To save 6 months’ worth of your fixed expenses in an emergency fund will take approximately 5 months.
What is an emergency fund?An emergency fund is a safety net used specifically to cover basic living expenses for at least 6 months in case future mishaps or unexpected expenses arise.
Financial experts generally recommend six months of basic living (fixed) expenses to put away in an emergency fund.
Data and Calculations:The amount to save in the emergency fund = $3,753.79 ($2,085.44 x 30% x 6)
50% of discretionary monies = $729.90 ($2,085.44 x 1 - 30%) x 50%
Months to save $3,753.79 saving $729.90 = 5 months ($3,753.79/$729.90)
Question Completion:Your realized income is $2,085.44, and your fixed expenses are 30%. You want to save 6 months’ worth in an emergency fund.
How many months will it take to fully fund it, excluding interest accrual?
Thus, o save 6 months’ worth of your fixed expenses in an emergency fund will take approximately 5 months.
Learn more about discretionary expenses and emergency funds at https://brainly.com/question/422550
Answer:
To calculate this, we first need to find the amount of discretionary money left after paying fixed expenses:
Discretionary money = Realized income - (Fixed expenses as a percentage of realized income)
Discretionary money = $2,085.44 - (30% x $2,085.44)
Discretionary money = $2,085.44 - $625.63
Discretionary money = $1,459.81
We want to put 50% of this toward the emergency fund each month, so:
Emergency fund contribution per month = 50% x $1,459.81
Emergency fund contribution per month = $729.91
To find out how many months it will take to fully fund the emergency fund, we divide the total amount needed by the monthly contribution:
Number of months = (Total amount needed) / (Emergency fund contribution per month)
Number of months = $18,292.65 / $729.91
Number of months = 25.06
Rounded up to the nearest whole month, it will take 26 months to fully fund the emergency fund.
Therefore, the answer is:
26 months
Question 2
A classroom has 15 girls and 11 boys.
(a) Find the ratio of boys to girls.
Answer:
11:15
Step-by-step explanation:
find the equation of a line that is parallel to this line and passes through the point (-3,1)
Answer:
Two possible equations:
Point-slope form is [tex]y-1=-\frac{2}{3} (x+3)[/tex]
Slope-Intercept form is [tex]y=-\frac{2}{3}x+-1[/tex]
Step-by-step explanation:
So to start we need to know what makes a line parallel. In an equation we know that for lines to be parallel they must have the same slope([tex]m[/tex]).
Then, we need to know the slope-intercept form of an equation. The point slope form is [tex]y-y1=m(x-x1)[/tex] where [tex]m[/tex] is the slope of the line and [tex]y1[/tex] and [tex]x1[/tex] represent the point on the graph. This is the equation we'll use for the line.
So now that we understand what we need to find, we need to find the slope of the existing line. To do this we use the equation [tex]m=\frac{y2-y1}{x2-x1}[/tex]. We can plug in the points (-2,3) and (1,1) on the graph to get [tex]m=\frac{1-3}{1+2}[/tex]. When we simplify this we get [tex]m=-\frac{2}{3}[/tex] so we know our slope is [tex]-\frac{2}{3}[/tex]. Lastly, all we need to do is plug the slope and the new point into our point slope equation to get [tex]y-1=-\frac{2}{3} (x+3)[/tex].
If you needed to go further and put this into slope-intercept form, you could solve the equation for y to get [tex]y=-\frac{2}{3}x+-1[/tex]
A line intersects the points
(7,6) and (11, -6).
What is the slope of the line in
simplest form?
m = [?]
Answer:
[tex]m=-3[/tex]
Step-by-step explanation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute and calculate
[tex]x_1=7[/tex]
[tex]x_2=11[/tex]
[tex]Substitute[/tex] [tex]into\ m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1=6[/tex]
[tex]y_2=-6[/tex]
Substitute
[tex]m=\frac{-6-6}{11-7}[/tex]
Calculate the sum or difference
[tex]m=\frac{-12}{4}[/tex]
Cross out the common factor
[tex]m=-3[/tex]
I hope this helps you
:)
Hello.
