Answer:
the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Step-by-step explanation:
The term of the sequence are given as : [tex]\dfrac{1}{2}[/tex], [tex]\dfrac{1}{2^2}[/tex], [tex]\dfrac{1}{2^3}[/tex], [tex]\dfrac{1}{2^4 }[/tex] , . . .
The nth term for this sequence is , [tex]\mathtt{a_n =( \dfrac{1}{2})^n}[/tex]
The nth partial sum of the sequence for [tex]\mathtt{a_1,a_2,a_3.... a_n}[/tex] is [tex]\mathtt{S_n}[/tex]
where;
[tex]\mathtt{S_n = a_1 +a_2+a_3+ ...+a_n}[/tex]
The first partial sum is: [tex]\mathtt{S_1= a_1}[/tex]
[tex]\mathtt{S_1= (\dfrac{1}{2})^1}[/tex]
[tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
Therefore, the first partial sum [tex]\mathbf{S_1= \dfrac{1}{2}}[/tex]
The second partial sum is: [tex]\mathtt{S_2= a_1+a_2}[/tex]
[tex]\mathtt{S_2= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2}[/tex]
[tex]\mathtt{S_2= \dfrac{1}{2} + \dfrac{1}{4}}[/tex]
[tex]\mathtt{S_2= \dfrac{2+1}{4} }[/tex]
[tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
Therefore, the second partial sum [tex]\mathbf{S_2= \dfrac{3}{4} }[/tex]
The third partial sum is : [tex]\mathtt{S_3= a_1+a_2+a_3}[/tex]
[tex]\mathtt{S_3= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3 }[/tex]
[tex]\mathtt{S_3= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}}[/tex]
[tex]\mathtt{S_3= \dfrac{4+2+1}{8}}[/tex]
[tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
Therefore, the third partial sum [tex]\mathbf{S_3= \dfrac{7}{8}}[/tex]
The fourth partial sum : [tex]\mathtt{S_4= a_1+a_2+a_3+a_4}[/tex]
[tex]\mathtt{S_4= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 }[/tex]
[tex]\mathtt{S_4= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}}[/tex]
[tex]\mathtt{S_4= \dfrac{8+4+2+1}{16}}[/tex]
[tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
Therefore, the fourth partial sum [tex]\mathbf{S_4= \dfrac{15}{16}}[/tex]
The fifth partial sum : [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5}[/tex]
[tex]\mathtt{S_5= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 }[/tex]
[tex]\mathtt{S_5= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}}[/tex]
[tex]\mathtt{S_5= \dfrac{16+8+4+2+1}{32}}[/tex]
[tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
Therefore, the fifth partial sum [tex]\mathbf{S_5= \dfrac{31}{32}}[/tex]
The sixth partial sum: [tex]\mathtt{S_5= a_1+a_2+a_3+a_4+a_5+a_6}[/tex]
[tex]\mathtt{S_6= (\dfrac{1}{2})^1 + (\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4 +(\dfrac{1}{2})^5 +(\dfrac{1}{2})^6 }[/tex]
[tex]\mathtt{S_6= \dfrac{1}{2} + \dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64} }[/tex]
[tex]\mathtt{S_6= \dfrac{32+16+8+4+2+1}{64}}[/tex]
[tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
Therefore, the sixth partial sum [tex]\mathbf{S_6= \dfrac{63}{64}}[/tex]
What is the sum of the complex numbers −9−i−9−i and −5−i−5−i?
Answer:
The sum of the complex numbers will be - 28 - 4i
Step-by-step explanation:
We have the sum −9−i−9−i + −5−i−5−i. Let's group like elements and simplify this expression,
−9−i−9−i + −5−i−5−i ( Group like terms )
- i - i - i - i - 9 - 9 - 5 - 5 ( Add like terms )
- i - i - i - i = - 4i, - 9 - 9 = - 18, and - 5 - 5 = - 10
- 18 - 10 = - 28 ( Substitute )
Solution : - 28 - 4i
The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.
