The Fritzes are buying a house that sells for $119,000. The bank is requiring a minimum down payment of 15%. To obtain a 40-year mortgage at 13.5% interest, they must pay 4 points at the time of closing.a Determine the required down payment.b) Determine the amount of the mortgage on the property with the 15% down payment.c) Find the cost of 4 points on the mortgage.
Answers
Explanations:
Given the following parameters:
Cost of house = $119,000
Minimum down payment = 15%
Interest on mortgage = 13.5%
Time required = 40 years
a) To get the required downpayment;
\(\begin{gathered} \text{ Downpayment = 15\% of \$119,000} \\ \text{ Downpayment }=\text{ 0.15 }\times119,000 \\ \text{ Downpayment =\$1}7,850 \end{gathered}\)Hence the required downpayment is $17,850
b) To get the amount of the mortgage on the property with the 15% down payment, we will take the difference in the cost and downpayment.
Amount of mortgage = Cost - Down payment
Amount of mortgage = $119,000 - $17,850
Amount of the mortgage = $101,150
c) To get the cost of 4-points on the mortgage, we need to first calculate the 13.5% interest on a 40-year mortgagee.
\(\begin{gathered} \text{Interest}=\text{PRT} \\ \text{Interest}=119,000\times0.135\times40 \\ \text{Interest}=\$642,600 \end{gathered}\)Cost of 4 points on mortgage = $119,000 + $642,600
Cost of 4 points on mortgage = $761,600
Related Questions
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
Answers
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
What do you mean by compound?A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.
Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.
We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:
3 ml x 3 ml x 3 ml
-------- = ----------
728 ml total, 8 ml overall
If we cross-multiply, we obtain:
8(x) = 3(728)
To find x, we use the formula x = 3(728)/8 = 273
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
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273 milliliters of compound A are needed to make 728 milliliters of the drug.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.
Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:
3 : (3+5) or 3:8
This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.
To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:
3/8 = x/728
where x represents the amount of compound A needed.
To solve for x, we can cross-multiply:
8x = 3*728
8x = 2184
x = 273
Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.
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what is the answer of 5ax +8ax+6ax=?
Answers
All have ax included so add the numbers together.
5ax + 8ax + 6ax = 19ax
If it’s mere addition then the answer should be “19ax”.
Lmk if I ryt!!
Please look at the graphs in the photo. Thank you!
Answers
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
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se trata?
7
Calcula el área de un rectángulo cuya base es 8 y altura 4
Answers
What’s the factor of the expression?
Answers
The answer to this question: B
Solve for 9x-3-8x=7-x
Answers
Answer:
5
Step-by-step explanation:
9x - 3 - 8x = 7 - x
9x - 3 - 8x + x = 7
2x - 3 = 7
2x = 10
x = 5
Answer:
hope u understand
Step-by-step explanation:
\(\: 1. \: x - 3 = 7 - x \\ \: 2. \: x + x - 3 = 7 \\ 3. \: x + x = 7 + 3 \\ 4. \: 2x = 7 + 3 = 10 \\ 5. \: 10 \div 2 = 5 \\ 6. \: x = 5\)
let me explain you now
1. collect like terms
2. move the variable to the left hand side and change its sign
3. move the constant to the right hand side and change its sign
4. collect like terms and add the numbers
5. divide the answer with 2
6. the solution
A wire is 71cm long . you wish to cut it into two pieces. One piece is bent into shape of triangle with legs of equal length .The piece is to be bent into shape of circle .
Answers
To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)
The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)
The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)
Solving for\(\(x\),\) we divide both sides of the equation by 3:
\(\(x = \frac{71}{3}\).\)
Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.
The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:
\(\(x = 2\pi r\).\)
Substituting the value of x we found earlier, we have:
\(\(\frac{71}{3} = 2\pi r\).\)
Solving for r, we divide both sides of the equation by \(\(2\pi\):\)
\(\(r = \frac{71}{6\pi}\).\)
Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.
In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.
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Find the volume.
PLEASE HELP I WILL GIVE BRAINLIEST TO THE RIGHT ANSWER
Answers
Jenny and Buddy collected 376 plastic bottles for recycling.
They recycled 131 bottles on Monday and 114 bottles on Tuesday.
How many bottles do they have left to recycle?
Complete the equations to solve. Enter your answers in the boxes.
Let
m
=
the number of bottles left to recycle after Monday.
Answers
Answer:
151
Step-by-step explanation:
114+131= 272 376-272=104
A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars.
a. Construct a PDF for each investment.
b. Find the expected value for each investment.
c. Which is the safest investment? Why do you think so?
d. Which is the riskiest investment? Why do you think so?
e. Which investment has the highest expected return, on average?
