The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.
As per the given data, the given formula is:
[tex]$T=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex] gives the time it takes in seconds.
Where,
T is the time it takes for a pendulum to make one full swing back and forth (in seconds).
L is the length of the pendulum, in feet.
Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.
Substitute the given parameters into the formula will give;
[tex]$1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex]
Now divide both sides by 2π.
[tex]$ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\[/tex]
[tex]$ 0.3024=\sqrt{\left(\frac{L}{32}\right)}[/tex]
Then taking square on both sides.
[tex]$ (0.3024)^2=\frac{L}{32} \\[/tex]
0.09144576 = [tex]$\frac{L}{32}[/tex]
Later multiply both sides by 32.
2.9262 = L
The approximate value of the length of a pendulum:
L ≈ 3
Therefore, the length of a pendulum is about 3 feet.
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find the difference of the polynomials 2a^2+3a and 3a^2-4a by subtracting the second from the first
Answer:
-a^2+7a
Step-by-step explanation:
Mensa is an organization that allows people to join only if their IQs are in the top 2% of the population. (You may need to use Table 8.1.)
(a)
What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? (Remember that the mean is 100 and the standard deviation is 15. Round your answer to two decimal places.)
(b)
Mensa also allows members to qualify on the basis of certain standard tests. If you were to try to qualify on the basis of the quantitative reasoning part of the GRE exam, what score would you need on the exam? (Remember that the mean is 151.3 and the standard deviation is 8.7. Round your answer to the nearest whole number.)
(a) To be eligible for Mensa, an individual's IQ must be in the top 2% of the population. This means that the IQ score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean IQ score is 100 and the standard deviation is 15, we can standardize the IQ score to find the z-score:
z = (IQ - mean) / standard deviation
z = (IQ - 100) / 15
The 97th percentile corresponds to a z-score of 2.33. To find the IQ score, we can reverse the standardization formula:
IQ = z x standard deviation + mean
IQ = 2.33 x 15 + 100
IQ = 146.95
So, the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa is 147.
(b) To be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam, an individual's score must be in the top 2% of the population. This means that the score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean score on the quantitative reasoning part of the GRE is 151.3 and the standard deviation is 8.7, we can standardize the score to find the z-score:
z = (score - mean) / standard deviation
z = (score - 151.3) / 8.7
The 97th percentile corresponds to a z-score of 2.33. To find the score, we can reverse the standardization formula:
score = z x standard deviation + mean
score = 2.33 x 8.7 + 151.3
score = 162.291
So, the score required to be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam is approximately 162. Round to the nearest whole number, the score would be 162.
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What is the solution to x=√-x+6
a. 2 and -3
b.-2 and 3
c. -3
d.2
The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number. So the answer is none of the options listed.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").
Here,
The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number.
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The length of a rectangular pool is 4 meters less than twice the width. if the pool's perimeter is 94 meters, what is the width?
Answer:
see below
Step-by-step explanation:
length = x
width = y
x = 2y -4
2*(x+y) =94
x+y = 47
so x = 47-y
so 47-y= 2y -4
so 3y = 51
y = 17
x=30
in a class of 24 students, 23 of them took an exam in class and 1 student took a make-up exam the following day. the professor graded the first batch of 23 exams and found an average score of 78 points with a standard deviation of 6.4 points. the student who took the make-up the following day scored 62 points on the exam
The average score for the class on the exam was 78 points with a standard deviation of 6.4 points. The student who took the make-up exam scored 79.25points.
1. Calculate the mean of the first 23 exams:
Mean = 78 points
2. Calculate the standard deviation of the first 23 exams:
Standard Deviation = 6.4 points
3. Calculate the mean of the entire class:
Mean = (78 x 23) + 62 = 1840 + 62 = 1902
Total = 24
Mean = 1902 / 24 = 79.25 points
The average exam score for the class of 24 students was 78 points with a standard deviation of 6.4 points. This means that most students in the class scored between 71.6 and 84.4 points on the exam. The student who took the make-up exam the following day scored 79.25points. This score is significantly lower than the average score of the class, suggesting that the student may have not done as well on the exam compared to the other students. It is also possible that the student faced additional challenges that the other students did not have to face, such as taking the exam on a different day. Regardless, the student's score was significantly lower than the average score of the class.
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arallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed by lines r and s are 1, 2, 3, 4; formed by lines r and t are 5, 6, 7, 8. Which angles are alternate interior angles? Angle3 and Angle5 Angle1 and Angle7 Angle3 and Angle7 Angle4 and Angle5
The angles are alternate interior angles
<4 and <6
<3 and <5.
