F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.
What is a Fibonacci sequence ?
The Fibonacci sequence is a number sequence in which each subsequent number is formed by adding the two numbers that came before it. The series is named after the Italian mathematician who devised it.
Fibonacci numbers are defined as follows:
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2) for n ≥ 2
Now, let's prove that F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using this definition:
F(n + 1) = F(n) + F(n - 1) (by definition)
F(n – 2) = F(n - 3) + F(n - 4) (by definition)
Adding these two equations, we get:
F(n + 1) + F(n – 2) = F(n) + F(n - 1) + F(n - 3) + F(n - 4)
Now, using the definition of F(n) = F(n-1) + F(n-2), we can substitute F(n-1) + F(n-2) for F(n):
F(n + 1) + F(n – 2) = F(n) + F(n) = 2F(n)
Therefore, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3, which is the desired result.
Hence, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.
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Is 100 ml equal to 1 liter?
The unit 100 ml is not equal to 1 liter.
What is unit of measurements?
A quantifiable language that expresses the magnitude of the amount is referred to as a standard unit of measurement. Understanding how the measurement relates to the thing is helpful.
Here the given is 100 milliliters
we know that to convert milliliters into liter we need to divide them by 1000. Then,
=> 100 ml
=> [tex]\frac{100}{1000} = \frac{1}{10}[/tex]
=> 0.1 liters ≠ 1 liter.
Hence the unit 100 ml is not equal to 1 liter.
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Find the area of the figure.
The area of the figure is __________ cm^2.
Answer:
A = 280cm^2
Step-by-step explanation:
we have 2 shapes, a parallelogram, and a rectangle
lets find our area of the rectangle
A = lw
A = 20(7.5)
A = 150
now for the parallelogram
A = bh
A = 20(6.5)
A = 130
now we add to find the entire A
A = 150+130
A = 280
Use the map shown below to find the distance between cities A and B to the nearest tenth. point A is at (0,0) and point B is at (-5,3)
Answer:-5, 3
Step-by-step explanation:
its the answer. Period
Determine which matrices are in reduced echelon form and which others are only in echelon form. 011 1 0 011 0000 1 1 40 0 1 011 b. 0010 Is matrix b in reduced echelon form, echelon form only, or neither? a.echelon form only b.reduced echelon form c.neither
Matrix b is in reduced echelon form.
Therefore the answer is b. reduced echelon form.
In a reduced echelon matrix, the leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0. Matrix b satisfies these conditions, so it is in reduced echelon form.
Reduced echelon form is a special type of echelon form for matrices, which is used in linear algebra to solve systems of linear equations. In a reduced echelon form matrix, the following conditions are satisfied:
All non-zero rows are above any rows of zeros
The leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0.
Each leading entry is the only non-zero entry in its column.
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On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change. At 7:30 a.m., the temperature was `-4`°F. By 7:32 a.m., the temperature was `45`°F. By 9:00 a.m. the same day, the temperature was `54`°F. By 9:27 a.m., the temperature was `-4`°F. How many degrees did the temperature change each minute from 9:00 to 9:27? Make sure to show whether the change was positive or negative.
From 9:00 a.m. to 9:27 a.m., the temperature changed from 54°F to -4°F, a change of 58°F. This change took 27 minutes.
The temperature change per minute was 58°F / 27 minutes = 2.15°F per minute.
The change was negative, because the temperature decreased from 54°F to -4°F.
can you taste ptc? ptc is a substance that has a strong bitter taste for some people and is tasteless for others. the ability to taste ptc is inherited. about 75% of italians can taste ptc, for example. you want to estimate the proportion of americans who have at least one italian grandparent and who can taste ptc. how large a sample must you test to estimate the proportion of ptc tasters within 0.04 with 90% confidence? answer this question using the 75% estimate as the guessed value for .
The sample size of 470 people is required to estimate the proportion of PTC tasters within 0.04 with 90% confidence.
To estimate the proportion of Americans who have at least one Italian grandparent and can taste PTC with a 90% confidence interval of 0.04, we need to calculate the sample size required using the formula for a proportion. Using the estimate of 75% for the proportion of Italians who can taste PTC as the guess for p, we can calculate that a sample size of 470 people is required.