Let's use the slope formula in order to find the slope:
[tex]\bf{\displaystyle\frac{y_2-y_1}{x_2-_x_1}[/tex]
Where
y₂ = the y-coordinate of the second point (-6)
y₁=the y-coordinate of the first point (6)
x₂=the x-coordinate of the second point (11)
x₁=the x-coordinate of the first point (7)
Plug in the values:
[tex]\bf{\displaystyle\frac{-6-6}{11-7} =\frac{-12}{4} =-3[/tex]
Therefore, m (the slope) is equal to -3.
I hope it helps.
Have an outstanding day. :)
[tex]\boxed{imperturbability}[/tex]
what is the magnitude of an account of -218 Dollars
Hey there!
The magnitude of 218 will always be 218 because the absolute value of a positive number is always itself. The magnitude of -218 will be 218 as well because the absolute value of a negative number is the positive version of the number without the negative sign. You are essentially dropping or ignoring the negative sign.
Therefore, the magnitude of an account of -218 Dollars is 218 dollars
A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 gallons of water was tied to the end of the rope at the ground. A group of hikers at the top of the cliff lifted the bucket by pulling up the rope, but when the bucket reached the top, only 12 gallons of water remained (the water spilled out steadily on the way up). If water weighs 8.3 lbs. / gallon. write a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground, and use it to find the work to get the bucket to the top of the cliff.
Answer:
A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
Step-by-step explanation:
Work done to lift the rope by distance x feet:
[tex]W_1=32(\frac{50-x}{2})[/tex]
Work done to lift the bucket by distance x feet:
[tex]W_2=(19-\frac{x}{5})(8.3)x[/tex]
On reaching top 7 gallons of water spilled out so , on going up by x feet [tex]\frac{7x}{35}=\frac{x}{5}[/tex] gallons of water spilled out.
a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:
[tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex]
Now the work to get the bucket to the top of the cliff i.e. x =35
[tex]W=16(50-35)+(19-\frac{35}{5})(8.3)(35)[/tex]
W=3726
Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
Question 44 of 44
Which of these is an optional deduction for money to be taken out of an
employee's paycheck?
A. Federal income tax
B. Medicare
C. Life insurance
D. Social Security
Answer : Life Insurance
Explanation : Have A Good Day
◊ YusuCr ◊
The optional deduction for money to be taken out of an employee's paycheck is life insurance.
Option C is the correct answer.
What is an employee's paycheck?An employee's paycheck is a document issued by an employer that lists the amount of money an employee has earned during a certain pay period and the amount of money that has been withheld for taxes, insurance, and other deductions.
It also includes the net amount of money that the employee is entitled to receive after all deductions have been made.
We have,
Life insurance is an optional deduction for money to be taken out of an employee's paycheck.
The other options listed (Federal income tax, Medicare, and Social Security) are typically mandatory deductions required by law.
Thus,
The optional deduction for money to be taken out of an employee's paycheck is life insurance.
Learn mroe about employee's paychecks here:
https://brainly.com/question/2819285
#SPJ7
Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).
Which rule was used to translate the image?
T4, –4(x, y)
T–4, –4(x, y)
T2, –4(x, y)
T–2, –4(x, y)
Answer:
T2, –4(x, y)
Step-by-step explanation:
Pre image has taken place ⇒ 2 units Horizontally right and 4 unit vertically down to obtain vertices of Image.
Hence, Answer = T2, –4(x, y)
~Lenvy~
Answer: T2, –4(x, y)
Step-by-step explanation:
right on edge 2023
Find a third degree polynomial with the given zeros and a leading coefficient of 4. 1/2, 3/2, 2
Answer:
[tex]4x^3-16x^2+19x-6[/tex]
Step-by-step explanation:
P(x)=a(x-r1)(x-r2)(x-r3)
This is a third degree polynomial of leading coefficient a, where r1, r2 and r3 are the roots.
So just replace it with the values you are asked for :
[tex]4\left(x-\frac{3}{2}\right)\left(x-\frac{1}{2}\right)\left(x-2\right)\\[/tex]
Then expand and you will find the answer : [tex]4x^3-16x^2+19x-6\\[/tex]
A rectangular table top has length 1.8 m and width 1.2 m.
