not a vector value.
(3, 5)·(4, -2) = (3)(4) +(5)(-2) = 12 -10 = 2
When the inner product is non-zero, the vectors are not perpendicular. (The yes answers with a non-zero value can be rejected out of hand.)
The appropriate choice is ...
2; no
Final answer:
The inner product of the vectors (3,5) and (4,-2) is 2. As the dot product is not zero, the vectors are not perpendicular. Therefore, the correct answer is c.2; no.
Explanation:
To find the inner product of two vectors, we use the dot product formula. The dot product of two vectors u = (a1, b1) and v = (a2, b2) is calculated as u · v = a1 × a2 + b1 × b2. For the vectors (3,5) and (4,-2), we calculate as follows:
Inner product = 3 × 4 + 5 × (-2) = 12 - 10 = 2.
Two vectors are perpendicular if their dot product is zero. Since the dot product here is 2, not zero, the given vectors are not perpendicular.
Therefore, the correct answer is: c.2; no.
in 56 years,Kevin will be 9 times as old as he is right now .
How old is he right now ?
Answer:
Kevin is 7
Step-by-step explanation:
In 56 years if Kevin is 7 now he will be 63 and 7X9 = 63
Marianne opened a retirement account that has an annual yield of 5.5%. She is planning to retire in 25 years. How much should she put into the account each month so that she will have $500,000 when she retires?
Answer:
Monthly deposit, P = $776.41
Step-by-step explanation:
Interest rate per annum = 5.5%
number of years = 25
Since she pays monthly, number of payments per annum = 12
Interest rate per period, r = (Interest rate per annum)/(number of payments per annum)
r = 5.5%/12 = 0.46%
Number of periods, n = number of years * number of payments per annum
n = 25 * 12 = 300
Future value of annuity, FVA = $500,000
Monthly deposit will be:
[tex]P = \frac{(FVA) * r}{(1+r)^{n} -1} \\P = \frac{(500000) * 0.46/100}{(1+0.46/100)^{300}-1 }[/tex]
P = $776.41
Answer:
MP = $778.77
she should put $778.77 into the account each month
Step-by-step explanation:
This problem can be solved using the compound interest formula;
FV = MP{[(1+r/n)^(nt) - 1]/(r/n)} .......1
Where;
FV = Future value
MP = monthly contribution
r = yearly rate
n = number of times interest is compounded per year.
t = number of years
Given
FV = $500,000
t = 25 years
r = 5.5% = 0.055
n = 12 months/year
From equation 1, making MP the subject of formula;
MP = FV/{[(1+r/n)^(nt) - 1]/(r/n)}
Substituting the given values we have;
MP = 500,000/(((1+0.055/12)^(12×25) -1)/(0.055/12))
MP = $778.77
she should put $778.77 into the account each month
The American Academy of Family Physicians released a survey, revealing that 76% of US adults admit they lie to their doctor about how often they exercise. Dr. Moffett believes the percentage seems high, so she decides to conduct her own hypothesis test to determine the true proportion. What should she write as the null and alternative hypotheses for this situation?
Answer:
H₀: p=0.76
Ha :p < 0.76
Step-by-step explanation:
A null hypothesis is the common accepted fact that the researcher works to prove it wrong. In this case, the survey revealed that 76% of US adults admit they lie to their doctor about how often they exercise. This forms the null hypothesis.
The alternative hypothesis suggest that a new theory is happening unlike the original one.In this case, Dr. Moffett believes the percentage seems high, so the alternative hypothesis is that the percentage is lower than 76%
Answer:
H0: p = 0.76; Ha: p < 0.76
Step-by-step explanation:
I took the quiz and got it right
Create a rational expression that satisfies the following criteria: 1) Domain is all reals except 1 and -1 2) x=1 is a vertical asymptote 3) X = -1 is a hole 4) There is a horizontal asymptote at y = 3
Answer:
y = (3x² + x - 2)/(x² - 1)
Step-by-step explanation:
(x - 1)(x + 1) = x² - 1
In the denominator
f(x)/(x² - 1)
f(x) has a factor (x + 1)
3 + (x + 1)/(x² - 1)
(3x² - 3 + x + 1)/(x² - 1)
y = (3x² + x - 2)/(x² - 1)
A filing cabinet has a height of 6 feet and a length of 2 feet. The volume of the filing cabinet is 36 cubic feet. What is the width of the filing cabinet?
Answer:
3 feet
Step-by-step explanation:
GIVEN: A filing cabinet has a height of [tex]6\text{ feet}[/tex] and a length of [tex]2\text{ feet}[/tex]. The volume of the filing cabinet is [tex]36\text{ feet}^3[/tex].