This means that we need to test 470 Americans who have at least one Italian grandparent to estimate the proportion of PTC tasters within 0.04 with 90% confidence. The formula for the sample size takes into account the desired level of confidence and the margin of error, which is the difference between the estimate and the true value that we are willing to accept.
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What is the relation ship between angle 1 and 2? And why is it that.
Answers:
Congruent
Similar
Corresponding angles
Alternate interior angles
In given geometric shape, angle 1 and 2 are alternate interior angles.
What are geometric shapes?In mathematics, geometric shapes are the patterns that show how everyday objects are shaped. Shapes are the forms of objects in geometry that have boundaries, angles, and surfaces. Both 2D and 3D shapes come in a variety of forms.
Regarding their regularity or uniformity, shapes are also categorised. Regular shapes like a square, circle, etc. are typically symmetrical. Asymmetrical shapes are irregular. They are also referred to as organic shapes or freeform shapes. For instance, a tree's shape is atypical or organic.
Now,
The angles formed when a transversal intersects two coplanar lines are known as alternate interior angles. They are on the inside of the parallel lines, but on the outside of the transversal. The transversal cuts through two Coplanar lines at different points.
Hence,
angle 1 and 2 are alternate interior angles.
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2. (10 points) Christine works in a medical lab. She has several blood samples. The volume of each sample was measured, and they are shown below. 2.350 milliliters 2.285 milliliters 2.332 milliliters 2.299 milliliters 2.317 milliliters A. Put the blood samples in order, from largest volume to smallest volume.
The volume of blood samples from smallest to largest can be ordered as 2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters
What is Ordering of Numbers?Ordering of numbers is the listing of numbers in a specific order, may be from smallest to largest or from largest to smallest.
The given volumes are :
2.350 milliliters, 2.285 milliliters, 2.332 milliliters, 2.299 milliliters and 2.317 milliliters
We have to look at the decimal part because the real part is same 2 for all the values.
So the order is,
2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters
Hence the order is 2.350 milliliters, 2.332 milliliters, 2.317 milliliters, 2.299 milliliters and 2.285 milliliters.
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a population of caribou have weights that are distributed like the bell shaped curve. the mean weight is 125 pounds with a standard deviation of 12 pounds. use the empirical rule to approximate the percent of weights that are between 101 and 137 pounds.
Approximately 68% of the weight fall between 101 and 137 pounds.
The empirical rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
To apply the empirical rule to this problem, we need to convert the weight range of 101 to 137 pounds into units of standard deviation. To do this, we subtract the mean weight of 125 pounds from each value and divide it by the standard deviation of 12 pounds.
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of:
(101 - 125) / 12 = -2
(137 - 125) / 12 = 1
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of -2 to 1.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 68% of the weight fall between 101 and 137 pounds.
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Approximately 68% of the weight fall between 101 and 137 pounds.
The empirical rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
To apply the empirical rule to this problem, we need to convert the weight range of 101 to 137 pounds into units of standard deviation. To do this, we subtract the mean weight of 125 pounds from each value and divide it by the standard deviation of 12 pounds.
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of:
(101 - 125) / 12 = -2
(137 - 125) / 12 = 1
So the weight range of 101 to 137 pounds corresponds to the standard deviation range of -2 to 1.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 68% of the weight fall between 101 and 137 pounds.
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Your newspaper article will end with recommendations to fans about buying
tickets. Your research indicates the average local baseball fan plans to attend
67 games during the season. What are your recommendations to the average
fan about buying tickets? Should they buy season tickets or single-game
tickets?
Make a recommendation for fans buying tickets in each section:
• main box
• bleachers
• left field reserve
Include all necessary work to support your answer.
I recommend the average fan buy season tickets when purchasing seats.
Based on the research, the average local baseball fan plans to attend 67 games during the season. For a fan who is planning to attend this many games, it would be more cost-effective to purchase season tickets rather than individual game tickets.
