To find the centroid of the region between the x-axis and the arch y=sin(x), 0≤x≤π. Then, we can use the formulas for the x-coordinate and y-coordinate of the centroid to find the centroid point.
The region between the x-axis and the arch y=sin(x) from x=0 to x=π looks like a half of a circle. To calculate the area of this region, we can integrate the function y=sin(x) from 0 to π:
A = ∫(0 to π) sin(x) dx = [-cos(x)](0 to π) = 2
The x-coordinate of the centroid is given by the formula:
X'= (1/A) ∫(0 to π) x*sin(x) dx
We can evaluate this integral using integration by parts:
u = x, dv = sin(x) dx, du = dx, v = -cos(x)
∫ xsin(x) dx = -xcos(x) + ∫ cos(x) dx = -x*cos(x) + sin(x) + C
Thus, the x-coordinate of the centroid is:
X' = (1/2) [-x*cos(x) + sin(x)](0 to π) = π/2
The y-coordinate of the centroid is given by the formula:
Y' = (1/A) ∫(0 to π) (1/2)sin^2(x) dx
We can use the identity sin^2(x) = (1-cos(2x))/2 to simplify the integral:
Y' = (1/4A) ∫(0 to π) (1-cos(2x)) dx = (1/4A) [x - (1/2)sin(2x)](0 to π) = 2/π
Therefore, the centroid of the region is located at the point (π/2, 2/π).
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Obtain the hexadecimal expression of decimal integer - 100 in the 8 bit signed binary integer system. What is the decimal integer expression of signed binary number 11010111? Obtain the 8bit fixed point binary number expression of decimal real number -3.47. The fixed point binary real number format is given by XXXX.XXXX
The hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system is "9C". The decimal integer expression of the signed binary number 11010111 is -41. The 8-bit fixed point binary number expression of decimal real number -3.47 is 10111011.
To obtain the hexadecimal expression of decimal integer -100 in the 8-bit signed binary integer system, we first need to represent -100 in binary form. Since the 8-bit signed binary integer system uses two's complement representation, we can find the binary representation of -100 by taking the two's complement of the binary representation of 100. The binary representation of 100 is 01100100, so the two's complement of this number is 10011100. Therefore, the binary representation of -100 is 10011100, and its hexadecimal expression is 9C.
To find the decimal integer expression of the signed binary number 11010111, we first need to determine its sign bit. Since the leftmost bit is a 1, the number is negative. To obtain its binary value, we can take the two's complement of the binary representation of 00101001, which is the binary representation of the absolute value of 11010111. The two's complement of 00101001 is 11010111, so the binary representation of -41 is 11010111 in the 8-bit signed binary integer system.
To obtain the 8-bit fixed point binary number expression of decimal real number -3.47, we first need to represent -3.47 in binary form. To do this, we can convert the integer part and the fractional part separately. The integer part of -3.47 is -3, which has a binary representation of 11111101 in the 8-bit signed binary integer system. The fractional part of -3.47 can be converted using the binary fraction representation method. Multiplying 0.47 by 2 yields 0.94, which has an integer part of 0. Multiplying 0.94 by 2 yields 1.88, which has an integer part of 1. Continuing in this way, we can obtain the binary fraction 01101101. Therefore, the binary representation of -3.47 is 11111101.01101101. To obtain the 8-bit fixed point binary number expression, we need to shift the binary point to the left by 4 bits, yielding 11010111.
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Solve for X. Options are: 9,10,11, and 12.
Answer: I think its 9 i could be wrong
Step-by-step explanation:
Answer:
Answer C. x=10
Step-by-step explanation:
Similar triangles
Given that the base lines are parallel, the base angles will be corresponding angles for the transversal and will be congruent. If one allows the up-down lines to continue to an intersection, one could form several triangles, all of which would be "Similar" to each other, due to their Angle-Angle congruence.
Similar triangles have all corresponding angles congruent between their triangles, and a consequence, all corresponding side-lengths between two triangles form a common proportion.
In other words, the ratio of the left side-length to the right side length is the same for both triangles.
Proportions
Despite that we don't actually have any full triangles, this concept extends for portions of a side length, so long as the bases are parallel.
