Sn = a(1 - rⁿ)/(1 - r) is the formula for the sum of a finite number of terms in a geometric series, where is the number of terms, is the first term, and is the common ratio.
The sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ be 2.407.
What is meant by finite geometric series?The equation be Sn = a(1 - rⁿ)/(1 - r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an finite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the series be Σ⁴ n=1 (2/3)ⁿ⁻¹
Σ⁴ n=1 (2/3)ⁿ⁻¹ = (2/3)¹⁻¹ + (2/3)²⁻¹ + (2/3)³⁻¹ + (2/3)⁴⁻¹
= 1 + (2/3) + (2/3)² + (2/3)³
= 1 + (2/3) +(4/9) +(8/27)
Where, the first term is a = 1
common ratio be r = 2/3
n th term be n = 4
Let the equation be Sn = a(1 - rⁿ)/(1 - r)
substitute the values in the above equation, we get
S4 = 1(1 - (2/3)⁴)/(1 - (2/3))
S4 = 1(1 - (16/81)⁴)/(1/3)
S4 = (65/81) × 3
S4 = (65/27) = 2.407
Therefore, the sum of the finite geometric series, Σ⁴ n=1 (2/3)ⁿ⁻¹ is 2.407.
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m < LRQ
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
The measure of < LRQ is 112.5.
What is an Intercepted Arc?
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]
The sum of the measures of the central angles of a circle with no interior points in common is 360 .
Here, 360 is divided into 8 equal arcs and each arc measures
360/ 8 = 45.
Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.
[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].
Therefore, the measure of < LRQ is 112.5.
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Fill in the blank: The opposite of __________________ a number is finding the square root. Squared means to raise to the power of ___.
squaring, 4
squaring, 2
cubing, 3
doubling, 2
Answer:
B. Squaring, 2
Step-by-step explanation:
When you Square a number, doing the opposite is finding the square root. When squaring a number, you multiply the number by itself, the number it raises the the power of 2.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book. With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book. For how many books produced will the costs from the two methods be the same?
The number of books published by a small publishing company is 3240.
Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of books be x.
With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.
That is, 44,714+11.50x
With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.
That is, 17,174+20x
Now, the number of books produced will the costs from the two methods be the same.
So, 44,714+11.50x=17,174+20x
⇒ 44,714-17,174=20x-11.50x
⇒ 8.5x = 27540
⇒ x=3,240
Therefore, the number of books published by a small publishing company is 3240.
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Write the correct messurement indicated by the arrows on the lines to the left
Answer:
Step-by-step explanation:
It is given that we need to find the correct measurement indicated by the arrows on the lines to the left.
Now, let us have a look at the figure;
6 inches5.2 inches4.6 inches4.3 inches4 inches3.6 inches3.1 inches2.6 inches2.3 inches1.7 inches1.4 inches1.2 inches1.1 inches0.5 inches0.3 inches0.2 inches0.1 cm0.7 cm1.7 cm2.3 cm3.1 cm3.4 cm4.2 cm4.7 cm5.5 cm6.4 cm7.2 cm8.2 cm8.5 cm9.1 cm9.6 cmTo know more about this topic, click here:
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A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates.
The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
What is area of rectangle?In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers
Given data
size of rectangular plate = 5 cm by 3cm.
the length should be within = 0.25 of 5 cm
How to solve for the minimum and maximum areaThis means the length, L of the rectangular plate can be mathematically represented as
5 - 0.25 ≤ L ≤ 5 + 0.25
4.75 ≤ L ≤ 5.25
Area of rectangle = Length × Width.
Width = 3
minimum length = 4.75
maximum length = 5.25
minimum length
= 4.75 * 3
= 14.25 cm^2
maximum length
= 5.25 * 3
= 15.75 cm^2
Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
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Find x. 24² + x² = 26²
The unknown variable's result of the equation 24² + x² = 26² is 10
To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.24² + x² = 26²
576 + x² = 676
x² = 676 - 576
x² = 100
x = [tex]\sqrt{}[/tex]100
x = 10
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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A meeting room is set up with 16 rows of seats. The number of seats in a row increases by two with each successive row. The first row has 12 seats. What is the total number of seats?
a. How can you find the number of seats in each row using an explicit formula?
