Therefore, the value of the expression E¹⁰ⁿ=1 8(1/4)ⁿ⁻¹ is 27.
What is fraction?A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written as two numbers, one above the other, with a horizontal line separating them. The number above the line is called the numerator and the number below the line is called the denominator. For example, the fraction 3/4 represents three parts out of four equal parts, or the ratio of three to four. Fractions can be used to represent a wide range of values, including numbers between whole numbers (such as 1/2 or 3/5), ratios between quantities (such as 2/3 cups of flour to 1 cup of sugar), and percentages (such as 75/100, which is equivalent to 75%, or three-quarters). Fractions are an important concept in mathematics and are used in many different contexts, such as in cooking, measurement, and finance.
Here,
The expression E¹⁰ⁿ=1 8(1/4)ⁿ⁻¹ means we need to evaluate the sum of the expression 8(1/4)ⁿ⁻¹, as n ranges from 1 to 10.
To do this, we can simply substitute each value of n into the expression and add up the results. Here are the first few terms of the sum:
n = 1: 8(1/4)⁰ = 8
n = 2: 8(1/4)¹ = 2
n = 3: 8(1/4)² = 1/2
n = 4: 8(1/4)³= 1/8
We can continue this pattern for the remaining values of n, and then add up all the terms:
8 + 2 + 1/2 + 1/8 + ... + (1/4)⁹
To simplify this expression, we can use the formula for the sum of a geometric series:
S = a(1 - rⁿ) / (1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term is 8, the common ratio is 1/4, and there are 10 terms. So we can substitute these values into the formula to get:
S = 8(1 - (1/4)¹⁰) / (1 - 1/4)
S = 8(1 - 1/1048576) / (3/4)
S = 8(1048575/1048576) * (4/3)
S = 8 * (3495250/1048576)
S = 27
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7. Margo can read 22 pages in 30 minutes.
How long would it take her to read a 100-page book?
Answer: x = 136.4 minutes
Step-by-step explanation:
x = (100/22)(30) minutes = 136.4 minutes
The ratio of the sides of two similar is 2/3. The area of the smaller triangle is 36cm. Find the area of the larger triangle?
Answer:
[tex]\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]
Step-by-step explanation:
Given.
Ratio of corresponding sides of two similar triangles = 2:3 or [tex]\dfrac{2}{3}[/tex]
Area of smaller triangle = 36 cm²
By the property of area of two similar triangle,
Ratio of area of both triangles = (Ratio of their corresponding sides)²
[tex]\dfrac{\text{Area of smaller $\triangle$ }}{\text{Area of larger $\triangle$ }} = \left(\dfrac{2}{3}\right)^2}[/tex]
[tex]\dfrac{36}{{\text{Area of larger $\triangle$ }}} = \dfrac{4}{9}[/tex]
Cross-multiplying we get
[tex]36 \times \dfrac{9}{4} = \text{Area of larger $\triangle$}\\\\81 = \text{Area of larger $\triangle$}\\\\\text{Area of larger $\triangle$} = 81 \:cm^2[/tex]
A circle has diameter 6 cm. Calculate the area of the circle. Give the units of your answer.
Answer: 9pi cm squared
Step-by-step explanation:
The radius is diameter divided by 2, so radius = 3cm.
Now, the equation for area is pi * r^2
3 squared is 9, so the area is 9pi cm squared.
Solve for the variable.
B.
3x
A
4x - 1
О
F
x2-x-2
D
The variable x has no true value in the similar shapes
How to solve for the variableFrom the question, we have the following parameters that can be used in our computation:
The figure
Using the figure, we have the following ratio
3x : 4x - 1 = 4x - 1 : x² - x - 2
Factorize
3x : 4x - 1 = 4x - 1 : x² + x - 2x - 2
So, we have
3x : 4x - 1 = 4x - 1 : x(x + 1) - 2(x + 1)
This gives
3x : 4x - 1 = 4x - 1 : (x - 2)(x + 1)
Express as fraction
3x/(4x - 1) = (4x - 1)/(x - 2)(x + 1)
So, we have
3x(x - 2)(x + 1) = (4x - 1)(4x - 1)
Using a graphing tool, we have
x = undefined
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if i make $2949 a second how long will it take to get $2,000,000
it will take approximately 678.24 seconds, or about 11 minutes and 18 seconds, to earn $2,000,000 if you make $2949 per second.