So, since the ratio of the left side-length to the right side length is the same for both triangles, we can set up the following equation because both ratios are equal:
[tex]\dfrac{short~left~side}{long~left~side}=\dfrac{short~right~side}{long~right~side}[/tex]
[tex]\dfrac{6}{15}=\dfrac{x}{25}[/tex]
Solving a one-variable equation
From here, we're solving a single variable equation, where the variable only shows up once. To solve for x, we need to disconnect the "dividing by 25" from it. To undo that, we apply the opposite operation: multiplication.
Multiply both sides of the equation by 25...
[tex]\dfrac{6}{15}*25=\dfrac{x}{25}*25[/tex]
Notice on the right side of the equation that x is divided by 25, and then immediately multiplied by 25. This will bring us right back to the value of x.
[tex]\dfrac{6}{15}*25=x[/tex]
Computing without a calculator
On the left side of the equation, to calculate it without a calculator, we could factor each number, and cancel common factors between the numerator and denominator:
[tex]\dfrac{2*3}{3*5}*5*5=x[/tex]
Notice that there is a 3 in the numerator and denominator. Since there is no multiplication, this is effectively starting with 2, multiplying by 3, and then immediately dividing by 3, which will just bring us back to 2, before dividing by 5. So, the 3s cancel, as collectively, they won't change the value of 2.
[tex]\dfrac{2}{5}*5*5=x[/tex]
Now, we have the same process with the 5s. 2 is first divided by 5, and then immediately multiplied by 5 (before being multiplied by another 5). The division by 5 and the first multiplication by 5 will cancel, as they collectively won't change the value of the 2.
[tex]2*5=x[/tex]
Lastly, 2*5 is 10
[tex]10=x[/tex]
If you were allowed to use a calculator to calculate it, then that simplifies the work to getting that answer.
Para pintar el portón del parqueadero la obra compró un tarro de pintura que asegura alcanzar hasta para 8 m² de superficie el portón del parqueadero mide 2.5 m por 3.5 m es suficiente la pintura que compró Laura?
The jar of paint is not enough to cover the area of the parking lot.
Is a jar of paint enough to cover a parking lot?
In this problem we find that Laura wants to paint a parking lot, whose area is represented by a rectangle:
A = w · h
Where:
w - Width, in meters.h - Height, in meters.If w = 2.5 m and h = 3.5 m, then the area of the parking lot is:
A = (2.5 m) · (3.5 m)
A = 8.75 m²
The area of the parking lot cannot be covered by a jar of paint.
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ind the relative rate of change f′(t)f(t) at t=1. assume t is in years and give your answer as a percent. f(t)=ln(t2 1) round your answer to one decimal place. f′(1)f(1)=
The relative rate of change f′(t)/f(t) at t=1 can be found by first calculating the derivative of the function f(t) and evaluating it at t=1.
f(t) = ln(t^2 - 1)
f'(t) = 2t / (t^2 - 1)
f'(1) = 2 / (1^2 - 1) = 1
Next, we can evaluate f(1) and use the formula for relative rate of change:
f(1) = ln(1^2 - 1) = ln(0) = undefined
Therefore, the relative rate of change f′(1)/f(1) cannot be calculated.
The function f(t) is undefined at t=1 because ln(0) is undefined. This means that we cannot calculate the value of f(1) and hence, cannot determine the relative rate of change f′(1)/f(1).
This is an example of a situation where the relative rate of change cannot be determined due to the function being undefined or having a singularity at the point of interest.
It is important to be aware of such situations when dealing with calculus and to check for any potential issues with the function or point of interest before attempting to calculate the relative rate of change.
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Calculer l'aire d'une crêpe cuite sur une crêpière de 40 cm de diamètre
Answer:
1257cm²
Step-by-step explanation:
L'aire d'un cercle = [tex]\pi[/tex]r²
= [tex]\pi[/tex][tex]\frac{d}{2}[/tex]²
= [tex]\pi[/tex][tex]\frac{40cm}{2}[/tex]²
= [tex]\pi[/tex](20cm)²
= [tex]\pi[/tex]400cm²
= 1256.63706144cm²
help how do I factor with the given zero!
y=x^4+2x^3-20x^2+64x-32
0=2+2i
The factored function is given as follows:
[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]
How to factor the function?The function for this problem is defined as follows:
[tex]y = x^4 + 2x^3 - 20x^2 + 64x - 32[/tex]
The zeros are given as follows:
x = 2 + 2i.x = 2 - 2i. -> complex conjugate theorem, if a complex number is a zero, the conjugate also is:Hence the function is factored as follows:
[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)[/tex]
[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)[/tex]
[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c[/tex]
Hence the value of a is given as follows:
a = 1.
