Total 13,608,000 has length of eight are there containing exactly six distinct characters.
Total number of string = 10
The length of the string should be = 8
The distinct characters = 6
So the same character should be = 2
There are total 10 numbers in which 6 are distinct, so
[tex]^{10}P_{6}=\frac{10!}{(10-6)!}[/tex]
[tex]^{10}P_{6}=\frac{10!}{4!}[/tex]
[tex]^{10}P_{6}[/tex] = 3,628,800/24
[tex]^{10}P_{6}[/tex] = 151,200
Hence, strings of length eight are there containing exactly six distinct characters = 151,200 × 10 × 9
Strings of length eight are there containing exactly six distinct characters = 13,608,000
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HELP ME PLEASE I DONT UNDERSTAND!!!!!
Choose all the expressions that equal 36.
Responses
A (14⋅32)2−28open paren 1 fourth times 32 close paren squared minus 28
B 23 + (58−54)2 + 122 3 + ( 58 - 54 ) 2 + 12
C 92 − (43 + 32) + 3005092 − ( 4 3 + 3 2 ) + 300 50
D 124 + (82 − 42) − 99124 + ( 8 2 − 4 2 ) − 99
E 53 − (2. 5 × 30) − 20
The expressions that equal 36 is:
E) 53 − (2. 5 × 30) − 20
Calculation of Algebra ExpressionEvaluated the mathematical expressions in each response to see if they equal 36.
A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.
B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.
C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.
D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.
Thus, only the expressions listed in my previous answer equal 36.
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find a solution to the initial value problem, [hint: interpret the left-hand side of the equation as the derivative of the product of two functions.]
The value of a in the equation in the simplest form will be 17 / 6.
We are given an equation:
x³ / x^(1/6) = x^(a)
We need to evaluate the left hand side to find the value of a in the equation in simplest form.
We know that:
x^ (a) / x^ (b) = x^ ( a - b)
Using this, we get that:
x^ (3 - 1/6) = x^ (a)
x^ (17/6) = x^ (a)
By comparing the bases, we get the value of a as:
a = 17 / 6.
Therefore, the value of a in the equation in the simplest form will be 17 / 6.
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Write the number five million four thousand three hundred
in standard form.e.g 2000=2x10*3
Five million four thousand three hundred can be written in standard form as 5,004,300.
Write the number five million four thousand three hundred in standard form?5,004,300 = 5 x 10^6 + 4 x 10^3 + 3 x 10^0.The number is composed of five millions (5,000,000), four thousand (4,000) and three hundred (300).In standard form, all numbers are written as a multiple of a power of ten. To convert the number to a multiple of a power of ten, the millions, thousands and hundreds are split apart. The millions is written as 5x10^6. This is because one million is equal to 10^6, and there are five millions. The thousands is written as 4x10^3.This is because one thousand is equal to 10^3, and there are four thousands. The hundreds is written as 3x10^0. This is because one hundred is equal to 10^0, and there are three hundreds. When the three parts are combined, the number is written as 5x10^6 + 4x10^3 + 3x10^0.This can be simplified to 5,004,300. This is the standard form of the number five million four thousand three hundred.To learn more about standard form refer to:
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Answer:
The number five million four thousand three hundred can be written in standard form as `5,004,300`. In scientific notation, it can be written as `5.0043 x 10^6`.
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How many boxes would Alan have to sell to earn less than $2050?
Answer: Alan would have to sell less than 540 boxes.
Step-by-step explanation:
what is the difference between mtm and most?
Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Maximum Operating Stress, or MOST, is the highest amount of stress to which a structure can be subjected without experiencing permanent deformation.
Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Structural analysis techniques, such as finite element analysis and structural testing, are often used to determine this. When designing and building a structure, MTM must be considered because it is crucial for structural safety. Maximum Operating Stress, or MOST, is the highest stress to which a structure can be subjected without experiencing permanent deformation. This is often decided by running a stress study on the structure and taking into account the materials that were utilised to build it. The building must be able to sustain the anticipated loads throughout its lifespan, which is of utmost importance. Additionally, it is crucial to prevent structural deterioration over time. When designing and building a secure structure, MTM and Most must both be taken into account.
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The formula V = 1/3 πr²h gives the volume V of a cone with height h and base radius r.
Solve the formula for h.
