Answers
The expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
What is a series?A sequence is defined as an arrangement of numbers in a particular order. A series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers.
For the given situation,
The series is 1/4 + 1/16 + 1/64 + 1/256.
⇒ [tex]\frac{1}{4}+\frac{1}{16} +\frac{1}{64} +\frac{1}{256}[/tex]
⇒ [tex]\frac{1}{4}+\frac{1}{4^{2} } +\frac{1}{4^{3} } +\frac{1}{4^{4} }[/tex]
Thus the sum of this series can be obtained by the expression,
[tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4^{n}})[/tex]
⇒ [tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4})^{n}[/tex]
Hence we can conclude that the expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
Learn more about series here
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Related Questions
Red Blue Yellow Green What is the probability of a player spinning the color blue and then rolling a 4?
A: 1/4
B: 1/24
C: 1/6
D: 1/16
Answers
Answer:
(1/4)×4=1/16
Step-by-step explanation:
Blue is 1 out of the 4 colours, it rolls for 4 times
A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51. Assume monthly gasoline bill amounts are normally distributed. The probability that his bill will be less than $50 a month or more than $150 for a single month is:
Answers
Answer:
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51.
This means that [tex]\mu = 125.32, \sigma = 49.51[/tex]
Less than 50:
p-value of Z when X = 50. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 125.32}{49.51}[/tex]
[tex]Z = -1.52[/tex]
[tex]Z = -1.52[/tex] has a p-value of 0.0643
More than 150
1 subtracted by the p-value of Z when X = 150. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 125.32}{49.51}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915
1 - 0.6915 = 0.3085
The probability that his bill will be less than $50 a month or more than $150 for a single month is:
0.0643 + 0.3085 = 0.3728
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
give the formula in finding the surface area of the cube
Answers
Answer:
A=6a²
Step-by-step explanation:
Lowercase a is the length of one side.
in a class of 24 students, how many different 3 person teams for a group project can the teacher make?
Answers
Answer:
The teacher can make 8 different 3 person teams
Step-by-step explanation:
Since there is a total of 24 students and the teacher wants to make as many 3 person groups as he/she can you would just do 24 divided by 3 which would equal 8 different teams of 3 people. So the teacher can make 8 different groups of 3 people
Which binomial is a factor of 3x^2 + 2x − 5 ?
3x-1
3x-5
x-1
x-5
Answers
Answer:
3x-1
Step-by-step explanation:
3x^2+2x-5=3x-1 x1-25
What is the arc measure of major arc ABC in degrees?
Answers
9514 1404 393
Answer:
249°
Step-by-step explanation:
Arc ABC = Arc AB + Arc BC
= 180° +69°
Arc ABC = 249°
If 2x + 5 = 82, then 12x = ?
A 5
B
10
C 15
D 20
Answers
Answer:
2x= 38.5
Step-by-step explanation:
I'm not sure where u got 12x but 2 x = 38.5:
2x + 5 =82
subtract 5 for 82
2x = 77
77 divided by 2 is 38.5
x = 38.5
hope this helps :)
Translate the phrase into a variable expression. Use the letter p to name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(1) for division
... the total number of plates minus the 4 saved for dessert...
Answers
p - 4 is the answer. No multiplication or division involved
Write exponential equation for geometric sequence where t(1)=140 and t(2)=98
Answers
Step-by-step explanation:
common ratio r = 98/140
first term a = 140
geometric sequence formula is an = ar^(n-1)
an = 98^(n-1)
where n is the number of terms in the sequence
Given the triangle below, what is the length
of the hypotenuse?
4 cm
5 cm
Answers
Answer:
6.4 cm
Step-by-step explanation:
i think you'd use pythagoras theorem if you don't know any of the angles . a^2 + b^2 = c^2 . so 4^2 + 5^2 = square root 41 ,, = 6.403124237 cm
i apologise if it is incorrect ^^
Answer:
Sq root of 41cm
Step-by-step explanation:
took the test
Which of the following are true statements about a 30-60-90 triangle?
