2. A man gets 1.8 million loan to buy a house, he paid interest at the rate of 9% per annum. In the first year, he paid the interest on the loan, he also paid back 140,000 of the money he borrowed. (1) how much did he pay in the first year altogether, (2) if he paid this money by monthly installment, how much did he pay per month.
Answers
(1) The amount of interest he paid in the first year altogether is 302,000.
(2) The monthly installment is 25,166.67 per month
How did we get the values?(1) The amount of interest he paid in the first year is 1.8 million x 9% = 162,000.
So, in the first year, he paid a total of 162,000 + 140,000 = 302,000.
(2) To calculate the monthly installment, we first need to find out the total amount he paid in a year and then divide it by 12:
302,000 ÷ 12 = 25,166.67
So, he paid 25,166.67 per month.
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Answer:
$296,318.52$24,693.21Step-by-step explanation:
You want to know the total paid during the first year of a $1.8M loan at 9% if the balance is reduced by $140,000 after 12 monthly payments. You also want to know the amount of the monthly payment.
Future valueThe remaining balance of an amortized loan is given by the formula ...
FV = PV(1 +r)^n - <future value of payments>
where r is the monthly interest rate, and n is the number of months.
Using the given loan values, we have ...
1,800,000 -140,000 = 1,800,000(1 +0.09/12)^12 -<payment value>
(2) Payment amountSolving for the future value of the payments, we find ...
<payment value> = 1,800,000(1.093806898) -1,660,000 = 308,852.42
This is the future value of the payments made, so some further calculation is required to find the amount of the payment.
<payment future value> = P((1+r)^n -1)/r = P(1.0075^12 -1)/0.0075
P = <payment future value>/12.5075864
P = 308,852.42/12.5075864 = 24693.21
The amount of the monthly payment was $24,693.21.
(1) Total paid12 monthly payments were made in the first year, so the total paid was ...
12 × $24,693.21 = $296,318.52 . . . . total paid in the first year
__
Additional comment
The attachment confirms these numbers. It is the output of an online remaining balance calculator. The difference of $0.04 between the bottom two numbers is a consequence of rounding. The given payment actually reduces the balance by $140,000.04.
Related Questions
To evaluate 8^2/3 find
Answers
To evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the powers they possess, many rules of exponents are given.
Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
The given value can be written as:
[tex]8^{\frac{2}{3} } = \sqrt[3]{8^{2} }[/tex]
Hence, to evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.
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the letters in the word miami are rearranged at random so that every possible anagram is equally likely. what is the probability that it still spells miami?
Answers
The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.
Let us count the total number of ways MIAMI can be arranged regardless of condition.
There are 2 M’s 2 I’s 1 A in word.
Total ways of arrangement will be = 5!/2!2!
Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1
Total ways of arrangement will be = 5 × 2 × 3
Total ways of arrangement will be = 30 ways
Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.
Thus, the probability will be = 3!/30
The probability will be = (3 × 2 × 1)/30
The probability will be = 6/30
The probability will be = 1/5
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the president of state university wants to forecast student enrollments for this academic year based on the following historical data: year enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 last year 21,000 what is the forecast for this year using exponential smoothing with alpha
Answers
The forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.
Exponential smoothing is a time series forecasting method that uses a weighted average of past observations to make predictions. In this case, the weight assigned to each observation is determined by a smoothing parameter, alpha, which is a value between 0 and 1.
The formula for exponential smoothing with alpha = 0.5 is given by:
F(t) = alpha * Y(t) + (1 - alpha) * F(t-1)
where F(t) is the forecast for time t, Y(t) is the actual observation at time t, and F(t-1) is the forecast for the previous time period.
Starting with the forecast for two years ago, we can use this formula to make a forecast for each year until this academic year.
F(2) = 0.5 * 20,000 + (1 - 0.5) * 16,000 = 18,000
F(3) = 0.5 * 18,000 + (1 - 0.5) * 18,000 = 18,000
F(4) = 0.5 * 16,000 + (1 - 0.5) * 18,000 = 17,000
F(5) = 0.5 * 15,000 + (1 - 0.5) * 17,000 = 16,250
F(6) = 0.5 * 21,000 + (1 - 0.5) * 16,250 = 18,625
So the forecast for this year (F(6)) is 18,625. Therefore, the correct answer is 18,625.