The value of b is given as follows:
-4 + b = 2
b = 6.
The value of c is given as follows:
8c = -32
c = -4.
Hence the factored expression is of:
[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]
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Is 2.5 greater than 1.75
Find the inverse laplace transform of ss2 12s 36= s --------------------- (s− )2 ss2 12s 36=f∣∣s 6 where f(s)=
he inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].
The inverse Laplace transform of f(s) = 6 / (s² + 12s + 36) first need to factor the denominator of f(s):
s² + 12s + 36 = (s + 6)²
We can rewrite f(s) as:
f(s) = 6 / [(s + 6)²]
The Laplace transform of the function [tex]6te^{(-6t)[/tex] has the Laplace transform:
[tex]L{6te^{(-6t)}[/tex] = 6 / (s + 6)²
The inverse Laplace transform of f(s), we get:
[tex]L^{-1}{f(s)}[/tex] =[tex]L^{-1}{6 / [(s + 6)^2]}[/tex]
= [tex]L^{-1}{6te^{(-6t)}[/tex]
= [tex]6(t-1)e^{(-6t)[/tex]
The inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].
The denominator of f(s) before we can compute the inverse Laplace transform of f(s) = 6 / (s2 + 12s + 36):
s² + 12s + 36 = (s + 6)²
F(s) may be rewritten as f(s) = 6 / [(s + 6)2].
The function 6te(-6t)'s Laplace transform has the following properties:
[tex]L{6te^{(-6t)}[/tex]= 6 / (s + 6)²
The inverse Laplace transform to the function f(s) we obtain:
L-1f(s) = L-16 / [(s + 6)²]
= L-16te(-6t)
= 6(t-1)e(-6t).
6(t-1)e(-6t) is the inverse Laplace transform of the function f(s).
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David is an hourly employee who moves to a different department but does
not receive a change in pay. How should his employee earnings record be
changed?
OA. His record should not be changed.
B. His pay schedule should change.
C. His personal information should change.
OD. His withholdings should change.
His record should not be changed. The correct option is A
What is employee ?
An individual who works for an employer pursuant to an employment contract, whether it be written or verbal, is referred to as an employee.
David is an hourly worker, and since his compensation is remaining the same, his employee earnings record shouldn't be altered. Even if he transfers to a different department, his hourly rate and rate of pay need to stay the same. The employee's record's department or job code may be the only thing to change in this scenario, but the earnings record itself is unaffected.
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PLEASE HELP 80 POINTS QUESTION DOWN BELOW
Answer:
the answer will be -3
Step-by-step explanation:
Out of 160 workers surveyed at a company, 29 walk to work. a. What is the experimental probability that a randomly selected worker at that company walks to work? b. Predict about how many of the 3800 workers at the company walk to work.
The experimental probability is 29/100 and the number of workers that walk is 1102
What is Experimental Probability?The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space.
The formula for this is given as;
P(E) = Number of occurrence of an event / Total number of times experiment is carried out.
a. Experimental probability = 29/100
b. To predict the total number of workers that walk, we can go as;
(29/100) * 3800 = 1102
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simplify 4x³ * 9x⁵
[tex]4x {}^{3} \times 9x {}^{5} [/tex]
find the minimum and maximum values of the function (,)=2 2f(x,y)=x2 y2 subject to the constraint 2 5=8
The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.
Taking partial derivatives of L with respect to x, y, and λ, we get:
∂L/∂x = 2xy^2 - 2λ
∂L/∂y = 2x^2y - 10λy
∂L/∂λ = 8 - 2x - 5y^2
Setting these equal to zero and solving for x, y, and λ, we get:
x = ±√(2λ/y^2)
y = ±√(2λ/5)
λ = xy^2/2
Substituting these back into the constraint equation, we get:
8 - 2x - 5y^2 = 0
8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0
Simplifying this equation, we get:
√(5λ) = √2
λ = 2/5
Substituting this back into the equations for x and y, we get:
x = ±1
y = ±1
Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):
f(1,1) = 1
f(-1,1) = 1
f(1,-1) = 1
f(-1,-1) = 1
Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
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The minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian as L(x,y,λ) = x^2 y^2 + λ(8 - 2x - 5y^2). We need to find the values of x, y, and λ that minimize or maximize L subject to the constraint 8 - 2x - 5y^2 = 0.