TO FIND: What is the width of the filing cabinet.
SOLUTION:
Let the width of filing cabinet be [tex]x\text{ feet}[/tex]
length of filing cabinet [tex]=6\text{ feet}[/tex]
height of filing cabinet [tex]=2\text{ feet}[/tex]
Volume of filing cabinet [tex]=\text{length}\times\text{height}\times\text{width}=36\text{ feet}^3[/tex]
putting values,
[tex]6\times2\times x=36[/tex]
[tex]12\times x=36[/tex]
[tex]x=3[/tex]
Hence the width of filing cabinet is 3 feet.
Find the Volume of the cylinder. Either enter an exact answer in terms of pie or use 3.14 for pie.
Can someone help me with this pls :(
Answer:
Step-by-step explanation:
we know that the formula for the volume of cylinder is
=[tex]\pi r^{2} h[/tex]
Given
radius(r) = 4
height(h) = 10
NOW
Volume = [tex]\pi r^{2} h[/tex]
= [tex]\pi *4^{2} *10[/tex]
=[tex]160\pi units^{3}[/tex]
or
if we use the value of pie then its answer is
= 160 * 3.14
= 502.4[tex]units^{3}[/tex]
Hope it was helpful:)
Here are the first five terms of Fibonacci sequence.
4, 4, 8, 12, 20
a) Write down the next two terms in the sequence ... , ...
The first three terms of a Fibonacci sequence are
n, 3n, 4n
b) Find the sixth term of this sequence
Answer:
a) 32, 52
b) 18n
Step-by-step explanation:
a)
12+20=32
20+32=52
b)
4th element = 3n+4n=7n
5th element = 4n+7n=11n
6th element = 7n+11n=18n
Answer:
a) 32, 52
b) 18n
Step-by-step explanation:
because 7n+n
3n+7
4
The city of Raleigh has 9000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 500 randomly selected registered voters was conducted. 217 said they'd vote for Brown, 242 said they'd vote for Feliz, and 41 were undecided.
Describe All citizens of Raleigh
A. All registered voters in Raleigh
B. All registered voters with telephones in Raleigh
C. The 500 voters surveyed
D. The 217 voters who said they'd vote for Brown
C. None of the abovethe sample for this survey.
Answer:
c
Step-by-step explanation:
plz mark me brainlesssss
From least to greatest, what are the measures of the next two angles with positive measure that are coterminal with an angle measuring 250°?
Answer:
610 and 970
Step-by-step explanation:
Answer:
610 and 970
Step-by-step explanation:
Find the value of x (no labels)
Answer:
x=31
Step-by-step explanation:
The interior angles of a triangle must add to 180 degrees, so
81+68+x=180
Add on the left
149+x=180
Now, solve for x by getting it by itself. To do this, subtract 149 from both sides
149-149+x=180-149
x=31
In Sakura's garden, for every 555 red flowers, there are 101010 yellow flowers. There are a total of 757575 yellow and red flowers in her garden. How many red flowers are in Sakura's garden?
Answer:
There are 25 red flowers in the garden.
Step-by-step explanation:
In this problem we have a common issue where the number is repeated 3 times in questions. So I'll sove it using the ratio 5 reds to 10 yellows and the data that there are 75 yellows and red flowers in the garden.
Since we know that for every 5 red flowers in a garden there are 10 yellow ones, then the ratio of yellow flowers to red flowers is
ratio = red/yellow = 5/10 = 1/2
yellow = 2*red
Since there are 75 yellow and red flowers in the garden we have:
yellow + red = 75
2*red + red = 75
3*red = 75
red = 75/3 = 25
There are 25 red flowers in the garden.
Answer:
25
Step-by-step explanation:
y=−5x+7 coordinates of x intercept
Answer:
The x intercept is (7/5,0)
Step-by-step explanation:
y=−5x+7
To find the x intercept, set y=0 and solve for x
0 = -5x+7
Subtract 7 from each side
0-7 = -5x+7-7
-7 = -5x
divide each side by -5
-7/-5 = -5x/-5
7/5 =x
The x intercept is (7/5,0)
Which algebraic expression represents this phrase?
the product of 40 and the distance to the finish line
THE ANSWER WOULD BE 40 × d
or 40d
what is 0.3% of 3.9*10^18
Answer:
1.17e+16
hope this helps! (if right pls mark brainy) thanks!
Which are simplified forms of the expression sec^2 theta sin 2theta? Select all that apply.