A force of 600 N is applied to the whole table top.
Calculate the pressure in N/m2 to the nearest integer.
The equation of pressure is given by:
[tex]p = \frac{f}{s} [/tex]
where p is the pressure.
f is the applied force.
s is the surface area to which the force is applied.
I will start off by calculating the surface area of the table top given by:
[tex]s = l \times w = 1.8 \times 1.2 = 2.16[/tex]
s=2.16 m²
We know that f=400 N, that is given.
[tex]p = \frac{400 \: n}{2.16 \: m {}^{2} } [/tex]
Plug this on your calculator (excluding the units lol)
[tex]p = 185.185 \frac{n}{m {}^{2} } [/tex]
[tex]p = 185 \frac{n}{m {}^{2} } [/tex]
Please click on this picture and explain why I got this answer wrong
Answer: $79.12
Step-by-step explanation:
We have to find total amount that was paid for dinner
5 people each order was worth $12.80
Therefore, total bill = 12.80*5
= $64
Tax: 7.5%
Therefore, the bill after tax was:
[tex]=64(\frac{100+7.5}{100})\\= 64(1.075)\\[/tex]
Bill with tax = $68.8
Gratuity = 15.0% of bill with tax
Therefore, gratuity = 0.15 * 68.8
= $10.32
Ended up paying in total = Gratuity + Bill with tax
= $68.8 + $10.32
= $79.12
help is needed here please and thank you!
[tex] \rm\frac{d}{dx} \left ( \bigg( \int_{1}^{ {x}^{2} {}{} } \frac{2t}{1 + { t}^{2} } dt\bigg) \bigg( \int_{ 1 }^{ lnx} \frac{1}{(1 + {t)}^{2} }dt \bigg)\right) \\ [/tex]
Applying the product rule gives
[tex]\displaystyle \frac{d}{dx}\int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \frac{d}{dx}\int_1^{\ln(x)}\frac{dt}{(1+t)^2}[/tex]
Use the fundamental theorem of calculus to compute the remaining derivatives.
[tex]\displaystyle \frac{4x^3}{1+x^4} \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \frac{1}{x(1+\ln(x))^2}\int_1^{x^2}\frac{2t}{1+t^2}\,dt[/tex]
The remaining integrals are
[tex]\displaystyle \int_1^{\ln(x)}\frac{dt}{(1+t)^2} = -\frac1{1+t}\bigg|_1^{\ln(x)} = \frac12-\frac1{1+\ln(x)}[/tex]
[tex]\displaystyle \int_1^{x^2}\frac{2t}{1+t^2}\,dt=\int_1^{x^2}\frac{d(1+t^2)}{1+t^2}=\ln|1+t^2|\bigg|_1^{x^2}=\ln(1+x^4)-\ln(2) = \ln\left(\frac{1+x^4}2\right)[/tex]
and so the overall derivative is
[tex]\displaystyle \frac{4x^3}{1+x^4} \left(\frac12-\frac1{1+\ln(x)}\right) + \frac{1}{x(1+\ln(x))^2} \ln\left(\frac{1+x^4}2\right)[/tex]
which could be simplified further.
1. The full Renegade dance Jalaiah created is 56 seconds long. For a 15-second-long TikTok, what percent of Renegade is used?
Answer:
3.7
Step-by-step explanation:
You have to divide
Answer:
i do not know tbh .
Step-by-step explanation:
correct answer gets brainliest
Answer:
Therefore If you exchange $522 for euros, then we will get
Step-by-step explanation:
mark me brainliest!!
Answer:
412.38Є
Step-by-step explanation:
The answer is simple, since 1$ = 0.79Є, multiply 0.79 by 522, or the other way around, if you want.
0.79*522
=412.38Є
Hope it helped.
y – 3(2y – 7) = 76
solve for Y!!
Answer:
y=-11
Step-by-step explanation:
Answer:
y = -11
Step-by-step explanation:
y – 3(2y – 7) = 76
y - 6y + 21 = 76
-5y + 21 = 76
-5y = 55
y = -11
what is -5½×2¾ ????
