The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.
The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.
In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.
The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.
Mathematically, we can write this sum as:
S = (6xi-3)/n for i = 1, 2, ..., n
And the limit of S as n approaches infinity can be written as:
lim n -> infinity S = lim n -> infinity (6xi-3)/n
Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.
In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].
Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:
∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3
And this value is 9, so the limit of S as n approaches infinity is 9.
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A new mixture of self - tanning & moisturizing lotions for everyday use is being developed . This mixture is made by mixing 700 ounces of everyday moisturizing lotion for $0.70 per ounce with self - tanning lotion worth $2 per ounce. If the new self - tanning & moisturizing lotion mixture is to cost $ 1.30 per ounce, how many ounces of the self-tanning lotion should be in the mixture?
The mixture should have ( ) ounces of the self - tanning lotion.
writw a rule for the sequence. then, find the unknown term.
4 1/2, 3 7/8, 3 1/4, 2
The rule for the arithmetic sequence in this problem is defined as follows:
[tex]a_n = 4.5 - 0.625(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The general rule of an arithmetic sequence is given as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
The common ratio for the sequence is given as follows:
d = 3.25 - 3.875 = 3.875 - 4.5 = -0.625.
The first term of the sequence is given as follows:
[tex]a_1 = 4.5[/tex]
Hence the rule is defined as follows:
[tex]a_n = 4.5 - 0.625(n - 1)[/tex]
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write a function C(t) to represent the cost of a taxicab ride. where the chance includes a fee of 2.50 plus $0.50 for each tenth of a mile t, Then give the slope and y-intercept of the graph of the function. answer
Answer:
C(t) = 0.50 * t + 2.50
Step-by-step explanation:
The function C(t) to represent the cost of a taxicab ride can be written as:
C(t) = 2.50 + 0.50 * t
where t is the distance traveled in tenths of a mile.
The slope of the graph of this function is 0.50, which represents the cost per tenth of a mile.
The y-intercept of the graph of this function is 2.50, which represents the fixed fee that must be paid regardless of the distance traveled.
So, the equation of the graph of this function is:
C(t) = 0.50 * t + 2.50
g(x) = 9+ 4x
h(x) =x + 21/5
Write (hog)(x) as an expression in terms of x.
(hog)(x) =
The expression for (h·g)(x) is 4x²+17.8x+19.8.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are g(x)=9+4x and h(x)=x+ [tex]2\frac{1}{5}[/tex].
Now, (h·g)(x)=h(x)×g(x)
= (x+ [tex]2\frac{1}{5}[/tex])×(9+4x)
= (x+11/5)×(9+4x)
= 9x+99/5+4x²+44x/5
= 9x+19.8+4x²+8.8x
= 4x²+17.8x+19.8
Therefore, the expression for (h·g)(x) is 4x²+17.8x+19.8.
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Lacey pays $15 for each hour of golf lessons and $10 for equipment rental. If the lesson is more than 3 hours long, she only pays $5 for equipment rental. Is the total cost of Lacey’s lesson a function of the number of hours scheduled? Use a table to help explain your answer. Show your work.
Answer:
60
Step-by-step explanation:
15x3=45
5x3=15
15+45=60
Find f’(x) for f(x)=4x^3-5x^2+7x-1
Select the correct answer from each drop-down menu.
In a sequence described by a function, the notation f(2) = 4 means that the
term of the sequence has a value of
. Sequences can be described as functions because
.
The function that describes the sequence maps each index or position to its corresponding value.
What does "sequence" signify in functional analysis?A sequence space is a vector space that contains endless sequences of real or complex numbers. It is used in functional analysis and related mathematical fields. It is, in essence, a function space whose constituents are functions from the natural numbers to the field K of real or complex numbers.
The notation f(2) = 4 indicates that a term in a sequence defined by a function has a value of 4 when the term's index or position is 2.
Because sequences are a collection of ordered pairs with the first element being the index or position of the term and the second being the term's value, they can be characterised as functions. The function that represents the series maps each index or location to its associated value, and these ordered pairs can be seen as points on a coordinate plane.
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How to determine if two verticals are similar
The endpoints of an edge are its end-vertices. When two vertices are endpoints of the same edge, they are said to be neighbouring.
How can the similarity between two graph vertices be determined?The limit of the normalised even iterations of a linear transformation can be used to obtain the similarity matrix. The square matrix in the particular case when G A=G B=G contains the similarity score between the vertices I and j of G as its I j)-th element.
What is the point where two sides meet in common?The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
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In art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint. Use Allison and Alexander’s percent of white paint to determine whose gray paint will be lighter. pls help
Alexander's white paint will be more lighter.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that in art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint.
We will compare the percent of white paint in a mixture.
We can write -
For Allisions mixture = n{1} = (2/3) x 100 = 66.67%For Alexanders mixture = n{2} = (11/17) x 100 = 64.71%n{2} < n{1}Therefore, Alexander's white paint will be more lighter.
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What is an angle that is adjacent to ∠CED?
The angle that is adjacent to the angle CED is the angle DEA.
What are adjacent angles?When two angles have a similar vertex and side, they are referred to as neighbouring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.