There are two answers.
a) 2 cot theta
b) 2-sec^2 theta
c) 2 tan theta
d) sec^2 theta-1
e) (sin2 theta) / (cos^2 theta)
Answer:
2 tan theta & sin2theta/cos^2theta
Step-by-step explanation:
Final answer:
The simplified forms of the expression sec^2(theta) sin(2theta) are 2 tan(theta) and sec^2(theta) - 1. These correspond to answer choices (c) and (d) respectively, by utilizing trigonometric identities to simplify the expression.
Explanation:
To find the simplified forms of the expression sec^2(theta) sin(2theta), we can use trigonometric identities. The identity for sin(2theta) is 2sin(theta)cos(theta). Since sec(theta) is the reciprocal of cos(theta), we can write sec^2(theta) as 1/cos^2(theta).
Therefore, the expression becomes:
sec^2(theta) sin(2theta) = (1/cos^2(theta)) * (2sin(theta)cos(theta))
We can simplify this further by canceling one cos(theta) from the numerator and denominator, which yields:
2sin(theta)/cos(theta)
Simplified, this is equal to 2 tan(theta), since tan(theta) = sin(theta)/cos(theta).
Using another trigonometric identity, sec^2(theta) = 1 + tan^2(theta), we can also express the original expression as:
sec^2(theta) - 1 which simplifies to tan^2(theta).
This means that the correct answers from the provided choices are (c) and (d).
Three identical bags each contain two marbles. One bag has two white marbles, one has two black marbles, and one has one of each. You are given a bag at random and draw a white marble. What fraction of the time will the second marble you draw from that bag also be white?
Answer:
2/3
Step-by-step explanation:
what is coterminal angle
Answer: Angles who share the same initial side and terminal sides.
What is the slope of the linear function represented in
the table?
-7
-1/7
1/7
7
Answer:
the answer is C. (1/7)
Step-by-step explanation:
I did it on edge
whats 2+2-1+4x4-12-7
Answer:
is the answer 0
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
2+2-1+4x4-12-7
4-1+4x4-12-7
3+4+4x4-12-7
7+4x4-12-7
11x4-12-7
44-12-7
32-7
25
hope help :) .^.
The miles-per-gallon obtained by the 1995 model Z cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon. What is the probability that a car will get less than 21 miles-per-gallon?
Answer:
0.42074
Step-by-step explanation:
In this question, we are asked to calculate the probability that a car will get less than 21 miles per gallon.
This is P(x < 21)
z = 21-22/5 = -1/5 = -0.2
Therefore the probability of getting less than 21 miles per gallon will be;
P(x<21) = P (z < -0.2)
= 0.42074
Plz help asap!!!!!!!!!!!!!!!!!!!
Answer:
A) 0.685
Step-by-step explanation:
P(no snow) = 1 - P(snow)
1 - 0.315
0.685
A school is selling tickets to a choral performance. On the first day, the school sold 6 adult tickets and 6 child tickets for $102. The school took in $96 on the second day selling 12 adult tickets and 3 child tickets. How much does each ticket cost ?
Answer:
adult $5
child $12
Step-by-step explanation:
make the adult as x and child as y.
this will makes 6x + 6y = 102
12x + 3y = 96
solve it and the answer comes out.
Let X={1,2,3}X={1,2,3}. Let P(X)P(X) be the set of all subsets of XX (i.e. Power set of XX). Let RR be a relation defined on P(X)P(X) by the following. For all sets AA and BB in P(X)P(X), ARBARB iff |A|=|B||A|=|B|. Is RR an equivalence relation?
Answer:
Yes
Step-by-step explanation:
For the equation to be equivalence then it must be
Reflexive, Symmetric and transitive
since |A|=|B|;
Every element in A is in B then R is reflexive
If f(1) = g(1), then g(1) = f(1), so R is symmetric.
If f(1) = g(1) and g(1) = h(1), then f(1) = h(1), so R is transitive.
R is reflexive, symmetric, and transitive,
thus R is an equivalence relation.
a) What are the key aspects of any parabola? What do the key aspects tell you about the graph
Answer:
Vertex of parabola
Step-by-step explanation:
The red dot shows the extreme of parabola that is known as vertex.
Amelia used 6 liters of gasoline to drive 48 kilometers.
At that rate, how many liters does it take to drive 1 kilometer?
liters
Answer:
Part 1: 8 km per liter
Part 2: 0.125 liters per km
Step-by-step explanation:
Part 1:
6x=48
x=48/6
x=8
Part 2:
8km per liter
?liters per km
1/8 = 0.125
0.125 liters per kilometer