The number is the standard from is given by the equation A = 8.254 x 10⁶
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 8.254 x 10⁶
On simplifying the equation , we get
A = 8.254 x 1000000
Multiplying the number , we get
A = 8,254,000
Now , the number can also be written as
A = 8254000
So , the standard form of the number A is given by the equation
A = 8.254 x 10⁶
Hence , the number is A = 8.254 x 10⁶
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
30. Write in standard form
1.15 x 10 to the power of negative 5
31. Write in standard form
2.2 x 10 to the power of negative 10
32. Write in standard form
4.3 x 10 to the power of 10
Answer:
30) 0.0,000,115
31) 0.00,000,000,022
32) 43,000,000,000
Step-by-step explanation:
30
1.15 x [tex]10^{-5}[/tex] The negative exponent is telling us that the number in standards form is smaller than 1.15. To write in standard form we move the decimal 5 places to the left.
0.0,000,115
31
2.2 x [tex]10^{-10}[/tex] This is like question 30, but we will move the decimal 10 places to the left this time.
0.00,000,000,022
32
4.3 x [tex]10^{10}[/tex] the exponent is positive this time. That means in standard from the number is much larger than 4.3. Move the decimal point 10 places to the right. If you do not see a decimal point, it means that it is at the end of the number.
43,000,000,000
What is the inverse function for -2f(x+5)-4
Answer:
Read carefully below
Step-by-step explanation:
In general, the inverse of a function f(x) is a function g(x) such that f(g(x)) = g(f(x)) = x for all values of x in the domain of f(x) and g(x). To find the inverse of a function, we need to switch the input and output variables and solve for the new output variable.
In this case, we are given the function -2f(x+5)-4. To find the inverse of this function, we need to switch the input and output variables and solve for the new output variable, which we will call y. We can do this by first moving all the terms to one side of the equation, and then solving for y:
-2f(x+5) - 4 = y
-2f(x+5) = y + 4
f(x+5) = (y + 4) / -2
This is the inverse function of -2f(x+5)-4. However, keep in mind that not all functions have inverses. In particular, a function must have the property that it is one-to-one (i.e. it maps unique inputs to unique outputs) in order to have an inverse. It is not clear from the given information whether the function -2f(x+5)-4 is one-to-one, so it is possible that it does not have an inverse.
Select the graph for the solution of the open sentence. Click until the correct graph appears.
|x| + 3 > 3
Answer: See attached for the graph.
Step-by-step explanation:
To find the answer to this question, we will isolate the variable x.
Given:
|x| + 3 > 3
Subtract 3 from both sides of the equation:
|x| > 0
Aboslute value:
x > 0, x < 0
This means the graph will be greater than or less than 0.
Plot all ordered pairs for the values in the domain.
A plot of all the ordered pairs for the values in the domain is shown in the graph attached below.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) to a function and the domain of a graph consist of all the input numerical values which are shown on the x-axis.
Based on the values given for the domain of this function, the ordered pairs would be calculated as follows:
When x = -8, we have;
y = 1/2(-8) + 1
y = -3
Ordered pair = (-8, -3)
When x = -4, we have;
y = 1/2(-4) + 1
y = -1
Ordered pair = (-4, -1)
When x = 0, we have;
y = 1/2(0) + 1
y = 1
Ordered pair = (0, 1)
When x = 2, we have;
y = 1/2(2) + 1
y = 2
Ordered pair = (2, 2).
When x = 6, we have;
y = 1/2(6) + 1
y = 4
Ordered pair = (6, 4)
Read more on domain here: https://brainly.com/question/16142034
#SPJ1
the unicode character set is a subset of the ascii character set. group of answer choices true false
It s true that a text file contains bytes of data that represent characters from a particular character set such as Unicode or ASCII. The correct option to this question is "True".
The text file contains texts that are represented by Unicode or ASCII. The Unicode or ASCII represents how the numbers, text, or other commands are displayed and written in a text file.
To represent text digitally in the text file, characters have their own unique character representation bit-pattern. These bit-pattern have a combination of 1s and 0s. And these patterns are represented by character codes that are either Unicode or ASCII.
You can learn more about ASCII Code at
brainly.com/question/26307436
#SPJ4
AXYZ is similar to ALMN. Angle Y is 89
degrees and Angle N is 32 degrees.
Record the measures for each angle in
the diagram.
