The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $2400/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $3000. If local mortgage rates are 4.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)
Answers
Using the monthly payment formula, the price range of houses that they should consider is:
[$513,666.78, $592,083.48].
What is the monthly payment formula?It is given by:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are given as follows:
r = 0.045 -> r/12 = 0.045/12 = 0.00375.n = 30 x 12 = 360.The minimum price, discounting the down payment, is found when A = 2400, hence:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
\(2400 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}\)
\(P = \frac{2400[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}\)
P = $473,666.78.
Considering the down payment, we add $40,000, hence the minimum value of the range is: $513,666.78.
The maximum price, discounting the down payment, is found when A = 3000, hence:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
\(3000 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}\)
\(P = \frac{3000[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}\)
P = $592,083.48.
Considering the down payment, we add $40,000, hence the maximum value of the range is: $592,083.48.
Hence the price range is:
[$513,666.78, $592,083.48].
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Related Questions
Mr. Lopez surveyed some of the students in the after-school program to figure out whether he should buy jumbo chocolate chip cookies or cinnamon twists for dessert. The circle graph shows the results. Cinnamon twists were chosen by 12 students. How students said he should buy jumbo chocolate chips cookies?
Answers
68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
What is a circle graph?
A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.
Let's say the total number of students = X.
From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.
Which means that
\(X*\frac{15}{100}=12\\ X=80\)
Therefore the total number of students is 80.
Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.
Which is equal to 80-12=68.
Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
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Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? choices
Answers
Answer: 2⁹5³ = 64,000
Step-by-step explanation:
There are 9 questions with 2 options (true or false) = 2⁹
There are 3 multiple questions with 5 options = 5³
true/false questions AND multiple choice questions
2⁹ x 5³ = 2⁹5³
This week the art museum giveaway thousand 200 tickets to the Greco’s exhibit which was 150% as many tickets as a key figure out how many tickets Elysium give away his work is your
Answers
Answer:
about 300
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
A baseball player gets 18 hits in the first 21 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 28 games?
In the first 28 games, he'll get how many hits.
Answers
Answer:
126
Step-by-step explanation: I am pretty sure this is right so my explanation for this answer is, I subtracted 28 by 21 to see how many games were left, I got 7. So then I multiplyed 18 by 7 to see the total of each to have the final answer.
(sorry if wrong)
Help please, I attached the question. Is it a!?

Answers
Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
\(0=ax^2+bx+c\)
The number of solutions it has can be determined using its discriminant:
\(\Delta = b^2-4ac\)
Where:
If the discriminant is positive, we have two real solutions. If the discriminant is negative, we have no real solutions. And if the discriminant is zero, we have exactly one solution.We have the equation:
\(2x^2+5x-k=0\)
Thus, a = 2, b = 5, and c = -k.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:
\(b^2-4ac=0\)
Substitute:
\((5)^2-4(2)(-k)=0\)
Solve for k. Simplify:
\(25+8k=0\)
Solve:
\(\displaystyle k = -\frac{25}{8}\)
Thus, our answer is indeed A.
2 bags is to 10 buttons as ? Bags is to 90 buttons
Answers
- left his house and drove to the store. He stopped and went inside. From he drove in the same direction until he got to the bank. He stopped and went the bank. Then he drove home. The graph below shows the number of blocks com home Connor is a minutes after he left his house, until he got back home.Connor left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Connor is a minutes after he left his house, until he got back home.
Answers
The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.
What is graph?Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.
It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.
The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.
Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.
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4
Each person in a fitness club is going to get a free gift.
Stan is going to order the gifts.
Stan takes a sample of 50 people in the fitness club.
He asks each person to tell him the gift they would like.
The table shows information about his results.
Gift
Number of people
17
sports bag
7.
gym towel
headphones
11
voucher
15
There are 700 people in the fitness club.
(1) Work out how many sports bags Stan should order.
Answers
Answer:
The answer would be 98.
Step-by-step explanation:
You divide 700 by 50. Then multiply by 7.
Answer:
238
Step-by-step explanation:
700 divided by 50 = 1414 multipled by 17 = 238what is the perimeter of the rectangle
Answers
Answer:
28 because 8 plus 8 plus 6 plus 6 sooooo 28:) brainly?
Step-by-step explanation:
A fair coin is spun four times. Circle the probability of getting four Heads.
A 1/2 B 2 C 1/8 D 1/6
Answers
Answer:the answer is 1/16
so none of the above
Step-by-step explanation:
1/8 I think as the chance of getting a heads on a fair coin is 1/2 and you do this 4 times so it is 1/8
What are the rules for multiplying and dividing negative numbers?
Answers
Answer: if you have 2 of the same sign its positive. it you have two different signs its negitive
Step-by-step explanation:
What is the size of matrix A?
What are the entries of the fourth row of matrix A?
What are the entries of the third column of matrix A?
What is the entry in the (3,4)th position of matrix A?
Answers
Therefore , the solution of the given problem of matrix comes out to be matrix A's (3,4)th place is -1.