The most commonly used explicit of an arithmetic sequence is given as,
an = a + (n - 1) d
Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,
2nd row seat = 12+ 1x2
3rd row seat = 12 + 2 x2
nth seat = 12 + (n-1) x 2
16th row seat = 12 + (16–1) x2 = 42
Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows
Average number of seats per row = (12 +42)/2= 27
So total seats = average per row x number of rows
= 27 x 16 = 432.
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Find the eighth term of each geometric sequence. 3,9,27, . . . . .
Answer:
6561
Step-by-step explanation:
You multiply by 3 each time.
Simplify by combining like terms. -(3 z-5)+z
The simplification by combining like terms of -(3z -5) + z is -2z + 5.
According to the given question.
We have an expression -(3z -5) + z.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression -(3z - 5) +z.
Here -3z and z both are the like terms.
So, we subtract coeffcients of z to simplify the given expression.
Therefore, the simplification of the expression -(3z - 5) +z is given by
-(3z - 5) + z
= -3z + 5 + z
= -3z + z + 5
= -2z + 5
Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.
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I will Mark BRAINLIST!!! Please Help its A Math Question!!!! Determine the approximate value of x using basic trigonometry.
hope it will help you...good luck
It takes Amelia 45 minutes to rake her yard every Saturday during the fall. It takes Andy 1 hour to rake the same yard. If Amelia and Andy work together, how long will it take them to rake the yard? Round your answer to the nearest minute.
Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane to obtain line segment A′B′. What is the length of A′B′? (1 point) a 2 units b 4 units c 6 units d 8 units
Hep please T^T
The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.
What is Translation ?
Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.
That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,
So, the measurement of segment A'B' would be 2 unit.
Verification :
Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,
Also, the rule of translation 6 unit right is,
(x,y) → (x + 6, y)
By the distance formula,
The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²
Thus, if A'B' is the transformed segment of segment AB,
Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)
So, the measure of segment A'B' =
√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²
Hence, the measure of AB = measure of A'B'.
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I'll give brainliest
What values of x and y satisfy the system of equations {x=−2y+13x+8y=11?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution of the simultaneous equation is given by (-7 , 4) .
A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.
For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.
The given pair of simultaneous equation is given as:
x=−2y+1
3x+8y=11
Let us solve the equations by the method of substitution:
From the first equation we take the value of x and put it in the second equation:
3x + 8y = 11
or, 3 ( -2y + 1 ) + 8y = 11
or, -6y +3 +8y = 11
or, 2y + 3 = 11
or, 2y = 8
or, y = 4
Substituting the value of y as 4 in the first equation we get:
x = − 2y + 1
or, x = - 2 × 4 +1
or, x = -8 +1
or, x = -7
Therefore the solution set of the pair of equations is given by (-7 , 4) .
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A store is having a sale on jelly beans and almonds today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
The system of equations that can be used to determine the cost for each pound of jellybeans and almonds is
5x + 3y = 16
2x + 6y = 22
The cost of one pound of jellybeans is $1.25.
The cost of one pound of almonds is $3.25.
What is the cost of one pound of jellybeans and almonds?Given this two equations:
5x + 3y = 16 equation 1
2x + 6y = 22 equation 2
Take the following steps to determine the required values:
Multiply equation 1 by 2
10x + 6y = 32 equation 3
Subtract equation 2 from equation 3
8x = 10
Divide both sides of the equation by 8: x = 10 / 8
x = 1.25
Substitute for x in equation 1:
5(1.25) + 3y = 16
6.25 + 3y = 16
3y = 16 - 6.25
3y = 9.75
y = 9.75 / 3
y = 3.25
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Does the infinite series converge or diverge? If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
Does the infinite series converge or diverge? The series converges.
If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
The sum of the infinite series is -1
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]
Since ,[tex]\vert r\vert < 1[/tex], the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]
The sum of the infinite series is -1
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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factorise and hence evaluate :
2,014^2-2,012^2
Answer:
8,052
Step-by-step explanation:
(2,014 - 2,012) x (2,014 +2,012)
2 x 4,026
8,052
Put the following numbers in order from least to greatest
1/2, -2, √5, -7/4, -24
Answer:
-24 < -2 < -7/4 < 1/2 < √5
Step-by-step explanation:
Negative integers are always less than 0 and positive integers. More the magnitude (numerical value) of a negative integer, lesser is that number.Hence the order of negativeintegers will be -24 < -2 < -7/4. 1/2 is 0.5 and root 5 is around 2.236. Hence, 1/2 < √5. The final order is -24 < -2 < -7/4 < 1/2 < √5whats the slope for (-6,-3) and (0, -1.5) in fraction form?
