2. Write an equation that represents the following situation
Starting value = 200
Rate = 2.5% decay per year
Years = 5 years
Answer:
The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.
Find the volume of each solid shape. Round your answer to two decimal places. (Use 3.14 for pi)
The volume of each shape (A right triangular prism and the trapezoidal prism are):
126 ft³; and546 ft³ respectively.A right triangular prism is a three-dimensional shape that has a triangular base and three rectangular faces. It is a prism because its two bases are identical and parallel. The formula for finding the volume of a right triangular prism is V = (1/2) * base * height * length.
A trapezoidal prism is a three-dimensional shape with trapezoidal bases and four rectangular faces. It is also a prism because its two bases are identical and parallel. The formula for finding the volume of a trapezoidal prism is V = ((b1 + b2) / 2) * height * length, where b1 and b2 are the lengths of the two parallel sides of the trapezoidal base.
Recall that the formula for the volume of a trapezoidal prism is:
V = (1/2)h(b1+b2)L
where:
V is the volume of the prismh is the height of the trapezoidb1 and b2 are the lengths of the parallel bases of the trapezoidL is the length of the prism.Hence, substituting the given values, we have:
V = (1/2)(20 + 19)(7) 4
V = (1/2)(39)(7) 4
V = (273/2) 4
V = 546ft³
Therefore, the volume of the trapezoidal prism is 546ft³
2) Recall that the formula for the volume of a right triangular prism is:
V = (1/2) * b * h * L
Where:
b is the length of the base of the triangle
h is the height of the triangle
L is the length of the prism (the distance between the triangular faces)
The factor of (1/2) is included since the base of the prism is a triangle.
Given the forumla above:
b = 9ft
h = 7ft
L = 4ft
Plugging in the values given:
V = (1/2) * 9ft * 7ft * 4ft
V = 126ft³
Therefore, the volume of the right triangular prism is 126ft³
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The gas company charges a $16 monthly service fee and $0.6924 per hundred cubic feet of natural gas used during a month. Which equation best represents, y, the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas?
The gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.
The equation that represents the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas is:
y = 0.6924x + 16
Where:
x is the number of hundred cubic feet of natural gas used during the month
0.6924 is the cost per hundred cubic feet of natural gas used
16 is the fixed monthly service fee charged by the gas company.
To calculate the monthly charges for a given amount of natural gas used, we can substitute the value of x into this equation and simplify. For example, if x = 200, then:
y = 0.6924(200) + 16
y = 138.48 + 16
y = 154.48
Therefore, the gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.
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what's the linear relationship for this im stuck
Answer:
slope = 15
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table
m = [tex]\frac{21-6}{2-1}[/tex] = [tex]\frac{15}{1}[/tex] = 15
the linear relationship is then of the form
y = mx + c ( m is the slope and c the y- intercept )
from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9
y = 15x - 9 ← linear relationship
Question 5 of 12
Question 1-5
The side lengths of the figure below are given in centimeters.
0 00
Submit Test
If the perimeter of this figure is 33 cm, what is the value of x?
9
03
-9
-3
< Previous
2x-3
A
2022-2023 Algebra ICBA 8
12
Pause Test
The value of x is approximately 4.83 centimeters.
Answer: B (03)
The value of x, we need to add up all the side lengths of the figure and set it equal to the given perimeter of 33 cm.
The top and bottom sides have length [tex]2x-3[/tex] cm each, and the left and right sides have length [tex]x+5 cm[/tex] each.
So, we can write the equation:
[tex]2(2x-3) + 2(x+5) = 33 [/tex]
Simplifying and solving for x:
[tex]4x - 6 + 2x + 10 = 33 [/tex]
[tex]6x + 4 = 33 [/tex]
[tex]6x = 29 [/tex]
[tex]x = 29/6 [/tex]
[tex]x ≈ 4.83 [/tex]
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What is the axis of symmetry for the function f(x)=7-4x+x^2
the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Why it is and what does symmetry mean?