The measurement of angles △XYZ are ∠X = 59°, ∠Y = 89°, and ∠Z = 32°.
The measurement of angles △LMN are ∠L = 59°, ∠M = 89°, and ∠N = 32°.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that, △XYZ and △LMN are similar triangle.
Since the triangles are similar, thus the measurement of triangles are similar.
Therefore,
∠X = ∠L, ∠Y = ∠M, ∠Z = ∠N.
∠Y = ∠M = 89° and ∠Z = ∠N = 32°.
The sum of all interior angles of triangle is 180°.
∠X + ∠Y + ∠Z = 180°
∠X + 89° + 32° = 180°
∠X + 121° = 180°
Subtract 121° from both sides:
∠X = 59°
∠X = ∠L = 59°.
To learn more about similar triangle, click on below link:
https://brainly.com/question/2279525
#SPJ1
Suppose that an individual has a body fat percentage of 15.7% and weighs 162 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
What is the answer to 19(2m−16)=13(2m+4)
Answer:
m = -21.
Step-by-step explanation:
To solve this equation, we can use the distributive property to expand the left side and the right side of the equation:
19(2m - 16) = 13(2m + 4)
38m - 304 = 26m + 52
Then we can combine like terms on both sides of the equation to obtain:
38m - 26m = 52 - 304
12m = -252
Finally, we can divide both sides of the equation by 12 to find the value of m:
12m / 12 = -252 / 12
m = -21
Therefore, the value of m that satisfies the equation is m = -21.
find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.
In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
The given function is f'(x) = 3x^3.
No integrating on both side,
f(x) = [tex]\int3x^3dx[/tex] + C
f(x) = 3x^4/4 + C
As given, the line 81x + y = 0 is tangent to the graph of f.
So, slope at point of tangent; f'(x) = -81
So, 3x^3 = -81
Divide by 3 on both side, we get
x^3 = -27
Taking cube root on both side, we get
x = -3
So putting the value of x in 81x + y = 0, we get
y = 243
Thus, f(x) passes through (-3, 243).
So, 243 = 3/4(81) + C
Multiply by 4 on both side, we get
972 = 243 + 4C
Subtract 243 on both side, we get
4C = 729
Divide by 4 on both side, we get
C = 729/4
So, f(x) = 3x^4/4 + 729/4
To learn more about function link is here
brainly.com/question/21145944
#SPJ4
The hypothetical city of hurstville is trying to decide how many city beautification projects should be approved each year. These projects involve planting gardens, commissioning murals, and building fountains. The city has two types of citizens. Type b citizens appreciate beauty more than type a citizens. There is an equal number of each type of citizen. The accompanying schedule depicts each type of citizen's marginal benefit for city beautification projects. The average cost of each project is $400. Use the information in the schedule to answer the questions. Marginal benefit scheduleqmbambb04006001300500220040031003004020050100600what is the optimal quantity of city beautification projects?3124city beautification is a public good because:it is nonrival in consumption and nonexcludable. It is rival in consumption and excludable. It is rival in consumption and nonexcludable. It is nonrival in consumption and excludable
Using the provided information we get,
a) Optimal quantity of city beautification projects is three.
b) 3124 city beautification is a public good because it is rival in consumption and non-excludable. So, Correct option is option (C).
The fictional city of Hurstville is trying to determine how many urban beautification projects it has. The city has two types of citizens, ones who appreciates beauty more than other type.
The average cost of each project = $400
We have given that
The combined marginal benefit curves are determined by horizontally adding up the in the individual marginal benefit curves. So, the optimal quantity of benefication projects is at the point where MSB is equal to MSE. Thus, the optimal outputs is 3 projects.
The city beneficiation is a public good because it is non-trivial in consumption and non-excludable.
To learn more about consumption , refer:
https://brainly.com/question/14975005
#SPJ4
Which expression is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power?
2 and three tenths raised to the eighth power divided by nine tenths raised to the ninth power
2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power
1.44
1.49
The equivalent expression to {(2 3/10)⁴ ÷ (9/10)⁵}⁴ is "2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power".
The correct answer choice is option B
Which is the equivalent expression?Exponents refers to the power to which a number, expression or symbol is to be raised. For instance, 4²; the exponent is 2 which is a power.
