The numeric value of the function f(x) = 4x² + 2x + 2 at x = x + 2 is given as follows:
f(x + 2) = 4x² + 20x + 22.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 4x² + 2x + 2
To obtain the numeric value at x = x + 2, we replace the two instances of x by x + 2, hence:
f(x + 2) = 4(x + 2)² + 2(x + 2) + 2
f(x + 2) = 4(x² + 4x + 4) + 4x + 4 + 2
f(x + 2) = 4x² + 16x + 16 + 4x + 6
f(x + 2) = 4x² + 20x + 22.
Missing InformationThe problem asks for the numeric value of the function f(x) = 4x² + 2x + 2 at x = x + 2.
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In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be above $250.000? O Impossible to determine without more information. O n = 50 O n=1000 O n=100 O n= 10
A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.
What is the median value?
The median value of a set of data is the middle value when the data is arranged in order. It is the value that separates the higher half of the data from the lower half. In other words, it's the value that has half the observations below it and half the observations above it.
In a residential neighborhood, the median value of a house is $200,000, which means that half the houses in the neighborhood are worth more than $200,000 and half are worth less.
For a sample median most likely to be above $250.000, the sample size would have to be small and skewed to the right tail, where the higher values are. In this case, the answer would be
Hence, A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.
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Please need help on this
Answer:
1) x² + 4x +1 = 1 (You have to put in +1)
2) True
Step-by-step explanation:
1)
2) A range is a representation of values between two points. When you're calculating the range of a parabola, you only know one of those points to start with. Your parabola will go on forever either up or down, so the end value of your range is always going to be ∞ (or −∞ if your parabola faces down.)
Answer: the answer is true
Step-by-step explanation: There are an infinite amount of numbers the parabola can hit, and there is no limit
hence the statement is true
A building surmounted is in the form of a cylinder by a cone of height 24.m. If the base diameter and total height of the building are 14m and 34 m respectively, find the outer surface area of the building.
Answer: The building is in the form of a cylinder surmounted by a cone. To find the outer surface area of the building, we need to find the total surface area of the cylinder and the cone and add them together.
The total surface area of the cylinder = 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(24) = 2π(49) + 2π(168) = 98π + 336π = 434π square meters
The total surface area of the cone = πr^2 + πr√(r^2 + h^2) = π(7^2) + π(7)(√(7^2 + 24^2)) = 49π + 49π(√(625)) = 49π + 49π(25) = 49π + 1225π = 1274π square meters
The outer surface area of the building is the sum of the total surface area of the cylinder and the cone, which is 434π + 1274π = 1708π square meters.
Step-by-step explanation:
match each term with its definition. experimental group dependent variable control group operational definition independent variable
A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.
A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.
Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.
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HELP ASAP !! WHATS THE END BEHAVIOR ?
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
What is end behaviour ?When referring to a function, "end behaviour" refers to the character of the value as the function parameter becomes closer to +∞ and -∞.
In the given table for f(x), we see that for every value of x, function f(x) is decreasing.
f(-2) = 48
f(0) = 12
f(2) = 3
f(3) = 1.5
In other words as the value of x increases, f(x) is approaching towards 0.
Now we take another function g(x) =
Now we plug in the values of x to get the values of g(x)
g(-1) =2^-1-5
= 1-10/2
= -9/2
= -4.5
g(0) = 2^0-5
= 1 - 5 = -4
g(2) = 2^2-5
= 4 - 5 = -1
g(3) = 2^3-5
= 8 - 5= 3
Now we find that g(x) is increasing with the values of x.
Now we take third function h(x).
By analyzing the given graph we find
h(-4) = 2
h(0) = 3
h(1) = 5
So when we are increasing the value of x function h(x) is increasing.
Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.
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factorise the following:
6 + 9y
Answer:
First find a number you can take out of both numbers.
In this case 3.
You get left with 2+3y
So the answer is 3(2+3y).
Find the surface area of the cylinder. Round your answer to the nearest tenth if necessary.A cylinder with diameter of 6 centimeters and height of 12 centimeters.
Answer:282.6 cm²
Step-by-step explanation:
The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.
Since the diameter is given, we can find the radius by dividing the diameter by 2, so r = 6/2 = 3 cm.
Then we can plug in the values into the formula:
2πr(r+h) = 2π(3)(3+12) = 2π(3)(15) = 90π cm²
To round the answer to the nearest tenth, we can use the following method:
If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.
If the digit in the thousandths place is greater than 5, we round up the hundredths digit.
