The amount of interest earned in 6 years will be $15.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.
Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.
Given that Ellie has $50 in a savings account that earns 5% annually. The simple interest is calculated as:-
Simple interest = ( P x R x T ) / 100
Simple interest = ( 50 x 5 x 6 ) / 100
Simple interest = $15
Hence, the value of the simple interest after 15 years will be $15.
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What are the six multiples of 8?
There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.
How do you solve multiples of 8?Knowing the multiplication table for 8 is necessary in order to determine the multiples of 8. Multiples of 8 are created by multiplying 8 by any natural number, resulting in 8n, where n is any natural number. As a result, the pattern is as follows: 8, 24, 40, 56, 72, 88, 104.The numbers that divide 8 perfectly without leaving a residue are considered to be its factors. The four components of 8 are 1, 2, 4, and 8.2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 89, and 97 are the prime numbers from 1 to 100.To learn more about multiples refer to:
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Which equation can be used to solve for x the total amount of paint in the mixture of the two colors
The equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).
We need to solve for x,
6+0.6x - 24=0.25x
After rearranging the equation we get,
0.35x=18
Divide both side by 0.35x
x=18/0.35
x = 51.43
The equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).
Inconclusion the equation that can be used to solve for x, the total amount of paint in the mixture of the two colors is: 0.15(40) + 0.6(x - 40) = 0.25(x).
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation is described as having one or more variables in French.
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Complete question: Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.
Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?
Find the general solution of the given differential equation. dy/dx + y = e^7x y = Give the largest interval I over which the general solution is defined.
The largest interval I over which the general solution is defined is (-∞, ∞).
What do you mean by differential equation?A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.
A differential equation can be thought of as an equation that describes how a function changes over time. For example, the velocity of an object is the derivative of its position with respect to time. If the position of the object is modeled by a function, then its velocity can be described by a differential equation.
ODEs deal with functions of a single variable and their derivatives, while PDEs deal with functions of multiple variables and their partial derivatives.
The given differential equation is a first-order linear ordinary differential equation with constant coefficients:
dy/dx + y = e⁷ˣ
This equation can be solved using the method of integrating factors. The integrating factor is given by e^∫1 dx = e^x. Multiplying both sides of the equation by the integrating factor, we get:
eˣ(dy/dx) + eˣ y = e⁸ˣ
Integrating both sides, we get:
eˣ y = e⁸ˣ - eˣ + C, where C is an arbitrary constant of integration.
Dividing both sides by eˣ, we get the general solution:
y = e⁷ˣ + Ce⁻ˣ
The largest interval I over which the general solution is defined is (-∞, ∞).
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find the curvature. r(t) = 9t i 7t j (2 t2) k
The curvature of a curve r(t) = 9t i 7t j (2 t2) k is 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2).
What do you mean by curvature?Curvature is a measure of the amount by which a curve deviates from being straight. It describes the degree to which a curve bends or twists at any point along its length.
In mathematics, curvature is a property of curves and surfaces that is used to describe their shape and local behavior. For example, the curvature of a circle is constant and is equal to the reciprocal of its radius. The curvature of a straight line is zero.
Curvature is a scalar quantity and is usually measured in units of inverse length, such as 1/meter. There are several ways to mathematically define and calculate curvature, including the concept of the curvature of a curve at a point, which is the rate of change of the direction of the tangent to the curve at that point.
The curvature of a curve is given by:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³
where r'(t) is the first derivative of r(t), r''(t) is the second derivative of r(t), and || || is the magnitude or length of a vector.
Given the curve r(t) = 9t i + 7t j + (2 t²) k, we can find its first and second derivatives:
r'(t) = 9 i + 7 j + 4t k
r''(t) = 4 k
So, the curvature of the curve r(t) is:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³ = ||9 i + 7 j|| × ||4 k|| / ||9 i + 7 j + 4t k||³ = 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2)
Since this expression depends on t, the curvature is a function of t, not a constant.