What is matrix?A matrix is a group of numbers arranged in rows and columns to form a rectangular array. The numbers make up the matrix's constituents or parts. Matrix algebra is widely used in many branches of mathematics, as well as in the sciences of architecture, physics, economics, and statistics.
Here,
Given that matrix A has 4 rows and 5 columns,
=> it has a dimension of 4 x 6.
=> -1, 2, 3, 4, and 5 are the values in the fourth row of matrix A.
=> 2, 0, 6, and -3 are the values in matrix A's third column.
The entry in matrix A's (3,4)th place is -1.
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A three-way intersection is sometimes called a
T-intersection
Y-intersection
Both a and b
Neither a nor b
Answers
Answer:
Both A and B
Step-by-step explanation:
Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.
The growth of a colony of bacteria is modeled by the function below, where t is the
is time in hours after the culture is begun and f(t) is the number of bacteria present.
After how many hours will there be 2000 bacteria in the colony? Round your answer
to the nearest hundredth (two decimal places).
f(t) = 500e^0.195t
Answers
namely, what is "t" when f(t) = 2000
\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t\)
for each graph determine the following
Answers
Answer + Step-by-step explanation:
• is it a function?
No , because f(2) = 1 and f(2) = -1
• Domain :
[1 , 5]
• Range :
[-4 , 4]
• y-intercept :
It doesn’t have y-intercepts ,because the graph doesn’t cross the y-axis.
• Zero :
x = 1 ,because f(1) = 0
• f(3) = ± 2
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Let's solve ~Here, for some values of x, we have more than one value of y. so we can conclude that it's not a function.
or
Draw vertical lines all over the graph, if the vertical lines cut the curve once then it is a function, and if more than once then it isn't a function.
Since the lines cut the curve more than once, it isn't a function
Domain :\(\qquad \sf \dashrightarrow \: ( 1 , 5 )\)
Range :\(\qquad \sf \dashrightarrow \: (-4 , 4)\)
Y - intercept :It doesn't cut y - axis, so it doesn't have y - intercept
Zeros :The values of x at which the curve cuts the x - axis are the zeros.
In the given graph zero is 1 Value of F (3) = ?If we plug the x - coordinate as 3, it has two y - coordinates : -2 and 2
So, F (3) = - 2 and 2
plz answer this question without putting links or files
Answers
Answer:
(6,14) (7,16) (8,18)
Step-by-step explanation:
The x values are going up by one, while the y values are going up by 2.
The graph of f(x) is shown.
For what values of x does f(x)=0?
Answers
Answer: X = -4, 0, 2
Step-by-step explanation:
Wherever the line touches the x-axis the f(x) or y = 0
Please answer this question.
Answers
Answer:
Step-by-step explanation:
\(1c-0.25c=0.75c\)
each function
f(x)=-4x-5;
ion for
Find ƒ(1)
for the given
Answers
When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.
The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.
Replacing x with 1, we have:
ƒ(1) = -4(1) - 5
Simplifying further:
ƒ(1) = -4 - 5
ƒ(1) = -9
Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.
Let's break down the steps taken to arrive at the solution:
1. Start with the function f(x) = -4x - 5.
2. Replace x with 1 in the function.
3. Evaluate the expression by performing the necessary operations.
4. Simplify the expression to obtain the final result.
In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.
It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.
Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.
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can u slove ASAP please
Answers
Answer:
B) 352
Step-by-step explanation:
45% = 0.45
640 x 0.45= 288
288 is how many students walked to school
So to find how many took the bus to school
640- 288= 352
Talwar wants to invest R5800 at simple interest rate of 12,2% per annum. How many years will it take for the money to grow to R26100
Answers
It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.
To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:
Time = (Amount - Principal) / (Principal × Rate)
Plugging in the values, we have:
Time = (R26,100 - R5,800) / (R5,800 × 0.122)
= R20,300 / R708.6
≈ 28.67 years
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Antonio le da cada dia a su perro siete decimos de bote de comida para perros ¿ para cuantos dias tiene con 7/2 de bote
Answers
La cantidad de comida de 7 / 2 de un bote sirve para un número de días de 5 días.
¿Cómo determinar la duración de un bote de comida para perros?
En este problemas tenemos que Antonio da una ración fija de comida a su perro, se indica que consume siete décimos (7 / 10) de un bote de comida cada día para alimentar a su perro. Tenemos aquí un situación de relación directa entre la cantidad de comida (y) y el número de días para provisiones (x).
A partir del enunciado, se deriva la siguiente ecuación:
y = (7 / 10) · x
Si tenemos que y = 7 / 2, entonces el número de días para provisiones es:
7 / 2 = (7 / 10) · x
x = 10 / 2
x = 5
La cantidad de comida de 7 / 2 de un bote sirve para un número de días de 5 días.
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Write a sentence of the form “–––––––––––––– is a function of –––––––.”
Type your response in the space below.
Answers
"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.
It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.
In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.
Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.
