A car dealer purchases 20 new automobiles for $8000
each. If he sells 16 of them at a profit of 20%, for how much he
sell the remaining 4 to obtain an average profit of 18%? [$8800
Answers
The car dealer needs to sell the remaining 4 cars for $12,100 each to obtain an average profit of 18%.
How much for remaining 4 cars?Let's break down the problem step by step:
1. The car dealer purchases 20 new automobiles for $8000 each, so the total cost of the 20 cars is 20 * $8000 = $160,000.
2. The car dealer sells 16 of the cars at a profit of 20%. To calculate the selling price of these cars, we need to add the 20% profit to the cost price. The profit per car is 20% of $8000, which is (20/100) * $8000 = $1600. So, the selling price of each of the 16 cars is $8000 (cost price) + $1600 (profit) = $9600.
3. The car dealer wants to obtain an average profit of 18% for all 20 cars. We have already sold 16 cars, and we need to calculate the selling price of the remaining 4 cars to achieve the desired average profit.
4. Let's assume the selling price of the remaining 4 cars is x dollars.
5. To calculate the total selling price of all 20 cars, we sum up the selling prices of the 16 cars and the remaining 4 cars. So, the equation is:
(16 * $9600) + (4 * x) = $160,000 + (20% * $160,000)
(16 * $9600) + (4 * x) = $160,000 + (0.20 * $160,000)
153,600 + 4x = 160,000 + 32,000
4x = 48,400
x = 48,400 / 4
x = $12,100
Therefore, the car dealer needs to sell the remaining 4 cars for $12,100 each to obtain an average profit of 18%.
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Related Questions
can someone help me find the fa tor of (128m^2n^5 - 200m^4n^3)?
Answers
Answer:
\(8m^2n^3\), \(4n-5m\), and \(4n+5m\)
Step-by-step explanation:
\(128m^2n^5-200m^4n^3\) <-- Given
\(m^2(128n^5-200m^2n^3)\) <-- Factor out m²
\(m^2n^3(128n^2-200m^2)\) <-- Factor out n³
\(8m^2n^3(16n^2-25m^2)\) <-- Factor out 8
\(8m^2n^3(4n-5m)(4n+5m)\) <-- Difference of Squares
Therefore, the factors are \(8m^2n^3\), \(4n-5m\), and \(4n+5m\)
HAAALP.... jk but it would be appreciated if you answer this geometry question. ._.
Answers
Answer:
33 units²
Step-by-step explanation:
Setting up an equation to find the area of given kite:
Area of the kite = \(\mathrm{\frac{(2ft+9ft)\times(3ft+3ft)}2}\)
Area of the kite = \(\mathrm{\frac{11ft\times6ft}{2}}\)
Area of the kite = \(\mathrm{\frac{66ft^2}^2}\)
Area of the kite = \(\mathrm{33\;ft^2}\)
Therefore, the area of our given kite is 33 square feet
Kavinsky
Answer:
33 units square
Step-by-step explanation:
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4. What is the volume of the prism? Type numbers only, NO UNITS OR SYMBOLS or your answer will be marked wrong.
Answers
The volume of the rectangular prism having a dimensions 12 by 8 by 2 is 192.
What is the volume of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
From the diagram:
Length l = 12 units
Width w = 8 units
Height h = 2 units
Plug these values into the above formul and solve for the volume:
Volume V = w × h × l
Volume V = 8 × 2 × 12
Volume V = 192 cubic units.
Therefore, the volume is 192.
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You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 3 percent, what is the price of the consol? Instructions: Round your answer to the nearest penny (2 decimal places). The price of the consol is $ b. You are concerned that the interest rate may rise to 4 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. Instructions: Round your answer for dollar amounts to the nearest penny (2 decimal places ) and answers for percentages to the nearest tenth (1 decimal place) The new price of the consol would be $ The price of the consol falls by 7% and the interest rises by 7% c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Instructions: Round your answer to the nearest tenth (1 decimal place) Your holding period return is %
Answers
a. The price of the consol is approximately $133.33.
b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.
c. Your holding period return is approximately -49.99%.