To find the axis of symmetry of the quadratic function f(x) = 7 - 4x + x²2, we can use the formula:
x = -b / 2a
where a and b are the coefficients of the x²2 and x terms, respectively, in the quadratic equation ax²2 + bx + c = 0.
In the given function, a = 1 and b = -4. Substituting these values into the formula, we get:
x = -(-4) / 2(1) = 2
Therefore, the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.
Symmetry is a property that describes a balanced and consistent arrangement of parts or elements that are similar in size, shape, and position. In mathematics, symmetry refers to the idea that a geometric object, function, or equation remains unchanged after some transformation, such as a reflection, rotation, or translation.
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Abigail wants to prove that a parallelogram is a rectangle if its diagonals are congruent. To start her proof, she draws parallelogram JKLM with congruent diagonals
Parallelogram JKLM is a rectangle because it has four right angles.
What is sss congruence theorem?The SSS (side-side-side) congruence theorem is one of the postulates of Euclidean geometry that states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
According to question:Abigali wants to prove that a parallelogram is a rectangle if its diagonals are congruent.
Since, JKLM is a parallelogram, JK≅ML.
Also by the reflexive property, KL is congruent to itself. So, since JL≅KM as well, ΔJKL ≅ ΔMLK by the SSS congruence theorem.
Now because the corresponding angles in congruent triangles are congruent, ∠JKL ≅ ∠MLK.
Also, since parallelograms have JK//ML,
Consecutive Interior Angles are supplementary.
So, since m∠JKL and m∠MLK are equal, they must both be 90°. Because the opposite angles in parallelograms are congruent, m∠MJK and m∠JML are both 90°. So, parallelogram JKLM is a rectangle because it has four right angles.
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Determine the union of j and k.
j = {7, 14, 21, 28, 35,42}
k = {14,28, 42, 56, 70}
The union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70} . Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.
What is a set ?
In mathematics, a set is a collection of distinct objects, called elements or members of the set. Sets are often denoted by curly braces {} enclosing the list of elements, separated by commas. For example, the set of natural numbers less than 5 can be written as {0, 1, 2, 3,
The union of two sets J and K, denoted by J ∪ K, is the set that contains all the elements that are in J or K, or in both.
In this case, J = {7, 14, 21, 28, 35, 42} and K = {14, 28, 42, 56, 70}. To find the union of J and K, we simply combine all the elements in both sets, removing any duplicates.
Therefore, the union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70}
Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.
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A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5 cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangle be?
The sides of the right triangle are 15 cm, 20 cm, and 25 cm.
What is triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
Let x be the length of the shorter leg of the right triangle.
Then, according to the problem statement, the longer leg is 5 cm more than the shorter leg, which means its length is x + 5 cm.
The hypotenuse is 10 cm more than the shorter leg, so its length is x + 10 cm.
By the Pythagorean theorem, we have:
x² + (x+5)² = (x+10)²
Expanding the squares and simplifying, we get:
x² + x² + 10x + 25 = x² + 20x + 100
Subtracting x² and simplifying further, we get:
x² - 10x - 75 = 0
Factorizing the left-hand side, we get:
(x - 15)(x + 5) = 0
Therefore, the possible solutions are x = 15 and x = -5, but x cannot be negative in this context, so we take x = 15 cm.
Then, the longer leg is x + 5 = 20 cm, and the hypotenuse is x + 10 = 25 cm.
Therefore, the sides of the right triangle are 15 cm, 20 cm, and 25 cm.
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If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
The prοfit exceeds the cοst as y > 1000 + 15x. Sο, οptiοn 4 is cοrrect.
What is profit?Gaining anything is knοwn as prοfit. When the Selling price ( SP ) οf the prοduct is mοre than the cοst price ( CP ) οf the prοduct, we gain prοfit. Oppοsite tο the prοfit is lοss i.e. lοsing anything is called lοss. When the Selling price ( SP ) οf the prοduct is less than the cοst price ( CP ) οf the prοduct, we get a lοss.