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Complete question:
The president of State University wants to forecast student enrollment for this academic year based on the following historical data: Year Enrollments 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with alpha = 0.5, if the forecast for two years ago was 16,000?
18,750
19,500
21,000
22,650
None of the above
Function Transformations
Given the point (-2,−1) is on the graph of f(x), find a point (written as an ordered
pair) that must be on each of the transformations of f(x) written below:
Ordered pair on the graph
y=f(x-4)-4
Ordered pair on the graph
y=f(x-4) +4
Ordered pair on the graph
y = f(x+4)-4
Ordered pair on the graph
y = f(x+4) +4
Answers
(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.
What do you mean by transformation?In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.
In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.
In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.
In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.
To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.
y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).
y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).
y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).
y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).
So, the ordered pairs that must be on each of the transformations of f(x) are:
y = f(x-4) - 4: (-6, f(-6) - 4)
y = f(x-4) + 4: (-6, f(-6) + 4)
y = f(x+4) - 4: (2, f(2) - 4)
y = f(x+4) + 4: (2, f(2) + 4)
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a woman making $2500 per month has her salary reduced by 10% because of sluggish sales. one year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. find her salary after the raise. g
Answers
After the raise, the salary of woman becomes $2700.
Salary Reduction and RaiseThe answer was determined through simple arithmetic calculations.
First, the initial salary of $2500 was reduced by 10%, which is calculated as $2500 * 0.1 = $250.So the new salary after the reduction was $2500 - $250 = $2250.Next, a 20% raise was given over the reduced salary of $2250, which is calculated as $2250 * 0.2 = $450.Finally, the raise was added to the reduced salary, resulting in $2250 + $450 = $2700.So, the woman's salary after the raise is $2700.This method of calculation can be applied to any similar scenario where an initial salary is reduced by a certain percentage and then increased by another percentage. The formula used can be generalized as:
Final Salary = (Initial Salary - Initial Salary * Reduction Percentage) * (1 + Raise Percentage)
It's a simple and straightforward method that can be easily applied to find the final salary in similar cases.
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Sales of the smart phone continued to grow exponentially beyond 2011.
In 2010, approximately 39.99 million smartphones of this brand were sold worldwide.
In 2011, approximately 72.9 million smartphones of this brand were sold worldwide.
In which year did the number of smartphones the brand sold exceed 200 million?
Answers
Answer: This question can be solved using exponential growth formula:
N = N0 * e^(rt)
Where N is the number of smartphones, N0 is the initial number, r is the growth rate, t is the number of years and e is the base of the natural logarithm (approximately equal to 2.718).
First, we need to find the growth rate:
r = (ln(N/N0)) / t
Using the data from 2010 and 2011:
r = (ln(72.9/39.99)) / 1
Next, we can find the year when the number of smartphones sold exceed 200 million:
N = 200 million
N0 = 39.99 million
t = (ln(N/N0)) / r
t = (ln(200/39.99)) / r
To find the year, we need to add t to the initial year 2010.
The number of smartphones the brand sold exceeded 200 million in the year 2023.
Step-by-step explanation:
The sum of two numbers is 33 and the difference is 9. What are the numbers?
Answers
Answer:
21 & 12
Step-by-step explanation:
let the sum of x and y be 33.. so,
x + y = 33
x - y = 9
x = 9 + y
x + y = 33
9 + y + y = 33
9 + 2y = 33
2y = 24
y = 24/2
y = 12
similarly,
x + y = 33
x + 12 = 33
x = 21
hence, sum: 21 + 12 = 33
difference : 21 - 12 = 9
if gas costs $3.25 per gallon, and it takes 21 seconds to pump one gallon of gas, how long will it take to pump $23.36 worth of gas (in seconds)?
Answers
We need to know how many gallons of gas $23.36 will buy, so we divide the amount by the cost per gallon: $23.36 ÷ $3.25 per gallon = 7.20 gallons.
Once we know how many gallons of gas we are buying, we can then find out how long it will take to pump that amount of gas. To do that, we multiply the number of gallons by the time per gallon: 7.20 gallons × 21 seconds/gallon = 151.2 seconds.
So, the answer to the question is 151.2 seconds, which is the total time it will take to pump $23.36 worth of gas at $3.25 per gallon and 21 seconds per gallon.
