The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
For given question,
We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]
We need to find the sum of given convergent series.
Given series is a geometric series with ratio r = sin(1)
The first term of the given geometric series is [tex]a_1=sin(1)[/tex]
So, the sum is,
= [tex]\frac{a_1}{1-r}[/tex]
= sin(1) / [1 - sin(1)]
This means, the series converges to sin(1) / [1 - sin(1)]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
= [tex]\frac{sin(1)}{1-sin(1)}[/tex]
= [tex]\frac{0.8415}{1-0.8415}[/tex]
= [tex]\frac{0.8415}{0.1585}[/tex]
= 5.31
Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
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How to do this question. First to answer this question will be marked as brainlist.
Answer:
10
Step-by-step explanation:
Every number with exponent zero is equal to 1
(7³×8)⁰ = 1
5⁰ = 1
then:
(3² + 5⁰) / (7³×8)⁰
= (3² + 1) / 1
= (9+1) / 1
= 10
3^2 = 9
3^2 = 95^0 =1
(7^3 x 8)^0 is 1
(anything to power of zero is one)
9 + 1 / 1 gives us the fraction 10/1
10/1 + 1/3 => make denominator the same, so I'll multiply 10/1 by 3
We get : 30/3 + 1/3 => 31/3
Thus answer is 31/3
Hope this helps!
Match each correlation coefficient to its corresponding description.
Katy buys 4 DVDs every 2 weeks. How many DVDs will she buy in 14 weeks?
Answer:
28 DVDs
Step-by-step explanation:
Given information from the question, we can deduce:
2 weeks = 4 DVDs
1 week =
[tex] \frac{4}{2} \\ = 2[/tex]
2 DVDs on average.
Which means,
14 weeks = 2 × 14 = 28 DVDs
Therefore, Katy will buy 28 DVDs in 14 weeks.
. The set of possible values of x is {-8, -3, 7}. If
5y = x-2, what is the set of possible values of y?
Answer:
{-2, -1, 1}
Step-by-step explanation:
Since we are given all the possible inputs {-8, -3, 7} we can use them one by one in the equation to find the outputs.
5y = x - 2 , if x is -8
5y = -8 - 2
5y = -10
y = -2
Next,
5y = x - 2, if x = -33
5y = -3 - 2
5y = -5
y = -1
Last,
5y = x - 2 when x =7
5y = 7 - 2
5y = 5
y = 1
So the set is {-2, -1, 1}
PLEASE HELP IM STUCK
Step-by-step explanation:
what is the problem ?
the solution of such a system of 2 equations is the point, where they cross.
this point has the same coordinates for both equations, and that is called the solution.
and we can clearly see that point in the graph :
(-1, 1)
formally we can solve that way
y = 2x + 3
y = -x
therefore,
2x + 3 = -x
3x + 3 = 0
3x = -3
x = -1
y = -x = - -1 = 1
so, we get
(-1, 1) as solution.
What is the area of the given triangle?
24 square units
12 square units
48 square units
17.2 square units
Answer: 12 square units
Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.
Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.
One number chosen randomly from the integers 1 to 20. Find the probability of getting a number that is odd and prime.
Answer:
35%
Step-by-step explanation:
All the prime numbers from 1 to 20 are:
2 3 5 7 11 13 17 19
7 / 20 = 35 / 100 = 35%
word problem for 2.35+-4.57
Answer:
=> -2.22
Step-by-step explanation:
=> 2.35 + ( -4.57)
=> 2.35 - 4.57
=> - 2.22
Use the method of undetermined coefficients to solve the given nonhomogeneous system. x' = −1 5 −1 1 x + sin(t) −2 cos(t)
It looks like the system is
[tex]x' = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} x + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
Compute the eigenvalues of the coefficient matrix.
[tex]\begin{vmatrix} -1 - \lambda & 5 \\ -1 & 1 - \lambda \end{vmatrix} = \lambda^2 + 4 = 0 \implies \lambda = \pm2i[/tex]
For [tex]\lambda = 2i[/tex], the corresponding eigenvector is [tex]\eta=\begin{bmatrix}\eta_1&\eta_2\end{bmatrix}^\top[/tex] such that
[tex]\begin{bmatrix} -1 - 2i & 5 \\ -1 & 1 - 2i \end{bmatrix} \begin{bmatrix} \eta_1 \\ \eta_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex]
Notice that the first row is 1 + 2i times the second row, so
[tex](1+2i) \eta_1 - 5\eta_2 = 0[/tex]
Let [tex]\eta_1 = 1-2i[/tex]; then [tex]\eta_2=1[/tex], so that
[tex]\begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} = 2i \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix}[/tex]
The eigenvector corresponding to [tex]\lambda=-2i[/tex] is the complex conjugate of [tex]\eta[/tex].