Prοfit can be calculated by the fοrmula,
Prοfit = Selling Price - Cοst price
P = SP - CP
Lοss can be calculated by the fοrmula,
Lοss = Cοst price - Selling price
L = CP - SP
As per the questiοn,
x = number οf units prοduced
expressiοn = 1000 + 15x
⇒ When y > 1000 + 15x, then prοfit exceeds cοst:
x = 50 & y = 1750
x = 100 & y = 2500
x = 150 & y = 3250
x = 200 & y = 4000
x = 0 & y = 1000
Therefοre, the graph in the 1st οptiοn is cοrrect as the prοfit exceeds the cοst.
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Complete question:
The cost of a small business is given by the expression 1000 + 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
3. A carpet company uses the following formula for
estimating the number of square feet, A, of carpeting
needed for a room x feet by y feet containing a stairway w
feet by z feet with n stairs:
A=xy+w[z(2n−1)+2n]
To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
What are the dimensions?
The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:
A = xy + w[z(2n - 1) + 2n]
Let's break down this formula to understand the different parts:
xy represents the area of the main part of the room, which is a rectangle with length x and width y.w represents the width of the stairway.z represents the depth of each stair.n represents the number of stairs.The expression z(2n - 1) represents the total vertical distance covered by all the stairs, including the top and bottom levels.The expression 2n represents the total horizontal distance covered by all the stairs.The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.
So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].
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Find the area of the shape below. Use NUMBERS ONLY in the blank. NO units.
30 ft
60 ft
60 ft
60 ft
60 ft
30 ft
The shape is like a plus sign
The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².
How to find the area ?You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.
The area of the composite shapes would therefore be :
= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )
= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )
= 1, 800 + 1, 800 + 4, 500
= 8, 100 ft ²
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HELP ASAP 25 PONITS PLEASE
Answer:
The Markdown amount: $9.45
Sale price: $13.05
Step-by-step explanation:
Convert 42% to decimal, which is 0.42
a = p(w). (formula)
a=22.5(0.42). or 22.5 x 0.42
a = 9.45
22.50 - 9.45 = 13.05
please help with this
Option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
What is a polynomial?A pοlynοmial is a mathematical expressiοn cοnsisting οf variables, cοefficients, and the οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents.
Pοlynοmials are an impοrtant part οf the "language" οf mathematics and algebra. They are used in nearly every field οf mathematics tο express numbers as a result οf mathematical οperatiοns. Pοlynοmials are alsο "building blοcks" in οther types οf mathematical expressiοns, such as ratiοnal expressiοns.
We have:
6x² − 8x
= 2(3x² −4x)
Then,
6x² - 3x + 8x -4
= 6x² +8x−3x−4
= 2x(3x+4) −3x −4
= 2x(3x+4)−(3x+4)
= (2x−1)(3x+4)
Thus, option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.
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Mr smith makes $20 and hour
working full time. He gets about 25% of his income taken out for taxes. He came up with the following monthly budget:
How much extra money does he have left over monthly to put into savings?
Please enter your answer without a dollar sign or spaces.
Amount of money that he have left over monthly to put into savings is $585.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
Given that,
Hourly rate of Mr. Smith = $20
If he works full time, then the number of working hours in a week is 40 hours.
So the number of working hours in a month = 40 × 4 = 160 hours
Rate for a month = 160 × $20 = $3200
Tax percent from the income = 25%
Income after tax = 3200 - (25% × 3200) = 3200 - 800 = $2400
Total budget of Mr. Smith = $1,410 + $405 = $1815
Income after the monthly budget = $2400 - $1815 = $585
Hence the money that is left is $585 for the savings.
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The complete question is given below :
Mr. Smith makes $20 an hour working full time. He gets about 25% of his income taken out for taxes. He came up with the following monthly budget.
Household:
Rent: $700
Cable: $85
Cell Phone: $175
Electric: $100
Food: $350
Total: 1,410
Automobile
Car: $200
Car Insurance: $100
Gas: $90
Maintenance: $15
Total: $405
How much money does he have left over monthly to put into savings?