An adjacent angle is complementary to another if the total of its adjacent angles is 90 degrees.
When the total of two adjacent angles is 180 degrees, they are supplementary to one another.
Two angles are said to be adjacent angles when they share a common vertex.
In the given figure the angle that shares the common vertex to angle CED is angle DEA.
Hence, the angle that is adjacent to the angle CED is the angle DEA.
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Someone walk me through this, please.
The final value of the investment is $689.10. Fill the table accordingly.
How to determine the final value of the investment?Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
First year
Interest earned = 9/100 * $580 = $52.20
Second year
Balance + Interest = $580 + $52.20
Total balance = $632.20 (Note: Total balance = Balance + Interest )
Interest earned = 9/100 * $632.20 = $56.90
Third year
Balance + Interest = $632.20 + $56.90
Total balance = $689.10
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y= -3x+7 = what number is for solving y?
Answer:
y=-3x+7
its the same thing
Step-by-step explanation:
If x= 45, then √x is between
4 and 5
44 and 46
22 and 23
6 and 7
The transpose of a product of matrices equals the product of their transposes in the same order. Choose the correct answer below: A.The statement is true. Matrix multiplication is not commutative so the product of the transposes must be applied in the same order as the initial product. B.The statement is true The product of the transposes can be applied in any order. C.The statement is false, The transpose of product of matrices equals the sum of the transposes of the matrices. D.The statement is false. The transpose of a product of matrices equals the product of their transposes in the reverse order
The statement is true. Matrix multiplication is not commutative, so the product of the transposes of the matrices must be applied in the same order as the initial product, not in a reverse order.
The statement that the transpose of a product of matrices equals the product of their transposes in the same order is true. Matrix multiplication is not commutative, which means that the order in which the matrices are multiplied matters. That is, for two matrices A and B, AB does not necessarily equal BA. Thus, when taking the transpose of a product of matrices, the order in which the transposes of the matrices are multiplied must be the same as the order in which the original matrices were multiplied. Otherwise, the result will not be the same. For example, if two matrices A and B are multiplied to give AB, the transpose of AB will be (AB)^T = B^T A^T, not A^T B^T. This is why the product of the transposes must be applied in the same order as the initial product.
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Three girls Share an amount of money. The eldest get b/3c of the total amount while the youngest gets gets b/6c of the total, what fraction does the third girl gets?
The fraction does the third girl gets is 3c - b/3c
What is fraction?A fraction can be defined as the part of a whole number or element.
The different types of fraction are;
Proper fractionsImproper fractionsComplex fractionsSimple fractionsMixed fractionsFrom the information given, we have that;
3 girls shares an amount of money
The eldest = b/3x
The youngest = b/6c
This is represented as;
1 - b/3c + b/6c
Add the fractions
1 - 2b - b /6c
add the values
1 - 3b/6c
1 - b/3c
3c - b/3c
Hence, the expression is 3c - b/3c
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Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) y=Ï€x
(b) y=xπ
(c) y=x2(2−x3)
(d) y=tant−cost
(e) y=s1+s
(f) y=x3−1√1+x√3
(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function
(b) g(x) = ∜x is a root function
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2
(e) v(t) = [tex]5^t[/tex]is an exponential function
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.
(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.
(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.
(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.
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The complete question is -
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) f(x) = [tex]log_2(x)[/tex]
(b) g(x) = ∜x
(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]
(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]
(e) v(t) = [tex]5^t[/tex]
(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]
Question 19). TPRS is a parallelogram. Identify m∠R.
Solve what is in the attatchment!!
the measurement of the ∠R will be 101 degrees.
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
Given TPRS is a parallelogram. in that ∠T = (4x +1) and ∠S = (3x +4)°
Since in a parallelogram, opposite angles are equal Thus,
∠P = ∠S = 3x + 4
∠R = ∠T = 4x +1
Since we know the sum of all angles of a quadrilateral is 360°
3x +4 + 4x +1 + 3x +4 + 4x +1 = 360
14x + 10 = 360
14x = 350
x = 350/14
x = 25
Thus,
∠R = 4x +1
∠R = 4 *25 + 1
∠R = 101°
therefore, the measurement of the ∠R will be 101 degrees.
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The population of deer is growing in a given region, and has a carrying capacity of 2500. If at the initial point of
observation (t = 0), there were 400, and 700 four years later, give the logistic model for the population P, and find the
number of deer after 10 years.
The logistic model for the population P is P = 75x = 400.
The number of deer population after 10 years is 1150.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Deer:
Population capacity = 2500
Initial population = 400
Population after 4 years = 700
Now,
We can make two ordered pairs:
(0, 400) and (4, 700)
Now,
We can write an equation as,
P = mx + c
m = (700 - 400) / (4 - 0) = 300/4 = 75
And,
(0, 400) = (x, y)
400 = 75 x 0 + c
c = 400
So,
P = 75x + 400
This is the equation for the number of deers after x years.
Now,
The number of deers after 10 years.
x = 10
P = 75 x 10 + 400
P = 750 + 400
P = 1150
Thus,
The number of deer after 10 years is 1150.