{(2 3/10)⁴ ÷ (9/10)⁵}⁴
= (2.3⁴ ÷ 0.9⁵)⁴
Multiply the powers
= 2.3¹⁶ ÷ 0.9²⁰
It can also be written as
(2.3)¹⁶ / (0.9)²⁰
Consequently, the expression which is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power is (2.3)¹⁶ / (0.9)²⁰
Read more on Exponent:
https://brainly.com/question/11464095
#SPJ1
Answer:
I am 100% sure it is b
Step-by-step explanation:
I have proof( i did the test) and took a picture
he lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 15 days. in what range would you expect to find the middle 50% of most pregnancies? between and . if you were to draw samples of size 36 from this population, in what range would you expect to find the middle 50% of most averages for the lengths of pregnancies in the sample? between and . enter your answers as numbers. your answers s
Using the normal distribution, the middle 50% would be expected to be in the range of 250 to 270 days.
Using the central limit theorem, for the samples of 36, the middle 50% would be expected to be in the range of 258 to 262 days.
What is normal distribution theorem?A sort of continuous probability distribution for a real-valued random variable is the normal distribution or the Gaussian distribution.
Normal Distribution of Probabilities
The z-score formula, which for a measure X, in a set with mean and standard deviation, is given by: can be used to address problems with normal distributions.
Z = (X - μ)/σ
The z-score calculates the measure's standard deviation from the mean.
A p-value, or percentile of X, is assigned to each z-score.
Mean (μ) = 260.
Standard deviation (σ)= 15 .
The normal distribution is symmetric, which means that the middle 50% is between the 25th percentile and the 75th percentile.
The 25th percentile is X when Z has a p-value of 0.25, so X when Z = -0.675.
The 75th percentile is X when Z has a p-value of 0.75, so X when Z = 0.675.
Lower bound:
Z = (X - μ)/σ
⇒ -0.675 = (X - 260)/15
⇒ X - 260 = -0.675*15
⇒ X - 260 = -10.125
⇒ X = 260 - 10.125
⇒ X ≈ 250
Upper bound:
Z = (X - μ)/σ
⇒ 0.675 = (X - 260)/15
⇒ X - 260 = 0.675*15
⇒ X - 260 = 10.125
⇒ X = 260 + 10.125
⇒ X ≈ 270
The middle 50% of pregnancies would be in the range of 250 to 270 days.
For sample of 36: By the Central Limit Theorem, the standard deviation of the sampling distribution of sample means of size n is given by .
Sample of 36, thus n=36, s=15/√36
⇒ s=15/6
⇒ s=2.5
Lower bound:
Z = (X - μ)/s
⇒ -0.675 = (X - 260)/2.5
⇒ X - 260 = -0.675*2.5
⇒ X - 260 = -1.69
⇒ X = 260 - 1.69
⇒ X ≈ 258
Upper bound:
Z = (X - μ)/s
⇒ 0.675 = (X - 260)/2.5
⇒ X - 260 = 0.675*2.5
⇒ X - 260 = 1.69
⇒ X = 260 + 1.69
⇒ X ≈ 262
The middle 50% of pregnancies would be in the range of 258 to 262 days.
To learn more about normal distribution visit:
brainly.com/question/12421652
#SPJ4
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answer:
2,3 and 7
Step-by-step explanation:
168 = 2x2x2x3x7
= 2²x3x7
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 18)(0,18) and (3, 6174)(3,6174).
The exponential function in the form y = ab^x is y = 18(7)^x
How to determine the exponential function in the formFrom the question, we have the following parameters that can be used in our computation:
Points: (0, 18) and (3,6174).
The above can be represented as
(x, y) = (0, 18) and (3,6174).
An exponential function is represented as
y = ab^x
Where
a = y when x = 0
This means that
a = 18
So, we have
y = 18b^x
At (3,6174), we have
6174 = 18b^3
So, we have
343 = b^3
Take the cube root of both sides
b = 7
This means that
y = 18(7)^x
Hence, the function is y = 18(7)^x
Read more about exponential function at
brainly.com/question/11464095
#SPJ1
A Venu revolve around the un, it travel at a peed of approximately 22 mile per econd. Convert thi peed to mile per minute. At thi peed, how many mile will Venu travel in 6 minute?
Answer:
22mile=1sec
x=360sec
criss cross method
(x)(1)=360×22
x=7920miles
Given the equation a line y+9=-3(x-4) Determine the characteristics of the line.
