The series that is related to a triangle with 10 cans in the bottom row can be expressed in summation notation as [tex]\sum\limits^{10}_{n=1} {n}[/tex]
Let us consider the simpler triangle formed by stacking cans as in the attached picture.
As we can see in the picture, if the bottom row contains 3 cans, then the triangle will have 3 rows. The number of cans in each row decreases by 1. We can expand this idea for a triangle with 10 cans in the bottom row.
In this case, there will be 10 rows and the number of cans in each row decreases by 1.
10th row : 10 cans
9th row : 9 cans
and so on.
We can express the number of all cans in this triangle as a series, starting from the top row (the first row):
1 + 2 + 3 + ... + 10
The explicit formula of the nth term is: a(n) = n.
Hence, in the summation notation, it can be written as:
[tex]\sum\limits^{10}_{n=1} {a(n)} = \sum\limits^{10}_{n=1} {n}[/tex]
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Evaluate (2/3)^2 Give your answer as a fraction in its simplest form.
i wasn't taught this ever
Answer: Most likely 0.44444 (The 4 is repeating.)
Step-by-step explanation:
Because first since its in parenthesis, you would do 2/3 which is 0.6666 repeating. Then you do that to the power of 2 which will give you 0.4 repeating!
Hope this works! If not, I apologize.
What’s is four fifths -one third
Answer:
[tex] \frac{7}{15} [/tex]
Step-by-step explanation:
The question is asking us to find the difference between 4/5 and 1/3.
[tex] \frac{4}{5} - \frac{1}{3} [/tex]
First we have to determine the LCM which is 15.
LCM is obtained by multiplying 5 and 3 from the denominators.
Then proceed as follows
[tex] \frac{4}{5} - \frac{1}{3} = \frac{12 - 5}{15} \\ = \frac{7}{15} [/tex]
The solution is therefore
[tex] \frac{7}{15} [/tex]
Help me please please
Evaluate the sum of the finite geometric series. Σ⁴ n=1 (2/3)ⁿ⁻¹
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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find the surface area of the compositite object. show work.
Write an explicit and a recursive formula for each sequence. 0,6,12,18,24, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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!!100 points!!
determine whether each equation represents a linear function.
-4x + 2y = 10
y = 2x^2 - 3x + 5
x = -5
y = 1.5x
!!!!please explain your reasoning!!!!
The equation -4x + 2y = 10 represents a linear function
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear function
x = -5 represents a linear function
y = 1.5x represents a linear function
The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power.
When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants.
-4x + 2y = 10 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
[tex]y = 2x^2 - 3x + 5\\[/tex] represents a non-linear functions as it lies in the plain (x-y) and it has power higher than 1. The highest power of the exponent is 2.
x = -5 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
y = 1.5x represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
Therefore, equations -4x + 2y = 10 , x = -5 , y = 1.5x are linear functions.
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The equation -4x + 2y = 10 represents a linear function
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear function
x = -5 represents a linear function
y = 1.5x represents a linear function
The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power.
When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants.
-4x + 2y = 10 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
[tex]y = 2x^2 - 3x + 5[/tex] represents a non-linear functions as it lies in the plain (x-y) and it has power higher than 1. The highest power of the exponent is 2.
x = -5 represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
y = 1.5x represents a linear function as it follows both the rule that is it lies in a plain(x-y) and also have exponents with power not higher than 1.
Therefore, equations -4x + 2y = 10 , x = -5 , y = 1.5x are linear functions.
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12 Express this product in scientific notation: (11 x 10¹¹) (12 × 10¹²).
A. 1.32 × 1023
B . 13.2 x 1025
C. 132 x 1025
D. -1.32 x 1025
Answer: The answer is c 1.32 x 10^25
Step-by-step explanation:
I need ur help please explain i don't understand check attachment
The graph of the given piecewise function is given at the end of the answer.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For this problem, the function is defined as follows:
f(x) = 2/3x, for x ≤ 0.f(x) = 3, for 1 ≤ x ≤ 3.f(x) = -2x + 5, for x ≥ 4.Hence:
To the left of x = 0, the function is increasing and linear.Between x = 1 and x = 3, the function is constant at x = 3.To the right of x = 4, the function is decreasing and linear.The function is given at the graph with the end of answer, with holes where the function is not defined, and multiple behaviors as it is piecewise.
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To rotate a point (90°, 180°) counterclockwise about the origin, multiply the y -coordinate by -1 and then interchange, the x - and y -coordinates.
To rotate a point 90° counterclockwise about the origin, multiply the y -coordinate by -1 and then interchange, the x - and y -coordinates are (x,y) -> (-y,x)
What does the term "coordinates" mean?