a. The price of the consol can be calculated using the formula for the present value of a perpetuity:
Price = Annual Payment / Interest Rate
In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:
Price = $4 / 0.03 ≈ $133.33
Therefore, the price of the consol is approximately $133.33.
b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:
New Price = Annual Payment / New Interest Rate
Substituting the values, we get:
New Price = $4 / 0.04 = $100
The percentage change in the price of the consol can be calculated using the formula:
Percentage Change = (New Price - Old Price) / Old Price * 100
Substituting the values, we have:
Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%
The percentage change in the interest rate is simply the difference between the old and new interest rates:
Percentage Change in Interest Rate = (4% - 3%) = 1%
Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.
c. The holding period return can be calculated using the formula:
Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100
The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:
Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67
Substituting the values into the holding period return formula:
Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%
Therefore, the holding period return is approximately -49.99%.
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I'LL MARK AS BRAINLIEST AND GIVE 50 POINTS
If tan x = -1/√3 and cos x is positive, find sin x
Answers
Answer:
\(\sin(x)=-\dfrac{1}{2}\)
Step-by-step explanation:
The tangent function, tan(x), can be expressed as the ratio of sin(x) to cos(x):
\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)
We are told that tan(x) = -1/√3.
There are two ways that tan(x) can be negative:
sin(x) is positive and cos(x) is negative.sin(x) is negative and cos(x) is positive.As we have been told that cos(x) is positive, then sin(x) must be negative.
To find the value of sin(x), equating the tan(x) ratio to the given value of tan(x), and rearrange to isolate cos(x):
\(\tan(x) = -\dfrac{1}{\sqrt{3}}\)
\(\dfrac{\sin(x)}{\cos(x)}=-\dfrac{1}{\sqrt{3}}\)
\(\cos (x)=-\sqrt{3}\sin(x)\)
Substitute the found expression for cos(x) into the trigonometric identity sin²(x) + cos²(x) = 1 and solve for sin(x):
\(\begin{aligned}\sin^2(x)+\left(-\sqrt{3} \sin(x)\right)^2&=1\\\\\sin^2(x)+3\sin^2(x)&=1\\\\4\sin^2(x)&=1\\\\\sin^2(x)&=\dfrac{1}{4}\\\\\sin(x)&=\sqrt{\dfrac{1}{4}}\\\\\sin(x)&=\pm \dfrac{1}{2}\end{aligned}\)
As we have already determined that sin(x) is negative, this means that the value of sin(x) is:
\(\boxed{\sin(x)=-\dfrac{1}{2}}\)
TRUE / FALSE. roofs having a span of 40 feet or less and a pitch of ? or greater, and roofs having a span of more than 40 feet and a pitch of 1/4 or greater are considered to be pitched.
Answers
The statement is true. Roofs with a span of 40 feet or less and a pitch of ? or greater, as well as roofs with a span of more than 40 feet and a pitch of 1/4 or greater, are considered to be pitched.
In roofing terminology, the pitch refers to the steepness or slope of a roof. A pitched roof has a slope that allows water to drain efficiently. The pitch is typically measured as a ratio of vertical rise to horizontal span.
According to the statement, roofs with a span of 40 feet or less and a pitch of ? (undefined or not specified) or greater are considered to be pitched. This means that as long as the roof has a certain degree of slope or steepness, it is categorized as a pitched roof.
Similarly, roofs with a span of more than 40 feet and a pitch of 1/4 or greater are also considered to be pitched. In this case, the requirement for a minimum pitch of 1/4 (or a steeper slope) applies to roofs with a larger span.
The classification of roofs as pitched or not pitched depends on their span and the minimum pitch requirements specified. Roofs that meet the specified criteria for span and pitch are considered to be pitched roofs.
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If the total number of books checked out of the library at your high school is 14,400 and the student population is about 2400. how many books on average does each student have?
Answers
The number of books taken by each student is 6.
What is an average?Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.
Given that the total number of books checked out of the library at your high school is 14,400 and the student population is about 2400.
The average is calculated by dividing the sum of the total number of items by the total counts of the items.
Average = 14400 / 2400
Average = 6
Therefore, the number of books taken by each student is 6.
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Please show clear solutions to these additional questions involving gas laws. A complete solution shows
all steps, including necessary unit conversions. Final answers must be rounded to correct significant
figures.