Answer:
Area of 7th hall = 37 m^2
Step-by-step explanation:
Total area of 7 halls = 7*55 = 385
Total area of 6 halls = 6*58 = 348
Area of 7th hall = 385-348 = 37 m^2
Answer:
The area of the seventh hall = 37m²
Step-by-step explanation:
for 6 halls
Mean area of 6 halls = 58m²
[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]
Let the area of the 7th hall be x
The sum of the areas of 7 halls = 348 + x - - - - - - (1)
[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]
notice that equation (1) = equation (2)
348 + x = 385
x = 385 - 348 = 37m²
Therefore, the area of the seventh hall = 37m²
how many quarts are there in 12 gallons and 3 quarts? enter the number only. Do not include units
Answer:
51
Step-by-step explanation:
At a high school movie night, the refreshments stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. 38 students bought both popcorn and a drink. What is the probability that a student buys a drink, given that he or she buys popcorn? Express your answer as a percent, rounded to the nearest tenth... best answer wins brainliest!!!
Answer:
47% and 62%
Step-by-step explanation:
1. Drink
The probability that a student buys a drink is 0.47
Step-by-step explanation:
The probability that a student buys a drink will be given by;
( the number of students who bought a drink)/(the total number of students)
We are told that;
Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. Therefore, the required probability is;
47/100= 0.47
0.47 = 47%
2. Popcorn
For popcorn probability, it's basically the same.
The probabilty that a student buys popcorn is 0.62
The probability that a student buys popcorn will be given by;
( the number of students who bought popcorn)/(the total number of students)
So therefore,
62/100 = 0.62
0.62 = 62%
How much state tax is withheld from $36,200 if the tax rate is 4%?
Answer:
$1448
Step-by-step explanation:
Tax=rate*amount=(4/100)*36200=1448
04.10 Which statement about the graph is true? CO 7 E 5 4 3 2 1 2 3 4 5 6 7 8 x The graph shows a proportional relationship because it is a line, and the difference between each point is the same. The graph shows a proportional relationship because it is a line, and each x-value is a multiple of 2. The graph does not show a proportional relationship because each point written as a ratio gives a different value. O The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.
Answer:
c
Step-by-step explanation:
cheese is rotten milk
Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
#1: Simplify the expression below. Type your answer as an integer.
7 + 1 - 18 : 6
Answer:
5
Step-by-step explanation:
Steps of calculation:
7 + 1 - 18 : 6 = 7 + 1 - 3 = 8 - 3 =5Answer is 5
7x2 - 4x +10+ 3x2 – 8
Find the slope of the line that passes through the points (1, -4) and (3,-1)
Hi there! :)
Answer:
[tex]\huge\boxed{m = \frac{3}{2}}[/tex]
Find the slope using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of each point:
[tex]m = \frac{-1 - (-4)}{3 - 1}[/tex]
Simplify:
[tex]m = \frac{3}{2}[/tex]
Therefore, the slope of the line is 3/2.
Answer:
3/2
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= ( -1 - -4)/(3-1)
= ( -1+4)/(2)
= ( 3/2)
Solve each system by graphing.
9514 1404 393
Answer:
no solution
Step-by-step explanation:
These lines have the same slope and different y-intercepts, so graph as parallel lines. As such, they will have no point of intersection, so there is NO SOLUTION to this system of inconsistent equations.
could I please have some help
Find the intervals on which the function f(x) = ax2 + bx + c (where "a" doesn't = 0) is increasing and decreasing. Describe the reasoning behind your answer.
Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
Use the following recursive formula to answer the question.
A1=-3/2
an=an-1+1/2
what’s is a9?
Step-by-step explanation:
a2=a1+1/2=-1
a3=a2+1/2=-1/2, then we have common difference 0.5
a9=a1+(n-1)d
a9=-3/2+(8)0.5=5/2
Please help with this
The shape has 11 sides.
Using the angle formula for polygons:
The sum of all the interior angles is:
11-2 x 180 = 9 x 180 = 1,620 degrees.
For one angle divide the total by number of sides:
1620 / 11 = 147.27 which rounds to 147.2
The answer is D.
The ages of some lectures are 42,54,50,54,50,42,46,46,48 and 48.Calculate the:
(a)Mean Age.
(b)Standard deviation.