Why it is?
We can use a simple formula to solve this problem:
Time = Amount / Rate
where Amount is the amount of money you want to earn ($2,000,000) and Rate is the rate at which you earn money per second ($2949).
Plugging in these values, we get:
Time = $2,000,000 / $2949 per second
Time = 678.24 seconds
Therefore, it will take approximately 678.24 seconds, or about 11 minutes and 18 seconds, to earn $2,000,000 if you make $2949 per second.
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Please solve this
the difference of twice a number and 6 is greater than -25. Write as an inequality
Answer:
x > -9.5
Step-by-step explanation:
2x - 6 > -25
2x > -19
x > -19/2
x > -9.5
In the screenshots it shows directions answer for each number
1) All the angles are,
∠ 1 = 72°
∠ 2 = 54°
∠ 3 = 54°
∠ 4 = 72°
2) All the angles are,
∠1 = 59°
∠2 = 90°
∠3 = 90°
∠ 4 = 31°
3) All the angles are,
∠ 1 = 22°
∠ 2 = 68°
∠ 3 = 68°
∠ 4 = 90° (right angle)
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
1) From first figure,
⇒ ∠ 3 = 54° (Two sides are equal hence two angles are also equal)
Hence, We get;
∠3 + ∠4 + 54° = 180°
54° + ∠4 + 54° = 180
∠4 = 180 - 108
∠4 = 72°
Hence, We get;
∠ 1 = ∠ 4
∠ 1 = 72°
And, ∠2 = ∠3 = 54°
2) From second figure,
∠ 4 = 90 - 59°
= 31°
And, We have;
∠1 = 59°
And, Diagonal bisect each other.
Hence,
∠ 2 = ∠ 3 = 90°
3) From third figure,
∠ 2 = 68°
Hence, 2 ∠ 1 = 180 - 136°
2 ∠ 1 = 44°
∠ 1 = 22°
And, We have;
Since, ∠ 2 = 68°
Hence, ∠ 3 = 68°
And. ∠ 4 = 90° (right angle)
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Do YOU currently have earned or unearned income? Where do you get this money from?
Answer:
Earned Income
Step-by-step explanation:
I get this money from chores I do around the house and my side job of selling sandwiches to my classmates (this is just an example you can personalize it)
How to convert 100 as a decimal?
The converted value of 100 percent to a decimal is equal to 1 which is denoted by 1.00.
Percent represents the given part out of hundred equally divided parts.Conversion of percent to decimal is divide the given number by 100.Converting 100 percent to decimal is divide 100 by 100 we get
1 percent is ( 1 / 100 )decimal
Substitute the required value of 100 percent we get,
⇒ 100 percent = ( 100 / 100 ) decimals
⇒ 100 percent = ( 1.00 ) decimals
Therefore, the conversion of 100 percent to decimal is given by 1.00 .
The above question is incomplete , the complete question is:
How to convert 100 percent as a decimal ?
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daniel has read 80% of a book. He has more 8 pages to finish. How many pages are there in the book?
Using the percentage formula it is obtained that there are 40 number of pages in the book.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
Let's use "x" to represent the total number of pages in the book.
According to the problem, Daniel has read 80 percentage of the book, which means he has read -
8/100 = 0.8x pages
He still has 8 pages left to finish, so we can set up an equation -
0.8x + 8 = x
Solving for x, we can subtract 0.8x from both sides -
0.8x + 8 - 0.8x = x - 0.8x
8 = 0.2x
Then, we can divide both sides by 0.2 to get -
x = 40
Therefore, there are 40 pages in the book.