Then find h when r = 2 inches and V = 45 cubic inches.
height = 10.74 inches
for steps refer attachment
The volume of a cone = (1/3) πr2h cubic units
Therefore, the volume of a cone = 20.93 cubic units
What is cone and formula?A cone has only one face, which is the circular base but no edges. A cone has only one apex or vertex point. The volume of the cone is ⅓ πr2h. The total surface area of the cone is πr(l + r) The slant height of the cone is √(r2+h2)Basically, the volume is equal to the product of the area and height of the shape. Volume = Base Area x Height. For shapes having flat surfaces such as cubes and cuboids, it is easy to find the volumeTo calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions togetherTo learn more about cone refers to:
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[BRAINLIEST] The first two terms of a geometric sequence are 27 and 9. What is the fourth term?
The required Fourth term of the given geometric sequence is 1.
What is geometric sequence?Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbours.
A geometric sequence always multiplies (or divides) by the same number to move from one term to the next. Therefore, 1, 2, 4, 8, 16,... is geometric since each step is a multiple of two; 81, 27, 9, 3, 1, 31... is geometric since each step is a multiple of three.
According to question:Sequesnce; 27 , 9
Common ratio(r) = 9/27 = 1/3
Then, we know that
[tex]a_{n}=ar^{n-1}[/tex]
So,
a₄ = 27(1/3)³
a₄ = 27/27 = 1
a₄ = 1
Thus, fourth term of the sequence is 1.
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Answer:
1
Step-by-step explanation:
1 is the correct one i got it right on test
Determine whether each value for x would make the inequality, -12x < 36, true or untrue.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-12x < 36}[/tex]
[tex]\huge\textbf{DIVIDE \boxed{\rm{\bf -12}} to both sides:}[/tex]
[tex]\mathsf{\dfrac{-12}{-12}x < \dfrac{36}{-12}}[/tex]
[tex]\huge\textbf{SIMPLIFY it:}[/tex]
[tex]\mathsf{x < \dfrac{36}{-12}}[/tex]
[tex]\mathsf{x > -3}[/tex]
[tex]\large\text{It is a(n) \boxed{\rm{o p e n e d}} circle SHADED to the RIGHT of your number line}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x > -3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
How do you find D when Diagonalizing a matrix?
The matrix D is important because it is the diagonal representation of the matrix A, which makes it easier to work with and understand.
When diagonalizing a matrix, the goal is to find a diagonal matrix (D) that is similar to the original matrix (A). This means that the matrix D will have the same eigenvalues as the matrix A and will be represented in a more simplified form.
To find the matrix D, you must first find the eigenvalues of the matrix A. These eigenvalues can be found by solving the characteristic equation, which is found by setting the determinant of the matrix (A - λI) to zero, where λ is the eigenvalue and I is the identity matrix.
Once the eigenvalues are found, you can then find the eigenvectors, which are non-zero vectors that satisfy the equation
=> Av = λv,
where v is the eigenvector.
Once you have both the eigenvalues and eigenvectors, you can then arrange them into the matrix D, where the eigenvalues are on the main diagonal and the eigenvectors are the columns.
To make sure that D is diagonal, you may need to scale the eigenvectors so that the entries are integers. This is called normalizing the eigenvectors.
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how many square feet of wallpaper will be used to cover a wall measuring 9 feet by 18 1/4 feet?
The area covered by the wallpaper will be 164.25 square feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, A wallpaper measures 9 feet by 18 1/4 feet.
Therefore, The area of the wallpaper will be,
= (9×73/4) square feet.
= 164.25 square feet.
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Given: △ABC, D∈ AB , E∈ BC F∈ AC , DE ∥ AC , AD ∥ FE AD=6, DE=5, AB=17 Find: AC
Please help ASAP!
Answer: The length of AC is approximately 5.196 units.
Step-by-step explanation:
To find the length of AC, we can use the fact that DE is parallel to AC and AD is parallel to FE, which forms a pair of corresponding angles. Therefore, we can set up a proportion using the fact that corresponding angles are congruent.
DE/AC = AD/FE
We know that DE = 5 and AD = 6, so we can substitute these values into the proportion:
5/AC = 6/FE
We can cross-multiply and solve for AC:
5 * FE = 6 * AC
Next, using the fact that triangle ABC is a triangle, we can use the Pythagorean theorem to find the value of FE.
