The radius of convergence is r = 6.
Find the radius of convergence by using the ratio tests?To find the radius of convergence, we use the ratio test:
r = lim |an / an+1|
where an = (-1)^n n^3 x^n / 6^n
an+1 = (-1)^(n+1) (n+1)^3 x^(n+1) / 6^(n+1)
Thus, we have:
|an+1 / an| = [(n+1)^3 / n^3] |x| / 6
Taking the limit as n approaches infinity, we get:
r = lim |an / an+1| = lim [(n^3 / (n+1)^3) 6 / |x|]
= lim [(1 + 1/n)^(-3) * 6/|x|]
= 6/|x|
Therefore, the radius of convergence is r = 6.
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An item is regularly priced at $93. Kira bought it at a discount of 45% off the regular price.
(50 points, thanks, 5 stars, brainliest, all that jazz, IF correct!)
If Kira had not have any discount, she would have bought the product at the normal selling price.
$ [tex]93[/tex]But that product was given a [tex]45[/tex]% discount on its regular price.
[tex]45[/tex]% [tex]=\frac{45}{100}=\frac{9}{20}[/tex]If the product had cost $[tex]100[/tex], the discount would have been $[tex]45[/tex].
So how many dollars would the discount be if it was $[tex]93[/tex]? We can determine this using a proportion.
[tex]93\frac{9}{20}=41.85[/tex]Kira will therefore be able to buy this product at a [tex]45[/tex]% discount for only;
[tex]93-(41.85)=51.15[/tex] dollars.Mia has $20 less than Brandi. Brandi has d dollars. Write a variable expression for the amount of money Mia has.
Answer: d-20
Step-by-step explanation:
if Mia has $20 less than Brandi, it means Brandi has d dollars, so we subtract Brandi 's money from $20.hope you understood.
If B is the midpoint of AC and AB = 5 Find BC and AC.
The length of BC is 5
The length of AC is 10
Midpoint of a line: Calculating length of a lineFrom the given information, we are to calculate the length of the given parts of line AC
From the given information,
B is the midpoint of AC
Thus,
We can write that
AB + BC = AC
and
AB = BC
Also, from the given information,
AB = 5
Therefore,
BC = 5
From the equation,
AB + BC = AC
Substitute the values of AB and BC
5 + 5 = AC
10 = AC
AC = 10
Hence, BC = 5 and AC = 10
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3
At a stream cleanup, the ratio of
adult volunteers to child volunteers
is 7:4. If 20 children volunteer, how
many adults are there?
Answer:
35
Step-by-step explanation:
a=adult c=children
7a:4c
?a:20c
20 is 5 times more than 4 which I found by doing 20/4
So now we multiply 7 by 5 to get 35
35a:20c
There are 35 adults
Given the figure at right.
Find the sum of angles
1, 2, and 3.
Write the rule to describe the transformation.
Answer:
Dilation of 3
Step-by-step explanation:
Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].
The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.
So, the scale factor is [tex]\frac{6}{2}=3[/tex].
The dilation shown in the image is a dilation with a scale factor of 3
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (3x, 3y)
What is dilation?Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
Generally, transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
Examining the figure, Using side DE as reference we can see that DE is 1 unit
After dilation side D' E' transformed to 3 units, showing an increment of 3.
The dilation is an enlargement and the scale factor is 3
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Is 16 a factor of 8?
No, number 16 is not representing as a factor of 8. The given statement is false as it is a multiple of 8.
As given in the question,
Given number is equal to 8,
Given factor is equal to 16:
Factors are those numbers which divides the given numbers without leaving any remainder. It exactly divides the given original number.
Here given factor 16 does not divides the given number 8.
Instead 8 divides the the number 16.
here '8' is the factor of the number 16.
And 16 represents as a multiple of 8.
Therefore, the given statement is false and 16 is not considered as a factor of 8 instead it is a multiple of 8.
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9 + m / 3 = 2 PLEASEEEEE HELPPPPP
Answer: M= -3
Solve for m by simplifying both sides of the equation, then isolating the variable.
What are the four types of triangles according to angle measure?
The 4 types of triangle are
Acute triangle
Obtuse Triangle
Right triangle
Equivalent triangle
What are the four types of triangles by angle measurement ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
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A local car dealership has 250 cars on the lot. 30% of the cars are SUVs. How many of the cars are not SUVs?
Answer:175 are not suvs
Step-by-step explanation:
Answer: 175
Step-by-step explanation:
2
A math teacher observed that as the number of hours students studied their multiplication facts increased, the
number of errors the students made on their multiplication tests decreased. Which scatterplot could support this
teacher's observation?
F
G
Number of Errors
Number of Errors
10
0
y
10
0
Multiplication Tests
12 3 4
Study Time (hours)
Multiplication Tests
1 2 3 4
Study Time (hours)
5
H
J
Number of Errors
Number of Errors
10
2
10
Multiplication Tests
2
●
0 1 2 3 4
Study Time (hours)
Multiplication Tests
●
0 1 2 3 4
Study Time (hours)
5
A scatterplot that shows the number of hours studied on the x-axis and the number of errors on the y-axis would best support the teacher's observation.