Answer:
The mean age is 48
The standard deviation is 4
Step-by-step explanation:
The answer is, (a) mean age is 48.
(b) standard deviation is 4.
What is a mean age?Average age of the population calculated as the arithmetic mean.Another parameter determining the average age of the population is the median age.What does standard deviation of age mean?In general, the standard deviation tells us how far from the average the rest of the numbers tend to be, and it will have the same units as the numbers themselves. If, for example, the group {0, 6, 8, 14} is the ages of a group of four brothers in years, the average is 7 years and the standard deviation is 5 years.How do you find the mean age?To find the mean add all the ages together and divide by the total number of children.
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Heng tried to define a reflection across line r.
• Any point N on line r maps to itself.
• Any point M not on the line of reflection maps to a point M' such that the midpoint L of MM' is
on liner.
Which counterexample shows that Heng's definition does not fully define a reflection?
Choose 1 answer:
Answer:
Any point N on line r maps to itself.
Step-by-step explanation:
Reflection is one of the examples of solid transformation in which a given point, segment, or figure is flipped over a reference point or line to produce its image. The distance of the object to the reference point or line is the same as the distance of its image to the point or line. And both have the same size, but different orientation.
The option that does not fully define a reflection is; any point N on line r maps to itself, because no image of point N is produced after the operation.
Answer:
C. This matches Heng's definition, but is not a reflection, because MM'MM
′
M, M, prime is not perpendicular to line rrr.
Step-by-step explanation:
How long will it take for a lump-sum investment to double in value at an interest rate of 1.5% per month, compounded continuously
Answer:
It will take 47 months ( 3 years and 11 months)
Step-by-step explanation:
We use the compound interest formula here.
Mathematically;
A = P( 1 + r)^t
Where A is the amount which is 2 times the principal here, so we can call it 2P
P is the lump-sum invested
r is the monthly interest rate given as 1.5% = 1.5/100 = 0.015
t = time , which we want to calculate
Substituting these values, we have;
2P = P(1 + 0.015)^t
divide both sides by P
2 = 1.015^t
Take the log of both sides;
log 2 = log (1.015)^t
log 2 = t log 1.015
t = log2/log1.015
t = 46.55
which is approximately 47 months
Khảo sát 600 sinh viên trường thấy có có 520 sinh viên thích các hoạt động của Hội Thanh Niên nhà trường. Với độ tin cậy 95%, ta có ước lượng tỷ lệ sinh viên toàn trường thích các hoạt động của Hội Thanh Niên thuộc khoảng
Answer:
I don't know ans OK bro because I can't understand your language what are you writing
V(x)=-x2+2x-4 and W(x)=-x3+2x2+x+5 Find V(x)-W(x)
Answer:
[tex]-x^3-x^2+x-9[/tex]
Step-by-step explanation:
Distribute -1
Combine Like Terms
[tex](x^2+2x-4)-(x^3+2x^2+x+5)\\= x^2+2x-4+-x^3-2x-x-5\\= -x^3-x^2+x-9[/tex]
Answer:
[tex]x^{3} -3x^{2} +x-9[/tex]
Step-by-step explanation:
-x^2+2x-4-(-x^3+2x^2+x+5)
Combine like terms
x^3-3x^2+x-9
I need some help with this please :)
Answer:18 ft
Step-by-step explanation: Perimeter=2(L+B)
Perimeter=2(7 + 2)
2×9=18
Answer:
18feet.
Step-by-step explanation:
To find the perimemter of a rectangle, you just add all the sides.
A rectangle has 4 sides in total, where 2 are equal, and the other 2 are als equal.
So, you just add 7+2+7+2, which gives 18.
This is why, the perimeter of this rectangle is 18feet.
Hope this helped, have a nice day!
A certain vector in the xy plane has an x component of 4 m and a y component of 10 m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about:
Answer:
New length of component y' = 7.2 m (Approx)
Step-by-step explanation:
Given:
Length of component x = 4 m
Length of component y = 10 m
New length of component x' = 8 m
Find:
New length of component y' = ?