Analyzing Errors
Detra and Trinh each wrote a rule to represent the relationship between input and output
values as shown in the graph below.
Output
14
12
10
8
6
2
Detra's Rule: Output = 3 x Input
How do you think Detra arrived at her
solution?
10 12 14
8
Input
Trinh's Rule: Output= Input + 3
How do you think Trinh arrived at her
solution?
Answer:
Detra's rule: Output = 3 x Input. This means that for every input value, the output value is three times greater. Detra likely arrived at this solution by noticing a pattern in the input-output values and determining that the output values were always three times greater than the input values.
Trinh's rule: Output = Input + 3. This means that for every input value, the output value is the input value plus three. Trinh likely arrived at this solution by noticing a pattern in the input-output values and determining that the output values were always three more than the input values.
Step-by-step explanation:
5. 56 oz = ____lb ____oz
A. 2 lb 1 oz
B. 2 lb 3 oz
C. 2 lb 6 oz
D. 3 lb 8 oz
56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.
What is pound?Pound is a unit of measurement for mass or weight commonly used in the United States and the United Kingdom. The symbol for pound is "lb".
According to question:In the English system of measurement, there are 16 ounces in one pound. To convert a weight in ounces to pounds, we need to divide the number of ounces by 16.
In this case, we have 56 ounces. So, by dividing 56 by 16, we obtain:
56 / 16 = 3 with a remainder of 8
This means that 56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.
In the US customary system, one pound is equal to 16 ounces, while in the imperial system used in the UK, one pound is equal to 14 ounces.
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Convert 56 ounces(oz) into pounds(Ib)
56 oz = ____lb ____oz
A. 2 lb 1 oz
B. 2 lb 3 oz
C. 2 lb 6 oz
D. 3 lb 8 oz
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r.
P = 4500 $, A = 4561.88 $, t = 3 months
The loan's simple interest rate is 5.232% per quarter.
What is the formula for the future value of a loan with simple interest?
A = P(1 + rt)
where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.
In this case, we have:
P = 4500
A = 4561.88
t = 3 months = 3/12 year =0.25 year
Substituting these values into the formula,
[tex]4561.88 = 4500(1 + 0.25r)[/tex]
Dividing both sides by 4500,
[tex]1.01308 = 1 + 0.25r[/tex]
Subtracting 1 from both sides,
[tex]0.01308 = 0.25r[/tex]
Dividing both sides by 0.25,
[tex]r = 0.05232 \: or \: 5.232\%[/tex]
Therefore, the loan's simple interest rate is 5.232% per quarter.
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stick of butter weight a quarter of a pound how much do 13 sticks of butter weight
Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Step-by-step explanation:
Mona had = 32 math problems.
Let math problems shw completed be x.
Before dinner: 3/4x maths.
remaining maths = x- 3/4x
= 4x-3x/4 = 1/3x.
find the value of 9u+4 given that -5u-8=2
Answer:
13
Step-by-step explanation:
Given
7u - 4 = 3 ( add 4 to both sides )
7u = 7 ( divide both sides by 7 )
u = 1
Then
9u + 4 = 9(1) + 4 = 9 + 4 =13
Solve the following system of equations and show all work.
y = 2x2
y =-3x -1
Answer:
Step-by-step explanation:
Start by substituting the first equation into the second equation to eliminate y:
2x^2 = -3x - 1
Move all terms to one side:
2x^2 + 3x + 1 = 0
Factor the quadratic equation:
(2x + 1)(x + 1) = 0
Solve for x by setting each factor to zero:
2x + 1 = 0 or x + 1 = 0
x = -1/2 or x = -1
Plug in the values of x to find the corresponding values of y:
For x = -1/2:
y = 2(-1/2)^2 = 1/2
For x = -1:
y = 2(-1)^2 = 2
The solutions to the system are (-1/2, 1/2) and (-1, 2).
please and thank you i really need it
Answer:
B
Step-by-step explanation:
Given that the probability of a student taking a physics class is 23, and the probability of a student taking a math class given that the student takes a physics class is 710, what is the probability of a student taking a math class and a physics class? Enter your answer as a fraction in simplest form.