Answers
Answer:
a. Construction of PDF (Probability Distribution Function) for each investment:
Software Company:
x P(x)
$5,000,000 0.10
$1,000,000 0.30
-$1,000,000 0.60
Hardware Company:
x P(x)
$3,000,000 0.20
$1,000,000 0.40
-$1,000,000 0.40
Biotech Firm:
x P(x)
$6,000,000 0.10
$0 0.70
-$1,000,000 0.20
b. Expected value for each investment:
Software Company:
x P(x) Expected value (xP(x)
$5,000,000 0.10 $500,000
$1,000,000 0.30 300,000
-$1,000,000 0.60 -600,000
Total expected value $300,000
Hardware Company:
x P(x) Expected value (xP(x)
$3,000,000 0.20 $600,000
$1,000,000 0.40 400,000
-$1,000,000 0.40 -400,000
Total expected value $600,000
Biotech Firm:
x P(x) Expected value (xP(x)
$6,000,000 0.10 $600,000
$0 0.70 $0
-$1,000,000 0.20 -200,000
Total expected value $400,000
c. The safest investment is the investment in the Hardware Company. Here, the probability of success is highest, with 60%.
d. The riskiest investment is the investment in the Software Company where the probability of failure is highest, with 60%.
e. The investment with the highest expected return on average is the investment in the Hardware Company. It has a total expected return of $600,000.
Step-by-step explanation:
a) Data and Calculations:
Investment amount = $1,000,000
Investment Options:
Software Company:
10% chance of returning $5,000,000
30% chance of returning $1,000,000
60% chance of losing $1,000,000
Hardware Company:
20% chance of returning $3,000,000
40% chance of returning $1,000,000
40% chance of losing $1,000,000
Biotech Firm:
10% chance of returning $6,000,000
70% chance of no profit or loss
20% chance of losing $1,000,000
Help me solve these two problems! Show the work
Answers
Answer:
see explanation
Step-by-step explanation:
2
4x² + 64 ← factor out the common factor of 4 from each term
= 4(x² + 16)
3
(a - 10)² = 121 ( take square root of both sides )
a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )
a = 10 ± 11
then
a = 10 - 11 = - 1
a = 10 + 11 = 21
if g(x)=8(1/2)^x then What is g(3)=
Answers
Answer:
g(3)= 4/3
Step-by-step explanation:
plug in the 3 for the x for get 4/3
Answer:
1
Step-by-step explanation:
put x=3,
8×1/2³ = 8/8 =1
Simplify y² + 11y - 6y + y²,
Answers
In order to simplify the expression
y² + 11y - 6y + y²,
we just have to add the terms with the same unkowns or combine like terms
terms with y: +11y and -6y
terms with y²: +y² and +y²
Now, we combine like terms:
terms with y: +11y - 6y = 5y
terms with y²: +y² + y² = 2y²
Then
y² + 11y - 6y + y²
= 2y² + 5y
Answer: y² + 11y - 6y + y² = 2y² + 5y
simplify 2 1/2 times 3/4
Answers
Answer:
\( \frac{5}{2} \times \frac{3}{4} \\ \frac{15}{8} \)
Answer:
15/8
Step-by-step explanation:
2.5/2 = 1.25
1.25/2 = 0.625
2.5 - 0.625 = 1.875
1.875 = 75/40 = 15/8
A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute.??t (min) 36 38 40 42 44?Heartbeats 2510 2647 2784 2915 3048??The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of t. (Round your answers to one decimal place.)??
(a) t = 36 and t = 42
(b) t = 38 and t = 42
(c) t = 40 and t = 42
(d) t = 42 and t = 44
Answers
Therefore , coordinate problem solution is A) 3140 pulses per minute , B) 2915 beats per minute , C) heartbeat of 2915 beats per minute (D) or 2915.5 beats per minute .
What do coordinates mean?When locating points or other mathematical objects precisely on a region, such as Euclidean space, a coordinate system is a technique that uses one or more numbers or coordinates. Locating a point or item on a the double plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y vectors are used to define a point's location on a 2D plane. a collection of numbers that indicate specific locations.
Here,
The slope method can be used to calculate the patient's heart rhythm after 42 minutes that use the secant line connecting the points with the specified values of t:
Heartbeat change / time change is the trend.
The heart rate can then be estimated using this slope value along with the number for heartbeats at t = 42 minutes.
A)Using coordinates 36, 2510, and 42, 2915 as examples:
Cardiac rate at 42 minutes = 2510 + (42 - 36) * 75 = 3140 Slope = (2915 - 2510) / (42 - 36) = 75
b) Using coordinates (38, 2647) and (42, 2915), respectively:
Cardiac rate at 42 minutes = 2647 + (42 - 38) * 67 = 2915 Slope = (2915 - 2647) / (42 - 38) = 67
c) Applying the values (40, 2784) and (42, 2915):
Heart rate at 42 minutes = 2784 + (42 - 40) * 65.5 = 2915.5 Slope = (2915 - 2784) / (42 - 40) = 65.5
Using coordinates (42, 2915), and (44, 3048), respectively:
Cardiac rate at 42 minutes = 2915 + (42 - 42) * 66.5 = 2915 Slope: (3048 - 2915) / (44 - 42) = 66.5
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A spherical chocolate covered candy hasa diameter of 8cm. 4Part of the candy is a chocolate shell thatis .5cm thick.What is the volume ofjust the chocolate shell?