So, the characteristic solution to the homogeneous system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix}[/tex]
The characteristic solution contains [tex]\cos(2t)[/tex] and [tex]\sin(2t)[/tex], both of which are linearly independent to [tex]\cos(t)[/tex] and [tex]\sin(t)[/tex]. So for the nonhomogeneous part, we consider the ansatz particular solution
[tex]x = \cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}[/tex]
Differentiating this and substituting into the ODE system gives
[tex]-\sin(t) \begin{bmatrix} a \\ b \end{bmatrix} + \cos(t) \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \left(\cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}\right) + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
[tex]\implies \begin{cases}a - 5c + d = 1 \\ b - c + d = 0 \\ 5a - b + c = 0 \\ a - b + d = -2 \end{cases} \implies a=\dfrac{11}{41}, b=\dfrac{38}{41}, c=-\dfrac{17}{41}, d=-\dfrac{55}{41}[/tex]
Then the general solution to the system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix} + \dfrac1{41} \cos(t) \begin{bmatrix} 11 \\ 38 \end{bmatrix} - \dfrac1{41} \sin(t) \begin{bmatrix} 17 \\ 55 \end{bmatrix}[/tex]
Which of the following represents the series in summation notation?
−2 + 4 − 8 + 16 − 32 + 64 − 128.
Answer:
ummation of n=1 to n=7 (-2)^n
Step-by-step explanation:
summation of n=1 to n=7 (-2)^n
For the first 150 miles of a trip, an car drives at v mph. For the next 200 miles, the car drives at (v
+25) mph. The average speed of the whole trip is 35 mph. Find the value of v.
(A) 20
(B) 25
(C) 30
(D) 35
If for the first 150 miles of a trip, an car drives at v mph, for the next 200 miles, the car drives at (v+25) mph and the average speed of the whole trip is 35 mph, then the value of v will be 20mph (A).
Given Information:
Average speed = 35 mph
Total distance = 150 + 200 = 350 miles
For the first 150 miles of a trip, an car drives at v mph speed
⇒ Time, t1 = 150/v hrs
For the next 200 miles, the car drives at (v+25) mph speed
⇒ Time, t1 = 200 / (v+25) hrs
Now, the formula for average speed is given as,
Total distance / Total time
= [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex]
⇒ [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex] = 35 mph
[tex]\frac{350 v (v+25)}{150(v+25) + 200v}[/tex] = 35
[tex]\frac{350v^{2} + 8750v}{150v +3750 + 200v}[/tex] = 35
350v² + 8750v = 35 (350v + 3750)
v² + 25v = 35v + 375
v² - 10v = 375
v² - 10v - 375 = 0
Now, the above equation for speed can be written as,
v² - 20v + 15v - 375 = 0
v(v-20) + 15(v-20) = 0
(v-20) (v+15) = 0
v = 20
or v = -15
Since, speed is a scalar quantity, it can't be negative. Thus, v = 20 mph
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A free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. the goalie is standing on the goal line at a point where he is 3 yards from the left post and 5 yards from the right post, to be sure that the angle that the kicker can kick and score is bisected. how far is the kicker from the right post, to the nearest yard?
IfIf a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.
Distance of the kicker from the right postUsing sine theorem
Let Left triangle=3/sinx=14/sin∝
Let Right triangle=5/sinx=y/sin(180°-∝°)
Let Sin∝°=sin(180°-∝°) sinx=sinx
Let y represent how far is the kicker
Hence:
3/5=14/y
y=5×14/3
y=70/3
y=23.3333
y=23 yards (Approximately)
Therefore If a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.
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Four individuals invest in real estate together and i agreed to split the prophets equally, n invest $12,000, x invest 6,000, y invest $25,000, and z invest $7,000. if the profit of the first year were $120,000, y receives _ ? _ less than if the profit were divided in proportion to how much they invested.
Y receives $30000 less than if the profit were divided in proportion to how much they invested.
What is Proportional Profit?In a proportional tax system, everyone is compelled to pay the same amount of taxes as a percentage of their income.
According to the given information:Profit will Divide into 4 equal parts.
The total Profit for the month is = $120,000
The party will receive a sum of = $30,000
This shows that Y also receive the same amount
Y = $30,000 (Profit received)
Now
If the Profits were divided in proportion to the investments made .
The proportion on investment made by Y.
The total investment made = $12000+$6000+$25000+$7000
= $50000
Out of this the Amount invested by Y = $25000
The Proportional Profit of Y.