1. If placing a balloon of gas into a freezer at –80.0 °C causes its volume to change to 76.4 % its
initial volume, then what was the balloon’s initial temperature in °C?
2. Suppose instead of volume, we built a thermometer that measures temperature by pressure
changes. A sample of gas is placed into a rigid glass vial along with a pressure sensor. At room
temperature (25.0 °C), the pressure of the gas is 1.01 atm. The gas thermometer is then placed
into a bath of hot oil. The pressure of the apparatus changes to 1.38 atm. What is the temperature
of the oil in °C?
Answers
1. The balloon's initial temperature was ____ °C.
2. The temperature of the oil is ____ °C.
1. To find the balloon's initial temperature, we can use the combined gas law, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature. Given that the volume changes to 76.4% of its initial volume and the final temperature is -80.0 °C, we can solve for the initial temperature. First, we convert the volume change to a decimal by dividing 76.4% by 100, giving us 0.764. Plugging in the values into the combined gas law equation, we can rearrange it to solve for the initial temperature.
2. To determine the temperature of the oil, we can use the ideal gas law, which states that the pressure times the volume divided by the temperature is equal to the gas constant times the number of moles. Since the volume remains constant and we are given the initial and final pressures, we can solve for the temperature. By plugging in the values into the ideal gas law equation and solving for the temperature, we can find the temperature of the oil in °C.
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g a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 29 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects? (report answer as a decimal value accurate to four decimal places.)
Answers
The probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects is 0.9660
This problem can be solved by permutations and combinations. This can also be solved using binomial probability experiment.
Let, then we could reasonably assume that follows a binomial distribution.
Given P = 0.01 and n = 29
P(x) = nCx.px.(1-p)^(n-x)
nCx = n! [x!-(n-x)!]
P = P(X<=1).
X<=1, if X = 0 and X = 1,
P(0) + P(1)
P(0) = 1.(0.01)^(0).(0.99)^(29) = 0.74717
P(1) = 29C1.(0.01)^(1).(1-0.01)^(29-1)
P(1) = 0.21887
P = P(0) + P(1)
P = 0.74717+0.21887 = 0.9660
So, therefore the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 4% rate of defects is 0.9660
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HELP ME PWEASE (what is A^2 + B^2 =)
YOUR WELCOME FOR THE POINTS
Answers
Answer:
i think it is 61
correct me if im wrong
Answer:
a2 + b2 = (a + b)2 -2ab.
Step-by-step explanation:
Your Welcome:)
- 2ab
At which root does the graph of f x x 5 3 x 2 2 touch the x axis?
Answers
The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.
Given that,
The function is f(x)= (x-5)³(x+2)²
We have to find at which root does the graph function touch the x-axis.
We know that,
What is a function?Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.
Take the function
f(x) = (x-5)³(x+2)²
f(x) = 0 if a curve touches the x-axis.
⇒ (x - 5)³(x + 2)² = 0.
But if ab = 0
So, a=0 and b=0
⇒ (x - 5)³ = 0 and (x + 2)² = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x=5 and x=-2.
Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.
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10 boys and 15 girls what in the ratio
Answers
Answer:
2:3
Step-by-step explanation:
simplified by 5 10÷5=2 and we'll you know the rest
Answer: 10:15?
i'm sorry if it's wrong, math isn't my best subject.
Step-by-step explanation:
e is 3 more than d.
f is 5 less than d.
Write an expression for e in terms of d
Answers
Answer:
Part A:
We are given that E is 3 more than D. This means that to get the value of E, we will simply add 3 to the value of D
Therefore:
E = D + 3
Part B:
We are given that F is 5 less than D. This means that to get the value of F, we will simply subtract 5 from the value of D
Therefore:
F = D - 5
Part C:
To get the value of E-F, we will simply subtract the equation we obtained from part B from the equation we obtained from part A
Therefore:
E - F = (D+3) - (D-5)
E - F = D + 3 - D + 5
E - F = 8
Hope this helps :)
Step-by-step explanation:
A circle is centered at D(-1, 3). The point G(-10, 1) is on the circle.
Where does the point J(-3, 12) lie?