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largest possible of x and smallest possible value of x
Answers
Answer:
A.) 16
B.) 18
Step-by-step explanation:
Mode is the number that shows up the most. For A.) they are saying the mode is 1. We see that for 1, the corresponding number is 17. Since no number can go larger than 17, that means x must be 16.
For B.) they are saying the mode is 2. the corresponding number is X. they want the smallest value possible, so what we do if find the largest number, which is 17, and simply add one
At a height of n metres above sea level, the atmospheric pressure is Pn
millibars.
At a height of (n + 1000) metres above sea level, the atmospheric pressure is
P(n + 1000) millibars
where P(n + 1000) = 0.88Pn
At sea level, the atmospheric pressure is 1013 millibars.
Calculate the atmospheric pressure at a height of 3000 metres above sea level.
Give your answer correct to 3 significant figures.
Answers
Pressure at 3000 meters above sea level will be 690.33 millibars.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, At a height of n meters above sea level, the atmospheric pressure is Pn millibars. At a height of (n + 1000) meters above sea level, the atmospheric pressure is P(n + 1000) millibars.
where,
P(n + 1000) = 0.88Pn
at n = 0
P(1000) = 0.88 P(n = 0)
Since,
P(n = 0) is 1013 milibar
thus,
P(1000) = 0.88 * 1013
At n = 1000
P(1000 + 1000) = 0.88 P(n = 1000)
P( 2000) = 0.88 * 0.88 *1013
at n = 2000
P(2000 + 1000) = 0.88 P(n = 2000)
P( 3000) = 0.88 *0.88* 0.88 *1013
Thus,
P(3000) = 690.33
Therefore, Pressure at 3000 meters above sea level could be 690.33 millibars.
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n a two-variable diagram, there is a straight line which is parallel to the vertical axis. the slope of this line is a. zero. b. infinite. c. indicative of a direct relationship between two variables. d. indicative of an inverse relationship between two variables.
Answers
The slope of a straight line that is parallel to the vertical axis is zero.
A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.
In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.
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In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC. What is the area of triangle DEC
Answers
Answer:
5
Step-by-step explanation:
The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:
E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )
= ( (0 + 2) / 2, (0 + 5) / 2 )
= (1, 2.5)
So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.
Consider APQR in the figure below.
The perpendicular bisectors of its sides are SV, TV, and UV. They meet at a single point V.
(In other words, V is the circumcenter of APQR.)
Suppose UV=30, PS= 64, and RV=78.
Find PU, PR, and QV.
Note that the figure is not drawn to scale.
Answers
The given values are below:
PU = 72PR = 128QV = 78How to get the valuesNote that point V is the intersection of the three perpendicular bisectors of a triangle which is also the center of the subtriangle circumference
So QV = RV = PV = 78
Point S is the midpoint of PR
So PR = 2,
PS = 2 x 64 = 128.
Because triangle QUV is a right triangle,
QV = 78.
UV= 30
QV^2 + UV^2 = QV^2
Therefore, PU = 72
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If one bestfriend went to the store with $5 and the other bestfriend went with $20 how many they had in total?
Answers
The amount of money they had in total is $25
How to calculate the amount of money that the best friends had in total?One bestfriend went to the store with $5
The other best friend went to the store with $20
The amount of money they had in total can be calculated as follows
= 20 + 5
= 25
Hence the amount of money the best friends had in total is $25
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Answer: 25$
Step-by-step explanation: 20 plus 5 equals 25.
Evaluate the expression when c=36 and d=24
Answers
The value of the expression after evaluating it according to the values of c and d is 42.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Since, no expression is given, let us assume that the expression is
c + d / 4
Now we have to evaluate the value of the expression according to the values of c and d,
For that, we will simply put the given values in the expression and solved it accordingly,
Put c = 36 and d = 24 in the expression we assumed,
c + d / 4 = 36 + 24/4
= 36 + 6 = 42
Hence, the value of the expression after evaluating it according to the values of c and d is 42.
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At the Hula Factory, the assembly line produces 212 leis in a batch. The leis are packaged in boxes with 30 each. If 14 batches are made in one day, how many leis will be leftover at the end of it?
Answers
Answer:
-2 leis.
Step-by-step explanation:
212 * 14 = 2,968 leis
2,968/30 = 99 boxes
99*30=2970
2968-2970=-2
There is a problem with the wording of this question. There isn't a total so it's really confusing...