For fans considering season tickets, here are some recommendations based on the seating section:
Main Box: If cost is not a concern and the fan is looking for a premium experience, purchasing season tickets in the Main Box section is the way to go. The fan will have the best view of the field and access to the best amenities.Bleachers: For the more budget-conscious fan who wants to attend the most games possible, purchasing season tickets in the Bleachers section is the best choice. These tickets are typically the least expensive and provide an energetic atmosphere with a close view of the field.Left Field Reserve: For fans who want a good balance between cost and comfort, season tickets in the Left Field Reserve section would be a good option. These tickets are often priced in between Main Box and Bleachers tickets and provide a good view of the field.Purchasing season tickets rather than individual game tickets is the most cost-effective choice for the average fan who plans to attend 67 games during the season. The best choice of section will depend on the fan's budget and personal preferences.
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In a direct variation, y= 1 /7 when x= 8/7 Write a direct variation equation that how the relationhip between x and y
A direct variation equation is: [tex]y = \frac{1}{8} x[/tex].
Direct variation exists between two variables when one quantity is directly dependent on the other. One quantity increases with respect to the other quantity and vice versa.According to the question,
x and y vary directly proportional then the equation is
y =kx ( where k is the constant of variation)
If x is not equal to zero the value of the constant of proportionality can be given as k = y/x.To find k use the given condition y = 1/7 when x = 8/7
we know that,
[tex]k = \frac{y}{x} = \frac{1/7}{8/7} = \frac{1}{8}[/tex]
Hence, the equation is: [tex]y = \frac{1}{8} x[/tex] .
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what is the formula to find the height of a cylinder via Surface Area (total) and radius?
Answer:
diameter=radius divided by 2
A car decreased in value by 38% to $9235 when it was resold. What was the original
price of the car to the nearest dollar?
the original price is really "x", which oddly enough is the 100%.
now it decreased to $9235, and we know that's 38% less than "x", so 100% - 38% = 62%, so $9235 is really the 62% of "x", hmmm what the dickens is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 9235& 62 \end{array} \implies \cfrac{x}{9235}~~=~~\cfrac{100}{62} \\\\\\ \cfrac{ x }{ 9235 } ~~=~~ \cfrac{ 50 }{ 31 }\implies 31x=461750\implies x=\cfrac{461750}{31}\implies x\approx 14895[/tex]
Meters and feet are two different scales for measuring distance. Five meters is approximately 16. 41 ft, and 12 m is approximately 39. 37 ft. Write an equation that shows the approximate distance in feet as a function of the distance in meters. Show your work
The approximate distance in feet as a function of the distance in meters is 3.28x + 0.01.
What is an equation that shows the approximate distance?Meters and feet are two different scales for measuring distance. Five meters is approximately 16. 41 ft, and 12 m is approximately 39. 37 ft.
Suppose the approximate distance in feet is y,
and the distance in meters is x
Suppose the function is y = ax + b
Given the information, we can know
S*r_{1} = 5; y_{1} = 16.41
x_{2} = 12
y_{2} = 39.37
S_{0} $ 16.41= 5a +b0 { Substitute }
39.37 = 12a + b*Theta
7a = 22.96
a = 3.28
So 16.41 = 5 * 3.28 + b {Substitute} b = 0.01
So the function is y = 3.28x + 0.01
The approximate distance in feet as a function of the distance in meters is 3.28x + 0.01
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Can I have help please
Answer:
Of course you can :)
Answer provided in image !^^
Step-by-step explanation:
3. In the image shade 9 because 3/4x12=9
in how many ways can 9 yellow marbles be divided among 4 distinguishable cups?
The number of ways 9 yellow marbles can be divided among 4 distinguishable cups is 126.
Dividing 9 marbles among 4 cups is a combination problem. The number of combinations is given by the formula C(n + r - 1, r - 1), where n is the number of items (marbles) and r is the number of groups (cups). In this case, n = 9 and r = 4. Plugging these values into the formula, we get:
C(9 + 4 - 1, 4 - 1) = C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220
This means that there are 220 ways to divide 9 yellow marbles into 4 distinguishable cups. However, since the cups are distinguishable, each combination is counted multiple times, once for each permutation of the cups. The number of permutations of n items taken r at a time is given by the formula n! / (n - r)!. In this case, the number of permutations is 4! = 4 * 3 * 2 * 1 = 24.