Computation:
Length vector of rotation = √x² + y²
Length vector of rotation = √4² + 10²
Length vector of rotation = √16 + 100
Length vector of rotation = √116
Length vector of rotation = √x'² + y'²
√116 = √x'² + y'²
116 = x'² + y'²
116 = 8² + y'²
New length of component y' = 7.2 m (Approx)
Solve the following system of equations using the elimination method. x – y = 11 2x + y = 19
━━━━━━━☆☆━━━━━━━
▹ Answer
(10, -1)
▹ Step-by-Step Explanation
x - y = 11
2x + y = 19
Sum up the equations:
3x = 30
Divide 3 on both sides:
x = 10
Substitute:
10 - y = 11
y = -1
Solution:
(x, y) (10, -1)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is the image of the point (-7, 4) after a rotation of 180° counterclockwise about the origin?
Answer: (7, -4)
Concept:
For each rotation angle, there is a specified rule that could be applied. Please refer to the attachment below for the list of rotation rules.
Solve:
Given point = (-7, 4)
Given rotation rule = (x , y) ⇒ (-x, -y)
(-7, 4) ⇒ (7, -4)
Hope this helps!! :)
Please let me know if you have any questions
5x+4(-x-2)=-5x+2(x-1)+12
Answer:
x=9/2
Step-by-step explanation:
Let's solve your equation step-by-step.
5x+4(−x−2)=−5x+2(x−1)+12
Step 1: Simplify both sides of the equation.
5x+4(−x−2)=−5x+2(x−1)+12
5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)
5x+−4x+−8=−5x+2x+−2+12
(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)
x+−8=−3x+10
x−8=−3x+10
Step 2: Add 3x to both sides.
x−8+3x=−3x+10+3x
4x−8=10
Step 3: Add 8 to both sides.
4x−8+8=10+8
4x=18
Step 4: Divide both sides by 4.
4x/4=18/4
x=9/2
There are 937 entries for a talent show.
What is the value of the 3?
Answer:
the value of the 3 is 30
Step-by-step explanation:
the second digit to the left of a decimal is always tens column
The revenue, cost, and profit functions for a line of cell phone cases is shown. Identify the location on the profit function where the profit from sales of the phone cases is a maximum.
Answer:
approximately x = 38
Step-by-step explanation:
The maximum profit is the vertex of the profit graph parabola. The maximum occurs at approximately x = 38.
The solution is x = 38
The location on the profit function parabola where the profit from sales of the phone cases is a maximum is given by x = 38
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the revenue, cost, and profit functions for a line of cell phone cases be given as two parabolic functions R ( x ) and P ( x )
The maximum profit is given by the parabolic function R ( x )
The profit is represented by = y
The price per phone is represented by = x
Now , when y is maximum ,
The value of y = $ 2,250,000
The value of x when y = $ 2,250,000 is x = 38
So , the value of x from the parabola where profit is maximum is x = 38
Therefore, the value of x = 38
Hence , the value of x from the function is x = 38
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Algebra II Part 1
On your paper, graph these coordinates:
(-1, 1), (-5, 2)
Type the correct equation of the line.
Note: Do not use fractions in your answer.
Answer:
4y+x-3=0
Step-by-step explanation:
The equation is y=mx+b
1) Use the coordinates from the first point
(-1,1)
1= -m+b
2) Use the coordinates frm the second point
(-5,2) (y=mx+b, use x=-5, y=2)
2=-5m+b
You have the system of equations
1=-m+b (multiply by -1) -1= m-b
2=-5m+b
Add the first equation (multiplied by -1) and the second one
-1+2= m-b-5m+b
1= -4m
m=-0.25
2=1.25+b
b=0.75
y=-0.25x+0.75
4y= -x+3
4y+x-3=0
Please help me solve this question ?
Answer:
Hi,
If you don't know how to derivate, i can show you using
lim (f(x+h)-f(x))/h if h ->0
Step-by-step explanation:
[tex]f(x)=2x^2+3x-2\\\\f'(x)=4x+3\\\\f'(1)=4*1+3=7\\\\f'(3)=4*3+3=15\\\\f'(5)=4*5+3=23\\[/tex]
Step-by-step explanation:
18