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Find the slope using points: (-10, 6) and (-5, 8)
Answer:
Step-by-step explanation:
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:
slope = (8 - 6) / (-5 - (-10)) = 2 / 5 = 0.4
So the slope of the line through the points (-10, 6) and (-5, 8) is 0.4
Find all real values of x that satisfy the equation (x^2 - 82)^2 = 324
The real values of x are -10 and 10
How to determine the real values of xFrom the question, we have the following parameters that can be used in our computation:
(x^2 - 82)^2 = 324
Take the square roots of both sides
So, we have
x^2 - 82 = 18
Add 82 to both sides of the equation
So, we have the following representation
x^2 = 100
Take the square root of both sides
x = -10 and x =10
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Find an equivalent fraction for each fraction using 12 as a common denominator of 4/6
The equivalent fraction to 4/6 with a denominator of 12 is:
4/6 = 8/12
How to find an equivalent fraction?If we have any fraction a/b, to find a equivalent fraction we just need to multiply both numerator and denominator by the same number (different than zero)
Here we want to find an equivalent fraction to 4/6, such that the new denominator is 12, then we can multiply both numerator and denominator by 2.
We will get:
4/6 = (2*4)/(2*6) = 8/12
So these two are equivalent fractions:
4/6 = 8/12.
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ind all values of for which this approximation is within of the right answer. assume for simplicity that we limit ourselves
Using the Taylor Remainder Theorem, the values of x ≤ 1.2145 for which this approximation is within 0.004458 of the right answer.
The function is f(x) = cos(x) at a=0.
The Taylor Series is:
f(x) = f(a) + f'(a)/1! (x - a) + f''(a)/2! (x - a)^2 + f'''(a)/3! (x - a)^3 + .............
Now, d/dx (cosx) = -sinx at a = 0
d/dx (cosx) = 0
d^2/dx^2 (cosx) = -cosx at a = 0
d^2/dx^2 (cosx) = -1
d^3/dx^3 (cosx) = sinx at a = 0
d^3/dx^3(cosx) = 0
d^4/dx^4 (cosx) = cosx at a = 0
d^4/dx^4 (cosx) = 1
d^5/dx^5 (cosx) = -sinx at a = 0
d^5/dx^5 (cosx) = 0
d^6/dx^6 (cosx) = -cosx at a = 0
d^6/dx^6 (cosx) = -1
Now putting the value
f(x) = 1 + 0/1! (x - 0) + (-1)/2! (x - 0)^2 + 0/3! (x - 0)^3 + 1/4! (x - 0)^4 + 0/5! (x - 0)^5 + (-1)/6! (x - 0)^6 + .............
Simplifying
f(x) = 1 - 1/2! x^2 + 1/4! x^4 - 1/6! x^6 + .............
|1/6! x^6| ≤ 0.004458
Multiply by 6! on both side, we get
x^6 ≤ 0.004458 × 6!
After solving
x ≤ 1.2145
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The complete question is:
Find T5(2): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a=0. Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.004458 of the right answer. Assume for simplicity that we limit ourselves to |x| ≤ 1.
Two line segments are parallel to each other. The first line segment has endpoints at (2, 3) and (1,9). The second line segment has endpoints at (5, 4) and (3,Y).
What is the value of y?
A
34
В.
16
10
6
If two line segments are parallel to each other and the first line segment has endpoints at (2, 3) and (1,9) while the second line segment has endpoints at (5, 4) and (3,Y), the value of y is:
16
Two lines are parallel if and only if they have the same slope. So, to find the value of y, we need to find the slope of the first line segment and use it to find the equation of the second line segment.
