Using similar triangles, we can set up the following proportion:
(tree height + Donna's height) / (distance from Donna to mirror) = Donna's height / (distance from mirror to top of tree)
Let h be the height of the tree.
Then we have:
(h + 6) / 6.6 = 6 / (37 + h)
Multiplying both sides by (37 + h) and simplifying, we get:
h + 6 = 222 / 6.6 - h / 6.6
Multiplying both sides by 6.6 and simplifying, we get:
6.6h + 39.6 = 222 - h
Solving for h, we get:
7.6h = 182.4
h = 24
Therefore, the height of the tree is approximately 24 feet.
progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Which of the following radical expressions has an absolute value symbol in its simplified form?
√81x
O √64x³
O 16x
O V-125x³
Answer:
[tex] \sqrt[4]{16x {}^{4} } [/tex]
giving brainlist! ⚠
Solve this Second Order Differential Equations, (but don't use Ai) coz I know if it's from there
The solution to the homogenous equation is M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n
What is the solution to the second order differential equation?To solve the second order differential equation:
d²M/dn² + 2n (dM/dn) = n
We can use the method of undetermined coefficients. First, we assume a particular solution of the form M = An + B, where A and B are constants to be determined. We then find the first and second derivatives of M:
dM/dn = A
d²M/dn² = 0
Substituting these into the differential equation, we get:
0 + 2n(A) = n
Solving for A, we find:
A = 1/2
So the particular solution is:
M = (1/2)n + B
To find B, we can substitute the particular solution into the original differential equation:
d²M/dn² + 2n (dM/dn) = n
0 + 2n(1/2) = n
So the homogeneous solution is:
Mh = C1n + C2
where C1 and C2 are constants to be determined. The general solution is the sum of the homogeneous and particular solutions:
The solution to the homogenous equation is;
M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n
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using (4.6), find the polynomial p2(x) that interpolates the following data. in each case, simplify (4.6) as much as possible. g
The required Lagrangian form of the polynomial p2(x) is given by
[(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2
The Lagrangian form of the interpolating polynomial p2(x) corresponding to the data in the table is,
p2(x) = L0(x) × y0 + L1(x) ×y1 + L2(x) ×y2
where Li(x) for i = 0,1,2 are the Lagrange basis polynomials defined by,
L0(x) = (x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)
L1(x) = (x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)
L2(x) = (x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)
Substituting the values of xi and yi from the table, we get,
p2(x)
= [(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2
Note that the indices of xi and yi in the Lagrange basis polynomials correspond to the indices of the data points in the table.
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The given question is incomplete, I answer the question in general according to my knowledge:
Write the Lagrangian form of the interpolating polynomial p2 corresponding to the data in the table below
x0 y0
x1 y1
x2 y2
Ezra works for a company that is headquartered in Canada.
One morning, he receives two checks from the company. The first
is his paycheck for 720 Canadian dollars and the second is a bonus
check for 225 Canadian dollars. He receives 600 U.S. dollars for sup
the first check. What amount, in U.S. dollars, will Ezra receive for his bounus check?
Amount, in U.S. dollars, will Ezra receive for his bounus check Ezra will receive 180 U.S. dollars for his bonus check.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make sense of numerical data by summarizing it and drawing conclusions from it. Statistics is used in a wide range of fields, from social sciences to medicine, engineering, and business.
To convert Canadian dollars to U.S. dollars, we need to know the exchange rate. Let's assume that the exchange rate is 1 Canadian dollar = 0.80 U.S. dollars.
First, we need to convert Ezra's paycheck from Canadian dollars to U.S. dollars:
720 Canadian dollars * 0.80 U.S. dollars/Canadian dollar = 576 U.S. dollars
So Ezra receives 576 U.S. dollars for his paycheck.
To find out how much he will receive for his bonus check, we need to convert it from Canadian dollars to U.S. dollars:
225 Canadian dollars * 0.80 U.S. dollars/Canadian dollar = 180 U.S. dollars
Therefore, Ezra will receive 180 U.S. dollars for his bonus check.