Since π is an irrational number it can't be rounded to the nearest tenth. But an approximation for π is 3.14 and 90π is approximately 282.6 cm².
a convex pentagon has exterior angles with measures 75°, 62°, 68°, and 101°. the measures of the last exterior angle is?
A convex pentagon has five exterior angles, and the sum of the measures of these angles is equal to 360 degrees.
We know that the measures of the exterior angles of a convex pentagon are 75°, 62°, 68°, and 101°, we need to find the measure of the last exterior angle.
To find the measure of the last exterior angle, we can use the formula:
Sum of all exterior angles = (n-2) x 180
where n is the number of sides in the polygon.
For a pentagon, n = 5, so the sum of all exterior angles is (5-2) x 180 = 540 degrees
So we can use this information to find the measure of the last exterior angle:
75 + 62 + 68 + 101 + x = 540
x = 244
Therefore, the measure of the last exterior angle is 244 degrees.
HELP, (a) only
In the pic above
A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane.
Explain about the Complex plain?A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane. The real and imaginary halves of a complex number are represented by displacements along the x and y axes, respectively, in what is essentially a modified Cartesian plane.
Similar to how we may represent the set of real numbers on a number line, we can represent the set of complex numbers on a complex plane. At the coordinates (0,0)left parenthesis, 0 comma, 0 right parenthesis, two number lines that make up the complex plane cross at a right angle.
You may think of the y-axis as the hypothetical axis.
The actual axes are on the x-axis.
In light of this, we can say:
A: (-2, 3i) (-2, 3i)
B: (-1, -i) (-1, -i)
C: (3, -4i) (3, -4i)
D: (4, I (4, i)
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HELP FAST!! WILL MARK BRAINLYISNT IF RIGHT ANSWER!
As a geologist, you catalog the weights of rocks. Since many countries use the metric system, the protocol is to have the weights in kilograms for consistency. According to the tag, 2 such rocks weigh 20 ounces each. What is the total weight of the rocks, in kilograms, if a kilogram is 35.2 ounces?
0.57
0.88
1.14
1.76
3.52
1.14 kg is the total weight of the rocks, in kilograms.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
2 such rocks weigh 20 ounces each.
i.e. weight of 2 rocks = 20*2
=40 ounces
now,
a kilogram is 35.2 ounces
the total weight of the rocks, in kilograms = 40/35.2
=1.14 kg.
Hence, 1.14 kg is the total weight of the rocks, in kilograms.
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Which is the graph of f(x) = 3(2-) *?
6
5
4
32
3
4
-3-2-1-1
-2
1 23 4 56
6
5
4
-3
2
4
-3-2-1
1 23
O
4
5 6
4
3
--3-2-1
7777
123 4 5 67
O
We graph points A(0,3) and B(1,2) to find the solution.
What is the intercept?
An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.
Here, we have
Given: f(x) = 3(2/3)ˣ
We first find the y-intercept
The y-intercept is the value of f(x) when the value of x is equal to zero
For x = 0
f(0) = 3(2/3)⁰ = 3
Point A(0,3)
Now, we find the value of f(x) when x = 1
f(1) = 3(2/3)¹ = 2
Point B(1,2)
Hence, we graph points A(0,3) and B(1,2) to find the solution.
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problem: you have a box of chocolates that contains 17 pieces of which:
7 are solid chocolate
4 are filled with cashews and
6 are filled with cherries.
all of the candies look exactly alike. you select a piece, eat it, select a second piece eat it and finally eat one last piece.
the question is what is the probability of selecting a solid chocolate and 2 cherry filled in any order
The probability of selecting one solid chocolate and 2 cherries is given as follows:
0.1544 = 15.44%.
How to obtain a probability?A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.
The outcomes resulting in one chocolate and two cherries being taken are given as follows:
Chocolate (7/17 probability), cherry (6/16 probability) and cherry (5/15 probability).Cherry (6/17 probability), chocolate (7/16 probability) and cherry (5/15 probability).Cherry (6/17 probability), cherry (5/16 probability) and chocolate (7/15) probability.Hence the probability is obtained as follows:
p = 7/17 x 6/16 x 5/15 + 6/17 x 7/16 x 5/15 + 6/17 x 5/16 x 7/15
p = 0.1544 = 15.44%.
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A car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solverA car dealership can offer a $36,000 car under a special promotion with four years financing at 0%, or can offer a discount off the price of the vehicle if the buyer finances the sale at .5% monthly over the four years. What discount off thepurchase price results in the buyer making the identical monthly payment under either purchase option. Please include excel solution in this using either goal seek or solver
The discount of the purchase price results in the buyer making the identical monthly payment under either purchase option, $4064.76.