= (25000/ 50000) x 120000
= $60,000
So Y receives 60000 - 30000
= 30000
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Last one
Because if we simplify
(4x³y-6xy³)/2xy(2xy(2x²-3y²))/2xy2x²-3y²Verified
Answer:
D is the correct Answer.
Step-by-step explanation:
4x^3+-6xy^3
2xy
When dividing exponents you will subtract. Leaving you with 2x^3-3y^2.
Therefore your answer is D.
Please answer this question ASAP!
The traffic lights at three different road crossings change after every 48, 72 and 108 seconds respectively. If they change simultaneously at 8 am, at what time will they change to again?
Answer:
8:07:12 am
Step-by-step explanation:
The lights will change simultaneously after any multiple of the least common multiple of their cycle times.
LCMThe least common multiple of a set of numbers is the product of the highest powers of their prime factors.
48 = 2⁴×3
72 = 2³×3²
108 = 2²×3³
The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...
LCM = 2⁴×3³ = 16×27 = 432
The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.
Evaluate 3(x-4) + 2x - x² for x = 3.
A. -6
B. 6
C. 2
D. -2
Answer:
A) -6
Step-by-step explanation:
its just by substituting 3 in place of x
3(3-4)+2(3)-(3)²
3(-1)+6-9
-3+(-3)= -6
pls gimme brailiest if it helped :)
Answer:
A. -6
Step-by-step explanation:
3(x-4) + 2x - x²
Evaluate
Let x =3
Substitute into the expression
3( 3-4) +2(3) - 3^2
Parentheses first
3( -1) +2(3) - 3^2
Exponents next
3( -1) +2(3) - 9
Multiply
-3 +6 -9
Add and subtract
-6
does anyone know the answer to this?
Answer:
C
Step-by-step explanation:
for AB to be parallel to CD then the slopes of both segments must be equal
using the slope formula to find the slopes , then
A (x₁, y₁ ) and B (x₂, y₂ )
[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
C (x₃, y₃ ) and D (x₄, y₄ )
[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]
then
[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]
[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C
Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother had $15 more than the other. How much has each saved?
Answer:
20 and 35 dollars.
Step-by-step explanation:
x + x + 15 = 55
2x + 15 = 55
2x = 55 - 15
2x = 40
x = 40/2
x = 20
One of the brothers has saved 20 dollars, while the other has 35 dollars.
if you borrow $100 for 3 years at an annual interest rate of 9%, how much will you pay all together
Answer:
$127
Step-by-step explanation:
interest = (100)(0.09)(3) = $27
total = principal amount + interest
total = 100 + 9 = $127
An account with an initial balance of $4,000.00 and a 3% interest rate has a balance of $4,121.66 at the end of one year. What is the effective annual yield? A. 97.05% C. 3.00% B. 2.95% D. 3.04%
The effective annual yield is 3.04%
What is effective annual yield?
Effective annual yield is the rate of return that considers the frequency of compounding, in other words, the number of times in a year that interest on the balance is compounded.
The easiest way to determine the effective annual yield in this case is to compare the end of the year balance with the initial balance at the start of the year
effective annual yield=(ending balance/initial balance)-1
ending balance=$4,121.66
initial balance=$4000
effective annual yield=($4,121.66/$4000)-1
effective annual yield=3.04%
Another way to determine the effective annual yield is use the below formula which considers that interest rate is 3% compounded monthly, in other words, n, the frequency of compounding is 12
EAR=(1+r/n)^n-1
r=3%
n=12
EAR=(1+3%/12)^12-1
EAR=3.04%
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Saul walks dogs to earn extra money. He
earned $220 last week by walking 16 dogs.
Write and solve an equation to determine
how much he charges to walk each dog
each week.
Answer:
the answer is 13.75
Step-by-step explanation:
So how here is the solutionSaul earned 220 of 16 dogs so
when you divide 220 with 16 the answer be 13.75
[tex]220 \div 16[/tex]
[tex]13.75[/tex]
So let's checkwhen you multiply 13.75 by 16 the answer be 220
[tex]13.75 \times 16 \\ 220[/tex]
please mark as brainlist I only want 2 more please
May it helpful to you
thank you
Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less to handle than paper ticketing. However, in recent times the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem, an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below.
14 14 16 12 12 14 13 16 15 14
12 15 15 14 13 13 12 13 10 13
A) What assumption is necessary before conducting a test of hypothesis?
B) What is the decision rule?
Reject H0: ? ? 15 and accept H1: ? < 15 when the test statistic is
Less than or Greater than (pick one)
C) Compute the test statistic:
D) Reject or accept the null hypothesis?
