Answer:
The difference between the price after value added tax (VAT) and the price after discount of an article gives us the actual amount of money saved by the customer.
The price after VAT is the price of the item including the tax imposed by the government, whereas the price after discount is the price of the item after any promotional or discounted price reduction. By subtracting the price after discount from the price after VAT, we can determine the actual amount saved by the customer, which is the discount amount minus any VAT paid on the original price.
For example, if an item originally cost $100 with a 10% VAT, the price after VAT would be $110. If the item was discounted by 20%, the price after discount would be $80. The difference between the price after VAT and the price after discount would be $30, which is the actual amount saved by the customer ($20 discount minus $10 VAT paid on the original price).
Step-by-step explanation:
To calculate the actual amount saved by the customer, we need to follow these steps:
Determine the original price of the item. For example, let's say the original price of the item is $100.
Calculate the VAT amount paid on the original price. To do this, multiply the original price by the VAT rate as a decimal. For example, if the VAT rate is 10%, then the VAT amount would be:
VAT amount = original price x VAT rate
VAT amount = $100 x 0.1
VAT amount = $10
So, the VAT amount paid on the original price of $100 is $10.
Determine the discounted price of the item. For example, let's say the item is discounted by 20%, so the discounted price is:
Discounted price = original price - (original price x discount rate)
Discounted price = $100 - ($100 x 0.2)
Discounted price = $80
So, the discounted price of the item is $80.
Calculate the actual amount saved by the customer. To do this, subtract the discounted price from the price after VAT. For example:
Actual amount saved = price after VAT - discounted price
Actual amount saved = $110 - $80
Actual amount saved = $30
So, the actual amount saved by the customer is $30, which is the discount amount minus the VAT paid on the original price.
Construct a polynomial function of least degree possible using the given information.
Real roots: −1, 1, 3 and (2,
f(2)) = (2, 7)
The polynomial function of least degree possible using the given information is: f(x) = -7/3 (x+1)(x-1)(x-3)
What is polynomial function?
A polynomial function is a type of mathematical function that consists of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.
To construct a polynomial function of least degree possible using the given information, we need to use the fact that the function has real roots at -1, 1, and 3. This means that the function can be factored as follows:
f(x) = a(x+1)(x-1)(x-3)
where a is a constant coefficient that we need to determine.
Next, we need to use the fact that the function passes through the point (2, 7) to determine the value of a. We substitute x=2 and f(x)=7 into the above equation and solve for a:
7 = a(2+1)(2-1)(2-3)
7 = -3a
a = -7/3
Therefore, the polynomial function of least degree possible using the given information is:
f(x) = -7/3 (x+1)(x-1)(x-3)
Note that this function has real roots at -1, 1, and 3, and passes through the point (2, 7).
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Martha's family set a goal to earn $7,507.50 in interest in account 2. How long will it take them to meet this goal?
It will take them to meet this goal 10.01 years (or approximately 10 years and 1 month)
To solve this problem, we'll need to use a formula:
Simple interest = Principal × rate × time (in years)
We can rearrange the formula as follows:
Time (in years) = Simple interest / (Principal × rate)
As per the formula, to calculate the time it will take the family to earn the interest, we'll need to know the principal and the rate. These values are not given in the question, so we'll assume that the principal is $10,000 and the interest rate is 7.5 percent (or 0.075 as a decimal).
Simple interest = Principal × rate × time (in years)
$7,507.50 = $10,000 × 0.075 × time (in years)
Divide both sides by $10,000 × 0.075 to isolate the time (in years):
time (in years) = $7,507.50 / ($10,000 × 0.075)
time (in years) = 10.01 years
So, it will take the family 10.01 years (or approximately 10 years and 1 month) to earn $7,507.50 in interest in account 2.
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What is the image point of (4,8) after a translation right 1 unit and up 5 units?(Explain+Rules)
Answer:
(5, 13)
Step-by-step explanation:
Points (4, 8)
Translation right 1 unit. Meaning x + 1
(4, 8) → (5, 8)
Up 5 units. Meaning y + 5
(5, 8) → (5, 13)
So, the final point at (5, 13)
Numbers that are greater than 11 over 16 and less than 15 over 16
Any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
What is the inequalities?In mathematics, inequalities are statements that cοmpare twο values and indicate whether οne value is greater than, less than, οr equal tο the οther value.
Tο find the numbers that are greater than 11/16 and less than 15/16, we need tο cοnsider all numbers between these twο values, excluding the endpοints. That is,
11/16 < x < 15/16
where x represents the number we are looking for. We can also write this using interval notation as:
(11/16, 15/16)
Hence, any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.
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Please Answer Quickly I need help
In the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.
What is reflexive property?Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set. In the parts that follow, let's learn more about equality and congruence's reflexive attribute.