Financing is the process of providing funds for business activities, making purchases, or investing. Financial institutions, such as banks, are in the business of providing capital to businesses, consumers, and investors to help them achieve their goals. The use of financing is vital in any economic system, as it allows companies to purchase products out of their immediate reach.
the PV=FV÷(1+r)^N,
here, PV is present value, FV is future value and r is the rate of discount or interst.
According to the given conditions,
if car financing at 0% ,
then car price=$36,000.
time period =48 months.
so, monthly payment =36000÷48
=$750.
if financing at regular rate then, monthly interest rate is 0.5%
time=48 month.
monthly payment, if we consider same payment=$750
the discount of the purchase price will be $4064.76.
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P=I^2xR what does I=?
Answer:
[tex]\sqrt{\frac{P}{R} }[/tex]
Step-by-step explanation:
[tex]P=I^2*R\\[/tex]
Divide both sides by R
[tex]\frac{P}{R} =I^2[/tex]
Remove the exponent by finding the square root of each side
[tex]\frac{\sqrt{P} }{\sqrt{R} } = I[/tex]
[tex]I=\sqrt{\frac{P}{R} }[/tex]
translate and solve a number by 3/5 is - 1/7
Answer:
False, if this is not what you mean comment and tell me
Step-by-step explanation:
It seems these days that students have to work more and more each week to be able to afford the costs of college. For a recent labor survey conducted by the
government, there were 78 respondents who were working while attending college. The frequency distribution below summarizes the number of hours worked
per week as reported by the respondents.
Number of hours
worked per week Frequency
(hours per week)
26 to 30
31 to 35
36 to 40
41 to 45
46 to 50
51 to 55
10
24
20
13
7
4
Based on the frequency distribution, using the midpoint of each data class, estimate the mean number of hours worked per week by the respondents. For your
intermediate computations, use four or more decimal places, and round your answer to one decimal place.
hours per week
The mean number of hours worked per week by the respondents will be 37.68.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Number of hours worked per week Frequency
26 to 30 10
31 to 35 24
36 to 40 20
41 to 45 13
46 to 50 7
51 to 55 4
The mean is given as,
Mean = [28 x 10 + 33 x 24 + 38 x 20 + 43 x 13 + 48 x 7 + 53 x 4]
(10 + 24 + 20 + 13 + 7 + 4)
Mean = 2939 / 78
Mean = 37.68
The mean number of hours worked per week by the respondents will be 37.68.
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What are the chances your flight will leave on time? To the right are a histogram and summary statistics for the percentage of flights departing on time each month from 2001 thru 2006. There is no evidence of a trend over time. (The correlation of On Time Departure % with time is r = - 0.006.) Complete parts a) through c) below. Find a 90% confidence interval for the true percentage of flights that depart on time. Interpret this interval for a traveler planning to fly. Choose the correct answer below. There is a 90% chance that the true mean monthly percentage of on-time departures is within the interval. We can be 90% confident that the interval contains the true mean monthly percentage of on-time departures. A randomly selected month has a 90% chance of having an on-time departure percentage within the interval. 90% of all months have on=time departure rates within the interval.
We can be 90% confident that the interval [76.4, 79.3] contains the true mean monthly percentage of on-time departures. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.
To find the 90% confidence interval, we first need to calculate the margin of error. To calculate this, we need to use the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. The standard deviation for the given data is 2.2 and the sample size is 72 (6 years × 12 months). So, the standard error is calculated as 2.2/√72 = 0.44. The margin of error is then calculated by multiplying the standard error by the critical value for 90% confidence, which is 1.645. The margin of error is therefore 0.44 × 1.645 = 0.72. The confidence interval is then calculated by adding and subtracting the margin of error from the sample mean. The sample mean is 77.8, so the 90% confidence interval is 77.8 ± 0.72, or [76.4, 79.3]. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.
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7 milimeter = 5 meter scale factor
The scale factor for 7 millimeters to 5 meters is 0.0014.
What is the scale factor?The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.
We can compute the scale factor (scaled-down) using the following formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
1 meter = 1,000 millimeters
5 meters = 5,000 millimeters (1,000 x 5)
The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)
The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)
Thus, the scale factor is 0.0014.
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Question Completion:What is the scale factor?
Convert the unit as shown below.
2772 cu in. =
gal
2772 cu in. =
gal
(Type a whole number or a decimal. Type your answer using the appropriate number of significant digits.)