The assumption that is necessary before conducting a test of hypothesis is that there is a significant amount of complaints for use of e-tickets.
How to illustrate the information?The assumption is that there is a significant amount of complaints for use of e-tickets.
H0: there is a significant amount of complaints for use of e-tickets.
H1: Number of complaints for use of e-tickets is not significant.
H1: parameter > value
Notice the inequality points to the right
Decision Rule: Reject H0 if test statistic > critical value
Decision Rule: Reject H0 if p -value = 0.05
The hypothetical mean is 15.00 and The actual mean is 13.50
The difference between these two values is -1.50.
The sample size is 20
Mean 13.50
SD 1.50
The test statistic will be -4.459.
Lastly z it's important to reject the null hypothesis since the test statistic is greater than the critical value of 1.7291.
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a=5
b=12
c=10
d=2
1. 2b-a
2. d(ab-c)
3. 3 + b/d
4. 4a/b+4d
5. b-c+d
amplificar la siguientes fracciones con tal que de un numero igual al final las fracciones son:
a. 1/2, 3/4, 5/10, 9/20
b. 3/8, 1/15, 3/20, 9/10
c. 7/9, 1/3, 5/6, 3/4
d.3/12, 1/5 7/15 1/20
The arrangement of the fractions given from the lowest to the highest is illustrated
How to illustrate the information?a. 1/2, 3/4, 5/10, 9/20.
We can change this to percentages.
1/2 = 1/2 × 100 = 50%
3/4 = 3/4 × 100 = 75%
5/10 = 5/10 × 100 = 50%
9/20 = 9/20 × 100 = 45%
Therefore, the arrangement will be 9/20, 5/10, 1/2, and 3/4.
b. 3/8, 1/15, 3/20, 9/10
3/8 = 37.5%
1/15 = 6.67%
3/20 = 15%
9/10 = 90%
The arrangement will be 1/15, 3/20, 3/8, and 9/10.
c. 7/9, 1/3, 5/6, 3/4
7/9 = 77.7%
1/3 = 33.3%
5/6 = 82%
3/4 = 75%
The arrangement will be 1/3, 3/4, 7/9, and 5/6.
d.3/12, 1/5 7/15 1/20
3/12 = 25%
1/5 = 20%
7/15 = 48%
1/20 = 5%
The arrangement will be 1/20, 1/5, 3/12, and 7/15.
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add 374 and 25 then subtract the sum from the largest single digit number. hint: largest single digit number is 9
Answer:
Sum of 374 and 25 = 374+25 = 399
now subtract 9 from the sum, i.e. 399 = 399 - 9 = 390 is your answer
Answer:
Step-by-step explanation:
374+25
=399
Now, subtracting the sum from 9
9-399
= -390
Suppose we roll one fair six-sided die, and flip six coins. what is the probability that the number of heads is equal to the number showing on the die?
The probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex] .
According to the question
we roll one fair six-sided die, and flip six coins
i.e
The Total Outcomes is the product of the sample spaces for the dice and the coins.
sample spaces for the dice = 6
sample spaces for the coins = 2⁶
S = 6.2⁶
S = 384
Now, The probability is
Therefore, the Favorable Outcomes
Consider the number of ways to get each total of heads from 1 to 6.
= 2⁶-1 (as TTT is excluded )
= 63
The probability that the number of heads is equal to the number showing on the die
As
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes
By substituting the values in the formula
Probability(Event) = [tex]\frac{63}{384}[/tex]
Probability(Event) = [tex]\frac{21}{128}[/tex]
Hence, the probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex]
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.A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500?
Answer:
given,
final interest = Prt
p = 7500
r = 15%
t= 8 yrs
Fi= 7500 x 0.15 x 8
= 1125 x 8
=9000
total savings = 9000 + 7500 = 16500
how does a budget help you
Answer:
it helps you control your spending, track your expenses, and save more money.
HELP PLEASE
if a function representing distance (feet) as a function of time (minutes), what does f(30) represent in terms of the situation?
We know
In a function
y=f(x)x represents the input and y represents output
So
f(30)x is time
So
f(30) represents distance traveled in 30mins
Grade 12 Financial Mathematic
n-up Q:
Austin buys a house for R 1 785 000 on the 1st September 2021. The bank gives him an interest rate of
6% p.a. compounded monthly. Mr Austin makes payments of R11 000 at the end of each month.
a) What is the balance on the loan on the 31st December 2036?
b) How long will it take Mr Austin to payoff the loan?
Answer:
a)0.00
b)13year,8month,2weeks and 6day