Answer:
Step-by-step explanation: y+9=-3(x-4)......given equation
This equation can be expanded further and simplified
y+9=-3x+12
We want to put the equation into the form y=mx+b so we can read its characteristics
To do this we need to get y on its own. We must take 9 from both sides
y+9-9=-3x-9+12
y=-3x+3
The equation has a gradient or slope or m =-3 and it cuts the y-axis at +3 or is the yintercept
Complete this working to write 9³ as a power of 3
9³=9x9
SO
SO
9³3 x 3 x 3 x
=
9³ = 3
where y =
Answer:
y= 6
Step-by-step explanation:
9³ = 3^y
3²^³ = 3^y
3⁶ = 3^y
therefore
y=6
If m<5 = (8x-14) and m<7 = (5x+34), what is the value of x and m<5?
Answer:
maybe 16
I hope I helped
Step-by-step explanation:
joining m < 5 = m < 7
8x – 14 = 5x + 34
8x – 5x = 34 + 14
3x = 48
divide both sides by 3
x = 48/3
x = 16
Marcia made 10 bracletes for 5 friends. Jen made 1 braclets for 4 friends.Are these ratios/rates equivalent.
The fraction or ratio for the bracelet aren't equivalent.
Are these fractions equivalent?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
Here Marcia made 10 bracletes for 5 friends. This will be:
= 10/5
= 2:1
Jen made 1 braclets for 4 friends. This will be:
= 1/4.
= 1:4
The fraction or ratio aren't equivalent.
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
need help with #4 (a,b,c). I’m in algebra 1 and this unit is Solving Systems by Substitution
Answer:
4a) [tex]P=2L+2W[/tex]
4b)
[tex]42=2L+2W\\L=2W+3[/tex]
4c)
[tex]L=15\\W=6[/tex]
Step-by-step explanation:
Note:
[tex]P=[/tex] Perimeter
[tex]L=[/tex] Length
[tex]W=[/tex] Width
The perimeter of a rectangle is the sum of all its sides.
We can say
[tex]P=L+L+W+W[/tex]
Which simplifies to
[tex]P=2L+2W[/tex]
This is the equation to find the perimeter of a rectangle.
We are given the perimeter which is 42.
We are also given that the length is the sum of twice its width and 3.
So we can write
[tex]42=2L+2W\\L=2W+3[/tex]
Lets solve using substitution.
Substitute [tex]L=2W+3[/tex] into the first equation.
[tex]42=2W+2(2W+3)[/tex]
Expand the right side of the equation then simplify.
[tex]42=2W+4W+6\\42=6W+6[/tex]
Subtract 6 from both sides.
[tex]36=6W[/tex]
Divide both sides by 6 to isolate [tex]W[/tex].
[tex]W=6[/tex]
Perform a back substitution. Substitute [tex]W=6[/tex] into the second equation, [tex]L=2W+3[/tex]
[tex]L=(2*6)+3\\L=12+3\\L=15[/tex]
A rating/review would be much appreciated! Have a good Christmas!
miae is baking .the recipe uses 3/4 cup sugar.miae wants to make 1/2 of a batch .how many cups of sugar does she need
To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. miae is baking .the recipe uses 3/4 cup sugar.Miae needs 3/8 cup of sugar for 1/2 of a batch.
To answer the question, Miae needs 3/8 cup of sugar for 1/2 of a batch, it is important to understand the concept of fractions. A fraction is a part of a whole, it is represented by a numerator and denominator, the numerator represents the number of parts and the denominator represents the total number of parts. In this question, the recipe calls for 3/4 cup of sugar for the entire batch, so to get 1/2 of the batch, Miae needs to divide the fraction by 2. To do this, we can either divide the numerator and denominator by 2, or multiply the fraction by 1/2. In this case, 3/4 multiplied by 1/2 is 3/8, so Miae needs 3/8 cup of sugar for 1/2 of a batch.
Learn more about fraction here
https://brainly.com/question/10354322
#SPJ4
Dustin has $1,000 in a savings account that earns 10% interest per year. The interest is not compounded. How much will he have in total in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
1,100
Step-by-step explanation:
1000 x 0.1 = 100
1000 + 100 = 1,100
find the sum of 2 over 3 + negative 1 over 3
Answer:
2/3 + -1/3 = positive 1/3
Answer:
To find the sum of 2/3 + (-1)/3, you can first convert the fraction to an equivalent fraction with a common denominator. In this case, the common denominator would be 3. 2/3 can be written as 2 x (3/3) = 2/3 and -1/3 can be written as -1 x (3/3) = -1/3. Then, you can add the numerators and the denominator will remain the same. So, the sum of 2/3 + (-1)/3 is 1/3.
find the work in ft-lb done by winding up a hanging cable of length 100 ft and weight-density 5 lb/ft
the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.