Lan
Answers
Answer:
C and F
Step-by-step explanation:
Answer:
A, F
Step-by-step explanation:
ratio of sides in a 30-60-90 triangle is 1 : [tex]\sqrt{3}[/tex] : 2
Choose a method you prefer to solve for a system of linear equations.
2x + 4y = -4
2x-y=6
Answers
Answer:
Elimination
x = 2
y = -2
Step-by-step explanation:
Elimination
2x + 4y = -4
2x - y = 6
Subtract the second equation from the first
5y = -10
Divide both sides by 5
y = -2
---------------------
Substitute for y = -2 in the second equation
2x - -2 = 6
2x + 2 = 6
subtract 2 from both sides
2x = 4
Divide both sides by 2
x = 2
NEED HELP DUE IN 6 MINUTES!!!!
Answers
Answer:
120
Step-by-step explanation:
volume of triangular prism = area of base times length
the base is a triangle and the area of a triangle can be calculated by using this formula
[tex]a=\frac{bh}{2}[/tex]
where b = base length and h = height
Dimensions of base
base length = 8cm and height = 3cm
Thus,
[tex]A=\frac{3*8}{2} \\3*8=24\\\frac{24}{2} =12\\[/tex]
The length of the triangular prism is 10cm
Thus volume = 10 * 12 = 120
It Takes Mike 18 minutes to finish reading 4 pages of a book. How long does it take him to finisn reading 30 pages?
Answers
Answer:
135
Step-by-step explanation:
First, divide.
18 ÷ 4 = 4.5
Then, multiply.
4.5 × 30 = 135
Have a great day!
What is the magnitude of -3 +4i?
Answers
Answer:
we have
-3+4i
let magnitude be |z|
|z|=[tex] \sqrt{( - 3) {}^{2} + 4 {}^{2} } [/tex]
|z|=5 unit
Answer:
The magnitude of -3 +4i is 5
Step-by-step explanation:
latoya made $80 for 5 hours of work. At the same rate, how much would she make for 13 hours of work
Answers
Answer:
$208
Step-by-step explanation:
First, divide.
80 ÷ 5 = 16
Next, multiply.
16 × 13 = 208
Lastly, have a wonderful day! :)
Answer:
At the same rate, Latoya would make $208 for 13 hours of work.
Step-by-step explanation:
Since Latoya made $80 for 5 hours of work, that means she made a unit rate of $16 per hour. By working at the same rate for 13 hours, she would make a total of [tex]16 * 13 =[/tex] $208.
The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis two points A and B are shown. The point A is on ordered pair 2, 1, and the point B is on ordered pair negative 1, 1. A straight line joins the points A and B. If the area of the rectangle to be drawn is 18 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (1 point) C(−1, −2), D(2, −2) C(−1, −8), D(2, −8) C(−1, −5), D(2, −5) C(−1, −6), D(2, −6)
Answers
9514 1404 393
Answer:
3. C(−1, −5), D(2, −5)
Step-by-step explanation:
The given points are 2 -(-1) = 3 units apart horizontally, so the remaining points will need to be 18/3 = 6 units below, vertically. Translating the given points down 6 gives ...
D = A -(0, 6) = (2, 1) -(0, 6) = (2, -5)
C = B -(0, 6) = (-1, 1) -(0, 6) = (-1, -5)
The two points required to make a rectangle with an area of 18 square units are ...
C(-1, -5), D(2, -5)
_____
The area of a rectangle is the product of length and width. If the area is 18 square units, and the width is 3 units, then the length must be 6 units. 3×6=18.
Please Help with explanation asap! Branliest to correct
Answers
Answer:
Solution given:
12 Ouches =$7200
per Ouches =$7200/6=$600
So
the required equation for the cost of any weight of gold is:
C.
600W=C is a required equation.
I AM GIVING 50 POINTS :))
The volume of the prism is 81m3
What is the volume of a pyramid that has the same base and height as this prism?
____m3
Answers
Answer:
16 x 25 x 37 = 14800 m^3
////////////////////////
A rectangular room is 11 feet by 14 feet. The ceilings are 9 feet high. If a gallon of paint covers 250 square feet. How many gallons of paint are needed to paint the room?
