Answer:
The series converges to [tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
It seems to be this series:
[tex]$ \sum_{n=1}^{\infty} \left(\dfrac{1}{2} \right)^{2n}$[/tex]
We have
[tex]$ \sum_{n=1}^{\infty} \left(\dfrac{1}{2} \right)^{2n} = \sum_{n=1}^{\infty} \left(\dfrac{1}{4} \right)^{n}$[/tex]
Using the Root test we can see that this series converges once
[tex]$ \lim_{n \to \infty} \sqrt[n]{|a_n|} < 1 \implies \sum_{n=1}^{\infty} a_n \text{ is convergent}$[/tex]
Then, [tex]$\lim_{n \to \infty} \sqrt[n]{\left(\dfrac{1}{4} \right)^{n}} = \lim_{n \to \infty} \dfrac{1}{4} = \dfrac{1}{4} < 1$[/tex]
The series is convergent.
Once the series is geometric, the first term is [tex]\dfrac{1}{4}[/tex] and the ratio is also [tex]\dfrac{1}{4}[/tex] in this case.
The sum of infinite geometric series is [tex]S = \dfrac{a_1}{1-r}[/tex] such that [tex]r < 1[/tex]
[tex]\therefore S = \dfrac{\frac{1}{4} }{1-\frac{1}{4}} = \dfrac{1}{3}[/tex]
What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π? (1 point) Select one: a. x = 3 pi over 2 , x = π b. x = pi over 2 , x = 3 pi over 2 c. x = 0, x = 2π d. x = 0, x = π
9514 1404 393
Answer:
b. x = π/2, x = 3π/2
Step-by-step explanation:
The maximum is found where the argument of the cosine function is a multiple of 2π.
2x -π = 2nπ
2x = (2n+1)π . . . . . . . add π
x = (2n+1) · π/2 . . . . . divide by 2
x = {π/2, 3π/2}
Write a linear equation in standard form for the line that goes through
(-14,-5) and (4,5).
O A. y- 5 = (x-4)
B. -5x+9y= 25
C. -5x +9y= 1
D. 5x-9y= 25
The linear equation of line passing through the (-14,-5) and (4,5) is given by -5x + 9y = 25
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -14 , -5 )
Let the second point be Q ( 4 , 5 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -5 - 5 ) / ( -14 - 4 )
Slope m = -10 / -18
Slope m = 5/9
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 5 = ( 5/9 ) ( x - 4 )
Multiply by 9 on both sides , we get
9y - 45 = 5x - 20
Adding 45 on both sides , we get
9y = 5x + 25
Subtracting 5x on both sides , we get
-5x + 9y = 25
Hence , the equation of line is -5x + 9y = 25
To learn more about equation of line click :
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Amber rode her bike around the park 4 times. It took her 9 minutes each time.
How many minutes did she ride in all?
Answer:
Amber rode for 36 minutes in total.
Step-by-step explanation:
Lets create a ratio table:
Time elpased (minutes) : Laps around park
9 : 1
36 : 4
Amber rode for 36 minutes in total.
đã đi 36 phút.
từng bước
9: 1
36: 4
Amber đã đi tổng cộng 36 phút.
What is the volume of the following rectangular prism? (please help)
Answer:
?
Step-by-step explanation:
i think ljhh ako naiintindihan
A class of 30 students ate 9 pizzas. How many pizzas would be needed for 40 students?
Answer:
12
Step-by-step explanation:
The ratio is 9:30
So for 40 people , it would be ?:40
Find the number that, when multiplies, by 30, equals 40. This is 1 1/3, or 1.3333... So multiply 9 by 1 1/3: 9 * 1 = 9, 1/3 * 9 = 3. ( + 3 = 12, so 12 pizzas
Answer:
12 i think
Step-by-step explanation:
What is the equation of the line that is perpendicular to the line defined by the equation 2y = 3x + 1 and goes through the point (3, 2)?