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Write an absolute value inequality for the graph below. Use ask for your variable.
The absolute value inequality for the graph is given as follows:
|x| < 3.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.
|x| = -x, x < 0.
It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
From the graph, the shaded region is less than 3 units from the origin, as |-3| = |3| = 3, hence the inequality is defined as follows:
|x| < 3.
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Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns $15 for each thirty-minute session and $25 for each sixty-minute session.
If she earned $230 this past weekend and had x thirty-minute sessions and x-2
sixty-minute sessions, what is the value of x?
What is the conversion of 300 meters to miles ?
The conversion of the units 300 meters to miles is equal to 0.1864miles ( round up to four decimal places ) .
Meters and Miles both are units used to measure the length or the distance between any two or more points.
Conversion factor relating meters and miles is equal to
One meter = 0.000621371 miles
To get the value of 300 meters in miles multiply by converting factor we get,
300 meters
= ( 300 ) × ( 0.000621371 ) miles
= ( 0.1864113 ) miles
= ( 0.1864 ) miles ( round up to four decimals places )
Therefore, the conversion distance 300 meters to miles is given by ( 0.1864 ) miles ( round up to four decimals places ) .
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Original equation:
3(a-2) + 14 =8-6a
Solution: 3a-2+14-8-6a
3a +12=8-6a
9a + 12 = 8
9a = -4
a = -4/9
so what do you need help with
why is 41 a prime number ?
The number 41 is a prime number because it can be divided only by the number one and itself to yield remainder zero.
A prime number is defined as the number which is an integer, greater than one and has the ability to divide only by one and the number itself. The division here indicates that remainder should be zero.
Now, we see that 41 is an integer and it is greater than one. Additionally, it can not be divided by other numbers expect one and itself. These reasons make 41 a prime number.
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1.you buy a car for $10,000. every year, the car loses 25% of its value. how would the function rule change if the car lost 10% of its value each year? and why does the function rule include 0.75 instead of 0.25?
2. You start a job making $10 per hour. at the end of each year, you earn a 10% raise. how will the function rule change if the annual raise is 8%?
The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.
What is Depreciation rate?The depreciation rate is the total amount depreciated each year, expressed as a percentage. For instance, if a business depreciated an asset at a rate of $15,000 per year for ten years, the total depreciation would be $100,000. This indicates that the rate would be 15% annually. To calculate depreciation using the straight-line method, the asset's salvage value, or what you expect it to be worth at the end of its useful life, must be deducted from the asset's cost.Depreciable basis, or the amount that may be written off, is the outcome. By how many years the asset will be useful, divide this sum.Present Value A = Rs. 52,488
Depreciation rate r = 10 % per annum
Time t = 4 years
Let initial value be P
We know the formula, A =[tex]$\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$[/tex]
We obtain by substituting the supplied values.
52,488 =[tex]$\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\[/tex]
52,488 = [tex]$\mathrm{P}(0.9)^4 \\[/tex]
[tex]$\mathrm{P}=\frac{52488}{0.6561} \\[/tex]
P = 80,000
The complete question is:
The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was
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if the given triangles form 90 degree angle
then it is right angle if not form 90 degree
angle then it is not
It is possible to determine if a triangle contains
a right angle using Pythagoras' theorem . If the
squares of the two shorter sides add up to the
Answer:
hypotenuse squared
Step-by-step explanation:
for example
if we have a triangle with sides 6,8, and 10
then
36+64=100
the complete equation is
[tex]\sqrt{a^{2} +b^2[/tex]=c
What is the rank of a 4 times 5 matrix whose null space is three-dimensional ? If A is a 6 times 7 matrix what is the largest possible dimension of Col(A) ? If P is a 5 times 5 matrix and Nul(P) is the zero subspace, what can you say about solutions of equations of the form Px = b for b R^5?
a) matrix is 4 x5 , null space is 3 dimensional then rank = 2. b) A is 6x7 matrix : the column vectors with leading 1's of the row vectors forms a basis for column space. Maximum possible dimension for Col(A) = 6.