AB^2 + BC^2 = AC^2
17^2 + BC^2 = (AC)^2
289 + BC^2 = AC^2
Now, substitute the value of FE into the equation we have,
5 * sqrt(AC^2 - 289) = 6 * AC
multiply the both sides of the equation by the reciprocal of 5,
sqrt(AC^2 - 289) = (6/5) * AC
Square both sides of the equation,
AC^2 - 289 = 36/25 * AC^2
subtract the left side from the right side
-289 = -(36/25) * AC^2
divide both sides by -(36/25)
AC = sqrt(289/(1-(36/25)))
AC = sqrt(289/11/25)
AC = sqrt(289/275)
AC = sqrt(289/11)
AC = sqrt(26)
AC = approx 5.196152422706632
Therefore, the length of AC is approximately 5.196 units.
Question in the picture
Answer:
Week 7
Step-by-step explanation:
Connie will have $170 in week 7, because in 3 weeks she will add $30 to her account.
Ling will have $117.5 in week 7, because in 3 weeks he will add $4.50 to his account.
170-117.5=52.5
52.5 is greater than 50, so it satisfies the question.
A patient took 400 mg of acetaminophen which ha the half life of 4 hour. How much acetaminophen will be in the patient in 4 hour? 2 hour? 1 hour?
If a patient took 400 mg of acetaminophen which has the half life of 4 hour, the amount of acetaminophen that will be in the patient is:
In 4 hour? 200 mgIn 2 hour? 100 mgIn 1 hour? 50 mgThe half-life of acetaminophen is 4 hours, which means that every 4 hours, half of the initial dose of 400 mg will still remain in the patient's body.
At 4 hours after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / 2 = 200 mg
At 2 hours after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / (2^(4/4)) = 200 mg / 2 = 100 mg
At 1 hour after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / (2^(4/4)) = 100 mg / 2 = 50 mg
In conclusion, the amount of acetaminophen in the patient's body decreases by half every 4 hours.
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f(x)=x^4-4x^3 5 estimate local extrema of each function and estimate the intervals on which the function is increasing and decreasing
The local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
Now, According to the question:
The function is :
[tex]f(x)=x^4-4x^3 +5[/tex]
Graphing Functions:
In order to graph a function, we first need to know the characteristics of that given function. On the other hand, we also need to simplify first the given function or rewrite it in general form for easier graphing.
Now, Graphing the function, we have
From the graph, the local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
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y = 3x + 4y, x + 2y = -1 using substitution
Answer:
x = 1
y = -1
Step-by-step explanation:
y = 3x + 4y
3x + 3y = 0
So, we have 2 equations that are
3x + 3y = 0
x + 2y = -1
Times the second equation by -3
3x + 3y = 0
-3x - 6y = 3
-3y = 3
y = -1
Now put -1 in for y and solve for x
x + 2(-1) = -1
x - 2 = -1
x = 1
Let's check
1 + 2(-1) = -1
1 - 2 = -1
-1 = -1
So, x = 1 and y = -1 is the correct answer.
out of 9799 wistles that a company manufactured, some were rejected for shipment to stores because they did not pass the quality controll standards of the company. estimate the number of wistles that did not pass
1862 are the number of wistles that did not pass.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that out of 9799 wistles that a company manufactured
19% were rejected for shipment to stores because they did not pass the quality controll standards of the company.
We have to find the number of wistles that did not pass
To find this we have to find 19% of 9799
19/100×9799
0.19×9799
1861.81
Hence, 1862 are the number of wistles that did not pass.
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In the figure, AE, BF, and CD are the medians of triangle ABC. How can you show that all three
medians intersect at point G?
Answer:
To show that all three medians of a triangle intersect at the same point, we can use the property that the midpoint of each median is the centroid of the triangle.
The centroid of a triangle is a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. This means that the centroid divides each median in a 2:1 ratio, with two thirds of the median length being on one side of the centroid and one third on the other side.
Since the centroid is the same for all three medians, it follows that all three medians must intersect at the same point, which is known as the centroid or the center of gravity of the triangle. This point is denoted by the letter G.
Therefore, we can conclude that all three medians of triangle ABC intersect at point G, which is the centroid of the triangle.
write an explicit formula for an, the nth term of the sequence 24,16,8
Answer:
f(n) = 32 - 8n
Step-by-step explanation:
24, 16, 8, 0
f(n) = 24 - 8 x (n-1)
f(n) = 32 - 8n
a frustum of a right circular cone is formed by cutting a small cone off of the top of a larger cone. if a particular frustum has a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches, what is its lateral surface area? (the lateral surface area of a cone or frustum is the curved surface excluding the base(s).)