options:
y = - 1/3 x + 3
y = -2/3x + 4
y = 1/3x – 1
y = 2x – 4
y = 6x + 5
Answer:
Step-by-step explanation:
In order to determine the perpendicular slope to the given line, we first need to determine the slope of the given line, which is not apparent in its current form. We need to solve the equation for y to determine the slope:
2y = 3x + 1 in slope-intercept form is
[tex]y=\frac{3}{2}x+\frac{1}{2}[/tex] . Therefore, the perpendicular slope, the opposite reciprocal of the given slope of 3/2 is -2/3. Passing through the point (3, 2):
[tex]y-2=-\frac{2}{3}(x-3)[/tex] and
[tex]y-2=-\frac{2}{3}x+2[/tex] so
[tex]y=-\frac{2}{3}x+4[/tex], the second choice down.
What is the value of the expression 3m-4.2 If m equals 2.1
Answer:
2.1
Step-by-step explanation:
Given :
3m-4.2 where, m=2.1
Now,
3(2.1)-4.2
6.3-4.2
2.1
Answer is 2.1
Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.
Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).
TV(X,X+a) = ?
Answer:
1
Step-by-step explanation:
Computing Tv(X, X + a ) for any a∈(0,1)
Given that : X∼Ber(0.5)
∴ The probability mass function
P(X = 1 ) = 0.5
P(X = 0) = ( 1 - 0.5 )
and expectation E[X] = 0.5
hence ; TV ( X, X + a ) = 1
what is the answered
pp lssss answer
[tex]\boxed{ \underline{ \bf \: Categorical}} \sf \: data \: set \: is \: the \: data \: set \\ \sf \: that \: deals \: with \: only \: non \: numerical \: values.[/tex]
Optoion C. Categorial data set is the right answer of the question given.
RaonbowSalt2222
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
x + y - z = -2
2x - y + 3z = 9
x - 4y - 2z = 1
Answer:
x = 1 , y = - 1 , z = 2
Step-by-step explanation:
[tex]\begin{pmatrix}1&1&-1&-2\\ 2&-1&3&9\\ 1&-1&-2&1\end{pmatrix}\\\\\\= \begin{pmatrix}2&-1&3&9\\ 1&1&-1&-2\\ 1&-1&-2&1\end{pmatrix}[/tex] [tex][ \ swap \ R_1 \ and \ R_2 \ ][/tex]
[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 1&-4&-2&1\end{pmatrix}[/tex] [tex][ \ R_2 = R_2 - \frac{1}{2} R_1 \ ][/tex]
[tex]=\begin{pmatrix}2&-1&3&9\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\end{pmatrix}[/tex] [tex][ \ R_3 = R_3 - \frac{1}{2} R_1 \ ][/tex]
[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&\frac{3}{2}&-\frac{5}{2}&-\frac{13}{2}\end{pmatrix}[/tex] [tex][ \ swap \ R_2 \ and \ R_3 \ ][/tex]
[tex]=\begin{pmatrix}2&-1&3&9\\ 0&-\frac{7}{2}&-\frac{7}{2}&-\frac{7}{2}\\ 0&0&-4&-8\end{pmatrix}[/tex] [tex][ \ R_3 = R_3 + \frac{3}{7}R_2 \ ][/tex]
Therefore,
[tex]-4z = - 8\\\\z = 2[/tex]
[tex]-\frac{7}{2} y - \frac{7}{2}z = -\frac{7}{2}\\\\y + z = 1\\\\y + 2 = 1 \\\\y = 1 - 2 = - 1[/tex]
[tex]2x - 1y + 3z = 9\\\\2x -1(-1) + 3(2) = 9\\\\2x + 1 + 6 = 9\\\\2x = 9 - 7\\\\2x = 2 \\\\x = 1[/tex]
Matt had 60 questions correct on a Percent’s Chapter Test that had 150 one-mark questions. What was his mark written as a percentage?
Answer:
His mark, as a percentage, was of 40%.
Step-by-step explanation:
Mark as a percentage:
His mark as a percentage is the number of questions correct multiplied by 100% and divided by the number of questions.