Mark Ran 875 miles this year in the track club. Mark Ryan in 52 track meets and ran the same number of miles in each. How many miles did mark run in each track meet? Brainly
Answers
Answer:
16.826
Step-by-step explanation:
I think you divide 875 by 52 which is 16.826 correct me if im wrong.
Answer:
16.8 miles in each track meet
Step-by-step explanation:
You divide 875 by 52 to see how many miles Mark ran in each track meet
875/52 = 16.8
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts
that are more than 2 standard deviations from the mean. The quality-control engineer
knows that the bolts coming off the assembly line have mean length of 12 cm with a
standard deviation of 0.10 cm. For what lengths will a bolt be destroyed?
Answers
The lengths that the bolt will be destroyed are given as follows:
Less than 11.8 cm.More than 12.2 cm.How to obtain the lengths?The lengths are obtained applying the proportions in the context of this problem.
Considering the mean length of 12 cm, and the standard deviation of 0.1 cm, the length that is 2 standard deviations below the mean is given as follows:
12 - 2 x 0.1 = 11.8 cm.
The length that is 2 standard deviations above the mean is given as follows:
12 + 2 x 0.1 = 12.2 cm.
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What Is a Kilometer in Math?
Answers
A kilometer (km) is a unit of length in the metric system, which is based on the meter as the basic unit of length.
It is equal to one thousand meters, or one million centimeters, and is used in many contexts around the world when referring to the measurement of distances between two points.
Kilometers are commonly used in the context of travel, as they are often used to measure the distance between two cities or countries, or to measure the length of a journey or route. In addition, kilometers are often used to measure the depth of bodies of water, and to measure the size of land features such as mountains and valleys.
In mathematics, the kilometer is used to measure the magnitude of certain quantities, such as the speed of an object or the acceleration of a body. It is also used to measure the size of certain objects, such as the radius of a circle or the length of a line.
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A kilometer is a unit of length in the metric system. In mathematics, a kilometer is a unit of length used to measure distance.
It is part of the metric system, which is the most widely used system of measurement in the world. A kilometer is defined as 1000 meters. This makes it a convenient unit of measurement for large distances, such as those between cities, or for measuring the length of roads and highways.
In mathematical calculations involving distances, kilometers can be used to express the length of a segment or the distance between two points. They can also be converted to other units of length, such as meters, centimeters, or miles, by using appropriate conversion factors.
In conclusion, a kilometer is a unit of length in the metric system that is used to measure large distances in mathematics and in everyday life.
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PLEASE HELP ME PLEASE THANK YOU
PART A
Craig went bowling with $35.50 to spend. He rented the shoes for $6.50 and paid $7.25 for each game.WRITE AN EQUATION TO DETERMINE X,THE GREATEST NUMBER OF GAME CRAIG COULD HAVE PLAYED. ONLY WRITE EQUATION HERE
Equation:__________
PART B
Determine what the greatest number of games he can play is. SHOW YOUR WORK
Answer:_________Games
Answers
Answer:
A. $6.50 + $7.25x ≤ $35.50
B. 4 games
Step-by-step explanation:
x = number of games played
$6.50 + $7.25x ≤ $35.50
7.25x ≤ 35.5 - 6.50
7.25x ≤ 29
x ≤ 29/7.25
x ≤ 4
I tried my best and this is what I got and how:
Part A Equation: $7.25x = $29.00
Part B Answer: x = 4
The greatest number of games Craig can play is 4.
If −8x+6y=4 is a true equation, what would be the value of −8x+6y+6?
Answers
the value of the algebraic equation −8x+6y+6 will be 10.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, −8x+6y=4 is a true equation
To find the value of the equation −8x+6y+6
=> −8x+6y+6
Since −8x+6y = 4 given
Thus,
=> 4 + 6
=> 10
Therefore, the value of the algebraic equation −8x+6y+6 will be 10.
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Please help thank you
Answers
Answer:
∠ A = 138° , ∠ C = 75°
Step-by-step explanation:
ABCD has parallel bases and is a trapezium
each lower base angle is supplementary to the upper base angle on the same side.
∠ A + 42° = 180° ( subtract 42° from both sides )
∠ A = 138°
∠ B + ∠ C = 180 , that is
12x - 3 + 9x - 6 = 180
21x - 9 = 180 ( add 9 to both sides )
21x = 189 ( divide both sides by 21 )
x = 9
Then
∠ C = 9x - 6 = 9(9) - 6 = 81 - 6 = 75°
Meena owns a small business selling bagels. She knows that in the last week 35
customers paid cash, 12 customers used a debit card, and 17 customers used a credit
card.