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Choose the item that has measurable volume.
cereal box
an index card
piece of paper
a napkin
Answer:
For an item to have measurable volume, the item must have space and must have a closed surface. Therefore, the item is the cereal box.
Step-by-step explanation:
hope its right!
A triangular piece of land has base 20meter and height 10meter. if the land is 15 dolar per square meter what is its value
The value of a triangular piece of land is, 1500 dollars.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We know that;
Area of triangular piece of land = 1/2 x length x height
Here, Length = 20m
Height = 10m
Hence, We get;
Area = 1/2 x 20 x 10
= 100 cm²
Since, The land is 15 dollar per square meter.
Hence, The total value is,
Value = 15dollars x 100
= 1,500 dollars
Thus, The value of a triangular piece of land is, 1500 dollars.
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Question
Simplify:
(-11r² +8rs + 4s² ) − (11r² − 4rs – 3s²).
Provide your answer below:
Step-by-step explanation:
To simplify the expression:
(-11r² +8rs + 4s² ) − (11r² − 4rs – 3s²), we need to perform the subtraction operation by distributing the negative sign to each term inside the parentheses:
-11r² + 8rs + 4s² - 11r² + 4rs + 3s²
Now we can combine like terms by adding or subtracting coefficients of the same variables:
(-11r² - 11r²) + (8rs + 4rs) + (4s² + 3s²)
Simplifying further, we get:
-22r² + 12rs + 7s²
Therefore, the simplified expression is -22r² + 12rs + 7s².
Suzanna says that 2/3 and 60% are equal. Is
she correct? Justify your thinking.
Answer:
2/3 is not equal to 60%
Step-by-step explanation:
2/3 of is equal to 66.6%
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Question reads..}[/tex]
[tex]\rm{Suzanna \ says \ that \ \dfrac{2}{3} \ and\ 60\% \ are \ equal.\ Is\ she \ correct?}\\\\\rm{Justify \ your \ thinking.}[/tex]
[tex]\huge\textsf{Let us make the problem easier to solve}[/tex]
[tex]\mathtt{\dfrac{2}{3} = 2\div 3 = 0.666667}\\\\\mathtt{ 0.666667\times100 = 66.67\%}\\\\\mathtt{\dfrac{2}{3} \approx 66.67\%}\\\\\\\\\mathtt{\dfrac{2}{3}\neq 60\%}[/tex]
[tex]\huge\text{Is she correct? Justify your thinking.}[/tex]
[tex]\huge\boxed{\mathtt{No, \she\ is \ incorrect\ because\ \dfrac{2}{3}\ is}}\\\\\huge\boxed{\mathtt{equivalent\ to\ approximately \ 66.67\%}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Your local hardware store is having a 35% off everything sale. But Wait!!!! For the next 3 days they
are offering a coupon to save an additional 30%. If the store applies the sale price then applies the
coupon, find each of the following. Let a represent the price of any item. Round all decimals to 4
decimal places.
Write an function that will directly calculate the final price on an item.
What percentage is actually being saved by the costumer?
1. The function that will directly calculate the final price on an item is " a * 0.455".
2. The percentage that is actually being saved by the custumer is 54.5%.
Function which will calculate the final price on an item:The final price of an item after the discount and coupon can be calculated using the following function:
Final price = a * (1 - 0.35) * (1 - 0.30)
Final price = a * 0.455
This function first applies the 35% discount, which reduces the original price (a) to 65% of its value. Then, it applies the 30% coupon to the discounted price, which reduces it to 70% of its value.