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Try adding up the first few odd numbers and see if the numbers you get satisfy some sort of pattern. Once you find the pattern, express it as a formula. Give a geometric verification that your formula is correct.
The required sum of the first n odd numbers is equal to n².
How we take numbers to make pattern?The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.
The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.
Thus, the sum of the first n odd numbers is equal to n².
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The table and equation below show the proportional relationship between time, in seconds, x, and distance traveled, in feet, y, for two drones.
drone 1
y = 6x
drone 2
x y
8 24
10 30
13 39
A drone 1 is traveling faster than drone 2
B drone 1 is traveling slower than drone 1.
c. the two drones are traveling at the same speed.
D. the speed cannot be compared because there is not enough imformation about drone 1
Drone 1 is traveling faster than Drone 2.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The table and equation below show the proportional relationship between time, in seconds, x, and distance traveled, in feet, y, for two drones.
For drone 1;
The equation is,
⇒ y = 6x
For drone 2;
x = 8, 10, 13
y = 24, 30, 39
Now, For drone 1;
The distance in 8 seconds is,
⇒ y = 6x
⇒ y = 6 × 8
⇒ y = 48
The distance in 10 seconds is,
⇒ y = 6x
⇒ y = 6 × 10
⇒ y = 60
Thus, Drone 1 is traveling faster than Drone 2.
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The scale of the map is missing. The actual distance from Granada Hills to Malibu is 54 miles, and it is 9 inches on the map. What is the scale of the map?
G = {x|x ∈ N and x is a negative}
The cardinal number of G = 0 for the given set G = {x|x ∈ N and x is a negative}.
What is a set?A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.
The set is given in the question, as follows:
G = {x|x ∈ N and x is a negative}
We have to determine the cardinal number of set G = {x|x ∈ N and x is a negative}
Cardinal numbers, also known as Cardinals of a Set, are the numbers used to count the number of elements in a Set.
Simply expressed, the cardinal number of a set equals the number of items in a set.
Let A = {a, b, c, d} be a set then Cardinal number of A is 4
Given G = {x|x ∈ N and x is a negative}
Here, x belongs to N, and a negative number
Since Natural Number (N) = 1, 2, 3, 4 ...
There is no negative value that corresponds to N.
Thus, G = { } or G is an empty set.
Hence, the cardinal number of G = 0
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The question seems incomplete, the complete question would be as:
Find the cardinal number of set G = {x|x ∈ N and x is a negative}
Nanuk has a savings account which gathers compound interest each year.
He opened the account with a deposit of
£2000.
After 4 years there is £2545.10 in the
account.
Work out the annual interest rate of the
savings account.
Give your answer as a percentage to 1
dp
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]
Frank is going to plant b vegetable seeds in one garden and 5b + 6 vegetable seeds in another . How many seeds is frank going to plant ?
The total number of seeds Frank is going to plant is 6b + 6 seeds.
How many seeds is frank going to plant ?From the question, we have the following parameters that can be used in our computation:
Graden 1 = b
Graden 2 = 5b + 6
Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.
The total number of seeds Frank is going to plant is:
b + (5b + 6) = 6b + 6
So Frank is going to plant 6b + 6 seeds.
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I need help with these questions ?!
Answer:
Step-by-step explanation:
kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiilllllllllllllllllllllllll
Answer:
The first one is 3/5 & The second one is 3/8 & The the third one is 1/8
Step-by-step explanation:
Hope this helps :)
29 is 0.40% of what number?
is really "x", which oddly enough is the 100%, but we also know that 0.40% of "x" is 29, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 29& 0.40 \end{array} \implies \cfrac{x}{29}~~=~~\cfrac{100}{0.40}\implies \cfrac{x}{29}=\cfrac{100}{~~ \frac{ 40}{100 } ~~}\implies \cfrac{x}{29}=\cfrac{10000}{40} \\\\\\ \cfrac{x}{29}=250\implies x=7250[/tex]
factorise this : 9x^2-4y^2
Answer:
(3x + 2y) (3x - 2y)
Step-by-step explanation:
a² - b² = (a + b) (a - b)
where a = 3x and b = 2y
Possible codes for "how do you deal with bullies"
Answer:
Step-by-step explanation:
I am not sure what you mean with that question but a short definition of bullying is:
Bullying can result in physical injury, social and emotional distress, self-harm, and even death. It also increases the risk for depression, anxiety, sleep difficulties, lower academic achievement, and dropping out of school.
If angle 2=125 degrees, angle 12=37 degrees, and angle 18=102 degrees, find the rest of the angles
The requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 = 102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
from figure,
∠2 = ∠5 = ∠11 + ∠12 = ∠15 = 125
From the above expression,
∠2 = ∠11 + 37°
125 - 37 = ∠11
∠11 = 88°
Similarly.
∠3 = ∠9 = ∠13 = ∠18 = 102°
∠4 = ∠7+∠8 = ∠14 = ∠17= 78°
∠1 = ∠6 = ∠10 = 16 = 55°
Thus, the requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 = 102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.
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FIND MULTIPLICITY AND ZEROS OF THE GRAPH!