Given that angle A is congruent to angle A using the reflexive property.
Thus, ΔAED ≅ ΔABC using the AA criteria.
Hence, in the given proof the blanks are ΔAED ≅ ΔABC using the AA criteria.
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Solve each inequality given that the function f is increasing over its domain[tex]f(4x-3)\geq f(2-x^2), D_{f}=(-8, 4) \\g(3x^2-2x)\geq g(3x-2), D_{g}=All real numbers[/tex]
The values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1
What are inequalities?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here, we have
Inequality 1: f(4x - 3) ≥ f(2 - x²), Df = (-8 , 4)
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x²
Rewrite as:
x² + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x² + 4x - 5 ≥ 0
Expand
x² + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
Inequality 2: g(3x² - 2x) ≥ g(3x - 2), Dg = all real numbers
g(3x² - 2x) ≥ g(3x - 2)
(3x² - 2x) ≥ (3x - 2)
Evaluate the like terms
3x² - 2x -3x + 2 ≤ 0
3x² - 5x + 2 ≤ 0
3x² - 3x -2x + 2 ≤ 0
3x(x-1) -2(x-1) ≤ 0
Solve for x
x≤1 or x≤2/3
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1
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Tomorrow, Sunita and Sunil will get married according to Hindu ritual. In Sunil's house, four banana plants have to be fixed in four corners for 'Linga Chauka in such a way that consecutive banana plants should be fixed at equal distances and banana plants in diagonally opposite direction should also be at the equal distances. If the coordinates of any two opposite banana plants are (3, 4) and (7, 2), then find the equation of the line made by the rice flour joining the remaining two opposite banana plants.
The equation of the line made by the rice flour joining the remaining two opposite banana plants is y = 2x - 7.
How to find the equation of the line?We are given the coordinates of two opposite banana plants, (3, 4) and (7, 2). Since the consecutive plants are fixed at equal distances, the other two plants will lie on the perpendicular bisector of the line segment joining (3, 4) and (7, 2).
First, let's find the midpoint of the line segment joining (3, 4) and (7, 2):
Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((3 + 7)/2, (4 + 2)/2) = (5, 3)
Find the slope of the line segment joining (3, 4) and (7, 2):
Slope = (y2 - y1)/(x2 - x1) = (2 - 4)/(7 - 3) = -2/4 = -1/2
Now, we can use the point-slope form of a linear equation to find the equation of the line made by the rice flour joining the remaining two opposite banana plants:
y - y1 = m(x - x1)
Here, m is the slope, and (x1, y1) is the midpoint (5, 3):
y - 3 = 2(x - 5)
y - 3 = 2x - 10
y = 2x - 7
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A new player joins the team and raises the mean to 22
A. The mean age of the team rounded to 1 decimal place is 20.9 years
B. The age of the new player is 23.1 years
A. How do i determine the mean age of the team?The mean age of the team can be obtained as illustrated below:
Age (x) = 19, 20, 21, 22, 23, Frequency (f) = 2, 3, 1, 4, 1Mean age =?Mean age = ∑fx / ∑f
Mean age = [(19 × 2) + (20 × 3) + (21 × 1) + (22 × 4) + (23 × 1)] / (2 + 3 + 1 + 4 + 1)
Mean age = 230 / 11
Mean age = 20.9 years
Thus, the mean age of the team is 20.9 years
B. How do i determine the age of the new player?The age of the new player can be obtained as follow:
Mean of previous player = 20.9 yearsNew mean = 22Age of new player =?New mean = (mean of previous + age of new player) / 2
22 = (20.9 + age of new player) / 2
Cross multiply
22 × 2 = 20.9 + age of new player
44 = 20.9 + age of new player
Collect like terms
44 - 20.9 = Age of new player
Age of new player = 23.1 years
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Complete question:
Pleas attached photo
Circumference area of circle use 3.14 for pi
The required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.
What is a circle?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
The points of the circle are at a fixed distance from the center.
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”.
So, the area would be:
= πr²
= 3.14*2.5*2.5
= 19.63495
= 19.63 ft²
The circumference would be:
= 2πr
= 2*3.14*2.5
= 15.70796
= 15.70 ft
Therefore, the required area and the circumference of the given circle are 19.63 ft² and 15.70 ft respectively.
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Please help with graph problem. Thank you loads!!!
Answer:
a. 250,000
b. 450,000
Step-by-step explanation:
which congruency theorem can be used to prove that △abd ≅ △dca?
a. SAS
b. Not enough information
c. SSS
d. AAS
the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.
In this question we accept two angles is given that is:
two triangles ∠ABD and
In this, an angle is common that is,
AD = AD
AB = CD
∠A is equal = ∠A (which is given)
That is the reason the SAS rule is right.
SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.