The probability of a student taking a math class and a physics class is [tex]\frac{7}{15}[/tex].
What is probability?
To determine the possibility of an event, one might utilise probability as a technique. Only the probability of an event occurring can be determined using it. A scale where 1 denotes a specific occurrence and 0 signifies impossibility.
We are given that the probability of the student taking a physics class is [tex]\frac{2}{3}[/tex].
Also, it is given that the probability of a student taking a math class given that the student takes a physics class is [tex]\frac{7}{10}[/tex].
So, probability of a student taking a math class and a physics class is:
⇒ Probability = [tex]\frac{2}{3}[/tex] * [tex]\frac{7}{10}[/tex]
⇒ Probability = [tex]\frac{14}{30}[/tex]
⇒ Probability = [tex]\frac{7}{15}[/tex]
Hence, the probability of a student taking a math class and a physics class is [tex]\frac{7}{15}[/tex].
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give me a furmula a triangle
Answer:
The formula for finding the area of a triangle is:
Area = 1/2 x base x height
where "base" is the length of one of the sides of the triangle, and "height" is the distance from that side to the opposite vertex.
Chicken costs c dollars per pound. Write an expression for the price of 3/4 pound of chicken.
Answer: [tex]\frac{3}{4}[/tex]c
Step-by-step explanation:
If one pound of chicken costs c dollars, and we are writing an expression for 3/4 a pound of chicken, our expression will be the price (c) multiplied by how much chicken there is (3/4):
3/4c
- In mathematics, an expression is a combination of numbers, variables (represented by letters), symbols, and operators, arranged in a way that represents some meaningful mathematical relationship or calculation.
- Expressions can be simple, like 3x or 4 + 5, or complex, like (3x + 4y) / (2x - 5y). Expressions are not equations or inequalities, as they do not contain an equal sign, but they can be used to build equations or inequalities.
Solving the Question:The price of 1 pound of chicken is c dollars. To find the price of 3/4 pound of chicken, we can multiply the price of 1 pound by 3/4:
[tex]\begin{aligned}\sf Price\: of\: \dfrac{3}{4}\: pound\: of\: chicken& =\sf \dfrac{3}{4} \times c \\&=\boxed{\bold{\:\dfrac{3}{4}c\:}}\end{aligned}[/tex]
Therefore, the expression for the price of 3/4 pound of chicken is 3/4c.
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https://brainly.com/question/13667588At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .53.
a. Find the probability that in a sample of 12 customers, none of the 12 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.)
The prοbability that in a sample οf 12 custοmers, nοne οf the 12 will οrder a nοnalcοhοlic beverage is 0.0042.
What is Binοmial Prοbability?Binοmial prοbability is a type οf prοbability that deals with the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes, cοmmοnly referred tο as success οr failure. It is calculated using the binοmial prοbability fοrmula.
This is a binοmial prοbability prοblem, where the prοbability οf success (οrdering a nοnalcοhοlic beverage) is 0.53, and the number οf trials is 12.
The prοbability οf nο custοmers οrdering a nοn-alcοhοlic beverage can be fοund using the binοmial prοbability fοrmula:
[tex]P(X = k) = (n choose k) * p^k * (1-p)^{(n-k)[/tex]
where:
n = number of trials
k = number of successes (in this case, 0)
p = probability of success (ordering a non-alcoholic beverage)
Plugging in the values, we get:
[tex]P(X = 0) = (12 choose 0) * 0.53^0 * (1 - 0.53)^{(12 - 0)[/tex]
[tex]= 1 * 1 * 0.47^{12}[/tex]
= 0.0042 (rounded to 4 decimal places)
Therefοre, the prοbability that in a sample οf 12 custοmers, nοne οf the 12 will οrder a nοnalcοhοlic beverage is 0.0042.