The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches
The lateral surface area of the frustum is calculated using the given formula:
Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii² + height²)
Lower base radius of frustum = 6 inches
Upper base radius of frustum = 3 inches
Height of frustum = 4 inches
Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]
= π × 9 × √[(9 + 16]
= 9π × 5
= 45π sq. inches
Hence, the lateral surface area of the given frustum is 45π sq. inches
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If the average weight of a panda is about 120kg, state what information you can deduce from the 40 pandas in the sample. Male pandas weigh, on average, between 80kg and 140kg, and females weigh, on average, between 70kg and 120kg. From the box plot, state the gender of the pandas in the sample
The box plot of the the gender of the pandas in the sample is illustrated below.
The term box plot in math is defined as a chart tool used to quickly assess distributional properties of a sample and the so-called box-and-whiskers plot shows a clear indication of the quartiles of a sample as well of whether or not there are outliers.
Here we have given that Male pandas weigh, on average, between 80kg and 140kg, and females weigh, on average, between 70kg and 120kg.
The the data for the box plot is written as,
=> 70, 80, 120 and 140.
By using this data we have plotted the box plot for the gender of the pandas in the sample.
And we have predicted the following values through it.
Minimum =70
Q1=75
Median =100
Q3=130
Maximum =140
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formulas used to calculate the free cash flow to firm (fcff)?
(OCF): OCF = Net Income + Depreciation & Amortization - Changes in Working Capital, (CapEx): CapEx = Investment in Property, Plant & Equipment + Investment in Intangible Assets. therefore, (FCFF): FCFF = OCF - CapEx
The Free Cash Flow to Firm (FCFF) is a measure of a company’s cash flow available for distribution to shareholders and debt holders. To calculate FCFF, the following three steps are taken:
1. Calculate Operating Cash Flow (OCF): OCF is calculated by taking net income, adding back depreciation and amortization, and subtracting any changes in working capital.
2. Calculate Capital Expenditures (CapEx): CapEx includes investments in property, plant, and equipment, as well as any investments in intangible assets.
3. Calculate Free Cash Flow to Firm (FCFF): FCFF is calculated by subtracting CapEx from OCF. This figure represents the cash flow available for distribution to shareholders and debt holders.
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An object i traveling around a circle with a radiu of 14 centimeter. If in 20 econd a central angle of 1/2 radian i wpt out, what are the linear and angular peed of the object?
The circumference of the circle is given by C = 2 * π * r, where r is the radius. In this case, the circumference of the circle is 2 * π * 14 = 88 cm.
Let's call the linear speed of the object v. Then, in 20 seconds, the object travels a distance of v * 20. This distance is equal to the arc length of the central angle of 1/2 radian:
v * 20 = (1/2) * (C/2π) = (1/2) * (88/2π) = 22/π cm
Solving for v, we get:
v = (22/π) / 20 = 22 / (20π) cm/s
The angular speed ω can be found by dividing the central angle by the time it took to travel that angle:
ω = 1/2 / 20 = 1/40 rad/s
So the linear speed of the object is v = 22 / (20π) cm/s, and the angular speed is ω = 1/40 rad/s.
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list five vectors in span{1, 2 }. for each vector, show the weights on 1 and 2 used to generate the vector. do not make a sketch. V1 = ( 3 1 2 ) , V2 = ( −4 0 1 )
The five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
We are given that two vectors
v1 = ( 3 1 2 ) and v2 = ( −4 0 1 )
We have to list five vectors in the span {v1, v2}
Let us choose five sets of weights as:
w = {0, 0}, {1, 0}, {0, 1}, {1, 1}, {1, -1}
So, the five vectors are:
V1 = 0 (v1) + 0 (v2) = (0 0 0)
V2 = 1 (v1) + 0 (v2) = (3 1 2)
V3 = 0 (v1) + 1 (v2) = (-4 0 1)
V4 = 1 (v1) + 1 (v2) = (3-4 1+0 2+1) = (-1 1 3)
V5 = 1 (v1) - 1 (v2) = (3+4 1-0 2-1) = (7 1 1)
Hence, the five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
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components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur?
The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.
(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).
The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.
The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.
The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.
(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.
So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.
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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
A container hold 5 mL of fluid. Doe it hold more than or le than 500 mL of fluid?
The container holds 5 mL of fluid, which is less than 500 mL of fluid.
5 mL is much smaller than 500 mL, so the container holds less than 500 mL of fluid.
