Answer:
2008 and 2010 is 52 units per year.
Step-by-step explanation:
To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.
The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.
Therefore, the change in sales over that period is:
f(2010) - f(2008) = 624 - 520 = 104
The average rate of change of sales between 2008 and 2010 is:
(104) / (2) = 52
So the average rate of change of sales between 2008 and 2010 is 52 units per year.
You give your home health patient an unopened 500mL bottle of Mucinex and tell them to take 2 teaspoons 4 times a day as ordered. Your patient then ask you, "How long will this bottle last?" What will you tell your patient? (Respond to both questions.)
Answer:
the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.
Step-by-step explanation:
Assuming that one teaspoon is equivalent to 5 milliliters (mL), then 2 teaspoons would be 10 mL. Therefore, the patient will be taking a total of 10 mL four times a day, which is 40 mL per day.
Since the bottle contains 500 mL, we can calculate how long the bottle will last by dividing the total volume of the bottle by the daily dose:
Number of days = Total volume of bottle / Daily dose
Number of days = 500 mL / 40 mL per day
Number of days = 12.5 days
Therefore, the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.
PLEASE HELP QUICK 30 POINTS
You know the lengths of the two legs of a right triangle, and you are trying to solve for the measures of the acute angles of that triangle. Without calculating the length of the hypotenuse, which trigonometric ratio and reciprocal trigonometric ratio would be most useful in this calculation? Why?
The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8 $220
82.8 $280
Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth.
A) ŷ = 3.8x − 109.2
B) ŷ = −3.8xx − 109.2
C) ŷ = 6.5x − 279.1
D) ŷ = −6.5x − 279.1
The linear regression equation is defined as follows:
C. ŷ = 6.5x − 279.1
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given on the table as follows:
(58.2, 112), (64.2, 135), (64.3, 138), (66.8, 146), (68.4, 166), (71.6, 180), (72.7, 188), (76.2, 199), (77.8, 220), (82.8, 280).
Inserting these points into a calculator, the line of best fit is given as follows:
ŷ = 6.5x − 279.1
Meaning that the correct statement is given by option C.
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Solve the integral equation using the generalized power rule
Answer:
a = 4x with a small 3 at the top ( x with a small 4 at the top + 3x ) with a small 30 + 3
b = B = 6x with a small 17 at the top + 192x with a small 15 at the top + 2520x with a small 13 at the top + 17280x with a small 11 at the top + 64800x with a small 9 at the top + 124416x with a small 7 at the top + 93312 with a small 5 at the top
sorry but I don't know c
Step-by-step explanation:
11. Which fraction has a value that's equal to ½?
O A. 568
O B. 15
O C. 4964
O D. 21/24
Answer: d is the answer
Step-by-step explanation: because if you do your math correctly it comes out to be 21/24
Jorge Holland is having a new furnace installed. The furnace costs $3,500.00. The bank requires a down payment of 20 percent and 36 monthly payments of $85.18 each. What is the APR on his loan?
Answer:
Down payment = $3,500 x 0.20 = $700.00So the amount of the loan is:Loan amount = $3,500.00 - $700.00 = $2,800.00Now we can use the formula for the present value of an annuity to find the APR:PV = PMT x [(1 - (1 + r)^-n) / r]where PV is the present value (in this case, $2,800.00), PMT is the monthly payment ($85.18), r is the monthly interest rate, and n is the number of months (36).Solving for r, we get:r = 0.01301 or 1.301%Since the monthly interest rate is 1.301%, the APR is:APR = 12 x 1.301% = 15.61%Therefore, the APR on Jorge Holland's loan is 15.61%.
The elevation at ground level is O feet. An elevator starts 90 feet below
ground level. After traveling 15 seconds, the elevator is 20 feet below
ground level. Which statement describes the elevator's rate of change in
elevation during this 15 second interval?
Answer: there you go :)
Step-by-step explanation:
Its D, 90-20=70 ft traveled downwards
5. Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest
monthly, and to calculate what annual interest rate he needs, he is using the Rule of 72.
Part ll: what equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?
Part lll: What annual interest rate does Miguel need to double his money by the time he retires?