In this problem:
60 questions correct out of 150. So
60*100%/150 = 40%
His mark, as a percentage, was of 40%.
DJ Kenisha is making a playlist for a radio show; she is trying to decide what 6 songs to play and in what order they should be played. If she has her choices narrowed down to 5 reggae, 15 hip-hop, and 13 blues songs, and she wants to play an equal number of reggae, hip-hop, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
Answer:
[tex]8.19 \times 10^{4}[/tex] different playlists are possible
Step-by-step explanation:
The order in which the songs are played is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 songs, so 2 reggae(from a set of 5), 2 hip hop(from a set of 15) and 2 blues(from a set of 13). So
[tex]T = C_{5,2}C_{15,2}C_{13,2} = \frac{5!}{2!3!} \times \frac{15!}{2!13!} \times \frac{13!}{2!11!} = 10*105*78 = 81900[/tex]
In scientific notations:
4 digits after the first, which is 8, so:
[tex]8.19 \times 10^{4}[/tex] different playlists are possible
Please help!! Will mark brainilest ☺️☺️
The shortest route from London to Edinburgh is 400 miles.
A lorry is expected to take 10 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 10 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
if it takes the lorry ten hours we divide 400 by 10
40 mph
if it takes 15% longer that means it will take
10*1.15=11.5
if we divide 400 by 11.5
we get 34.7826086957
or 34.8
so the lorry travels 5.2 mph faster then the expected speed
Hope This Helps!!!
Which row of the table reveals the y-intercept of function f?
Answer:
No solution is possible from the informatin provided.
Step-by-step explanation:
You didn't include the table,
Answer:
y intercept is found from the pair that has a 0 for the x variable.
Step-by-step explanation:
if a choice was (0,2) this would be the point where the line intercepts the y axis.
x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis
Which point represents the value of -(-2) on the number line?
Answer:
2
Step-by-step explanation:
-(-2)
negative x negative always give positive .
=>2
You can easily represent 2 on number line
2) A block of ice weighs 12 400 kg. It has the shape of a cylinder, with a radius of 1.2 m and
a height of 3 m. What is the density of the ice? Give your answer to one decimal place.
Answer:
= 3.6
Step-by-step explanation:
Do you know how to find the volume of a cylinder? Like any prism, it's area of base x height, in this case the base is a circle of radius 1.2m.
Density is simply mass / volume (kg / m3 ).
clarify its 1.2 x 3 = 3.6
12400 / 3.6 = 3.444 occuring
Can someone help PLSSS
Answer:
Step-by-step explanation:
Area stage = 1/2 h (ab +cd)
Area = 5(14+22)
meeting center Area = 180
room = 25*32 = 800
800-180 = 620 tile
620*$4.90 = $3038
So no not enough money....
Note: even if it was $2999 it still would not be enough because
you have to cut tiles to fit in corners and edges... Just having fun with that comment, the math problems sometimes don't take reality into account (ha ha ha)
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of accidents provided the following data. Sunday= 64, Monday=53, Tuesday=55, Wednesday=49, Thursday=55, Friday=68, Saturday=76. Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the -value? Compute the value of the test statistic (to 3 decimals).
Answer:
Hence,
a)
Test statistic [tex]X^{2}[/tex] = 9.269.
p value = 0.148
b)
Sunday= 15.23%, Monday= 12.62%, Tuesday= 13.10%, Wednesday=11.67%,
Thursday= 13.10%, Friday= 16.19%, Saturday= 18.09%.
Step-by-step explanation:
a)
relative observed Expected Chi square
Category frequency(p) [tex]O_{i}[/tex] Ei=total*p [tex](O-E)^{2}[/tex] [tex]R^{2}_{i} =(O_{i} -E_{i} )^{2} /E_{i}[/tex]
1 0.142857143 64.0 60.00 16.00 0.267
2 0.142857143 53.0 60.00 49.00 0.817
3 0.142857143 55.0 60.00 25.00 0.417
4 0.142857143 49.0 60.00 121.00 2.017
5 0.142857143 55.0 60.00 25.00 0.417
6 0.142857143 68.0 60.00 64.00 1.067
7 0.142857143 76.0 60.00 256.00 4.267
Total 1.000 420 420 556 9.269
Test statistic [tex]X^{2}[/tex] = 9.269.
p value = 0.148 from excel: chidist(9.269,6)
b)
Percentage %= Frequency of traffic occur on category x 100 / Total number of frequency given.