The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
What is the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) as required in the task content?It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.
On this note, it follows from the slope formula that slope;
m = (y2 - y1)/(x2 - x1)
Therefore, the slope of the line segment joining the two points is;
m = (-1.5 - (-3))/(0 - (-6))
m = 1.5/6
m = 1/4.
Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
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Find the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi. (PLEASE SHOW WORK IF POSSIBLE)
The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
Volume of a coneThe formula for calculating the volume of a cone is expressed according to the formula
V = 1/3 pir²h
where
r is the radius of the cone = 10/2 = 5in
h is the height = 2in
Substitute to have;
V = 1/3pi(5)² × 2
V = 50/3pi
Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
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Please help!!!
For questions 10-13 use f(x)=4(1/2)^x
Which expression is equal to this expression, according to the associative property? 5+(3-1)
Answer:7
Step-by-step explanation:
3-1= 2
5+2=7
How many solutions does each of the following equations have?
6(x-3)+12=6x-6
Answer:
All real numbers are solutionsStep-by-step explanation:
How many solutions does each of the following equations have?
6(x-3)+12=6x-6
6x - 18 + 12 = 6x - 6
-18 + 12 = -6
-6 = -6
0 = 0
Identify the appropriate mixed number for the picture shown.
A. 54
B. 14
C. 114
D.45
Answer:
c
Step-by-step explanation:
its one full square and 1/4
Evaluate the function at each specified value of the independent variable and simplify.
f(x) = x² + 1
a) f(1) =
b) f(-3) =
c) ƒ (6³) =
d) f (x - 1) =
25446 to 1 significant figure
Answer: 30,000 rounded to 1 significant figure
I hope this helped!
Draw a line representing the rise and representing the run of the line. State the slope of the line in simplest form.
Find the measure of each numbered angle. (Lesson 4-2)
m ∠ 6
The measurement of angle ∠2 is 67.50°.
What exactly do we mean by an angle?In Euclidean geometry, an angle is a figure formed by two rays called the sides of the angle that share a common endpoint called the vertex of the angle.Angles formed by two rays are located in the plane in which the rays are located.When two planes intersect, angles are formed.These are referred to as dihedral angles.So,
An octagon has 8 sides.Sum of interior angles = 180° x (n-2) = 180° x (8-2) = 180° x 6 = 1,080°1,080° ÷ 8 sides = 135° interior angle.Angle 2 = 135° / 2 = 67.50°Therefore, ∠2 is 67.50°.
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The correct question is given below:
Given the regular polygon, find the measure of each numbered angle.
m ∠ 2
Determine the probability of following event, flipping a coin and not landing on heads
According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}
Therefore, the probability can be written as:
Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]
Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Kendra buys 5 yards of yellow fabric and 8yards of purple fabric The yellow
costs $2 more per yard than the purple fabric,
She pays a total of 62.80 what
would be the combined cost of 2 yards of yellow and yards of purple
fabric?
The combined cost of 2 yards of yellow and 1 yard of purple fabric is $17.69.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Length of yellow fabric = 5 yards
Length of purple fabric = 8 yards
Let x be the cost of per yard purple fabric.
Then, cost of per yard yellow fabric = 2 + x
Now since, Total amount paid is $62.80
Therefore,
5(2 + x) + 8x = 62.8
expanding the brackets we get,
10 + 5x + 8x = 62.8
Solving we get,
10 + 12x = 62.8
or, 12x = 52.8
⇒ x = 62.8/12
⇒ x = $5.23
Thus the cost of per yard purple fabric = $5.23
Similarly, cost of per yard yellow fabric = 2 + 5.23 = $7.23
Thus, combined cost of 2 yards of yellow and 1 yard of purple
fabric = 2*$5.23 + $7.23
= $10.46 + $7.23
= $17.69
Thus, the combined cost of 2 yards of yellow and 1 yard of purple fabric is $17.69
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In a bag, the ratio of purple counters to green counters was 3:4. 8 more purple counters were then added to the bag, and the ratio of purple counters to green counters became 5 : 4. How many green counters are in the bag?
Answer:16
Step-by-step explanation:
since the increase is 2 units for purple counters
8 ÷ 2 = 4
4×4=16