Answers
We want to calculate the volume of the spherical shell of chocolate.
The chocolate shell is spherical with a thickness of 0.5cm
Volumes of spherical shells can be calculated with the formula;
\(V_{shell}=\frac{4}{3}\pi(R^3-r^3)\)The outer diameter is 8cm. The outer radius is therefore 4cm
The inner diameter is 8-2(0.5)=7cm. The inner radius is therefore 3.5cm
Therefore, we can find the volume of the chocolate shell as;
\(V_{shell}=\frac{4}{3}\pi(4^3-3.5^3)=88.5\operatorname{cm}^3\)Therefore,
\(V_{shell}=88.5\operatorname{cm}^3\)ab=r+d
Solve for a
Please include work
Answers
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\(ab = r + d\)
Divide sides b
\( \frac{ab}{b} = \frac{r + d}{b} \\ \)
\(a = \frac{r + d}{b} \\ \)
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Write an equation for "nine times a number decreased by five is the same as six times the same number increased by seven.
Answers
Answer: 9*x-5 = 6*x+7
Step-by-step explanation:
First we have to understand what it is saying.
9 times x (being a number) minus 5 equal to 6 times x plus 7
Now lets put it into an equation.
\(9*x-5 = 6*x+7\)
the equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940. In this equation, a represents the average age and x represents the years since 1940. Estimate the year in which the average age of brides was the youngest
Answers
Answer:
Please help me important question in image
Step-by-step explanation:Please help me important question in image
Please help me important quePlease help me important question in image
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Please help me important question in image
Please help me important question in image
Answer:
The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.
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True or False?
(–3)^22 is greater than (–2)^33
Answers
Answer:
true
Step-by-step explanation:
(-3)^22 -> to the power of an even number -> answer is positive
(-2)^33 -> to the power of an odd number -> answer is negative
positive # > negative #
Answer:
True
Step-by-step explanation:
First let's compare them.
(-3)²² (-2)³³-3 raised to an even power will give a positive number.
-2 raised to an odd power will give a negative number.
Therefore, (-3)²² > (-2)³³ is a true statement.
he entire graph of the function is shown in the figure below.
Write the domain and range of using interval notation.
Someone please help me. I really nee help. this question is due tonight before 8 and im stuck.
Answers
The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].
The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).
In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.
So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.
In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].
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On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?
Answers
a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:
235 = a * b ^ 0
395 = a * b ^ 10
Solving for a and b, we get:
a = 235
b = (395/235)^(1/10) = 1.067
Therefore, the exponential model for new cases in Milwaukee is:
y = 235 * 1.067 ^ x
b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:
y = 235 * 1.067 ^ 19 = 1018.5
Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.
c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.
I'm stuck and I need help right now
Answers
Answer:
See below.
Step-by-step explanation:
Make a table with values at certain values of x from -2 to 2.
Write in the table f(x) and g(x), and then h(x).
Then, plot the points for h(x).
See the picture below.
D E and F are three points on a straight line such that
DE= 3e + 6f
DF = -10.5e-21f
Find the ratio of
length of DF: length of DE
Answers
The ratio of length of DF to length of DE is e + 2f : -3.5e - 7f.
What is ratio?
One can calculate that how much of one quantity is included in the other by comparing the two amounts of the same unit and obtaining the ratio.
We are given that the Length of DE is 3e + 6f and the Length of DF is
-10.5e - 21f.
So, from this, we get the ratio as
⇒3e + 6f : -10.5e - 21f
Now by taking 3 common from both the sides, we get
⇒e + 2f : -3.5e - 7f
Hence, the ratio of length of DF to length of DE is e + 2f : -3.5e - 7f.
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Roselyn is driving to visit her family, who live 150 kilometers away. Her average speed is 60 kilometers per hour. The car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter. Fuel costs 0.60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answers
Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out
Distance travelled with 20 l of petrol in solution and final answer.
Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.
The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.
Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.
As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.
Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.
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Find the area of the shaded part in the given diagram
Answers
Answer:
30cm^2
Step-by-step explanation:
area of large rectangle = length x width
= 5 X 9 = 45 cm^2
area of small rectangle = length x width
= 3 X 5 = 15 cm ^2
45 - 15 = 30cm^2
50pounds to 35 pounds
Answers
Answer:
I am assuming you mean the difference, In that case it is 15 pounds.
50- 35= 15
Jill is 11 years younger than Pete. The sum of their ages is 29. What’s the age of Pete.
Answers
Answer:
The sum of their ages is 29, which we can express as the equation:
P + (P - 11) = 29
Simplifying the equation:
2P - 11 = 29
Adding 11 to both sides:
2P = 40
Dividing both sides by 2:
P = 20
Therefore, Pete's age, represented by "P," is 20 years old.
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
In triangle FGH, m∠F=59°
and m∠H=77
Complete the equation to determine m∠G
Answers
Answer: 44 degrees
Step-by-step explanation: 59+77+x=180
x=44