Category Percentage%
Sunday 15.23%
Monday 12.62%
Tuesday 13.10%
Wednesday 11.67%
Thursday 13.10%
Friday 16.19%
Saturday 18.09%
Given that abcd ~Jklm. Find the value of x, y, and z
Answer:
x = 7.2
y = 10
z = 6
Step-by-step explanation:
Since ABCD ~ JKLM, therefore, the ratio of their corresponding sides would be equal. Thus:
JK/AB = KL/BC = LM/CD = JM/AD
Substitute
12/x = y/6 = 15/9 = 10/z
✔️Find x:
12/x = 15/9
12/x = 5/3
Cross multiply
x*5 = 3*12
5x = 36
x = 36/5
x = 7.2
✔️Find y:
y/6 = 15/9
y/6 = 5/3
Cross multiply
y*3 = 5*6
3y = 30
y = 30/3
y = 10
✔️Find z:
15/9 = 10/z
5/3 = 10/z
Cross multiply
5*z = 10*3
5z = 30
z = 30/5
z = 6
If 20% of a length is 23cm ,whathat is the complete length
Step-by-step explanation:
20% of the length is 23 cm
100% of the length is 23×5 = 115 cm
Which congruence statement is correct?
Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
To finance the purchase of several new cars ,the Lincoln car rental agency borrowed $ 110 000 for 9 months at an annual interest rate of 5% . What is the simple interest due on the loan?
Answer: 4125
Step-by-step explanation:
S.I = P X R /100 X T
S.I = 110000 x 5/100 x 9/12 = 4125
= 4125
Answer:
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A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%
Compute the product AB by the definition of the product ofmatrices, where Ab1 and Ab2 are computed separately, and by therow-column rule for computing AB.
Matrix A= [2 -2]
[3 4]
[4 -3]
Matrix B =
[4 -1]
[-1 2]
Answer:
[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]
Step-by-step explanation:
Given
[tex]A =\left[\begin{array}{cc}2&-2\\3&4\\4&-3\end{array}\right][/tex]
[tex]B = \left[\begin{array}{cc}4&-1\\-1&2\end{array}\right][/tex]
Required
[tex]AB[/tex]
To do this, we simply multiply the rows of A by the column of B;
So, we have:
[tex]A * B = \left[\begin{array}{ccc}2*4 + -2*-1&2*-1+-2*2\\3*4+4*-1&3*-1+4*2\\4*4-3*-1&4*-1-3*2\end{array}\right][/tex]
[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]
which equation is the inverse of 5y+4=(×+3)^2+1/2?
Answer:
The inverse is -3 ±sqrt(5x+7/2)
Step-by-step explanation:
5y+4=(x+3)^2+1/2?
To find the inverse, exchange x and y
5x+4=(y+3)^2+1/2
Solve for y
Subtract 1/2
5x+4 -1/2=(y+3)^2+1/2-1/2
5x+8/2 -1/2=(y+3)^2+1/2-1/2
5x+7/2 = (y+3)^2
Take the square root of each side
±sqrt(5x+7/2) =sqrt( (y+3)^2)
±sqrt(5x+7/2) = (y+3)
Subtract 3 from each side
-3 ±sqrt(5x+7/2) = y+3-3
-3 ±sqrt(5x+7/2) = y
The inverse is -3 ±sqrt(5x+7/2)
If line r is parallel to —- ?
Answer:
the correct answer is 10
f(a)=|x-6|-|x+5|
evaluate
Can someone help with this
Answer: 28
Step-by-step explanation: ADB = 1/2 ACB