Choose 1 answer:
A Inside the circle
B. On the circle
C. Outside the circle
Answers
i could be wrong but i think 12 is too far since (-10, 1) is on the circle
in 5-8, find each reciprocal. 5/9 8 7/3 1/12
Answers
the answer
155
324
5/9 (87/3(1/12)= 155/324
would lecture notes collected during your bachelor degree study; be a type of date?
Answers
No, lecture notes collected during a bachelor degree study are not a type of date. Lecture notes are a collection of the notes taken by a student during the lectures in the course of their bachelor degree study.
They are not the same as dates, which are the specified days on which something happens or is planned to happen. Lecture notes are usually written in the form of summaries of a lecture, which are usually made up of the important points that the student has noted down during the lecture.
They may also include diagrams, equations, and other visual aids that the student has used to illustrate the material covered. Lecture notes are not the same as dates, as they are not related to any specified days. They are simply summaries of the lecture topics discussed by the professor in the course of the student’s bachelor degree study.
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What is another way to write the equation
Answers
Answer:
the 2nd one
Step-by-step explanation:
all the other ones don't make 6
Determine which relation is a function. Question 1 options: {(–3, 2), (–1, 3), (–1, 2), (0, 4), (1, 1)} {(–3, 2), (–2, 3), (–1, 1), (0, 4), (0, 1)} {(–3, 3), (–2, 3), (–1, 1), (0, 4), (0, 1)} {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}
Answers
Option d) {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)} is the correct answer.
A function is a mathematical relation that maps each element in a set to a unique element in another set.
To determine which relation is a function between the given options, we need to check whether each input has a unique output.
In option a), the input -1 has two outputs, 3 and 2, which violates the definition of a function.
In, Option b) has two outputs for the input 0, violating the same definition.
In, Option c) has two outputs for the input 0, but it also has two outputs for the input -2, which violates the definition of a function as well.
In, Option d) is the only relation that satisfies the definition of a function, as each input has a unique output. Therefore, Option d) is the correct answer.
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a class has 30 students. what is the probability that at least two people in this class share the same birthday?
Answers
To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.
If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:
365/365 * 364/365 * 363/365 * ... * 336/365
This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).
Calculating this probability gives us:
(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937
So the probability that no two people in the class share the same birthday is approximately 0.2937.
Using the complement rule, the probability that at least two people in the class share the same birthday is:
1 - 0.2937 = 0.7063
Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.
Possible OutcomesFor each of the following events, determine how many possible outcomes there will be:1. Flipping a coin three times.2. Rolling a 6-sided die twice.3. Rolling a 6-sided die and flipping a coin.
Answers
The question said we should find the possible outcome of each of the following:
(1) Flipping a coin three times.
Recall, when flipping a coin, there are two possible outcomes (heads or tails).
So flipping a coin three times means:
2³ = 8
Therefore, the possible outcomes of flipping a coin three times is 8.
(2) Rolling a 6-sided die twice.
recall, there are 6 outcomes for a first roll and 6 for the second so, the total number of possible outcome is:
6 * 6 = 36
Therefore, the possible outcomes of rolling a 6-sided die twice is 36.
(3) Rolling a 6-sided die and flipping a coin.
When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6).
So, putting these together, we will have:
2 * 6 = 12.
Therefore, the possible outcomes of rolling a 6-sided die and flipping a coin 12.
Which of the following natural landmarks can be found in the Great Plains of Texas O Guadalupe Peak O Sam Houston National Forest Grand Prairie O Palo Duro Canyon
Answers
Answer:
the Palo Duro Canyon is found in the Great Plains of Texas.
Answer:
texas
Step-by-step explanation:
texas
helpppppppppppppppppp
Answers
Answer:
Step-by-step explanation:
a. Expand the area of the graph that has some small deviations from an otherwise coherent line. By magnifying those particular points, a sense of greater error is portrayed.
b. Shrink the axes so that data are moved closer together.
b) 7+2x/3 =5
helppppp
Answers
Answer:
4
Step-by-step explanation:
7+2x/3=5
7+2x. = 15
2x. =8
x. = 4
i hope it is helpful
Answer:
\( \frac{3x + 4}{2} = 9.5 \\ 3x + 4 = 19 \\ 3x = 15 \\ \boxed{x = 5}\)
\( \frac{7 + 2x}{3} = 15 \\ 2x + 7 = 45 \\ 2x = 38 \\ \boxed{x = 19}\)
What are the equation and slope of the line shown on the grid?