What percentage is actually being saved by the custumer?Original price = $100
Sale price (35% off) = $100 * (1 - 0.35)
Sale price (35% off) = $65
Final price = $65 * (1 - 0.30)
Final price = $45.50
Savings = $100 - $45.50
Savings = $54.50
Percentage saved:
= (Savings / Original price) * 100%
= ($54.50 / $100) * 100%
= 54.5%
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In her geology class, Nora learned that quartz is found naturally in a variety of colors. Nora's teacher has a giant box of colorful quartz pieces that he and his students have collected over the years. Nora picks a piece of quartz out of the box, records the color, and places it back in the box. She does this 18 times and gets 3 purple, 2 yellow, 5 white, and 8 pink quartz pieces.
Based on the data, what is the probability that the next piece of quartz Nora picks will be yellow?
Write your answer as a fraction or whole number.
The probability that the next piece of quartz Nora picks will be yellow is [tex]\frac{1}{9}[/tex].
What is probability?
Probability is a tool that can be used to calculate the likelihood of an event. It can only be used to assess the likelihood that an event will take place. a scale where 0 represents impossibility and 1 represents a particular occurrence.
We are given that Nora picks pieces 18 times from the box and gets 3 purple, 2 yellow, 5 white, and 8 pink quartz pieces.
So, for the event,
⇒ Probability of yellow pieces = [tex]\frac{2}{18}[/tex]
⇒ Probability of yellow pieces = [tex]\frac{1}{9}[/tex]
Hence, the probability that the next piece of quartz Nora picks will be yellow is [tex]\frac{1}{9}[/tex].
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The radius of a circle is 5 in. Find its area in terms of pi
Answer:
Step-by-step explanation:
[tex]A=\pi r^2=\pi \times 5^2=25\pi[/tex]
Solution: [tex]A=25\pi[/tex] units²
A famous ice cream business releases data showing that 75% of pistachio ice cream is purchased by people above the age of 65. Which statement is true?
A. The first quartile is 65.
B. The minimum age of pistachio ice cream purchasers is 65.
C. The third quartile is 65.
D. The interquartile range is 65.
Answer: A. The first quartile is 65.
Reason:
25% of the data is below the 1st quartile.
75% of the data is above the 1st quartile.
The third quartile is 65 is the true statement.
Option C is the correct answer.
We have,
The first quartile (Q1) represents the 25th percentile of the data, meaning 25% of the data falls below this value.
The third quartile (Q3) represents the 75th percentile of the data, meaning 75% of the data falls below this value.
Since 75% of pistachio ice cream is purchased by people above the age of 65, it means that the third quartile (Q3) of the data is 65.
Thus,
The third quartile is 65 is true.
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During their softball season, Jessica had double the amount of hits Sam had. If Jessica and Sam together had 63 hits, write and solve an equation to find the amount of hits each girl had. (IM IN A HURRY WILL GIVE BRAINLIEST IF ANSWERED)
Sam had 21 hits, and Jessica had 42 hits
What is Linear Equatiοn?A linear equatiοn is a mathematical equatiοn that can be written in the fοrm οf "ax + b = c", where "a", "b", and "c" are cοnstants and "x" is the variable being sοlved fοr. Linear equatiοns describe a straight line relatiοnship between variables.
Let's use variables tο represent the number οf hits that Jessica and Sam had.
Let's say that Sam had x hits.
Accοrding tο the prοblem, Jessica had dοuble the amοunt οf hits Sam had, sο Jessica had 2x hits.
Tοgether, they had 63 hits, sο we can write an equatiοn:
x + 2x = 63
Simplifying the equatiοn:
3x = 63
Dividing bοth sides by 3:
x = 21
Sο Sam had 21 hits, and Jessica had dοuble that amοunt, οr 42 hits.
Therefοre, Sam had 21 hits, and Jessica had 42 hits
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Is (2+8), 3y a constant?
Step-by-step explanation:
3y is not a constant for it has a variable.
However, (2+8) = (10) is a constant
Shania is having trouble understanding her algebra assignment. To help her understand, she asks Mark why x2 x y3 is not equal to (xy)5. Which of the following responses would be best for Mark to give?