Miguel has to put up the equation r = 72/16.
4.5% is the interest rate.
What is the 72-hour rule?For calculating how long it would take for an investment to double in value, the rule of 72 is utilised. To get the doubling time, divide 72 by the interest rate.
To use the rule of 72, you simply divide the number 72 by the annual interest rate. For example, if the interest rate is 6%, the rule of 72 predicts that it will take approximately 12 years (72 ÷ 6 = 12) for the investment to double in value.
Part2:
equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires is n = 72 / r
Part3:
annual interest rate does Miguel need to double his money by the time he retire
r = 72 / n
72 / 16 = 4.5%
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PWSB has a deal where they give you $100.00 to start a savings account. In addition, you decide toput money in the bank for 5 weeks and finish with $50.00.
a. Assuming you save the same amount every week, write an equation where y is the total
money in the savings account and x represents the number of weeksyou saved money.
b. What do the slope and y-intercept represent in the context of the problem?
Someone please help me with this it is a linear equation I think and the formula is y=Mx+b
y = $100.00 - $10.00x is the equation for the total amount of money in the savings account after x weeks.
The y-intercept represents the initial deposit of $100.00 and the slope is -10
How to find the expressiona. Let's call the amount of money saved each week "s" and
let's call the total amount of money in the savings account after "x" weeks "y".
Since the amount saved each week is the same, we can express the total amount of money in the savings account as:
y = $100.00 + sx
We know that at the end of the 5th week, the total amount in the savings account is $50.00. So we can set up the following equation:
$50.00 = $100.00 + 5s
solving for s:
$50.00 - $100.00 = 5s
-$50.00 = 5s
-10 = s
So the equation for the total amount of money in the savings account after x weeks is:
y = $100.00 - $10.00x
b. In the context of this problem, the slope represents the amount of money that is saved each week.
In this case, the slope is -10, meaning that $10.00 is saved each week. The y-intercept represents the initial deposit of $100.00.
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Question 2: Stony opened a bank account with a particular bank! at the beginning of 2015. The bank pays 8% simple interent on a yearly basis. If Stony's initial is $1575, how much money would be in Stony's account by september of 2020.
There would be $2203.50 in Stony's account by September 2020 using simple interest formula.
As the bank charges an annual 8% simple interest, we may apply the following formula:
Simple interest is calculated as follows: Principle is the initial investment, Rate is the annual interest rate, and Time is the duration in years.
Here, the principal (P) is $1575, the interest rate (r) is 8%, and the time (t) is 5 since we need to know how much money Stony will have in his account by September 2020, which is five years from now.
We may calculate Stony's interest earnings over a five-year period using the simple interest formula:
Interest is calculated as follows: $1575 x 0.08 x 5 = $628.50
Stony's account will therefore have the following balance by September 2020: Total Amount = Principal + Interest = $1575 + $628.50 = $2203.50
Therefore by September 2020, Stony would have $2203.50 in his account.
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Suppose that the dollar value (t) of a certain house that is ‹ years old is given by the following exponential function.
v(t) =427,500(1.08)^t
At spinet torture middle school, 35% of the classrooms are for sixth graders, if there are 49 sixth grade classrooms, how many classrooms in total?
actually, there are a total of "x" classrooms, which oddly enough is the 100%, and we also know that 35% of that is 49, so
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 49& 35 \end{array} \implies \cfrac{x}{49}~~=~~\cfrac{100}{35} \\\\\\ \cfrac{ x }{ 49 } ~~=~~ \cfrac{ 20 }{ 7 }\implies 7x=980\implies x=\cfrac{980}{7}\implies x=140[/tex]
Urgenttt! Please help.
What is 1.3333… expressed as a fraction in simplest form? SHOW YOUR WORK.
(Hint: You will use two equations to answer this question. One of them is: x = 1.3)
Step 1: To convert 1.33 repeating into a fraction, begin writing this simple equation:
n = 1.33 (equation 1)
Step 2: Notice that there are 2 digitss in the repeating block (33), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.
100 × n = 133.333 (equation 2)
Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.
100 × n = 133.333
1 × n = 1.33
99 × n = 132
132
99
could be the answer, but it still can be put in the simplest form, i.e., reduced.