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the complete question is:
Which congruency theorem can be used to prove
that ABD =DCA?
a. SAS
b. Not enough information
c. SSS
d. AAS
the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 18 minutes, (b) between 22 and 31 minutes, and (c) more than 30 minutes.
The probability that a randomly selected athlete uses a stair climber for,
(a) P(X < 18) = 0.2514
(b) P(22 < X < 31) = 0.4332
(c) P(X > 30) = 0.0918
Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.
(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).
Z-score for 18 minutes = (18 - 22) / 6 = -0.67
Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.
Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.
(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).
Z-score for 22 minutes = (22 - 22) / 6 = 0
Z-score for 31 minutes = (31 - 22) / 6 = 1.5
Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.
Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.
(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).
Z-score for 30 minutes = (30 - 22) / 6 = 1.33
Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.
Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.
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What is the solution to X equals the square root of negative X +6
Answer:
The equation X = √(-X + 6) can be solved using algebraic manipulation. Here are the steps:
Square both sides of the equation to eliminate the square root:
X^2 = -X + 6
Add X to both sides of the equation:
X^2 + X = 6
Rearrange the equation in standard quadratic form:
X^2 + X - 6 = 0
Factor the quadratic equation:
(X + 3)(X - 2) = 0
Use the zero product property to solve for X:
X + 3 = 0 or X - 2 = 0
X = -3 or X = 2
Step-by-step explanation:
A town with a population of 80,250 people has 500 city blocks. Each block is one-tenth mile long by one-tenth mile wide. Find the population density of the town in the people per square mile.
Answer:
First, we need to find the area of one block:
Area of one block = length x width = (1/10) mile x (1/10) mile = 1/100 square mile
Since there are 500 blocks in the town, the total area of the town is:
Total area of town = 500 blocks x (1/100) square mile/block = 5 square miles
To find the population density, we divide the population by the total area:
Population density = population / total area
Population density = 80,250 / 5 = 16,050 people per square mile
Therefore, the population density of the town is 16,050 people per square mile.
evaluate the function graphically.
find (-3)
The function f(-3) when evaluated graphically has its value to be 4 on the graph
How to Evaluate a Function GraphicallyTo evaluate a function graphically, you need to follow these steps:
Plot the function on a coordinate plane (this is the given graph)Identify the function value from the graphIn this case, the function f(-3) has its value to be 4 on the graph
This means that
f(-3) = 4
Hence, the function has a value of 4
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-6(3x - 9y-10) slove
Answer:
-18x + 54y + 60
Step-by-step explanation:
you get this answer by distributing the -6 to all 3 properties.
-6 x 3x = -18x
-6 x -9y = 54y
-6 x -10 = 60
What's the area of a regular triangle with a side length of 15? (Explanations step-by-step are appreciated!)
the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.
A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:
Area = (√(3) / 4) × side²
where "side" is the length of one side of the triangle.
Let's plug in the given value of side length, which is 15, into the formula:
Area = (√(3) / 4) × 15²
Area = (√(3) / 4) × 225
Area = 97.4279 (rounded to 4 decimal places)
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A tour company charges a base price of $60 per person but then lowers it by $4 per each additional pers who goes on the tour (up to 8 people). For example, if only one person goes, her ticket is $60, but if t people go, each of their tickets is $56 and if three people go, each of their tickets is $52. Let n be the num of people who go on the tour
Thus, the cost would be $60 + $56 = $116 for a group of two persons and $60 + $52 + $52 = $164 for a party of three for number n.
The pricing structure for the tour company is based on a base price of $60 per person, which is then discounted by $4 for each additional person up to a maximum of 8 people. This means that for a group of 2 people, the price would be $60 + $56 = $116, while for a group of 3 people, the price would be $60 + $52 + $52 = $164.
The pricing structure incentivizes larger groups to go on the tour, as they can benefit from the discounted price per person. However, the discount stops at 8 people, which means that larger groups do not receive any further discounts. This is likely because the tour company may have a limit on the number of people they can accommodate on a single tour.
It is important for customers to be aware of the pricing structure when considering booking a tour with the company. They should also consider the benefits and drawbacks of going with a larger group versus a smaller one, such as the potential for a more personalized experience with a smaller group versus a more social experience with a larger group. Overall, the pricing structure is designed to be fair and encourage group bookings, while also accommodating the needs of the tour company.
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A man in a lighthouse tower that is 30 ft. He spots a ship at sea at an angle of depression of 10°. How far is the ship from the base of the lighthouse?
Answer:
170.16 ft
Step-by-step explanation:
tan10° = 30/x
x = 30x/ tan 10° = 30/0.1763
=170.16 ft
Given u = 3i − 8j and v = −4i + 8j, what is u ⋅ v?
Answer:
-12i - 64j
Step-by-step explanation:
Find the volume of this composite shape.