Answer:
In 2x*3y, you must multiply each term together. 2*3=6 and x*y=xy. So, 2x*3y=6xy.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Match the equation with the graph
Answer choices are:
Y=3x -5
Y= x
Y= -5x + 3
Y= -x + 2
Y= x - 1
Y= 2x + 2
Y= (x + 3)^2 -2
Y= 1/2x + 2
Y= x
Assume that you are a garment manufacturer. Based on the marker, you need to
order 3,500 yards of fabric in 60 inches with a density of 200 gm/m² to fulfill your
order. The fabric mill is only able to quote you fabric price in weight at S$6 per kg
and he can meet your 200gm/m² density and the 60 inches fabric width
requirements. How much fabric must you order in kg? What is the total cost of the
fabric purchased?
I NEED HELP ASAP
Answer:
The garment manufacturer must order 640.56 kg of fabric and the total cost of fabric purchased would be S$3,843.36.
Explanation:
To find out how much fabric must be ordered in kg, we need to first convert the yards to meters, then calculate the weight of the fabric in kg.
1 yard = 0.9144 meters 3,500 yards = 3,202.8 meters
Density = 200 gm/m² = 0.2 kg/m²
Total weight of fabric = 3,202.8 meters x 0.2 kg/m² = 640.56 kg
Therefore, the garment manufacturer must order 640.56 kg of fabric.
The cost of fabric per kg is S$6.
Therefore, the total cost of fabric purchased is:
Total cost = 640.56 kg x S$6/kg = S$3,843.36
Paint is used to create a circle on a square canvas. The diagram shows the dimensions, in feet (ft), of the canvas. The shaded part of the diagram represents the part of the canvas that is painted blue. which value is closest to the area, in square feet, of the part of the canvas that is painted blue?
a) 5.2
b) 7.7
c) 17.2
d) 26.6
Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.
Explain about the circle:A circle is an a double shape made up of a collection of points that are spaced regularly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the defined distance between each point and the origin is referred to as the radius.
Given data:
Radius of the circle r = 6/2 = 3 ft.canvas is painted with blue colour leaving the circular part.Area of painted region = Area of square - Area of circle
Area of painted region = side² - π*r²
Area of painted region = 6² - 3.14*3²
Area of painted region = 36 - 28.26
Area of painted region = 7.74
Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.
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I’ve been having trouble solving #54 can anyone help me?
The summation of the values in the table is -0.65
How to get the value of the summation?Just take the sum between the products of the values in the correspondent rows, the first row gives:
-1*0.999 = -0.999
The second row gives:
349*0.001 = 0.349
Then the sum between these two gives:
-0.999 + 0.349 = -0.65
That is the summation.
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Juniper Middle School serves students in 7th and 8th grades.
a. 55% of the students at Juniper are in the 8th grade. The remaining 117 students are in 7th grade. How many
students attend Juniper Middle School?
b. In September, there was an average of 4.8 daily unexcused absences. In October, this daily average was 6. By what
percent did the average daily unexcused absences change from September to October?
There are 260 students who attend Juniper Middle School. The average daily unexcused absences increased by 25% from September to October.
How to calculate . How many students attend Juniper Middle Schoola. Let's assume that the total number of students at Juniper Middle School is "x."
Given that 55% of the students are in the 8th grade, we can write:
0.55x = number of 8th grade students
And since the remaining 117 students are in 7th grade, we can write:
x - 0.55x = 117
0.45x = 117
x = 260
Therefore, there are 260 students who attend Juniper Middle School.
b. To find the percent change from September to October, we can use the formula:
percent change = ((new value - old value) / old value) x 100%
Substituting the given values, we get:
percent change = ((6 - 4.8) / 4.8) x 100%
percent change = (1.2 / 4.8) x 100%
percent change = 25%
Therefore, the average daily unexcused absences increased by 25% from September to October.
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 155 grams of a radioactive isotope, how much will be left after 5 half-lives?