The slope of the first line segment can be found using the formula:
Slope = (y2 - y1) / (x2 - x1)Slope = (9 - 3) / (1 - 2) = 6 / -1 = -6)Since the two lines are parallel, they have the same slope, so we can use the slope to find the equation of the second line segment.
y - y1 = m(x - x1)y - 4 = -6(x - 5)Expanding the equation and solving for y, we get:
y = -6x + 34Now that we have the equation of the second line segment, we can use the x-coordinate of one of its endpoints (3) to find the corresponding y-coordinate.
y = -6(3) + 34y = 16So, the value of y is 16.
Complete Question:
"Two line segments are parallel to each other. The first line segment has endpoints at (2, 3) and (1,9). The second line segment has endpoints at (5, 4) and (3,Y).
What is the value of y?
A. 34
В. 16
C. 10
D. 6"
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PLEASE HELP 30 pts for this
a) The length of the base is 10 units and the height is 7 units. The area is 35 square units.
B) The length of the base is 10 units and the height is 6 units. The area is 30 square units.
C) The length of the base is 10 units and the height is 3 units. The area is 15 square units.
D) The length of the base is 4 units and the height is 11 units. The area is 22 square units.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The base and height are highlighted in each triangle.
A)
The length of the base is 10 units.
The length of height is 7 units.
The area of the triangle is 1/2 × 10 × 7 = 35 square units.
B)
The length of the base is 10 units.
The length of height is 6 units.
The area of the triangle is 1/2 × 10 × 6 = 30 square units.
C)
The length of the base is 10 units.
The length of height is 3 units.
The area of the triangle is 1/2 × 10 × 3 = 15 square units.
D)
The length of the base is 11 units.
The length of height is 4 units.
The area of the triangle is 1/2 × 11 × 4 = 22 square units.
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Cost of a theater ticket is an example of O a) O quantitative data. b) nominal data. O c) categorical data. d) either categorical or quantitative data.
The correct option: a) O quantitative data; defines the cost of the theater ticket.
Define the term quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data.
In most cases, the data is accompanied with measuring units, such as metres with in case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.Specifically, this phrase should refer to data that is composed of numerical quantities like measurements or counts, as opposed to qualitative data. Sometimes, less precisely, it is used to describe things when the variables are quantities instead of data derived from qualitative qualities, like height, weight, or price.Thus, the cost of any theater ticket defines an example of quantitative data.
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Which is a reasonable domain for the function f(x) = 10x + 8?
Choices:
0 < x < 6
0 < x < 24
0 < x < 64
0 < x < 248
The domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.
The domain of a function is the set of all possible input values for which the function is defined. For the function f(x) = 10x + 8, the domain will be all real numbers greater than or equal to 0. This can be seen by examining the equation: if x = 0, then f(x) = 8. Therefore, the domain of the function will be all x values such that x ≥ 0. To calculate the upper bound for the domain, we can solve for x by subtracting 8 from both sides of the equation, resulting in 10x = -8. Dividing both sides by 10 gives us x = -0.8. Therefore, the domain of the function f(x) = 10x + 8 will be all x values such that 0 ≤ x < 248.
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The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?.
The legs' lengths are 7 and 24 respectively. As a result, choice C is the right answer.
What is the Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most well-known triplets are (3,4,5).Completed question ;
The hypotenuse of a right triangle measures 25. Which could be the lengths of the legs?
A. 3 and 4
B. 5 and 5
C. 7 and 24
D. 10 and 15
Given data :
The hypotenuse of a right triangle measures 25.
A) 3²+4²= Square of the hypotenuse
25=Square of the hypotenuse
Hypotenuse=5 units
B) 5²+5²= Square of the hypotenuse
50=Square of the hypotenuse
Hypotenuse=5√2 units
C) 7²+24²= Square of the hypotenuse
625=Square of the hypotenuse
Hypotenuse=25 units
D) 10²+15²= Square of the hypotenuse
325=Square of the hypotenuse
Hypotenuse=√325 units
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which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?a. V = π∫dc[f(y)]^2dyb. V = π∫dc[f(y)]dyc. V = π∫dc[f(y)]dy^2d. V = π∫dc[f]2dy
The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π ∫dc [tex][f(y)]^{2}[/tex]dy.