To simplify this fraction, divide the numerator and denominator by 33 (the GCF - greatest common factor).
n = 132
99
= 132 ÷ 33
99 ÷ 33
= 4
3
. So, 1.33 = 4/3
as the lowest possible fraction.
write a linear equation based on the given information.
through: (5,-1) and (2,2)
Answer:
y = (-1/3)x + 2/3
Step-by-step explanation:
We can use the slope-intercept form of a linear equation to find the equation of the line passing through the points (5, -1) and (2, 2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we have:
slope = (2 - (-1)) / (2 - 5) = -1/3
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of a linear equation to find the y-intercept.
Using the point (5, -1), we have:
-1 = (-1/3)(5) + b
Solving for b, we get:
b = -1 + 5/3 = 2/3
Therefore, the equation of the line passing through the points (5, -1) and (2, 2) is:
y = (-1/3)x + 2/3
If 30% of all commuters ride to work in carpools, find the probability that if eight workers are selected, three will ride in carpools.
The probability that out of 8 workers, 3 will ride in carpools is 0.254.
What is probability?
The mathematical concept of probability is used to determine the likelihood of an event. It is solely useful for calculating the probability that an event will occur. From 0 to 1, where 0 represents impossibility and 1 represents a particular occurrence.
We are given that 30% of all commuters ride to work in carpools.
Now, if eight workers are selected, then the probability that three will ride in carpools is determined by using the following
P (X = 3) = [tex]n C_{x} p^{x} (1-p)^{(n-x)}[/tex]
We have n = 8, x = 3 and p = 0.3
So, using the formula, we get
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (1-0.3)^{(8-3)}[/tex]
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * [tex](0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * 0.027 * 0.16807
⇒P (X = 3) = 0.254
Hence, the probability that out of 8 workers, 3 will ride in carpools is 0.254.
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3.1. 1 Three friends Anna, Manna and Hanna are doing the decorations for matric farewell dance. Anna put up two - fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer. [13]
Answer:
Step-by-step explanation:
To determine if the job is complete, we need to add up the fractions of the decoration that each person put up:
Anna: 2/5
Manna: 1/4
Hanna: 3/10
Now we can find the total fraction of the decoration that they put up by adding these fractions:
2/5 + 1/4 + 3/10 = 16/40 + 10/40 + 12/40 = 38/40
So they have completed 38/40 of the decoration. To find the fraction of the job that is still left to do, we can subtract this from 1:
1 - 38/40 = 2/40
Therefore, there is still 2/40 of the decoration left to do, or 1/20 of the total job.
Can someone help with this?!
In AJKL, JK II MN. Given that MJ = 10, NK=25, and LN = 20, find LM.
M
Z
K
=0
LM=
Answer:
Please mark as brainliest
I need help with this please
Answer:
Ricky is taller by 11 inches ( a)
Step-by-step explanation:
1 foot = 12 inches
5 feet= 60 inches
Ticky is 68 inches
Ricky is 79 inches
ricky-Ticky= 79- 68= 11 inchesss!
What is different about the Statue of Liberty
compared to other outdoor statues?
A its in a park
B its on a pedestal
C it is made of copper
D It is much bigger.
The difference between the Statue of Liberty compared to other outdoor statues is that it is made of copper which is option C.
Statue of liberty explained.
The Statue of Liberty is a colossal neoclassical sculpture located on Liberty Island in New York Harbor in the United States. It was a gift from the people of France to the people of the United States, dedicated on October 28, 1886, and has since become one of the most recognizable symbols of the United States and its ideals of freedom and democracy.
The statue was designed by French sculptor Frédéric-Auguste Bartholdi, with the help of engineer Gustave Eiffel. The statue depicts a female figure dressed in a flowing robe and holding a torch in one hand and a tablet in the other, upon which is inscribed the date of the American Declaration of Independence (July 4, 1776).
The Statue of Liberty is unique among outdoor statues in that it is made of copper sheets that have oxidized over time to form a green patina. This patina has become an iconic symbol of the statue and is a result of the natural process of copper corrosion. The statue was originally a shiny brown color, but the oxidation of the copper has gradually changed its appearance over time.