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). There are various coordinate systems that mathematicians, physicists, and engineers frequently utilize.Rotation of 90° counter-clockwise about origin-
Think about the location (X, Y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 in order to rotate this point by 90 degrees around the origin in the opposite manner.
This would be expressed mathematically as follows
(x ,y) → ( -y ,x)
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Round 170.65 up to 3 digits
Answer:
Rounding up to 3 decimals = 170.650
Rounding up to Hundreds = 200
Michael is driving to Dallas. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Michael has 61 miles to his destination after 15 minutes of driving, and he has 49.8 miles to his destination after 29 minutes of driving. How many miles will he have to his destination after 33 minutes of driving?
In linear equation, 16.6 miles will he have to his destination after 33 minutes of driving.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."for linear equation rate of change is constant .
rate of change of distance from destination with respect to time
= 49.8 - 61/29 - 15
= -11.2/14
= -0.8
now the distance from destination after 57 minutes driving
= 49.8 + (-0.8)( 33 - 29 )
= 19.8 -3.2
= 16.6 miles
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ow that pn pnQ ) v (pnr
Answer:
brwhwthfv fvqfbqrhwt vwrvqdvqrgdqg
Use the diagram and the given angle measure to find the other three measures.
$m\angle1=143\degree$ Line segments drawn on a pair of scissors. Two line segments intersect creating obtuse vertical angles 1 and 3 and acute vertical angles 2 and 4.
$m\angle2=$
a
$\degree$
$m\angle3=$
$\degree$
$m\angle4=$
$\degree$
The three measures of the angle are,
Angle 2 = 37°
Angle 3 = 153°
Angle 4 = 37°
When two straight lines or rays intersect at a single endpoint, an angle is created. The intersection of two points is where an angle's vertex is located. The Latin word "angulus," which means "corner," is where the term "angle" originates. The building's corner provided protection, whether it was a projecting portion or a partially covered area. 2a: Dihedral angle and the figure created by two lines that originate from the same point.
I guess refers to two intersecting angle which form 4 angles.
Angles 1 and 2 are supplementary angles whose sum is 180°.
Angle 1 + Angle 2 = 180°
143° + angle 2 = 180°
Angle 2 = 180° - 143°
Angle 2 = 37°
Angles 1 and 3 are vertical angles, therefore treat them as such.
Therefore, it is easy to find their measures because vertical angles are congruent in measures.
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15.84 + 156 =??
Pls help
Answer:
171.84
Step-by-step explanation:
156 + 15 = 171
171 + 0.84 = 171.84
There was a base fee of $17.95 and there was an additional charge of 92 cents for each mile driven. Shen had to pay $173.43 when he returned the truck. For how many miles did he drive the truck?
Th number of miles driven by truck is 169.
What is defined as the unitary method?The unitary method is an approach that involves determining the value of a single unit and then calculating the value of the necessary number of units based on that value.The unitary method's formula is to identify the value of a single unit and afterwards multiply that value by the number of units to get the required value.For the given question:
The base fee of the drive = $17.95.
The additional charges are 92 cents for each mile driven.
The additional charges = $0.92
Let 'x' be the miles driven by the truck.
Thus, the total additional charges for the drive of x miles will be: 0.92x.
So, the total charge for truck drive is;
The total charge are given as $173.43.
Total charge = base charge + additional charge
$173.43 = $17.95 + 0.92x
0.92x = $173.43 - $17.95
0.92x = 155.53
x = 169.05
x = 169 miles.
Thus, the total number of miles driven by the truck are 169 miles.
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y=x-3
y=-4x+3
Determine whether the pair of lines listed is parallel, perpendicular or neither.
The given equations are neither parallel nor perpendicular with each other.
According to the question, to calculate the slope of the given equations.
y = x - 3 and Y = 4x + 3
Now, equate the given equations with the standard slope equation that is: y = mx + c
Using above equation, the slope for first equation is: m1 = 1
And the slope for the second equation is: m2 = 4
When the value of the slopes are equal, means lines are parallel. Similarly, when the value is negative one, then the lines are perpendicular to each other otherwise neither parallel nor perpendicular.
Hence, the given equations are neither parallel nor perpendicular with each other.
What is the slope of a line?
The slope of a line is the ratio of the y-axis coordinates and the x-axis coordinates. It is also called as gradient which tells the steepness of a straight line. Depending upon the values, it is categorized as parallel, perpendicular or no line.
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PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
also show regular work
The average person laughs 15 times a day. Is this continuous or discrete?
Answer: Discrete
Step-by-step explanation: Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting.