One side of a right triangle is known to be 25 cm exactly. The angle opposite to this side is measured to be 60 with a possible error +_ 0.5
a. Use differentials to estimate the errors in the adjacent side and the hypothenuse.
b. Estimate the percentage errors in the adjacent side and hypothenuse.
The estimate errors in the adjacent side and the hypothenuse are ≅ ±0.29 cm and ≅ ±0.145 cm respectively. The percentage errors in the adjacent side and hypothenuse are 2.009% & 0.502%.
Hypothenuse y₁ = 25/sin x = 25cosec x
Adjacent y₂ = 25/tan x = 25cot x
Opposite angle is 60° = π/3
Possible error, dx ≅ ±0.5° = 0.5 × π/180 = ±π/360
Differentiating y₁ = 25cosec x
dy₁ = -25(cosec x · cot x)dx
dy₁ = -25(cosec (π/3) · cot (π/3))×±π/360
= -25(2/√3)(1/√3)(±π/360)
= ≅ ±0.145 cm
Similarly
dy₂ = -25 cosec²x .dx
dy₂ = -25 cosec²(π/3) .×±π/360
= -25(2/√3)²×±π/360
≅ ±0.29 cm
So the errors in the hypothenuse = ±0.145 cm
Error in the adjacent side = ±0.29 cm
Percentage error in the adjacent side = 0.29/(25/√3) = 2.009 %
Percentage error in the hypothenuse = 0.145/(25/sin60) = 0.502%
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For each transformation below, state whether the lengths, angles or both are invariant.
How the transformations below affect length, angles or both?
Translation - shifting same figure, lengths remain as is, angles remain as is;Reflection - mirroring the figure, lengths remain as is, angles remain as is;Rotation - rotation of the figure, lengths remain as is, angles remain as is;Enlargement - resizing the figure, lengths become larger, angles remain as is.Input Output Rule
Input Output
−4 2
−1 2
−1 −2
1 0
2 3
Question 1
Does the table represent a function? If not, justify your reasoning.
Responses
A No, because (−1, 2) and (−1, −2) have the same input value.No, because (−1, 2) and (−1, −2) have the same input value.
B No, because (−4, 2) and (−1, 2) have the same output value..No, because (−4, 2) and (−1, 2) have the same output value..
C Yes, the table represents a function.Yes, the table represents a function.
D Yes, because on a graph (1, 0) will intercept the y-axis at 0.
Answer:
A. No, because (-1) and (-1, -2) have the same input value.
Step-by-step explanation:
Functions:So what exactly is a function? It's very similar to a relation where there is input and for each input we have some output and sometimes multiple. The difference is in a function there is only one output for each input. Now the outputs of two different inputs can be the same, such that the input 2 and 3 will both output 4 or any value, but we cannot have an input such as 2 outputting 3 and 4 since we can only have one output for each input.
In the table given, the input "-1" outputs "2" and -2" which means the table does not represent a function.
This makes "A" the correct answer to whether it's a function or not and explanation.
WHAT IS THE ANSWER FOR THE 2nd ONE?! PLS HELP!!
The total volume of both storages will be 76 cubic ft.
What is volume?A volume is defined as the amount of space occupied by a three-dimensional solid shape. It is difficult to visualize in any shape, but it can be compared between shapes.
A compass box, for example, has a larger volume than an eraser placed inside it. We divide any two-dimensional shape into equal square units to calculate its area.
The volume of the larger box will be calculated as:-
Volume = side³
Volume = (4)³
Volume = 64 cubic ft
The volume of the smaller box = 12 cubic ft
Total volume = 64 + 12 = 76 cubic ft
Hence, the total volume of the boxes is 76 cubic ft.
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Suppose that A is countable set. Show that the set B is also countable if there is an onto function f from A to B
Let A and B be two countable sets. Then there exists a bijective function f from A to B.
Since f is onto, for every element b in B, there exists a unique element a in A such that f(a)=b. This implies that the number of elements in B is equal to the number of elements in A, i.e. B is also countable.
Formally, if A = {a1, a2, ..., an}, then B = {f(a1), f(a2), ..., f(an)}. Since f is onto, B has n elements, which implies that B is countable.
Let A be a countable set and let B be a set with an onto function f from A to B. Since A is countable, it can be written as an infinite sequence of distinct elements an, where n is a natural number. To show that B is also countable, we can construct a one-to-one correspondence between the elements of A and B. We can do this by assigning bi to the element ai in A, for each i. Thus, we can write B as an infinite sequence of distinct elements bn, where n is a natural number. Therefore, B is countable.