The numerator and denominator of a unit conversion factor have the same quantity in different units. Multiplying by a conversion factor has no effect on the number's inherent value because the factor is comparable to multiplying by 1.
The numerator is the intended unit, whereas the denominator is the supplied unit.
The primary guideline is to multiply when converting from a bigger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit. You will reduce the number, and as you are aware, division is all about reducing numbers.
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Justin Wallace started a business to offer development of online stores for small businesses. Record the following transactions in the journal of the business. Include an explanation with each journal entry
September 1 Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business
September 2 Purchased computer equipment on account, $9,800.
September 2
Paid cash for September's office rent of $3,900.
September 3 Recorded $6,400 revenue for services rendered to clients on account
Begin with the investment that Justin Wallace deposited in a business bank account.
September 1: Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business. Record the entry. (Record debits
first, then credits. Select the explanation on the last line of the journal entry table. Leave unused cells blank.)
Debit
Date
September 1:
Accounts :
Debit:
Credit:
On September 1 the debit and cash is as follows
Debit: Cash $32,000
Credit: Owner's Equity $32,000
How can we explain each statement?On September 1, Justin Wallace invested $32,000 cash into the business to start the business. This transaction increases the business's Cash account and increases the Owner's Equity account, which represents the owner's investment in the business.
September 2:
Debit: Accounts Payable $9,800
Credit: Cash $9,800
On September 2, the business purchased computer equipment on account for $9,800. This transaction increases the Accounts Payable account, which represents the business's obligation to pay the supplier, and decreases the Cash account.
September 2:
Debit: Cash $3,900
Credit: Rent Expense $3,900
On September 2, the business paid cash for September's office rent of $3,900. This transaction decreases the Cash account and increases the Rent Expense account, which represents the cost of renting office space.
September 3:
Debit: Service Revenue $6,400
Credit: Accounts Receivable $6,400
On September 3, the business recorded $6,400 revenue for services rendered to clients on account. This transaction increases the Service Revenue account, which represents the business's revenue from providing services, and increases the Accounts Receivable account, which represents the business's right to receive payment from clients for services rendered.
What is mensuration?Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.
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describe whether your percent yield for the product was high or low. if it was either high or low, explain what might have caused the high/low percent yield.
A product-focused process is commonly used to produce: high-volume, low-variety products.
There are other types of processes. This process is completely developed around the product, it is considered a continuous process with high volume of products that have low variety. It presents a high facility utilization (this is considered an advantage), organized by product, which receives a high-fixed price, but the variable cost is low.
Product focused prodction is one that focuses on improving the product by arranging sets of people into production lines to increase efficiency of production.
Equipment and people are grouped based on products being produced. For example in a manufacturing plant assembly lines are formed that focuses on one product.
This tends to be used for products that have low differentiation and are to be produced on high volume.
Example automobile plants, clothing factories, and food factories.
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what is the sum of all the elements from the first six rows of pascal's triangle?
The sum of all the elements present in the first six rows of the Pascal's triangle is equal to 63.
Pascal's triangle elements are represented by :
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Sum of all the elements of first six rows are:
First row : 1
Second row : 1 + 1 = 2
Third row : 1 + 2 + 1 = 4
Fourth row : 1 + 3 + 3 + 1 = 8
Fifth row : 1 + 4 + 6 + 4 + 1 = 16
Sixth row : 1 + 5 + 10 + 10 + 5 + 1 = 32
Sum of all the six row elements = 1 + 2 + 4 + 8 + 16 + 32
= 63
Therefore, the sum of all the elements of the first six row of Pascal's triangle is equal to 63.
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evaluate sin x cos y da where r [0, / 2][0, / 2]
According to trigonometry, the value of sin y cos x.
The term called trigonometry is defined as the type of mathematics that deals with the relationship between the sides and angles of triangles.
Here we know that the function is written as
=> sin x coy y
where r [0, 1/2] [0, 1/2]
Here by Using Fubini’s theorem we can write this as an iterated integral to get,
=> [tex]\int\limits^{1/2}_0\int\limits^{1/2}_0 {sinxcosy} \, da[/tex]
Here the Fubini's theorem states that the double integral over a region is equal to an iterated integral, which is computed in a similar manner with definite integrals of functions of single variable.
When we integrate the expression, then we get
=> [tex]\int\limits^{1/2}_0 {cos(1+y)sin(1+x)} \, da[/tex]
Again we have to integrate this one, then we get the value as,
=> sin y cos x.
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