A force applied across a distance is what is referred to as work.
In this problem,
the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).
Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.
Learn more about distance here
https://brainly.com/question/28956738
#SPJ4
Can someone help??
Answers:
A. 1 cm and 5 cm
B. 8 cm and 15 cm
C. 3 cm and 4 cm
D. 5 cm and 17 cm
Answer:
A. 1 cm and 5 cm
Step-by-step explanation:
Let me know if my work makes sense!
PLS HELP ALMOST DUE AND REALLY IMPORTANT.
What is the constant of proportionality for the data in the table? Time (weeks) 2 5 10 Trees Planted 130 325 650 k= 70 k = 130 k = 65 k = 195
The constant of proportionality for the data in the table is 65. This can be determined by dividing the number of trees planted by the number of weeks for each data point in the table. For example, for the first data point where 2 weeks have passed, 130 trees have been planted, which means the constant of proportionality is 65 (130 / 2 = 65). This value is the same for all of the data points in the table, which means it is the constant of proportionality for the data.
For a concert, 19 boys and 22 girls bought tickets from the music club. The total cost of the tickets was $256. This total cost includes a $10 tax. What was the cost of each ticket, not including the tax?
Part A
Which of the following steps are needed to solve this problem? Select all that apply.
A.
Subtract 19 from 22 to find out how many more girls than boys went to the concert.
B.
Add 19 and 22 to find the total number of students who attended the concert.
C.
Add $10 to $256 to find the total cost of the tickets without the tax.
D.
Subtract $10 from $256 to find the total cost of the tickets without the tax.
E.
Divide $256 by 10 to find the total cost of the tickets without the tax.
Part B
What was the cost of each ticket, not including the tax?
A.
$4
B.
$5
C.
$6
D.
$7
A) First we need to subtract the tax, the correct option is D.
B) by dividing the total cost without the tax by the number of people, we wiill see that each ticket costs $6, the correct option is C.
Which is the first step?We want to find the total cost of each ticket not including the tax, then the first thing that we need to doo is take the total cost ($256) and subtract the $10 of the tax, we will ge:
$256 - $10 = $246
Then the correct option is D
"Subtract $10 from $256 to find the total cost of the tickets without the tax."
Part B:
Now we can divide that amount by the number of people so we get how much each ticket costs:
19 + 22 = 41
We will get:
$246/41 = $6
Then the correct option is C.
Learn more about taxes:
https://brainly.com/question/26316390
#SPJ1
Which is closest to the volume of the cylinder below?
A. 6.28 cubic cm
B. 12.56 cubic cm
C. 62.8 cubic cm
D. 125.6 cubic cm
The illustrated volume of the cylinder is 769cm³.
How to calculate the volume?One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinite curvilinear surface.
It should be noted that the formula for finding the volume of a cylinder is πr²h
where π = 3.14
r = radius
h = height
Let's assume that the height is 5cm and radius is 7cm. The volume will be:
V = πr²h
Volume = 3.14 × 7² × 5
Volume = 769cm³
Note that your information was incomplete and an overview was given.
Learn more about cylinder on:
https://brainly.com/question/9554871
#SPJ1
helpp
i need it rnn
and if u could plot the point too thats good
js those for now tyy
Step-by-step explanation:
5.
y = 3
yes, that's it for this here too.
it means that any value for x is valid, and all have the assigned y value 3.
6.
remember, the usual equation for a line is
y = ax + b
"a" being the slope, "b" the y-intercept (the y-value when x = 0).
we see the y-value for x = 0 is 3. that is "b".
for the slope we need 2 points and calculate the x- and y- coordinate differences.
always look for points with integer coordinates.
I see e.g. (0, 3) and (3, 2).
x changes by +3 (from 0 to 3).
y charges by -1 (from 3 to 2).
the slope "a" = -1/+3 = -1/3
the equation is then
y = (-1/3)x + 3
7.
we do exactly the same things.
we see the y-value for x = 0 is +1. that is "b".