What is error in math?Error in math is an incorrect answer to a mathematical equation or problem. It can be caused by a variety of factors, such as inaccurate calculations, misreading instructions, or not understanding the problem. Error in math can be frustrating and can lead to poor grades, but it can also be an opportunity for learning and growth. With the proper guidance and understanding, students can learn from their mistakes and become better mathematicians.
The scatterplot would likely show a negative correlation, with the number of errors decreasing as the number of hours studied increases. This indicates that as students study more, their performance on multiplication tests improves. It could also show an outlier or two, which could indicate that some students are able to learn multiplication facts more quickly than others.
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Sarah ued propertie of operation to write the following three equivalent expreion to
Sarah's error in the expression 3 so the correct answer is option D
Complete Question: Sarah used properties of operations to write the following three equivalent expressions to.
A. There are no errors. All of the expressions are equivalent.
B. Expression 1. Sarah can’t apply the Distributive Property if there are three addends.
C. Expression 2. Sarah can’t combine -4 and -6. She must combine -4 with 8.
D. Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6).
Expressions 1, and 2 are equivalent because they are using the distributive property to expand the term within the brackets before applying the 1/2 coefficient.
Expression 3 is not equivalent because it does not use the distributive property and does not have the same terms as the other expressions.
Sarah's error in expression 3 is that she did not use the distributive property and the terms inside the brackets are not the same as the other expressions, hence the results are different.
Therefore, Sarah's error in the expression 3 so the correct answer is option D
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The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.
A linear model can be represented by the equation y = mx + b, where y is the dependent variable (megawatt hours generated by hydropower), x is the independent variable (years since 2007), m is the slope of the line, and b is the y-intercept.
To find the slope (m) and y-intercept (b) for this problem, we can use the two points given: (2007, 248) and (2012, 277).
m = (277 - 248) / (2012 - 2007) = 29 / 5 = 5.8
b = 248 - (5.8)(2007) = 248 - 11456 = -11208
So the linear model representing the number of megawatt hours generated by hydropower as a function of the number of years since 2007 is:
y = 5.8x - 11208
where x is the number of years since 2007.
Expand and combine like terms.
(9c^2+c^6)(9c^2-c^6
Answer: -c^12+9c^4
Step-by-step explanation:
Answer: 81 c^4 - c^12
Step-by-step explanation:
(9c^2+c^6)(9c^2-c^6)
Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)
This is the difference of squares
(a+b) (a-b) = a^2 - b^2
(9c^2) ^2 - ( c^6)^2
81 c^4 - c^12
answer PLEASE????? thanks
Answer:
2 4/5
Step-by-step explanation:
2/5 x 2 = 4/5 + 2 = 2 4/5
_______________
Hope this helps :)
At the craft tore, Anita bought a bag of yellow and green marble. The bag contained 70 marble, and 30% of them were yellow. How many yellow marble did Anita receive?
There are 21 yellow marbles anita receives
given that
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.
at the craft store , Anita bought a bag of yellow and green marble
The bag contained 70 marble,
30% percentage of them were yellow.
now, we need to find How many yellow marble did Anita receive
= 70 * 30%
= 70 * [tex]\frac{30}{100}[/tex]
= 7 *3
= 21
There are 21 yellow marbles anita receives
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6 times a number plus 15 is equal to 6 times a number minus 41
The given statement as an expression is 6x + 15 = 6x - 41
How to represent the statement as an expressionFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
6 times a number plus 15 is equal to 6 times a number minus 41
Represent the number with x
So, we have the following representation
6 times x plus 15 is equal to 6 times x minus 41
is equal to implies =
So, we have:
6 times x plus 15 = 6 times x minus 41
Plus implies +, minus implies - and times *
This gives
6x + 15 = 6x - 41
The question does not require that we solve the expression
So, we leave it at 6x + 15 = 6x - 41
Hence, the required expression is 6x + 15 = 6x - 41
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I’ll give brainliest :)
Write the rule for the linear function
Answer:
y = f(x) = a + bx
Step-by-step explanation:
Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).
What are the 6 steps to solving equations?
Answer:
The six steps to solving equations are:
Simplify both sides of the equation, if necessary, by combining like terms.
Isolate the variable on one side of the equation.
Use inverse operations to solve for the variable.
Check your solution by substituting it back into the original equation.
Write the solution in interval notation.
Graph the solution on the number line.
Note that steps 5 and 6 are only applicable when solving inequalities, not equations.
Step-by-step explanation:
PLEASE HELP
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
The constant of proportionality of the graph is 12.
How to find the constant of proportionality?Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one in which two quantities vary directly with each other.
Proportional relationship can be represented mathematically as follows:
y = kx
where
k = constant of proportionalityTherefore, let's use (3, 36) to find the constant of proportionality.
Hence,
y = kx
36 = 3k
divide both sides by 3
3k / 3 = 36 / 3
k = 12
Therefore, the constant of proportionality is 12.