Therefore, while the Statue of Liberty is also located in a park and on a pedestal, and it is larger than many outdoor statues, these characteristics are not unique to the statue and can be found in other outdoor statues as well.
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What is the range of the function y=e4x7
A- Y <0
B- Y > O
C- y <4
D- Y> 4
We have been given the function We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.
Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.
Therefore, the range of the function is given by y>0B is the correct option.
If ABCD is a rectangle, AD=9, AC=22
If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, the missing measures are m<ADC = 90°, m<BAC = 24°, m<CDB = 240°, and m<AEB = 132°.
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental theorem in geometry that says that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
That is to say mathematically,
[tex]a^{2} + b^{2} = c^{2}[/tex]
where a and b are the lengths of the two sides of the triangle (the sides adjacent to the right angle), and c is the length of the hypotenuse.
Thus, substituting our values for this formula,
[tex]x^{2} +9^{2} =22[/tex]
[tex]x^{2} +81= 484[/tex]
[tex]x^{2} = 484-81[/tex]
[tex]x^{2} =403[/tex]
[tex]x=20.1[/tex] = AB
Thus,
BC = 9
AB = 20.1
BD= 22
EC = 11
m<ADC = 90°
m<BAC = 24° (90-66)
m<CDB = 240°
m<AEB = 132° (180-24-24)
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You asked an incomplete question. The complete question reads;
If ABCD is a rectangle, AD=9, AC=22, and <BCA = 66°, find each missing measure. I also attached an image of the question.
Suppose a = 5 and A = 75 degrees.
Find:
The side lengths of given triangle is;
a=5 units
b=18.72 units
c=18.99 units
What is triangle?A triangle is a closed, two-dimensional figure with three straight sides and three angles. It is one of the basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles, including equilateral triangles (where all three sides are of equal length and all three angles are 60 degrees), isosceles triangles (where two sides are of equal length), and scalene triangles (where all three sides and angles are different). Triangles are used in many different areas of mathematics and science, including trigonometry, geometry, and physics.
Here,
We can use the trigonometric ratios of sine, cosine, and tangent to find the values of b and c. First, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle C:
C = 180 - A - B = 180 - 75 - 90 = 15 degrees
Next, we can use the definition of the sine ratio:
sin(A) = opposite/hypotenuse
to find c:
sin(75) = 5/c
c = 5/sin(75) ≈ 18.99
Finally, we can use the Pythagorean theorem:
a² + b² = c²
to find b:
b² = c² - a²
= (18.99)² - 5²
≈ 350.66
b ≈ √350.66 ≈ 18.72
Therefore, a ≈ 5, b ≈ 18.72, and c ≈ 18.99.
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Please help!! No one answered my last question
Answer:
3 final songs
Step-by-step explanation:
Answer: There will be 3 songs on the final CD.
Step-by-step explanation: The band expects to put 12 songs on their next CD. They write and record 25% more songs than they expect, which means they wrote and recorded 12 + (0.25 x 12) = 15 songs. During the editing process, 80% of the songs are removed. 80% of 15 is (0.80 x 15) = 12 songs. Subtracting the removed songs from the recorded songs, we get 15 - 12 = 3 songs that will be on the final CD. Therefore, there will be 3 songs on the final CD.
I NEED HELP ASAP
An athlete dives from the 3-meter springboard her height y, and horizontal distance x, can be approximated by the function y=-1.2x^2+3.12x +3. both the height and distance are in meters.
A:
how far has she traveled horizontally when she reaches her maximum?
B:
what is her maximum height, round to the nearest tenth of a meter
Part A: distance travelled by athlete when she reaches her maximum is 1.3 m.
Part B: her maximum height: 5 m.
Explain about the quadratic equation?In mathematics, a quadratic equation is one with degree 2, which means that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where such a, b, and c are all numbers which can't be zero. All of these are examples of quadratic equations:Th equation is-
y = -1.2x² + 3.12x +3.
horizontal distance - x
Part A: distance travelled by athlete when she reaches her maximum:
Comparing given equation with standard form of quadratic equation:
x = -b/a
x = -3.12/2(-1.2) = 1.3
Thus, distance travelled by athlete when she traveled horizontally and reaches her maximum of 1.3 m.