16 ft
24 ft
Answer:
that question is incomplete
16) During a theater season, New York theatergoers bought 11.7 million tickets for $588.5 million. To the nearest dollar, what was the mean price for a theater ticket in New York???
mean price for a theatre ticket in New York is $ 50.299
Mean can be expressed as the total sum of observations for the total number of observations.
In other words its the sum by the count
It gives the average measure of each entity.
The mean Price is sometimes called Average Price.
Total number of Tickets = 11.7 million
Total Cost = $588.5 million
Mean Price = Total Cost / Total Number of Tickets
= 588.5 million / 11.7 million
= $ 50.299
mean price for a theatre ticket in New York is $ 50.299
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Evaluate 0.3y + y/z
When Y=10 and z=5.
Therefore, when y = 10 and z = 5, the value of the expression 0.3y + y/z is 5.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operators that are grouped together to represent a mathematical quantity or relationship. Expressions can be simple, such as a single number or variable, or they can be more complex, involving multiple operations and variables. Expressions are often used in mathematics to represent relationships between variables, to evaluate quantities, and to solve equations.
Here,
Substituting y = 10 and z = 5 in the given expression, we get:
0.3y + y/z = 0.3(10) + 10/5
= 3 + 2
= 5
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I really need help a.s.a.p
The area of the semicircle that has a radius of 3 kilometers is calculated as: 14.13 square kilometers.
How to Find the Semicircle's Area?To find the area of a semicircle, you can follow these steps:
Recall that a semicircle is half of a circle. Therefore, the formula for the area of a circle can be modified to find the area of a semicircle by dividing the formula by 2.The formula for the area of a circle is A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.To find the area of a semicircle, divide the formula for the area of a circle by 2. Therefore, the formula for the area of a semicircle is A = 1/2(πr^2).The semicircle's area = 1/2(πr²) = 1/2 * (3.14 * 3²)
= 14.13 square kilometers.
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a bookstore is deciding what price it should charge for a certain book. after research, the store finds that if the book's price is dollars (where ), then the number of books sold per month is . what price should the store charge to maximize its revenue?
To maximize the revenue, the bookstore should charge $13 for the book.
Given:
p = book's price in dollars, where
p is less than or equal to 26.
number of books sold per month = 130-5p
Price that maximizes revenue = ?
Revenue = Price × QuantityofUnitsSold
Revenue = p(130-5p)
Revenue = [tex]130p - 5p^2[/tex] , This is quadratic equation so, The vertex of the parabola, which gives the price that maximizes revenue, can be determined by calculating the value of x-coordinate of the vertex.
Let x = p
The formula for the x-coordinate of the vertex is [tex]-b/2a[/tex]
where,
a = -5
b = 130
c = 0
x = [tex]-b/2a=-130/-10 = 13[/tex]
So, to maximize the revenue, the bookstore should charge $13 for the book.
Maximum revenue will be:-
Revenue = Price × QuantityofUnitsSold
Revenue = p(130-5p)
where p = 13
Revenue = (13)(130-5(13))
Revenue = $845
The maximum revenue at (price = 13) will be $845.
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I need help plsssssssssssssss
Answer:3.14sq^2
Step-by-step explanation:b x c x a = 3.14
John borrows R3000 from the bank .he must repay the loan after 3 years . the bank changes compound interest at 10% per annum .how much interest will John pay over the three years
Answer:
Step-by-step explanation:
10 percent of 3000 = 300
3000+300=3300
3300+300=3600
3600+300=3900
interest = 3900-3000
= R900
he will pay R900 interest over 3 years.
i think this is the answer.
In 2002 a company's sales revenue was $540,000 and its marketing expenses were $97,200. Marketing expenses are what percentage of total sales?
Answer:
18%
Step-by-step explanation:
first you divide 97,200 from 540,000= 0.18 x 100=18%
In a class of student 17 like volleyball like basketball and 10 like both games . show in venn-diagram and find the number student who do not like both games
The number of students who do not like both games is 3
What is a Venn Diagram?John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.
How to solveStudents who like only volleyball=17-10=7
Students who like only basketball=15-10=5
Students who like both sports =10
Students who like one or more sports =7+5+10=22
Students who do not like any sport =25-22=3
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In a class of 25 students, 17 like volleyball, 15 like basketball and 10 like both games. Find the number of students who don't like any of the games.
If the quadrilateral below is a trapezoid, solve for x.
X =
PLEASE HELP
Answer:
x = 7
Step-by-step explanation:
In a trapezoid
each lower base angle is supplementary to the upper base angle on the same side , then
∠ S + ∠ V = 180
8x - 21 + 145 = 180
8x + 124 = 180 ( subtract 124 from both sides )
8x = 56 ( divide both sides by 8 )
x = 7