So, the total number of ways to divide 9 yellow marbles into 4 distinguishable cups is 220 / 24 = 9. This means that there are 126 distinct ways to divide 9 yellow marbles among 4 distinguishable cups.
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simplify 60 with [tex]\sqrt{x} 60[/tex]
Write an equation for the quadratic function with the roots at x= 0, x = 5
The equation for the quadratic function with the roots at x= 0 and x = 5 will be y = x² - 5x.
How to get polynomials with zeroes?Let a, b, c, and d be the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The zeroes of the quadratic equation are 0 and 5, then the quadratic equation is given as,
y = (x - 0)(x - 5)
y = x (x - 5)
y = x² - 5x
The equation for the quadratic function with the roots at x= 0 and x = 5 will be y = x² - 5x.
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What is the equation of the line that passes through the point (1,-3) and has a slope of -3?
An equation of the line that passes through the point (1, -3) and has a slope of -3 is y = -3x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the information provided above, we have the following slope and data points on the line:
Points = (1, -3).Slope, m = -3At point (1, -3), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-3) = -3(x - 1)
y + 3 = -3x + 3
y = -3x + 3 - 3
y = -3x
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The derivative of a function of f at x is given by f′(x)=limh→0f(x+h)−f(x)h provided the limit exists.
Use the definition of the derivative to find the derivative of f(x)=8x^2+2x+7.
Enter the fully simplified expression for f(x+h)−f(x). Do not factor. Make sure there is a space between variables.
f(x+h)−f(x)= ?
The derivative of a function of f at x is given by f′(x) = lim(h→0) f(x+h)−f(x)h provided the limit exists.
What is derivative of a function?A function's immediate rate of change at one particular location is referred to as the derivative of that function. At a certain point along the curve, the derivative provides the precise slope. The symbol for the derivative of a function is dy/d x, which stands for the derivative of the function with respect to the variable.
Given that,
f(x + h) - f(x) = 16xh + 8h² + 2h
f(x)=8x²+2x+7.
then derivative is given by:
f'(x) = lim(h→0) [f(x + h) - f(x)] / h
f'(x) = lim(h→0) [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7] / h
f'(x) = lim(h→0) 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7 / h
f'(x) = lim(h→0) 16xh + 8h² + 2h / h
f'(x) = lim(h→0) 16x + 8h + 2
f'(x) = 16x + 8
f(x + h) - f(x) = [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7]
f(x + h) - f(x) = 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7
f(x + h) - f(x) = 16xh + 8h² + 2h
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In ΔABC, a = 6 inches, m∠A=121° and m∠B=36°. Find the length of b, to the nearest 10th of an inch.
Answer:4.1
Step-by-step explanation:
Answer: 4.1
Step-by-step explanation:
each year, a magazine complies a list of the 400 richest americans. a of september 19,2012 the mean is
The mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
The mean of the 400 richest Americans is calculated by summing up all of the net worth of each person on the list, and then dividing it by the total number of people on the list. The formula used to calculate the mean is:
Mean = (Sum of Net Worth) / (Total Number of People on the List)
For example, on September 19, 2012, the total net worth of the 400 richest Americans was $1.7 trillion. If we divide this by the total number of people on the list (400), then the mean net worth of the 400 richest Americans is $4.25 billion.
Therefore, the mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.
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Graph 2 lines to find x and y values that make both y= -2/3x + 3 and y= 2x -5
The values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.
What is system of simultaneous equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given is the system of simultaneous equations as -
{y} = -{2/3}x + 3
{y} = 2x - 5
Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines.
Therefore, the values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.
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pls hurry this is urgent
The angle measures are ∠QRS = 66° and ∠SQR = 95°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
The triangle QRS with side SR on ray ST.
∠QRS + 114° = 180°
∠QRS = 66°.
Now, the sum of all the angles of the triangle is 180°.