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Question is present in the image
Answers
The equation that is equivalent to P = B + Brz is:
r = (P - B) / Bz
To see why, we can rearrange the original equation as follows:
P = B + Brz
P - B = Brz
(P - B) / Bz = r
Therefore, r = (P - B) / Bz is equivalent to P = B + Brz.
Now let's check the given options:
x = P/Br + 1/r
This equation is not equivalent to P = B + Brz.
r = (P - B) / Bz
This is the correct equation that is equivalent to P = B + Brz.
r = Bz / (P - B)
This equation is not equivalent to P = B + Brz.
B = P / (rz + 1)
This equation is not equivalent to P = B + Brz.
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Có 2 chuông gà: chuồng 1 có 5 trống 10 mái ,chuồng 2 có 6 trống 14 mái. Có 1 con ở chuồng 2 nhảy sang chuồng 1 . từ chuồng 1 bắt ngẫu nhiên ra 2 con. Tính xác suất bắt được
a . 2 con trống
Answers
f(x) = 6x + 5 and x(y) = 4y2 – 25 For the given functions, find f(x) if y = 3.
Answers
Answer:
if my math is right the answer is f(x) =11(19)
Step-by-step explanation:
f(x) =6x+5
divide x form both sides
f=6+5
f=11
x(y) =4y2-25
x(3) =4 (3) 2-25
divide 3 from both sides
x=4(1) 2 -25
add the 4 and 2
x=6(1)-25
x=6-25
x=19
f=11 x=19
HELP PEOPLE PLEASE PLEASE PLEASE BRAINIEST IF RIGHT ONLY IF RIGHT DO NOT, I REPEAT DO NOT ANSWER IF YOU DONT KNOW OK THANK YOU HURRY! BTW DUE TODAY PLEASE PLEASE PLEASE PLEASE
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answers
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
The sum of -7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7.
Answers
Answer:
\(\huge\boxed{No \ solutions}\)
Step-by-step explanation:
Our first goal is to transform these words into numbers for an expression.
Let's break it down.
-7 times a number
We'll assume that the number is \(n\). -7 times a number can be represented as \(-7n\).
8 times the sum of the number and 1
We can break this complex statement down.
8 times the sum of the number and 1
The sum of the number and 1 will be \(n+1\). 8 times that will be \(8(n+1)\). Since it says at the beginning the sum of, we add \(8(n+1)\) to \(-7n\).
\(-7n + 8(n+1)\)
Is the same as the number minus 7.
"Is the same" means we use an equal sign. The number minus 7 will be \(n-7\). So we get \(-7n + 8(n+1)=n-7\)
Now we can solve for n by reversing the equation until we have n isolated on one side.
\(-7n + 8n + 8 = n-7\)
\(n + 8 = n-7\)
\(8 = -7\)
We end up with 8 = -7. This is not possible. Therefore, there are no real values of x that satisfy this equation.
Hope this helped!
3 1/8 divided by (x - 4 7/28) = 17/18 + 1 5/6
(Key on how to write the mixed numbers: Three is a whole number and then the fraction is 1/8, 4 is the whole number and 7/28 is the fraction, 1 is the whole number and 5/6 is the fraction)
Please provide the work and the answer! :)
Answers
x = 301/56
Algebraic expressionsAlgebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expression
Given the algebraic expression,
\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)
Step 1:
Simplify the expression by converting the mixed numbers into improper fractions:
25/8 ÷ ( x - 119/28) = 17/18 + 11/6
Step 2: Simplify the right side of the equation
25/8 ÷( x - 119/28) = 17/18 + 33/18
25/8 ÷( x - 119/28) = 50/18
Step 3: Multiply both sides of the equation by (x - 119/28)
25/8 = 50/18 × (x - 119/28)
Step 4: Multiply both sides of the equation by (18/50)
25/8 × (18/50) = (x - 119/28)
Step 5: Simplify the left side of the equation
9/8 = (x - 119/28)
Step 6: Add 119/28 to both sides of the equation
9/8 + 119/28 = x
Step 7: Calculate the value of x:
x = 9/8 + 119/28
= 63/56 + 238/56
= 301/56
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11. Shrimp are often found in tropical climates and can be raised on farms or caught in the wild.
Elena was taking inventory of 1-pound shrimp packages at the end of the day at a seafood
market. She recorded the country of origin and whether the package contained shrimp that
were farm-raised or wild-caught.
• 27 packages of shrimp were farm-raised in Mexico.
• 40 packages of shrimp were farm-raised in Honduras.
• 52 packages of shrimp were farm-raised in Ecuador.
• 13 packages of shrimp were wild-caught in Mexico.
6 packages of shrimp were wild-caught in Honduras.
• 28 packages of shrimp were wild-caught in Ecuador.
a. A package of shrimp is selected at random from those inventoried. What is the probability
that a package of wild-caught shrimp came from Honduras?
Answers
The probability that a package of wild-caught shrimp came from Honduras is 0.0036.
How to calculate the probability?The probability that a package of wild-caught shrimp came from Honduras will be:
= Number of wild caught in Honduras/ Total number
= 6/(27 + 40 + 52 + 13 + 6 + 28)
= 6/166
= 0.036
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