I see e.g. these points : (0, 1) and (3, 2).
x changes by +3 (from 0 to 3).
y changes by +1 (from 1 to 2).
the slope "a" is +1/+3 = 1/3.
the equation is
y = (1/3)x + 1
8.
and again the same things.
we see the y-value for x = 0 is +3. that is "b".
I see e.g. these points : (0, 3) and (-3, 0).
x changes by -3 (from 0 to -3).
y changes by -3 (from 3 to 0).
the slope "a" is -3/-3 = 3/3 = 1.
the equation is
y = x + 3
Please help me. I know it’s 4 months but I don’t know what the total amount paid is including interest. If anyone could add the steps that would be awesome!
Divide by 12 to go from the APR to the monthly interest rate
(9.5%)/12 = 0.7916667%
The decimal form is 0.007916667 approximately.
Multiply this with the starting balance $1367.90 and we get:
0.007916667*1367.90 = 10.8292 which rounds to 10.83
The interest payment for the 1st month is $10.83; which means the principal payment would be 400-10.83 = 389.17
This principal payment will then drop the balance from $1367.90 to 1367.90-389.17 = 978.73 dollars.
The value $978.73 is now the starting balance of the 2nd month. This process of...
(a) Compute the interest(b) Subtract the interest from the $400 monthly payment to get the principal (with the exception of the last month as shown below)(c) Subtract the principal from the starting balance to get the ending balance.is repeated until the balance is $0.
This is what the table would look like
[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6}\text{Month} & \text{Starting} & \text{Interest} & \text{Principal} & \text{Payment} & \text{Ending }\\& \text{Balance} & & & & \text{Balance}\\\cline{1-6}1 & 1367.9 & 10.83 & 389.17 & 400 & 978.73\\\cline{1-6}2 & 978.73 & 7.75 & 392.25 & 400 & 586.48\\\cline{1-6}3 & 586.48 & 4.64 & 395.36 & 400 & 191.12\\\cline{1-6}4 & 191.12 & 1.51 & 191.12 & 192.63 & 0\\\cline{1-6}\end{array}[/tex]
Many credit card companies and banks offer free calculators on their website, or you can find similar free calculators online elsewhere, that will quickly calculate a table like shown above. It is called an amortization table or amortization schedule.
With the exception of the 4th month, each row has the principal and interest add to the $400 monthly payment. The last row will have a payment of 1.51+191.12 = 192.63 dollars.
The total amount paid back would be 400+400+400+192.63 = 1392.63 dollars. This is the sum of the values in the "payment" column.
-------------------------------------------------------------------------
Here's another way to determine the answer.
The monthly payment formula is
[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}[/tex]
where,
P = monthly paymentL = loan amount, aka starting balancei = monthly interest rate in decimal formn = number of monthsIn this case,
P = 400L = 1367.90i = 0.007916667 approximately (calculated earlier)n = unknownLet's solve for the variable n. We'll need logarithms to isolate the exponent.
Part 1
[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}\\\\\\\displaystyle 400 = \frac{1367.90*0.007916667}{1 - (1+0.007916667)^{-n}}\\\\\\\displaystyle 400 = \frac{10.8292087893}{1 - (1.007916667)^{-n}}\\\\\\\displaystyle 400(1 - (1.007916667)^{-n}) = 10.8292087893\\\\\\[/tex]
Part 2
[tex]\displaystyle 1 - (1.007916667)^{-n} = 10.8292087893/400\\\\\\\displaystyle 1 - (1.007916667)^{-n} = 0.0270730\\\\\\\displaystyle -(1.007916667)^{-n} = 0.0270730-1\\\\\\\displaystyle -(1.007916667)^{-n} = -0.9729270\\\\\\\displaystyle (1.007916667)^{-n} = 0.9729270\\\\\\[/tex]
Part 3
[tex]\displaystyle \log((1.007916667)^{-n}) = \log(0.9729270)\\\\\\\displaystyle -n*\log(1.007916667) = \log(0.9729270)\\\\\\\displaystyle n = -\log(0.9729270)/\log(1.007916667)\\\\\\\displaystyle n = 3.4805965\\\\\\[/tex]
Each decimal value is approximate.
That value of n then rounds up to the nearest integer n = 4
We do not round to n = 3 since that would be one month short, as shown in the table above.
You can use a graphing calculator to quickly solve that equation for the variable n. It can be used as a way to visually confirm the answer.