Part B: her maximum height:
y = -1.2x² + 3.12x +3.
Put x = 1.3
y = -1.2(1.3)² + 3.12(1.3) +3.
On solving:
y = 5.028
y = 5 m
Thus, her maximum height, round to the nearest tenth of a meter is 5 m.
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How many ways is there to answer 20-question multiple choice test if there are 5 choices for each question?
Answer:
95,367,431,640,625 (or approximately 9.5 x 10^13)
Step-by-step explanation:
If there are 5 choices for each question in a 20-question multiple-choice test, then there are 5 possible answers for each question. To find the total number of ways to answer the test, we need to multiply the number of choices for each question together.
Therefore, the total number of ways to answer the 20-question multiple-choice test is:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
which is equal to 95,367,431,640,625 (or approximately 9.5 x 10^13) ways to answer the test.
refers to the standard normal distribution find a z value such that the probability of obtaininig a large z value of 0.20?
Therefore , the solution of the given problem of probability comes out to be the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
What is probability exactly?The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.
Here,
The z-value for a chance of 0.20 in the right tail of the distribution can be found using a calculator or a standard normal distribution table.
The probability number in the right tail that is
=> closest to 0.20 using a standard normal distribution table is 0.1995.
This probability's equivalent z-value is roughly 0.84.
As an alternative, we can calculate the z-value using a computer. With a chance of 0.20, a mean of 0, and a standard deviation of 1, and the inverse normal function—also known as the normal quantile function—we obtain:
=> Z=invNorm(0.20) 0.84
As a result, the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
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Which solid figure could be formed from the net shown?
(A) cube
(B) triangular prism
(C) rectangular pyramid
(D) square pyramid
_______________________________
(reporting wrong/spam answers)
(giving brainliest to correct answers)
_______________________________
A) Cube
the two squares will form the top and one side.
Each square right, top and bottom of the square will form the sides
After working through the suggested questions,Zanele realises that the questionnaire is not suitable.List two reasons why you that the given questionnaire is Not suitable
Below are some general reasons why a questionnaire might not be suitable:
Poorly constructed questionsLaslty Inadequate samplingWhat is the questionnaire about?Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.
Lastly Inadequate sampling: If the sampling technique used to select respondents is not representative of the target population, then the results obtained may not be generalizable or applicable to the larger population. The sample size and composition may also affect the validity and reliability of the results.
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what is the meaning of bookkeeping
Answer:
Hope this helps
Step-by-step explanation:
the activity or occupation of keeping records of the financial affairs of a business.
Im not sure which bookkeeping you mean but bookkeeping focuses on recording and organising financial data.
[tex]x-\frac{3x-2}{4} =\frac{6-5x}{3}[/tex]
This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get , x ≈ 1.29
Tο sοlve linear equatiοns with fractiοns, we need tο multiply bοth sides οf the equatiοn by the least cοmmοn multiple (LCM) οf all the denοminatοrs tο eliminate the fractiοns¹.
Hοw are linear equatiοns that have fractiοns οn bοth sides sοlved?When an equatiοn invοlves fractiοns οn bοth sides, multiply each side by the denοminatοrs' lοwest cοmmοn multiple (LCM).
The LCM οf 4 and 3 is 12. Multiplying bοth sides by 12, we get:
12(x - (3x-2)/4) = 12((6-5x)/3)
Simplifying, we get:
12x - 3(3x-2) = 4(6-5x)
Expanding and cοllecting like terms, we get:
-6x + 6 = -20x + 24
Adding 20x tο bοth sides, we get:
14x + 6 = 24
Subtracting 6 frοm bοth sides, we get:
14x = <cοde>**18**</cοde>
Dividing bοth sides by <cοde>**14**</cοde>, we get:
<cοde>**x = 18/14**</cοde>
This is an imprοper fractiοn. Tο simplify it, we divide the numeratοr by the denοminatοr and get:
<cοde>**x = <u>9</u>/<u>7</u>**</cοde>
This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get:
x ≈ 1.29
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