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Guys pls help me
1) 13 - 5x-4/6 = 10x - 8
2) 6(14x-21) = 14(18x - 6)
1. The value of x is 1.35
2. The value of x is 0.25
How to find x value in equation?The first step in finding the value of x in an equation is to isolate the variable. To do this, you will need to use the appropriate rules of algebra to rearrange the equation so that x is on one side of the equation and all other terms are on the other side. Then, you can solve the equation by using the appropriate method (e.g. factoring, quadratic formula, etc.) to solve for x.
1) 13 - 5x- 4/6 = 10x - 8
13+ 8- 4/6 = 10x + 5x
21-4/6 = 15x
20.3 = 15x
x = 1.35
2) 6(14x-21) = 14(18x - 6)
84x - 126 = 252x - 84
-126 + 84 = 252x - 84x
-42 = 168x
x = 0.25
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write the equation in slope-intercept form
m = -1/2; (0,-5)
determine the displacement (in m) of the object after a time of 6 seconds. (if negative, then enter a negative answer.)
Displacement is the difference between the initial position and the final position of an object.
We can determine the displacement with the following formula:
Displacement = Final position - Initial position
In this case, the initial position is 0 m and the time is 6 seconds. We can find the displacement using the equation of motion:
Displacement = Initial Velocity × Time + ½ × Acceleration × Time2
Given that the acceleration of the object is 4 m/s2, the equation of motion becomes:
Displacement = 0 + ½ × 4 × 62
Therefore, the displacement of the object after 6 seconds is 72 m.
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Which of the following are true statements?
Check all that apply.
A. f(x) = 2√√x has the same domain and range as f(x)=√x
B. The graph of f(x) = 2√ will look like the graph of f(x)=√x
but will stretch it vertically by a factor of 2.
C. The graph of f(x) = 2√x will look like the graph of f(x)=√x
but will shrink it vertically by a factor of 1/2.
D. The graph of f(x) = 2√x will look like the graph of f(x)=√x
but will shrink it horizontally by a factor of 1/2.
Statements A and C are correct.
How to solve the problem?We have to select the true statements from the given four statements in options.
step 1:
I think the statements A and C are true from the mathematical point of view.
If the original function is y=[tex]\sqrt{x}[/tex] and then by reflecting it about the x-axis
the equation will become y= - [tex]\sqrt{x}[/tex] and then shrinking it vertically by a
factor of 1/2 the function will finally become y= 1/2 [tex]\sqrt{x}[/tex]
Hence, statement A is true.
step2:
Again, the original function y= [tex]\sqrt{x}[/tex] has domain x ≥ 0 and range y ≥ 0, but in the transformed equation y=-1/2 [tex]\sqrt{x}[/tex] has domain same as original equation i.e. x ≥ 0 but the range is different i.e. y ≤ 0.
Hence, statement C is also true.
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Christmas lights are produced in a large quantity and as a result one-fifth are faulty. If
individual lights are taken out one by one from this large quantity, find the probability
that when the first three lights are taken out
a there is one faulty light
b there are two faulty lights
c there is at least one faulty light.
The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
What is probability?The likelihood that an event will occur is measured by probability. It is difficult to make a complete prediction for many events. By using it, we are only able to forecast the likelihood of an event, or how likely it is, to occur. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probability. For students in class 10, probability is a crucial subject because it clarifies all of the fundamental ideas. In a sample space, there is a probability of 1 for each event.
a. Let there be 100 lights, 1/5th are faulty = 20
There is one faulty in first three, P = 3/100 × 20/100
= 0.006
= 0.60%
b. There are two faulty lights, P = 3/100 × 20/100 × 20/100
= 0.0012
= 0.12%
c. There is at least one faulty light = 3/100 ×1/5
= 0.006
= 0.60%
Thus, The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
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Siegell's Locksmith Shop is taking out a mortgage on a new building. It is going to be an interest-only, 12-year balloon mortgage for $350,000. The APR is 3.35%. The last payment will be the balloon payment of the full principal.
a. Find the total number of monthly payments, not including the final balloon payment.
b. Find the amount of each monthly payment if the payments are interest-only. Round to the nearest cent.
c. Find the difference between the regular monthly payment and the balloon payment, to the nearest hundred dollars.
d. If the mortgage was not a balloon mortgage, what would be the amount of the monthly payment, rounded to the nearest cent?
Total number of monthly payments, not including the final balloon payment is $1,195.77
How to solve the problem?The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.
Step1
M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02
M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1
Step2:
3,618.02 × 12 × 12 = 520,994.88
The total paid is the product of the monthly payment and the number of payments.
520,994.88 - 350,000 = 170,994.88
= 170,994.88÷143
= 1,195.77
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