What is rank of matrix?A matrix's rank is defined as the largest number of its characteristic equation columns (or rows). A matrix's rank is limited to a handful of its rows and columns.
A square matrix has columns (rows) that are only linearly independent if the matrix is not unique. To put it another way, any nonsingular matrix of order m has rank m. The symbol for a matrix A's rank is (A).
A null matrix has 0 rank. No non-zero rows or columns exist in a null matrix. There are no distinct rows or columns as a result. Hence, a null matrix has a rank of 0.
a) matrix is 4 x5 , null space is 3 dimensional then rank = 2
b) A is 6x7 matrix : the column vectors with leading 1's of the row vectors forms a basis for column space.
Maximum possible dimension for Col(A) = 6
c) If null space = {0,0,0,0,0}, then
The for Ax= B, column vector B is the solution for the system.
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Divide 15a6b4 by 5a2b.
Answer:
Step-by-step explanation:
15a6b4/5a2b
you can scrap the a and b
15*6*4/ 5*2=
now you keep simplifying the fraction
3*6*4/2=
3*6*2=
36
Leon has already had 4 science quizzes this semester. Going forward, he expects to have 4 quizzes per month.
Write an equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x.
The equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x is y = 4x.
An equation is a mathematical statement that shows the relationship between two or more values.
In this case, Leon has already had 4 science quizzes this semester and expects to have 4 quizzes per month going forward.
We can use an equation to show how the total number of science quizzes, y, depends on the number of months that have passed, x.
The equation for this would be y = 4x, where x is the number of months that have passed and y is the total number of science quizzes.
This equation shows that for each month that passes, the total number of science quizzes increases by 4
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A 6-pack of bouncy balls costs $2. 76. What is the unit price?
A 6 pack of bouncy ball costs 2.76$ and the unit price of a bouncy ball is $0.46
To find the unit price of the bouncy balls, we need to divide the total cost by the number of bouncy balls in the pack. Since there are 6 bouncy balls in the pack and the cost is $2.76, we can calculate the unit price as follows: Unit price = total cost ÷ number of units
Unit price = $2.76 ÷ 6
Unit price = $0.46
Therefore, the unit price of a bouncy ball is $0.46.
Unit price is a measure of the cost of a single unit of a product. It is calculated by dividing the total cost of a product by the number of units in the package. The unit price is helpful when comparing the costs of different package sizes or brands of the same product. It allows consumers to make informed decisions about their purchases based on the value they receive for their money. Unit pricing is required by law in some countries, including the United States, to ensure transparency in pricing and to protect consumers from deceptive marketing practices. Overall, knowing the unit price of a product can help consumers save money and make more informed purchasing decisions.
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how to calculate optimum replacement interval
The economic life cycle analysis does not take into account factors such as technological advancements or changes in regulatory requirements, which can affect the optimal replacement interval.
Yet, it is important to review and update the analysis periodically to ensure that the replacement interval remains optimal.
There are the normal steps for calculating the optimum replacement interval using the economic life cycle analysis:
1. Estimate the annual maintenance and repair costs for the item, based on historical data or industry standards.
2. Estimate the annual operating costs for the item, such as energy or fuel costs.
3. Compare the total cost of ownership for the item over its expected useful life to the cost of replacing the item with a newer or more efficient model.
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dont understand this sorry please help
The range of the following graph is [-2, 3]
What is Range?In mathematics, the range of a function is the set of all possible output values (also called the codomain) that the function can produce for its input values. The range is a subset of the codomain, and it describes the vertical extent of the function's graph. The range can be finite or infinite, and it can contain repeating values or be a continuous interval.