Taking partial derivatives of L with respect to x, y, and λ, we get:
∂L/∂x = 2xy^2 - 2λ
∂L/∂y = 2x^2y - 10λy
∂L/∂λ = 8 - 2x - 5y^2
Setting these equal to zero and solving for x, y, and λ, we get:
x = ±√(2λ/y^2)
y = ±√(2λ/5)
λ = xy^2/2
Substituting these back into the constraint equation, we get:
8 - 2x - 5y^2 = 0
8 - 2(±√(2λ/y^2)) - 5(±√(2λ/5))^2 = 0
Simplifying this equation, we get:
√(5λ) = √2
λ = 2/5
Substituting this back into the equations for x and y, we get:
x = ±1
y = ±1
Now we can evaluate the function f(x,y) = x^2 y^2 at the four possible points (1,1), (-1,1), (1,-1), and (-1,-1):
f(1,1) = 1
f(-1,1) = 1
f(1,-1) = 1
f(-1,-1) = 1
Therefore, the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
the minimum and maximum values of f(x,y) subject to the constraint 8 - 2x - 5y^2 = 0 are both equal to 1.
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HELP ME I DONT UNDERSTAND THIS EQUATION
write the value of each exspression
2²/2 by the power of 5
A.8
B.6
C. 1/8
D.-8
The value of the expression is 1/8. Option C
What are index forms?Index forms are simply defined as mathematical forms used in the representation of numbers that are too large or too small in more convenient ways.
Index forms are also referred to as scientific notation or standard forms.
The rules of index forms are;
Add the exponent values, when multiplying forms of like basesSubtract the exponent values, when subtracting forms of like bases.From the information given , we have;
2²/2⁵
Subtract the exponents
2²⁻⁵
2⁻³
Represent the value
1/8
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what is the probability of an event occuring 4 standard deviations from the mean in a normal distribution
The probability of an event occurring 4 standard deviations from the mean in a normal distribution is extremely low. Specifically, the probability of an event occurring 4 standard deviations from the mean in a normal distribution is approximately 0.006%.
In a normal distribution, 68% of the values are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.7% are within three standard deviations of the mean. So, an event that is 4 standard deviations from the mean is extremely unlikely to occur.
This is because the empirical rule states that in a normal distribution, approximately 68% of observations will fall within 1 standard deviation of the mean, 95% of observations will fall within 2 standard deviations of the mean, and 99.7% of observations will fall within 3 standard deviations of the mean. Thus, the probability of an observation falling more than 3 standard deviations from the mean is very small, and the probability of it falling 4 or more standard deviations from the mean is even smaller. This demonstrates the importance of considering outliers and extreme values when analyzing data in a normal distribution.
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The lengths of 2 sides of a triangle are 15 inches each. The third side measures 10 inches. What type of triangle is this? Explain your answer in geometric terms.
Answer:A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
This ultimately implies that, any polygon with three (3) lengths of sides is a triangle.
In Geometry, there are three (3) main types of triangle based on the length of their sides and these are;
Equilateral triangle.
Scalene triangle.
Isosceles triangle.
An isosceles triangle has two (2) congruent sides that are equal in length and two (2) equal angles while the third side has a different length.
Step-by-step explanation:
Need help with question
Answer:
-1 ± 2√10
Step-by-step explanation:
first of all, do -2 on top divided by 2 on bottom to get 1st part of answer -1.
now (2√40) / 2 = 1√40 which just equals √40.
√40 = √(4 X 10) = √4 X √10 = 2 X √10 = 2√10.
so our final answer becomes -1 ± 2√10
a baseball team has a 20-person roster. a batting order has nine people. how many different batting orders are there? answer: question 8 options: 60949324800 670442572800 362880 7257600
Thus, there are 60,949,324,800 different batting orders possible. The correct option is A.
The number of different batting orders for a 20-person baseball roster with 9 people in each batting order can be calculated using the concept of permutations. In this case, we have 20 players to choose from, and we need to arrange 9 of them in a specific order.