Hope this helps!
pls help, i rlly dont know what this is
Answer:B
Step-by-step explanation:
Answer:
Step-by-step explanation:
option b is correct
9/4 = 2.25
13.5/6 = 2.25
do the last one yourself
THIS IS EASY ++ WILL GIVE BRAINLIEST ! TYSM
Answer:
5
-5
13
-5
-13
13
5
-13
Step-by-step explanation:
Answer:
5, -5, 13, -5, -13, 13, 5, -13
Step-by-step explanation:
9 - 4 = 5 4 - 9 = -5 9 - (-4) = 9 + 4 = 13 -9 - (-4) = -9 + 4 = -5 -9 - 4 = -13 4 - (-9) = 4 + 9 = 13 -4 - (-9) = -4 + 9 = 5 -4 - 9 = -13Hope this helped and have a good day
Solve the following inequality algebraically.
x^2+2x-24< 0
Answer:
-6<x<4
Step-by-step explanation:
x^2+2x-24=0
(x-4)(x+6)=0
x-4=0
x+6=0
x=-6,4
x<-6 false
-6<x<4 true
x>4 false
so -6<x<4
WILL GIVE BRAINIEST TO BEST ANSWER, PLEASEEE HELP
also show steps/work
The solution of the equation for h is as follows:
h = 2r
How to find h in the equation?The equation is represented as follows:
2πr³ = πr²h
where
r = radiush = heightTherefore, let's make h the subject of the formula
2πr³ = πr²h
Divide both sides by πr²
2πr³ / πr² = πr²h / πr²
h = 2r
Therefore, the solution of the equation for h is as follows:
h = 2r
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Sean is thinking of a 3 digit number. the digit in the hundreds place is 1 more than the digit in the ones place. the value of the digit in the ones place is 25 less than the value of the digit in the tens place. what number is sean thinking of?
635 is the 3 digit number Sean is thinking of.
What is a digit?A digit is one of the elements of a set that makes up a numeration system. Thus, in a certain context, a digit is a number. The digits in the decimal (base-10) Arabic numbering system are the constituents in the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Let a, b , c the digits of hundreds place, tens place and ones places.
Let the digit in the tens place be x, thus b = x
The digit in ones place is 25 less than the value of the digit in the tens place
c = x - 25
And finally, he digit in the hundreds place is 1 more than the digit in the ones place
a = (x - 25) +1
If a, b , c are digits of there respective places the the value of their digits are
a(100), b(10) c(1)
Now, b can be any no. which is more than 25 so as to make positive ones place, lets say 30
b = 30 = x
Thus x = 3, so
a = ( x - 25) +1
= ( 30 - 25) +1
= 6
c = 30 - 25
= 5
Thus, 635 is the 3 digit number Sean is thinking
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The points (-10, q) and (10, -9) fall on a line with a slope of -1/5. What is the value of q?
help plss ima need help on other questions to
Answer:
5 1/15
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form:
76
15
Decimal Form:
5.0
¯
6
Mixed Number Form:
5 1/15
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point.
y=-x^2-6x-16
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{-16} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ -6}{2(-1)}~~~~ ,~~~~ -16-\cfrac{ (-6)^2}{4(-1)}\right) \implies \left( - \cfrac{ -6 }{ -2 }~~,~~-16 - \cfrac{ 36 }{ -4 } \right) \\\\\\ (-3~~,~~-16+9)\implies (-3~~,~~-7)[/tex]
Given that ZCEA is a right angle and EB bisects ZCEA,
which statement must be true?
OZBEA CEA
O ZCEB CEA
OmzCEB= 45°
O m/CEA = 45°
The statement is true and option (C) is correct. i.e m∠CEB = 45° .
To prove
Reason
As shown in the diagram
∠CEA = ∠CEB + ∠AEB
Bisector
A bisector is a tool that divides any object into two equal parts.
As given
∠CEA is a right angle, and EB bisects it, dividing it into two equal parts.
Thus
∠CEB = ∠AEB = 45 °
Therefore
m ∠CEB = 45 °
Hence proved.
Therefore the correct option is option (C) is correct.
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Evaluate each expression for a=3 and b=-5 . 3(a-b)
Evaluating the expression 3(a - b) for a = 3 and b = -5 is equal to 24.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression 3(a - b), substitute the value of the variable a and the value of variable b.
3(a - b)
3[3 - (-5)]
Performing the arithmetic operations, we can have the value of the expression.
3[3 - (-5)]
= 3(3 + 5)
= 3(8)
= 24
Hence, the expression 3(a - b) when a = 3 and b = -5 is equal to 24.
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List the domain and range of each relation. (3,-2),(4,4),(0,-2),(4,1),(3,2)
Range = { -2 , 4 , -2 , 1 , 2} is for the relation .
what is domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).relation. (3,-2),(4,4),(0,-2),(4,1),(3,2)
domain = { 3 , 4 , 0 , 4 , 3 }
Range = { -2 , 4 , -2 , 1 , 2}
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