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Calculate the total water use in Spain if the per capita water use is 810m ^ 3 and the population of Spain is 46.5 million
Total water use in Spain = 810m^3 x 46.5 million = 37,425,000,000 m^3. it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.
1. Given that the per capita water use is 810m^3 and the population of Spain is 46.5 million.
2. Calculate the total water use by multiplying the per capita water use by the population of Spain.
3. Total water use in Spain
= 810m^3 x 46.5 million = 37,425,000,000 m^3
The total water use in Spain is calculated by multiplying the per capita water use (810m^3) by the population of Spain (46.5 million). This yields a total water use of 37,425,000,000 m^3. This number indicates the volume of water used in Spain annually by its citizens. Water use can have a variety of impacts on the environment, such as depletion of water resources, and it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.
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Challenge You have 2 different savings accounts. For Account A, the simple interest earned after 6 months is $4.88. For Account B, the simple interest earned after 27 months is $24.75. If the interest rate is 3.9% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The principal of account A is $250.26
The principal of account B is $500
The account that would earn you more interest in the first month is account B
What are the principals?
Simple interest is the interest earned on an amount of money in a savings account.
Simple interest = principal x time x interest rate
Principal is the amount deposited
Principal = simple interest / ( time x interest rate)
Principal of account A = 4.88 / (6/12 x 0.039) = $250.26
Principal of account B = 24.75 / (27/12 xx 0.022) =$500
Interest earned in the first month:
Account A = (1/12) x 250.26 x 0.039 = .81
Account B = (1/12) x 500 x 0.022 =0.92
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How do you find the endpoint of a titration?
The endpoint of a titration can be found by various methods like visual indicators, conductometric titration, volumetric titration, etc.
The endpoint of a titration is the point at which the reaction between the acid and base is complete. In other words, it is the point at which the acid and base have been neutralized, and the solution reaches a neutral pH of 7.0. There are several ways to determine the endpoint of a titration, including:
Visual indicators: Certain indicators, such as phenolphthalein or methyl orange, change color at a specific pH, indicating the endpoint of the titration.Potentiometric titration: A pH sensor or electrode is used to measure the pH of the solution during the titration. The endpoint is determined when the pH reaches a specific value, such as 7.0 for a neutralization reaction.Conductometric titration: A conductivity sensor is used to measure the conductivity of the solution during the titration. The endpoint is determined when the conductivity reaches a maximum or minimum value.Amperometric titration: An electrode is used to measure the current during the titration. The endpoint is determined when the current reaches a maximum or minimum value.Volumetric titration: The endpoint is determined by measuring the volume of the titrant required to neutralize the acid or base.To find the endpoint, it is important to use a suitable indicator that changes color in the range of pH close to the endpoint of the titration. It's also important to use a burette to measure the volume of the titrant added and use it to plot the titration curve.
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HELP HELP 15 POINTSSSSSS
Answer:
I believe B, E, and F is the answer
What are the 3 types of image?
There are the Following three types of images they are written as follows:
1. Image of an element: If x is a member of X, then the image of x under, f, denoted, f(x), is the value of f when applied to x. f(x) is alternatively known as the output of f for argument x.
2. Image of a subset: Throughout, let: f: X→Y be a function. The image under f of a subset A of X is the set of all f(a) for a ∈ A.
It is denoted by f[A],} or by f(A) when there is no risk of confusion.
3. Image of a function: The image of a function is the image of its entire or full domain, also called as the range of the function. This last usage should be evaded because the word "range" is also commonly used to mean the codomain off.
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if you can solve this that would be great
Answer:
x<30
Step-by-step explanation:
3/6x-1/6x<10
1/3x<10
x<30
solve for u.
2u + 2.17 = 16.17
Answer:
[tex]\boxed{\bf u=7}[/tex]
Step-by-step explanation:
[tex]\sf 2u+2.17=16.17[/tex]
Subtract 2.17 from both sides:-
[tex]\sf u+2.17-2.17=16.17-2.17[/tex]
[tex]\sf 2u=14[/tex]
Divide both sides by 2:-
[tex]\sf \cfrac{2u}{2}=\cfrac{14}{2}[/tex]
[tex]\sf u=7[/tex]
Therefore, u = 7
______________________
Hope this helps!
Have a great day!
Which is the longest side in ∆ XYZ right angled at X?
The longest side in a right triangle is the hypotenuse, which is the side opposite the right angle.
In ∆ XYZ, if X is the right angle, then the hypotenuse would be the side connecting points Y and Z. This is because in a right triangle, the hypotenuse is always the side opposite the right angle and is also the longest side in the triangle. This can be proven using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than
once.
y = 3x - 1
2y - 6x = 4
2y = -x + 6
4y + 2x = 12
y = 2x + 3
x+y=-9
inconsistent
consistent
independent
dependent
So on solving the provided question we cans say that in the following linear equation values are y = -1, -3 , 3
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here ,
as we know that x = 0
so, y = 3x - 1 = -1
2y - 6x = 4 => y = 2
2y = -x + 6 = y = 3
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solve for y 6/y+4=5/y-7