The formula for permutations is: P(n, r) = n! / (n - r)!, where n is the total number of items (20 players), r is the number of items to be arranged (9 players), and ! denotes the factorial of a number (the product of all positive integers up to that number).
Applying this formula for your problem:
P(20, 9) = 20! / (20 - 9)!
Calculating the factorials:
20! = 2,432,902,008,176,640,000
11! = 39,916,800
Now, divide the factorials:
P(20, 9) = 2,432,902,008,176,640,000 / 39,916,800
P(20, 9) = 60,949,324,800
So, there are 60,949,324,800 different batting orders possible. The correct option is A.
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Shape C is rotated 90° clockwise about the point (1, 3) to give shape D. Use this information to complete the sentence below. Shape D can be rotated about the point y 9 8- 7- 6+ 5- 4- 3- 2- 14 с shape C. D O clockwise to give
Shape D can be rotated [tex]\underline{270^{o}}[/tex] clockwise about the point (1, 3) to give shape C.
To find the values of blanks, the rotational relationship between Shape C and Shape D should be considered. Shape C is rotated 90° clockwise about the point (1, 3) to give Shape D.
We can conclude that Shape D can be rotated 270° because a full rotation is [tex]360^{o}[/tex]. It means turning around until your point in same direction again.
So, C [tex]\xrightarrow{90^{o}\ clockwise }[/tex] D [tex]\xrightarrow{270^{o}\ clockwise }[/tex] C
The center if rotation should stay the same.
This means that if we rotate Shape D 270° clockwise about the point (1, 3), we will obtain Shape C.
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the quadratic $x^2-3x 1$ can be written in the form $(x b)^2 c$, where $b$ and $c$ are constants. what is $b c$?
The value of b = -3/2 and c = -5/4
To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:
(x + b)² = x² + 2bx + b²
Comparing this to the given expression x² - 3x + 1, we see that we need:
2bx = -3x, so b = -3/2
b² + c = 1, so substituting b = -3/2 gives:
(9/4) + c = 1
so c = 1 - 9/4
= 4/4 - 9/4
= -5/4
The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).
Therefore, the value of b = -3/2 and c = -5/4
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Given question is incomplete, the complete question is below
the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?
Find the value of x.
log 3 x = 4
Answer:
81
Step-by-step explanation:
We can solve for x by first using the definition of logarithms, which states that log base a of b is equal to c if and only if a raised to the power of c equals b.
Using this definition, we can rewrite the given equation as:
3^4 = x
Simplifying this expression, we get:
81 = x
Therefore, the value of x is 81.
how to identify the constant of proportionality based on a verbal description of the proportional relationship practice
To identify the constant of proportionality based on a verbal description of the proportional relationship, we need to look for keywords that suggest proportionality.
These keywords include "directly proportional," "inversely proportional," "proportional to," or "varies directly/inversely." Once we have identified the keywords that suggest proportionality, we can then look for the quantities that are related and the specific values they take. From there, we can set up a proportion and solve for the constant of proportionality.
For example, if we are told that the time it takes to complete a task is directly proportional to the number of workers, and it takes 6 workers 4 hours to complete the task, we can set up the proportion: time/number of workers = constant of proportionality. Plugging in the values we have, we get 4/6 = k, which simplifies to 2/3 = k.
Therefore, the constant of proportionality in this case is 2/3, and we can use this to find the time it would take with a different number of workers.
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How do you solve 4.62 times 3.78 in standard algorithm
The value of 4.62 times 3.78 equals 17.4828.
We have to find 4.62 times 3.78 in standard algorithm
To multiply 4.62 by 3.78 using the standard algorithm, follow these steps:
4.62
x 3.78
------
27756 (multiply 8 by 2)
+184368 (multiply 7 by 2, then 8 by 6, and add to the previous result)
-------
17.4828 (the final answer)
Hence, the value of 4.62 times 3.78 equals 17.4828.
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A water storage tank is in the shape of a hemisphere (half a sphere). If the radius is 19 ft, approximate the volume of the tank in cubic feet.
Answer: 14,358 cubic feet
Step-by-step explanation:
Volume of hemisphere = 0.5 x volume of sphere
Volume of hemisphere = 0.5 x 4/3 pi r^3
Volume of hemisphere = 0.5 x 4/3 pi 19^3
Volume of hemisphere = 0.5 x 4/3 pi 6859
Volume of hemisphere ≅ 14,358 cubic feet
josiah is a teacher and takes home 44 papers to grade over the weekend. he can grade at a rate of 8 papers per hour. write a recursive sequence to represent how many papers josiah has remaining to grade after working for n hours.