Answer:
Mixed fraction: -15 1/8
Improper fraction: 121/8
A hypothesis test in which rejection of the null hypothesis occurs for values of the
point estimator in either tail of the sampling distribution is called
a. The null hypothesis
b. The alternative hypothesis
c. A one-tailed test
d. A two-tailed test
A news organization interested in chronicling winter holiday travel trends conducted a survey. Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays. Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays. Construct a 99% confidence interval for the difference in population proportions of people in the eastern half of a country who fly to visit family members for the winter holidays and people in the western half of a country who fly to visit family members for the winter holidays. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.) z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576
Answer:
(-0.481 , -0.144)
Step-by-step explanation:
Confidence Interval for difference is proportion formula is given as:
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
For p1
Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays.
n1 = 96 people
p1 = x/n
x = 42 people
p1 = 42/96
= 0.4375
1 - p1 = 0.5625
For p2
Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays.
n2 = 108 people
p2 = x/n
x = 81 people
p2 = 81/108
= 0.75
1 - p2 = 0.25
99% confidence interval = 2.576
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
= 0.4375 - 0.75 ± 2.576 ×√[0.4375(1 -0.4375)/96 +0.75 (1 - 0.75)/108]
= -0.3125 ± 2.576 × √0.4375× 0.5625/96 + 0.75 × 0.25 /108
= -0.3125 ± 2.576 × √0.0025634766 + 0.0017361111
= -0.3125 ± 2.576 × √0.0042995877
= -0.3125 ±2.576 × 0.0655712414
= -0.3125 ± 0.1689115178464
Confidence Interval
-0.3125 - 0.1689115178464
= -0.4814115178
Approximately to 3 decimal places = -0.481
= -0.3125 + 0.1689115178464
= -0.1435884822
Approximately to 3 decimal places = -0.144
Therefore, the 99% confidence interval for difference in proportion = (-0.481 , -0.144)
Let f be the continuous function defined on [-6,6]. Let g be the function given by g(x) = [tex]\int\limits^x_{-1} {f(t)} \, dt[/tex] . Write an equation for the tangent to the graph of g at x=4
Answer:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]
And we want to write the equation for the tangent to the graph of g at x = 4.
First, determine g(4):
[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]
This is equivalent to the area of f from -1 to 4:
[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]
Note that areas under the x-axis are negative.
Find g'(4):
[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]
Note f is a line for 3 < x < 6 with a slope of 1.
Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]
In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Evaluate the expression for the given value of x. 8x + 4 for x = 8 The solution is
Answer:
68
Step-by-step explanation:
bidmas rule
8×8=64
64+68
Help ! What do we know about the slopes of two lines if we are told that the lines are parallel?
Answer:
they have the same slope
Step-by-step explanation:
because if they are parallel they have the same slope
Select the correct answer from the drop-down menu.
The design of a building that has a square pyramid roof as a roof is shown. The cost of material for the outside of the building and for the roof
ranges from $25 per square foot to $50 per square foot. The budget for this material is $500,000. The rectangular front of the building has a
length twice as long as its height. The slant height of the roof is the same as the height of the rectangular front of the building.
What is the maximum possible length of the rectangular front of the building to the nearest foot?
feet
The maximum possible length of the rectangular front of the building is
The maximum length of the rectangular front is the highest length of the rectangular front, and the value is 128.1 feet
How to determine the maximum possible length?Let the dimension of the rectangular front be x and y.
Such that:
y = 2x
So, the area of the rectangular front is:
A = xy
[tex]A = 2x^2[/tex]
The surface area of the pyramid roof is:
A = 4bh
Where:
b = base =25
h = height =18
So, we have:
[tex]A = 4* 25 * 18[/tex]
[tex]A = 1800[/tex]
The total surface area of the figure is:
[tex]T = 1800 +2x^2[/tex]
The range of the cost of material is: $25 per square foot to $50 per square foot.