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
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The volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π∫dc [f(y)]² dy
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
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Which is the graph of f(x) = 2(3)?
The graph of the exponential function:
f(x) = 2*(3)^x
Is the first one.
Which one is the graph of f(x) = 2*(3)^x?We want to find the graph of the exponential function:
f(x) = 2*(3)^x
To identify it, you can evaluate the function in some different values of x.
if x = 0
f(0) = 2*(3)^0 = 2
if x = 1
f(1) = 2*3^1 = 6
if x = 2
f(2) = 2*(3)^2 = 18
So we have the 3 points:
(0, 2), (1, 6), (2, 18)
The only graph that passes through these points is the first one, so that is the correct option.
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Can anyone tell me how to do this
The required dimensions in the figure are
angle FXD = 44 degreesEG = 14angle FZG = 21How to find the required dimensionsDG = FG = EG incenters
solving for angle FXD using SOH CAH TOA
The side XG is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
sin 22 = FG / XG
XG = 14 / sin 22
XG = 37.37
sin x = DG / XG = 14 / 37.37 hence x = 22
therefore angle FXD is 44 degrees
EG = DG = 14
angle FZG
< DYE + < FXD + < FZE = 180 sum of angles of a triangle
94 + 44 + < FZE = 180
< FZE = 180 - 94 - 44
< FZE = 42
< FZE = 2 * < FZG
< FZG = 42 / 2
< FZG = 21
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There are 13 yellow and 7 pink flowers in The garden Jacob picks 9 flower hóquei mano flawer are in The garden nos?
Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3. 143. 143, point, 14 for \piπpi.
units^3
3
Answer:
4 is there answer I think
Step-by-step explanation:
Which graph is a function of x?
Help me please
Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
The value of x is 15
The value of y is 7.
The unknown sides:
x = 15
5y - 3 = 33
y + 9 = 16
x - 2 = 13
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Similar triangles mean the ratios of the corresponding sides are equal.
Now,
(5y - 3)/(y + 9) = 30/x = 26/(x - 2)
Taking two ratios.
(5y - 3)/(y + 9) = 30/x
5xy - 3x = 30y + 270
Taking two ratios.
30/x = 26/(x - 2)
30x - 60 = 26x
30x - 26x = 60
4x = 60
x = 15
Now,
Substituting x = 15
5xy - 3x = 30y + 270
5 x 15 x y - 3 x 15 = 30y + 270
75y - 45 = 30y + 270
75y - 30y = 270 + 45
45y = 315
y = 7
Now,
x = 15
5y - 3 = 35 - 3 = 33
y + 9 = 7 + 9 = 16
x - 2 = 15 - 2 = 13
Thus,
x is 15 and y is 7.
The unknown sides are 15, 33, 16, and 13.
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determine if linear
An equation is considered linear if it is in the form of y=mx+b where m is the slope of the equation and b is the y-intercept.
Properties of Linear EquationsThere are several properties possessed by linear equations, which are as follows:
Adding and subtracting the numbers of the two sides will not change the value equation. Multiplication and division of the two sides does not change the value of the equation The value of the equation does not change if both sides are added or subtracted by the same number If an equation is moved, addition changes to subtraction, multiplication changes to division, and vice versa.Learn more about linear equation at
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Your realized income from your primary job is 2,034. 24/month. Your fixed expenses are 30% of your primary jobs realized income. You have a second job that pays $9. 50/hr with deductions of FICA (7. 65%), federal tax withhold (11. 5%), and a state tax withholding (7. 75%). If you want to save enough in the next 10 months to have an emergency fund that will cover 5 months using only 20% of your discretionary monies from your primary job, how many hours per month do you need to work at your second job to meet your monthly savings goal?
You need to work 84 hours per month at your second job to meet your monthly savings goal.