Answer: After each half-life, the amount of radioactive isotope will be reduced to half its previous amount. Therefore, after 5 half-lives, the amount remaining will be:
155 grams / 2^5 = 4.84 grams (rounded to two decimal places)
So, after 5 half-lives, approximately 4.84 grams of the radioactive isotope will be left.
Step-by-step explanation:
Find the volume of the composite. The solid below is a square prism with a cylinder
cut out of it. Round to the nearest whole centimeter.
Answer:
17,242 cm³
Step-by-step explanation:
Step 1:
Volume of square prism = (area of base) * height
Volume of square prism = (25 * 30) * 25
Volume of square prism = 750 * 25
Volume of square prism = 18,750 cm³
Step 2:
Volume of cylinder = (area of base) * height
Volume of cylinder = (π * (8/2)²) * 30
Volume of cylinder = 16π * 30
Volume of cylinder = 480π
Volume of cylinder ≈ 1,508 cm³
Step 3:
Volume of composite = (Volume of square prism) − (Volume of cylinder)
Volume of composite = 18,750 cm³ − 1,508 cm³
Volume of composite = 17,242 cm³
A random sample of 36 exam scores is taken from the normally distributed population with unknown mean and a populations standard deviation know and equal to 3. The sample mean score is 68. Find a 90% confidence interval estimate for the population mean of exam scores.
Please round to the nearest hundredths and write your answer in the form ( , ); for example (31,34) or (25,46). Do not type in any extra spaces.
Hope this answer helps.
Chase decided he was going to start selling cups of lemonade this weekend too. He calculated his profit using the given table
number of cups sold (c) 15 20 25 30 35
total profit earned S(c) $5.05 $9.05 $13.05 $17.05 $21.05
$5.05 15
+ $9.05 20
+ $13.05 25
+ $17.05 30
+ $21.05 + 35
$65.25 125
NUMBER OF CUPS SOLD :-125
TOTAL PROFIT:- $65.25
PLEASE HELP IM SO CONFUSED LATE ASSIGNMENT
Answer:
34%
Step-by-step explanation:
80+10 = 90 (The number of people who do not like meat on their pizzas
Add all the numbers (150+25+80+10) = 265
You do # of people who don't like meat on their pizzas / # of total people
90/265 = 0.339622642
When rounded (Since they're asking for per cent which is 100 because 100 cents make 1 dollar) it will be 0.34 because 0.34 is in it's hundredth place
0.34 x 100(because it is per-cent)
Gives you 34%
You are driving your car through a roundabout that has a radius of 10 m . Your physics textbook is lying on the seat next to you.What is the fastest speed at which you can go around the curve without the book sliding? The coefficient of static friction between the book and the seat is 0.20..
The fastest speed at which you can go around the curve without the book sliding is equal to 4.43 m/s.
How to determine the fastest speed around the curve without the book sliding?According to Newton's Second law of motion, the centrifugal force which acts on a physical object that is moving around a curve in the x-direction (x-coordinate) and y-direction (y-coordinate) is modeled by the following mathematical equations:
∑Fx = Fc = mv²/r (x-direction)
∑Fy = Fmax = n - W = mg = 0
Fmax = μmg
Where:
m represent the mass.g represent the acceleration due to gravity.v represent the velocity.r represent the radius.Generally speaking, the maximum speed of a physical object would be attained when its static friction is maximum. Therefore, we would have the following:
Fmax = μmg = mV²/r
Making V the subject of formula, we have:
Maximum speed, V = √μgr
Maximum speed, V = √(0.2 × 9.8 × 10)
Maximum speed, V = 4.43 m/s.
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I need help with this problem. Please answer if you know how to do this.
It should be noted that 768 hand-held color televisions can be sold at $320 per television.
How to solve the word problemA word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
It should be noted that to find the number of hand-held color televisions sold at $320 per television, we need to substitute p = 320 into the supply model or demand model and solve for N.
Using the supply model:
N = 2.4p = 2.4(320) = 768
Therefore, at a price of $320 per television, the supplier is willing to produce 768 hand-held color televisions per week.