5y + y + 66 = 180
6y = 114
y = 19
So, ∠SQR = 95°.
Therefore, ∠QRS = 66° and ∠SQR = 95°.
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Enter the numerator and the denominator of the fraction in simplest form that is equal to 0. 84 repeating
The fraction that is equal to 0.84 repeating is 8/9 in simplest form.
If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase "lowest words" when referring to the simplest form.
0.84 repeating can be represented as a fraction in simplest form by using the following method:
Let x = 0.84 repeating,
Then 10x = 8.4 repeating.
Subtracting the two equations,
we have 9x = 8.
Dividing both sides by 9,
we have x = 8/9.
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1. A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches.
What is the surface area of the pyramid?
Enter your answer in the box.
2.A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
3.A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
The total surface area of the hexagonal pyramid is 237.5 in²
How do equations work?An expression that depicts the relationship between two or more numbers and variables is called an equation. Depending on the degree, an equation may be linear, quadratic, cubic, or another type.
A solid figure's surface area is calculated by summing up all of its distinct surfaces.
Given the hexagonal pyramid with a base of 6 inches and each isosceles triangle having a height of 8 inches. Hence:
Area of pyramid base = 93.5 in²
The lateral face has 6 triangle faces, hence:
Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²
Total area of lateral face = 6 * 24 in² = 144 in²
Total surface area = 144 in² + 93.5 in² = 237.5 in²
The surface area is 237.5 in²
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let's let x represent the length of one of the sides of the cube (in cm), let s represent the surface area of the cube (in square cm), and let v represent the volume of the cube (in cubic cm).
Surface area of the cube can be S = 6x², if the side length of the cube is 7.7 cm, the surface area would be is S = 6(7.7)² = 391.16.
What do you mean by Surface Area?The surface area of an object refers to the total area of its exposed outer surface. It is a measure of the amount of space that an object's surface covers. Surface area is a two-dimensional concept, and is different from the object's volume, which is a three-dimensional concept.
The surface area of an object depends on its shape, and can be calculated using mathematical formulas specific to different shapes. For example, the surface area of a cube is the sum of the areas of its six faces, while the surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere.
Surface area is an important concept in a variety of fields, including physics, chemistry, and engineering. In physics, it is used to calculate the heat transfer between objects, while in chemistry it is used to calculate the amount of reactant needed to cover a given surface area in a reaction. In engineering, surface area is important in the design of heat exchangers, reactors, and other equipment where heat or chemical reactions take place on surfaces.
V = x³
So, if the side length of the cube is 7.7 cm, the volume would be:
V = (7.7)³ = 455.169
The surface area of the cube can be calculated as:
S = 6x²
So, if the side length of the cube is 7.7 cm, the surface area would be:
S = 6(7.7)² = 391.16
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The complete question is:
Find Sn for the arithmetic series where a1=3 , an=3 , n=14
The value of the sum of the series is 42
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
In this series, a1=3 , an=3 , n=14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 3)
= 14/2 * 6
= 7 * 6
= 42
So, the sum of the first 14 terms of the arithmetic series is 42
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15. The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values (1 point) that n may have.15. The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values (1 point) that n may have.
An inequality that expresses the interval of values that n may have is 7 < n < 17.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < n < b + c
12 - 5 < n < 12 + 5
7 < n < 17.
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Allie is completing a long division problem that may or may not have a remainder. In each box, drag the appropriate digit to show the correct way to divide
Answer choices may be used more than once.
Follow the example of long division to understand the method and concept of the same.
Let us understand the long division with an example. For this, let us take 13032 as the dividend and 24 is the divisor. Now, performing long division.
On division the quotient will be 5. Now, subtracting 120 from 130, the remainder will be 10. Now, we will take the dividend 103.
Dividing 103 by 24, the overall quotient will be 54. On subtraction we get 7. Taking 2, thus, the combined dividend is 72.
Dividing 72 by 24, the quotient will be 3. Thus, overall quotient will be 543. The remainder will be zero. Thus, the long division of 13032 by 24 yields 543 as quotient without remainder.
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