Fixed expenses = 2,034.24 x 30% = $610.72
Discretionary income = 2,034.24 - 610.72 = $1,423.52
Savings goal per month = $1,423.52 x 20% = $284.70
Net pay per hour = $9.50 - ($9.50 x 7.65%) - ($9.50 x 11.5%) - ($9.50 x 7.75%) = $7.33
Hours per month = $284.70 ÷ $7.33 = 84 hours.
To calculate, first find the number of your fixed expenses by multiplying your primary job income by 30%. This is $610.72. Then subtract your fixed expenses from your primary job income to find your discretionary income, which is $1,423.52. Multiply that by 20% to find the amount you want to save each month, which is $284.70.
Finally, divide that amount by your net pay per hour after taxes from your second job, which is $7.33, to find the number of hours you need to work, which is 84 hours.
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what is the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal and 8th octagonal numbers?
The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
What is triangle ?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4^2 = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4² = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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let -1 4 4 , 2 -7 -12 , and -2 6 . for what value of is in the plane spanned by and ?
Value of is in the plane spanned will be -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].
If y is on the plane covered by v1 and v2, v1 and v2 can be combined linearly to form y.
Y is equal to av1 plus bv2, where a and b are constants.
[4,-1,h] = a[1,2,-1] + b[-2,-1,1]
According to the laws of vector addition and multiplication, [4,-1,h] = [a - 2b,2a - b, -a + b]. A vector is equal if each of its components is equal.
4 = a - 2b
-1 = 2a - b
h = -a + b
From the first two equations, we can solve for a and b to obtain h:
a = -2
b = -3
h = -1
As we can see, -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].
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Full Question:
For what value of h is y in the plane spanned by v1 and v2?
an urn contains 5 red, 6 blue, and 8 green balls. if a set of 3 balls is randomly selected, what is the probability that each of the balls will be
The probability that each of the balls will be of a different color is approximately 0.084.
To calculate the probability that each of the balls will be of a different color, we need to consider all possible combinations of 3 balls from the urn. There are a total of 19 balls in the urn, so there are 19 choose 3, or 19!/(3! * (19-3)!) = 191817/3! = 969 possible combinations.
Of these 969 combinations, there are
5 choose 1 * 6 choose 1 * 8 choose 1 = 5 * 6 * 8 = 240 combinations where each of the 3 balls is of a different color. So, the probability that each of the balls will be of a different color is 240/969 = 0.084, or approximately 0.084.
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The area of the pool is 113.04 ft².
How to find the area of the pool?The diagram shows a circle inside a square. The circular surface is the pool and it is surrounded by the square deck. The diameter of the pool can be chosen from 12 to 24 feet.
The blue shaded region is the area of the pool. Therefore, let's find the area of the pool as follows:
area of the pool(area of a circle) = πr²
where
r = radius of a circleTherefore,
r = diameter / 2 = 12 / 2 = 6 feet
Hence,
area of the pool(area of a circle) = 3.14 × 6²
area of the pool(area of a circle) = 3.14 × 36
area of the pool(area of a circle) = 113.04 ft²
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write 6x+3y=24 in slope-intercept form
Answer:
the answer to it is y = -2x + 8
Step-by-step explanation:
Answer:
6x-3y=12 equals -3y=-6x+12 equals y=2x-4. In slope-intercept form; y=mx+c, m is slope and c is the y-value of the intercept; (0,y). So the slope is 2, and the y-intercept is -4 or (0,-4). answer.
Step-by-step explanation:
pls, tell me if wrong have a good day/night<3
Solve for
x
2
(
x
+
4
)
=
−
6
Answer: -7
Step-by-step explanation: multiply first then you have 2x+8= -6.
subtract 8 from both sides. you now have 2x= -14. divide by 2. X = -7 ( look at attached image if confused)
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=4x, y=5x2
Answer:
Step-by-step explanation:
y=0,16/5
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