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Bigger corp has numerous clients they sell to on account. At 12/31/21, Bigger1s accounts receivable balance is $550,000
and their balance in their Allowance for Bad Debt account is a credit balance of $25,000
Based on past experience and other factors, the corp estimates that 8% of its account receivable is uncollectable after preparing an Aging of their A/Rec
They determine this to be a material amount and therefore use the Allowance Method
a) prepare the accounting for estimating Bad Debt Exp under the Allowance Method
b) show the Corp's Net Realizable Value after (a) above
c) After accounting for their Allowance at 12/31/21, on 7/1/22 Bigger identifies Customer F to be written off. F owes
them $20,000. Show the accounting for Cust F's write-off under the Allowance Method
d) show the Corp1
s Net Realizable Value after writing off Customer F
#3:
1) What is an 11
aging of accounts receivable11
?
2) State 2 for and 2 reasons against selling on account
3) How does Notes Receivable differ from Accounts Receivable?
a) To estimate Bad Debt Expense under the Allowance Method, Bigger Corp needs to create an adjusting entry at the end of the period. The entry will increase Bad Debt Expense and create a contra-asset account, Allowance for Doubtful Accounts. The entry will be:
Bad Debt Expense 44,000
Allowance for Doubtful Accounts 44,000
The calculation for the entry is: 8% * $550,000 = $44,000.
b) After the adjustment in (a), the net realizable value of Bigger Corp's accounts receivable is:
Accounts Receivable $550,000
Allowance for Doubtful Accounts ($69,000)
Net Realizable Value $481,000
c) To write off Customer F's debt of $20,000 under the Allowance Method, Bigger Corp needs to create another journal entry that decreases both accounts receivable and the allowance account. The entry will be:
Allowance for Doubtful Accounts 20,000
Accounts Receivable - Customer F 20,000
d) After writing off Customer F's debt, the net realizable value of Bigger Corp's accounts receivable is:
Accounts Receivable $530,000
Allowance for Doubtful Accounts ($69,000)
Net Realizable Value $461,000
An aging of accounts receivable is a report that categorizes a company's accounts receivable by the length of time the invoices have been outstanding. The report typically breaks down the receivables by 30-day periods, such as 0-30 days, 31-60 days, 61-90 days, and 91+ days. This report is used to help management identify which accounts are overdue and may require follow-up action, and to estimate the amount of bad debt expense that may need to be recorded.
Selling on account has several advantages, such as increasing sales revenue and customer loyalty. It also allows customers to buy products or services they need without having to pay immediately, which can be beneficial for both parties. However, there are also disadvantages, such as the risk of non-payment, the need to manage accounts receivable and collection efforts, and the potential for bad debt expense. Additionally, selling on account may require additional resources to manage, such as billing and collections staff.
Notes Receivable is a written promise to pay a specified amount of money at a specific future date. Accounts Receivable, on the other hand, represent amounts owed to a company by its customers for goods or services sold on credit. Notes Receivable usually carry interest and have a longer-term repayment schedule compared to Accounts Receivable, which are typically due within a shorter time frame, such as 30 days.
I really need help please help
Answer:
M = 1/8t - 223.05
Step-by-step explanation:
The volume of a figure is 975 ft³. If the
dimensions are multiplied by 2/5, what will be
the volume of the new figure?
Volume= answer... ft3
The volume of the new figure is approximately 63.36 ft³.
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Equation:If the dimensions of a figure are multiplied by a scale factor of k, then its volume will be multiplied by a factor of k³.
In this case, the dimensions are multiplied by 2/5, which is the same as multiplying by a scale factor of 0.4 (2/5 = 0.4). Therefore, the volume of the new figure will be:
V' = (0.4)³ * V
where V is the original volume.
Substituting V = 975 ft³, we get:
V' = (0.4)³ * 975 ft³
V' ≈ 63.36 ft³
Therefore, the volume of the new figure is approximately 63.36 ft³.
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