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what are the answers to these questions?
a) dV/dt=?
b) dV/dt=?
c) dV/dt=?
The value of differentiation A) dV/dt = 2πrh(dr/dt) ,B) dV/dt = π(r²(dh/dt) , C) π(2rh(dr/dt) + r²(dh/dt))
What is a differentiation?A mathematical procedure called differentiation is used to determine the derivative of a function with respect to a variable. The rate at which one quantity changes in relation to another is determined using this method.
If we have a function f(x) = x2, for instance, its derivative f'(x) = 2x tells us how quickly the function changes in relation to x.
The following formula determines the volume V of a right circular cylinder with radius r and height h:
V = πr²h
The cylinder's radius is r in this instance, and its height is h.
When we change the formula's specified values, we obtain:
V = πr²h
= (12)(2) = 2 cubic metres.
As a result, the right circular cylinder has a 2 cubic unit volume.
Let's now think about how dv/dt and dr/dt relate when h is constant and r varies over time.
When we take into account time t and differentiate both sides of the formula V =πr²h, we obtain:
dV/dt = d(r²h)/dt
(r²)(dr/dt)(dh/dt) = dV/dt
h is a constant, hence dh/dt = 0.
Therefore,
dV/dt= ((2r)(dr/dt)(dh/dt)
= 2rh(dr/dt)
B)
Let's now think about how dv/dt and dh/dt relate when r is constant and h varies over time.
When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:
dV/dt equals d(r²h)/dt
r²(dh/dt) = dV/dt
As r is constant, dr/dt is equal to 0.
Therefore,
r2(dh/dt) = dV/dt
C)
Given that r and h are time-varying, let's look at the relationship between dv/dt, dh/dt, and dr/dt.
When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:
dV/dt equals d(r²h)/dt
dV/dt is equal to (r²)(dh/dt) + (r²)(dr/dt)
Therefore,
((2rh(dr/dt) + r2(dh/dt))
= dV/dt)
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Variable costs as a percentage of sales for Lemon Inc. are 63%, current sales are $603,000. and fixed costs are $202,000. How much will operating income change if sales increase by $37,400?
Answer: $13, 658 increase
First, we need to calculate the current total variable costs:
Total Variable Costs = Sales x Variable Costs as a % of Sales
Total Variable Costs = $603,000 x 0.63
Total Variable Costs = $380,490
Next, we can calculate the current operating income:
Operating Income = Sales - Total Variable Costs - Fixed Costs
Operating Income = $603,000 - $380,490 - $202,000
Operating Income = $20,510
If sales increase by $37,400, the new sales figure will be $640,400 ($603,000 + $37,400). We can then calculate the new total variable costs:
New Total Variable Costs = New Sales x Variable Costs as a % of Sales
New Total Variable Costs = $640,400 x 0.63
New Total Variable Costs = $404,232
Finally, we can calculate the new operating income:
New Operating Income = New Sales - New Total Variable Costs - Fixed Costs
New Operating Income = $640,400 - $404,232 - $202,000
New Operating Income = $34,168
Therefore, the operating income will increase by $13,658 ($34,168 - $20,510) if sales increase by $37,400.
To find the surface area of a refrigerator, what units will be used; check all that applies
Group of answer choices
square feet (sq ft)
meters (m)
square inches (sq in)
millimeters (mm)
surface area of a refrigerator,
square feet (sq ft)
square inches (sq in)
What is surface area ?the total area or the solid that the surface of the solid occupies.
we know that refrigerator have cuboid shape so,
surface area of cuboid =2(lb+bh+hl)
where l is length ,b is breath ,and h is height of cuboid .
The units generally used to measure the surface area of a refrigerator are:
square feet (sq ft)
square inches (sq in)
Therefore, the options are square feet (sq ft) and square inches (sq in) correct.
Meters (m) and millimeters (mm) are typically not used for measuring the surface area of a refrigerator.
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