The values of y coordinate depicts the values of range
So, the range of the following graph is [-2, 3]
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Big idea math (image)
Answer:
DB = approximately 16
Step-by-step explanation:
DEC is a right triangle => DC=10. Because all four sides are equal in a rhombus, then AD=AB=10. Then, because angle BAD is 53*2=106 degrees, we can use cosines. DB=sqrt(10^2+10^2-2*10*10cos(106deg))=15.9727102009.
algebra 1 need help please
Answer:
y = 3x - 1
Step-by-step explanation:
In order to write this equation in slope intercept form, we first need to find the slope. I will take two points (2,5) and (1,2). We can find the slope either by counting the slope with [tex]\frac{rise}{run}[/tex] or we can calculate it using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]
For the sake of simplicity, we will count it using [tex]\frac{rise}{run}[/tex]. Counting the slope between the two points, we get [tex]\frac{3}{1}[/tex] which simplifies to 3.
The y intercept crosses between the point (0, -1), so our y intercept is -1.
Thus, our equation of the line will be [tex]y=3x-1[/tex]
What is 68 weight in lbs?
The conversion of the weight 68 kg from Kilogram to lbs will be equal to 149.914 lbs.
The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.
One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.
One pound is equal to 0.45359237 kilograms.
To convert kilograms (kg) to pounds (lbs), you can use the following formula:
To convert kilograms to pounds, multiply your figure by 2.20462
To convert 68 kg to lbs, you can multiply 68 by 2.20462:
68 kg X 2.20462 lbs/kg
= 149.914 lbs
Therefore, 68 kg is equal to 149.914 lbs.
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The complete question may be:
What is 68 Kg weight in lbs?
karen peyton and annie all ran in a race karen ran the race in 43.52 seconds peyton time running the race was 2.17 seconds more than karen time what was peyton time
i really need help
Answer:
Peyton = 45.69 seconds to run the race
Step-by-step explanation:
Karen = 43.52 seconds
Peyton = k + 2.17
Peyton = 43.52 + 2.17
Peyton = 45.69 seconds
Answer:
45.69
Step-by-step explanation:
If Peyton's time running the race was 2.17 seconds more than Karen's time, then we can calculate Peyton's time by adding 2.17 seconds to Karen's time.
Karen's time: 43.52 seconds
Peyton's time: 43.52 + 2.17 = 45.69 seconds
Therefore, Peyton's time running the race was 45.69 seconds...
pls answer
The patch 2 is divided diognally into two triangles of equal areas.Tulips are planted in one triangular area.What is the area in which tulips are planted?
The area in which tulips are planted is 4247.625 square meters.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
To calculate the area of the triangle described as;
= 1/2 x length of the base segment x height of the triangle.
Given:
All the grass patches have equal areas.
From the diagram;
the shape of patch 2 is rectangular.
And the dimensions of the rectangle are 120.5 meters by 70.5 meters.
Two triangles of equal areas are formed by the division of patch 2 diagonally.
The area in which tulips are planted is,
= 1/2 x base x height
= 1/2 x 120.5 x 70.5
= 8495.25/2
= 4247.625 square meters.
Therefore, the area is 4247.625 square meters.
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please help!! answer the question below
Answer:
Below
Step-by-step explanation:
Similar triangles due to A - A - A
Set up ratios
QR is to RS as QP is to TS
(x+2) / (2x-5) = 3/5 Cross multiply to get
5x+10 = 6x-15 subtract 5x from both sides of the equation
10 = x - 15 add 15 to both sides
25 = x
A law firm is going to designate associates and partners to a big new case. The daily
rate charged to the client for each associate is $800 and the daily rate for each
partner is $1800. The law firm designated twice as many partners as associates to the
case and was able to charge the client $17600 per day for these lawyers' services.
Write a system of equations that could be used to determine the number of associates
assigned to the case and the number of partners assigned to the case. Define the
variables that you use to write the system.
Answer:
Answer:
Associates=7
Partners=10
Step-by-step explanation:
Let the number of associates be x while partners be y. Since they are a total of 17 then
x+y=17
Therefore, x=17-y
Also considering the charges then
800x+1800y=23600
Subsituting x with 17-y then
800(17-y)+1800y=23600
13600-800y+1800y=23600
1000y=10000
Y=10
X=17-y=17-10=7