Answers
what grid ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀
Answer: The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope. y = mx+b is the equation to get slope.
Step-by-step explanation:
which two of the following expressions are equivalent to \sin(\theta)sin(θ)sine, left parenthesis, theta, right parenthesis?
Answers
The two expressions that are equivalent to sin(θ) are sin²(θ) and 1 - cos²(θ). These expressions represent different trigonometric identities that relate the sine function to other trigonometric functions.
The given expression sin(θ) can be rewritten in two equivalent forms: sin²(θ) and 1 - cos²(θ).
sin²(θ): This expression represents the square of the sine function. It means taking the sine of θ and squaring the result. The square of the sine function is equivalent to multiplying sin(θ) by itself, which matches the given expression sin(θ).
1 - cos²(θ): This expression is based on a trigonometric identity known as the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1. By rearranging the equation, we can isolate sin²(θ) as 1 - cos²(θ). Therefore, this expression is also equivalent to sin(θ).
These equivalent expressions arise from the fundamental relationships among trigonometric functions and their identities. By manipulating these identities, we can derive various equivalent forms of a given trigonometric expression, as seen with sin(θ).
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please help me please
Answers
Answer:
1st Q: C. Algebraic Expression; it consists of numbers and a variable.
2nd Q: D. The number of times Chris washes the car.
Step-by-step explanation:
1st Question:
Numerical Expression: Contains numbers and operations. Numerical expressions are your typical 2 + 2 equations. The ones you start learning in Kindergarten with just numbers and different operations such as addition, subtraction, division, and multiplication.
EX: 108 - 24 = ?
? = 84
Algebraic Expression: Contains numbers, operations, and variables. They are the same as normal, numerical expressions with the exception that it also has letters, or variables.
EX: 2x + 3 = 7
x = 2
__________________________________
2nd Question:
Amount Chris earns per wash: $10.00
# of times Chris washes the car: x
So 10x means what...?
10 = earns per wash
x = times washed the car
Multiply 10 by x to find the total Chris earns for the number of times he washes the car, x.
(Just as a reference, this would be counted as an Algebraic Expression).
Hope this helps! :)
(Lmk if you don't understand the explanation for the 2nd Q)
A bag holds 20 jelly beans: 5 red, 10 green, 4 blue, and 1 black. What is the probability of choosing two consecutive blue jelly beans without replacement
Answers
Answer:
10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19
Step-by-step explanation:
Explanation is above. If you need any more help let me know.
PLEASE HELP ME WITH THIS ASAP
Answers
Answer:
x=46
Step-by-step explanation:
4(x+1)-3x=50
first you gotta take care of the () so multiple by 4
(4x+4) -3x=50
combine like terms, subtract 4-3 to get 1 so you have 1x left
4 + x = 50
and then solve for x
x=46
( i checked it to make sure it was right so dw)
If A is symmetric matrix, then A^3 is a _______ matrix.
Answers
If A is a symmetric matrix, then A³ is also a symmetric matrix.
To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.
Now, let's look at A³:
A³ = A * A * A
We can replace each A with A^T, since they are equal:
A³ = A^T * A^T * A^T
Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:
A³ = (A^T * A^T * A^T)^T
A³ = (A^T)^T * (A^T)^T * (A^T)^T
Since the transpose of a transpose is the original matrix, we can simplify:
A³ = A * A * A
Therefore, A³ is also a symmetric matrix.
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A rectangular piece of metal is 25in longer than it is wide . Squares with sides 5in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 750in, what were the original dimensions of the piece of metal
Answers
Answer:
Step-by-step explanation:
Let width be x
Let lenght be 25 + x
Total ax = (25+x) * x
Square with 5in long are cut from the four corner formed = 750in
(25+x-10) * (x-10) * 5 = 750
(15+x) (x-10) = 150
15x-150+x^2-10x =150
15x -150-150+x^2-10x+0
x^2+15x-300=0
(ax^2+bx+c=0)