So, the maximum cost is:
[tex]50 * (1800 +2x^2) = 500000[/tex]
Divide both sides by 50
[tex]1800 +2x^2 = 10000[/tex]
Subtract 1800 from both sides
[tex]2x^2 = 8200[/tex]
Divide both sides by 2
[tex]x^2 = 4100[/tex]
Take the square root of both sides
x = 64.03
Recall that:
y = 2x
So, we have:
y = 2 * 64.03
y = 128.06
Approximate
y = 128.1
Hence, the maximum possible length of the rectangular front of the building is 128.1 feet
Read more about maximum area at:
https://brainly.com/question/19819849
Answer: 82
Step-by-step explanation:
Find the LCD for the following pair of fractions 1/10 and 17/45
Answer:
Step-by-step explanation:
LCD: 90
10: 10, 20, 30, 40, 50, 60, 70, 80, 90
45: 45, 90
9/90 and 34/90
Parallel Lines and Transversals Find the measure of each angle indicated. Pls help me on these at least a couple of them I really need help I'll give brainliest if it is correct
Answer:
75°, 112°, 125°, 113°, 89°, 98°, 90°, 130°
Step-by-step explanation:
The marked angle pairs are one of ...
vertical angles -- congruentlinear pair -- supplementaryconsecutive interior -- supplementaryalternate interior -- congruentcorresponding -- congruentalternate exterior -- congruent1) vertical angles (congruent): ? = 75°
2) linear pair (supplementary): ? = 180° -68° = 112°
3) consecutive interior (supplementary): ? = 180° -55° = 125°
4) alternate interior (congruent): ? = 113°
5) corresponding (congruent): ? = 89°
6) alternate exterior (congruent): ? = 98°
7) alternate interior (congruent): ? = 90°
8) alternate interior (congruent): ? = 130°
_____
Additional comment
For parallel lines in general, all of the obtuse angles are congruent, and all of the acute angles are congruent. All of the obtuse angles are supplementary to the acute angles. (In (7), all angles are right angles, so all are congruent.) These facts can help you with problems like this one.
Learning the language (names/relationships) of these angles will be helpful to you in the future.
how many more grains of rice are in a fifty-pound bag of valencia rice than in a fifty pound bag of basmati rice
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains
Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
Find out more on equation at: https://brainly.com/question/2972832
What is the slope of the line that passes through the points (9, 5)(9,5) and (21, 1) ?(21,1)? Write your answer in simplest form.
Answer:
i know this but do not lol
Step-by-step explanation:
Answer:
did u mean to put (9,5) and (21,1) in there twice? but if so ur answer is m= -1/3
TRY USING SYMBOLAB I USE ALL THE TIME
In the triangle above, what is sin A
Answer:
[tex]\large\boxed{\sf sin(A)=0.5}[/tex]
Step-by-step explanation:
A right angled triangle is given to us and we would like to find out the value of sin(A) .
From the triangle we can see that the measure of angle BAC is 30° . Therefore ,
[tex]\longrightarrow A = 30^o[/tex]
On using sin both sides ,
[tex]\longrightarrow sin(A) = sin30^o[/tex]
As we know that the value of sin30° = 1/2. So;
[tex]\longrightarrow sin(A)=\dfrac{1}{2} [/tex]
Simplify by converting it into decimal ,
[tex]\longrightarrow \underline{\underline{sin(A) = 0.5}} [/tex]
Hence option B is correct .
And we are done!
Ok what is the time and how do I actually get this free trial lol
the time is only 9:30 and fine in it lol
Jackson weighed all of his pet guinea pigs and found the average weight to be 2.4 pounds. If the standard error of the sample mean was 0.2227 and the sample standard deviation was 0.63 pounds, how many guinea pigs does Jackson have
Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.
In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]
[tex]0.2227\sqrt{n} = 0.63[/tex]
[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]
[tex]n = 8[/tex]
Jackson has 8 guinea pigs.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
find three consecutive integers whose sum is 1266
Answer:
(x)t(xt1)t(xt2)=1266
Step-by-step explanation:
here here we will use the algebra to find three consecutive integers whose sum is 1266 we start by assigning x to the first integer since there are consecutive it means that the second number will be x plus 1 and the third will be x plus 2 they shall all add up to 1 2 6 6 therefore you can write the equation as a following