The recursive sequence to represent how many papers Josiah has remaining to grade after working for n hours is aₙ = aₙ₋₁ - 8
Let aₙ be the number of papers Josiah has remaining to grade after working for n hours.
In the first hour, Josiah grades 8 papers, so the number of papers remaining is:
a₁ = 44 - 8 = 36
In the second hour, Josiah grades another 8 papers, but this time he is grading papers from the remaining pile:
a₂ = a₁ - 8
= 36 - 8 = 28
In general, after n hours, Josiah will have graded 8n papers, and the number of papers remaining to be graded will be:
aₙ = aₙ₋₁ - 8
This is because he starts with a₀ = 44 papers, and each hour he grades 8 papers, reducing the number of papers remaining by 8.
Therefore, the recursive sequence to represent how many papers Josiah has remaining to grade after working for n hours is aₙ = aₙ₋₁ - 8
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The equation A = P(1+0.0430) represents the amount of money earned on a savings account with 4.3% annual simple interest. If the account balance is $15,160 after 12 years, what is the value of
the principal?
O$1,211
O $1,228
O $9,000
O $10,000
The amount of the principal investment is the sum of $10,000. The Option D is correct.
How do we calculate our principal investment?The equation "A = P(1+0.0430t)" represents the amount of money earned on a savings account with 4.3% annual simple interest, where a is the amount after t years, p is the principal investment, and 0.043 is the interest rate.
Given that the amount after 12 years is equal to $15,160, we can use the equation to solve for the principal investment:
[tex]\sf A = P(1+0.0430t)[/tex]
[tex]\sf \$15160 = P(1+0.043\times12)[/tex]
[tex]\sf\$15160 = P(1 + 0.516)[/tex]
[tex]\sf \$15160= P \times 1.516[/tex]
[tex]\sf P = \dfrac{\$15160}{1.516}[/tex]
[tex]\sf P = \$10000[/tex].
Therefore, the amount of the principal investment is the sum of $10,000.
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Volume of Prisms. I need help with finding the volume please
The volume of the prism is 259 units³.
How to find the volume of a prism?The volume of the prism can be calculated as follows:
volume of a prism = base area × height
The prism is a triangular base prism. The area of the base of the prism is 37 units² and the height of the prism is 7 units.
Therefore,
Base area of the prism = 37 units²
height = 7 units
Hence,
volume of a prism = 37 × 7
volume of a prism = 259 units³
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find all solutions of the equation x 2 − 2 x 8 = 0 and express them in the form a b i
The solutions of the equation [tex]x^2 - 2x - 8 = 0[/tex] expressed in the form a + bi are 4 + 0i and -2 + 0i
To find the solutions of the equation [tex]x^2 - 2x - 8 = 0,[/tex] we can use the quadratic formula:
[tex]x = (-b \pm \sqrt{(b^2 - 4ac)) / (2a), }[/tex]
where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c = 0.[/tex]
In this case, the coefficients are:
a = 1
b = -2
c = -8
Plugging these values into the quadratic formula, we get:
[tex]x = (-(-2) \pm \sqrt{ ((-2)^2 - 4(1)(-8))) / (2(1)) }[/tex]
= (2 ± √(4 + 32)) / 2
= (2 ± √36) / 2
= (2 ± 6) / 2
We have two possible solutions:
x = (2 + 6) / 2 = 8 / 2 = 4
x = (2 - 6) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation[tex]x^2 - 2x - 8 = 0[/tex] are x = 4 and x = -2.
Expressing them in the form a + bi, where a and b are real numbers and i is the imaginary unit, we have:
x = 4 + 0i
x = -2 + 0i
Since both solutions are real numbers, there is no need to express them in the form a + bi. The solutions are 4 and -2.
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A rectangular certificate is 9 inches wide and 7 inches tall. What is its area?
Answer: 45 in.
Step-by-step explanation:
Step 1:
Length × Width = Area How to find Area
Step 2:
5 in. × 9 in. Equation
Answer:
45 in. Multiply
Which graph shows the line of best fit for the data ?
Answer:
Top right
Step-by-step explanation:
It goes through most of the plotted data