Answers
Answer:
3 gallons or 3.032
Step-by-step explanation:
find the total surface area (758)
divide by 250 or subtract 250 till it is under that number
Please help!!!!!!!!!!!!
Answers
Answer: 990 ways
Step-by-step explanation:
For the first chicken, there are 11 slots it could be, or 11. For the next chicken, there are 10 available, or 10. Same thing for the third chicken, with 9. Thus, simply do 11*10*9 to get 990.
Clark has two 16-ounce cans of corn. He uses 18 ounces of it to
make a corn soup and the rest to make a casserole.
a. How many ounces of corn did he use to make the casserole?
Answers
Answer:
14
Step-by-step explanation:
Answer:
14 Ounces
Step-by-step explanation:
16 x 2 = 32 Ounces of corn
32 - 18 = 14 Ounces
can someone help me.?!
Answers
[tex]{\boxed{\mathcal{\red{h\:=\:9.5}}}}[/tex] ✅
Step-by-step explanation:-[tex]h + \frac{1}{2} = 10 \\ ⇢ h + 0.5 = 10 \\ ⇢ h \: = 10 - 0.5 \\ ⇢ h = 9.5[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Matthew has 5 1/4 bags of fertilizer to spread around his yard. Each bag of fertilizer will cover 115.4 ft 2. How many square feet will Matthew be able to cover if he uses all of the fertilizer?
Answers
Answer:
605.85 (ft 2)
Step-by-step explanation:
5 1/4 * 115.4 = 605.85 (ft 2)
Factor the following expression.
10.25 + 513 – 14.12 – 7
A. (5.33-7)(2x2 + 1)
B. (5.04 + 7)(2.5 - 1)
C. (5.3 + 7)(2x2 - 1)
D. (5x4 - 7)(2x + 1)
Answers
Answer:
Step-by-step explanation:
ask cymath it will help you with any mathmatical problem
How many square feet of outdoor carpet will we need for this hole
Answers
Rationalize the denominator of the expression 2 - √ 3 / √ 6
Answers
Step-by-step explanation:
[tex] \to \dfrac{2 - \sqrt{3} }{ \sqrt{6} } [/tex]
Conjugate of √a is √a. So, conjugate of √6 is √6. Multiplying √6 with both numerator and denominator.[tex] \to \dfrac{2 - \sqrt{3} }{ \sqrt{6} } \times \dfrac{ \sqrt{6} }{ \sqrt{6} } [/tex]
[tex] \to \dfrac{ \sqrt{6}( 2 - \sqrt{3} )}{ {(\sqrt{6})}^{2} } [/tex]
[tex] \to \dfrac{ 2 \sqrt{6} - \sqrt{18} }{ 6 } [/tex]
[tex] \to \dfrac{ 2 \sqrt{6} - 3 \sqrt{2} }{ 6 } [/tex]
[tex] \to \dfrac{ \sqrt{6}}{3} - \dfrac{ \sqrt{2} }{ 2 } [/tex]
Hence, rationalised!can someone please help I will do anything
Answers
Answer:
678.24 cubic centimeters
Step-by-step explanation:
HELP
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answers
Answer:
tan
Step-by-step explanation:
take 19 degree as reference angle
using tan rule
tan 19=opposite/adjacent
0.34=14/x
x=14/0.34
x=41.17
x=41.2
A dilation has center at the origin. Which of the following is the image of the point P(1.- for a scale
factor of
A
D: (P) = P(x3)
B
D}(P) = P',
C
D:(P) = P1C-
D
D}(P) = PG-)
Answers
Answer:
C. [tex]D_\frac{1}{7} (P)=P'(\frac{1}{4},-\frac{5}{14} )[/tex]
Step-by-step explanation:
[tex]\frac{7}{4}*\frac{1}{7}=\frac{7}{28} =\frac{1}{4}[/tex]
[tex]-\frac{5}{2} *\frac{1}{7} =-\frac{5}{14}[/tex]