If next week, she is expecting 700 customers, about how many would you expect to
pay with a debit card? Round your answer to the nearest whole number.
Answers
131 customers would expect to pay with a debit card out of 700 Customers.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
customers paid by cash=35
customers used a debit card = 12
customers used a credit card = 17
If she is expecting 700 customers then number of customers used Debit card will be
= 700 x 12/ (35+12+17)
= 700 x 12/64
= 131.25
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Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software.
Answers
Answer:
$49.59
Step-by-step explanation:
$20.75+$10.59+$18.25=$49.59
what is 60/40 simplified
Answers
Answer:
3/2
Step-by-step explanation:
You can divide the numerator and denominator by its GCF(Greatest common factor) which in this case is 20.
60/ 20 = 3
40/20 = 2
3/2
Select all possible cross-sections of a sphere
Answers
Circle: a cross-section that goes through the center of the sphere and creates a circular shape.
Point: a cross-section that goes through the center of the sphere and creates a single point.
2b x b
is this answer only 2b ^ 2 or is there any other answer without using exponentiation
Answers
The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.
Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.
So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.
The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.
The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.
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Please solve both questions 6 and 7
Answers
Answer:
6. 4x + 28 + x + 19 + 3x + 13
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x = 117
Step-by-step explanation:
6. 4x + 28 + x + 19 + 3x + 13 = 180
8x + 60 = 180
8x = 120
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x + 423 = 540
x = 117
Denise has $250 in her checking account. Each time she buys a bottle of water, she spends $2. If Denise buys
x bottles of water, how much money will remain in her account?(1 نقطة)
Answers
The remaining amount of money in Denise's account is $250 - (2x).
Therefore, if Denise buys x bottles of water, she will have $250 - (2x) remaining in her account.
Denise has $250 in her checking account.
Each time she buys a bottle of water, she spends $2.
If Denise buys x bottles of water, the total amount of money spent is 2x.
To calculate the remaining amount in Denise's account, we need to subtract the total amount of money spent (2x) from the original amount of money in her account (250).
Therefore, the formula to calculate the remaining amount is $250 - (2x).
Substituting the value of x in the formula, we get the remaining amount of money in Denise's account.
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For every bottle of water Denise buys her balance decreases by $2. So If Denise buys x bottles of water, her balance decreases by $2 * x.
Let's call the amount of money remaining in Denise's account after buying x bottles of water M.
The equation to find M is:
M = 250 - 2x
This equation says that the money remaining in Denise's account is equal to her initial $250 balance minus the amount she spent on buying x bottles of water, which is $2 per bottle.
In other words, for every bottle of water Denise buys, her balance decreases by $2. So, if she buys x bottles of water, her balance decreases by $2 * x.
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In a group of 50 students, 20 like only Maths and 15 like only Science. If the number of students who do not like any of the two subjects is double of the number of students who like both subjects, find the number of students who like at most one subject by using a Venn-diagram.
Answers
To solve this problem using a Venn diagram, we need to start by drawing a rectangle to represent the group of 50 students, and then draw two overlapping circles to represent the subjects of Math and Science. Let's label the regions of the Venn diagram as follows:
M: Students who like MathS: Students who like ScienceMS: Students who like both Math and ScienceNeither: Students who like neither Math nor ScienceWe know that 20 students like only Math, 15 students like only Science, and the number of students who like both subjects is unknown. We also know that the number of students who like neither subject is double the number of students who like both subjects. Let's use this information to fill in the Venn diagram:
The number of students who like at least one subject is the sum of the students who like only Math, the students who like only Science, and the students who like both subjects: 20 + 15 + MS.The number of students who like neither subject is double the number of students who like both subjects: 2MS.We can set up an equation using this information:
20 + 15 + MS + 2MS = 50
Simplifying this equation, we get:
3MS = 15
MS = 5
Now we can fill in the Venn diagram:
M MS
\ /
\/
/ \
S----MS
We know that MS = 5, so the number of students who like at most one subject is:
20 (like only Math) + 15 (like only Science) + MS (like both subjects) = 20 + 15 + 5 = 40.
Therefore, 40 students in the group of 50 like at most one subject.