What are Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
As, from the property of parallel line we have the following properties
Alternate Interior angleCorresponding AngleCo- interior angle.So, from the figure the pair angles shows alternate interior angle
<4 and <6
<3 and <5.
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Nolan buys a $12,000, 13-week treasury bill at 5%. What’s his effective rate? Round your answer to the nearest hundredth of a percent.
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
what is interest ?Divide the original by the lending rates, the duration of time, and other factors to arrive at simple interest. Simple gain = principal + interested + hours is the marketing formula. This system makes it simpler to calculate interest. The most popular technique to figure out this is as a portion of the principal sum. He can only pay his share of the 100% interest, for example, if he borrow $100 from a friend he agrees to repay him with 5% interest. $100 (0.05) = $5. When you borrow more money, you should pay interest, and when you give it out, you must make payments. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Simple interest = $12,000 × 0.05 × 13/52 = $150
Simple discount note = ($12,000 - $150) × 13/52 = $2962.5
Effective rate of interest = $150 / $2962.5
Effective rate of interest = 0.0506 or 5.06%
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
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K
Consider the numbers
Select all that apply.
Which are rational numbers?
A. 8
7
D. 0
G. √9
J.-√34
5
M. √3
8
4,√3, -2.57, 22, 19.2.-19, 125, 27.131331333-34. √2.-7.0,√/9.
B. 4
E.125
H. 7.131331333...
K. -2.57
N. 2
C.-19
OF. 22
1. 5
9
OL.
26
0. 19.2
The rational numbers in this problem are given by these following letters:
A, B, C, D, E, G, I, K, L, O.
What are rational and irrational numbers?Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.
The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.
The irrational numbers are justified as follows:
7.1313313333... is a non-terminating decimal.The remaining are non-exact roots.More can be learned about rational numbers at brainly.com/question/12088221
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What is an equation for the linear function whose graph contains the point (2, 5) with a slope of -5?
Answer:
y=-5x+15.
Step-by-step explanation:
1. if the given slope is (-5), then it is possible to make up the required equation in slope-interception form: y=-5x+interception, where 'interception' is unknown number;
2. in order to calculate the 'interception' it is enought to substitute the given coordinates of the point into the last equation (y=5; x=2):
5=-5*2+interception; ⇒ interception=15. Then
3. finally, the required equqaiton is y=-5x+15.
Can you help me with this
Answer:
two plus two equals five
Step-by-step explanation:
The half-life of Carbon is 5730 years. If 10 grams of Carbon are present at time t = 0, how many will be present in 2,000 years?
The amount of Carbon that will be presented in 2,000 years is given as follows:
7.85 grams.
What is an exponential function?An exponential function is defined as follows:
y = a(b)^(x/n).
In which:
a is the initial amount.b is the rate of change.n is the time needed for the rate of change.Considering the initial amount of 10 grams and the half life of 5730 years, the parameters for this problem are given as follows:
a = 10, b = 0.5, n = 5730.
Hence the function is defined as follows:
y = 10(0.5)^(x/5730)
Then the amount after 2,000 years is given as follows:
y = 10(0.5)^(2000/5730)
y = 7.85 grams.
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Which answer is equal to cot(x)?
The cotangent of an angle is obtained dividing the cosine of the angle by the sine of the angle, that is:
cot(x) = cos(x)/sin(x).
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The cotangent function is the inverse of the tangent function, that is:
cot(x) = 1/tan(x)
cot(x) = 1/(sin(x)/cos(x))
cot(x) = cos(x)/sin(x).
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There are five boxes. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
The difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
Given:
The weight of boxes is :
1st box = 200 kg
2nd box = 300 kg
3rd box = 250 kg
4th box = 350 kg
5th box = 500 kg
Since , heavier weight = 500 Kg
lighter weight = 200 Kg
Average weight of four heaviest boxes =1400/4=350kg
Average weight of four lightest boxes =1100/4=275kg
∴ Difference =(350−200)/2=150/2=75kg
Hence , the difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
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How many adults binge drink four times per month?
A. 1 in 10
B. 1 in 6
C. 1 in 4
D. 1 in 8
suppose that {~v1, ~v2, ~v3} is a linearly dependent set of vectors in rn and ~v4 is vector in rn. show that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
True, that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
What is a linearly independent set?
A collection of vectors is said to be linearly independent in vector space theory if no nontrivial linear combination of the vectors equals the zero vector. The vectors are considered to be linearly dependent if such a linear combination occurs.
(i.e., all coefficients = 0). A single element set {v} is linearly independent if and only if v ≠ 0.
Now,
As given that
x1v1 + x2v2 + x3v3 = 0 with x1, x2, x3 not all zero, then x1v1 + x2v2 + x3v3 + 0 v4 = 0 and still the coefficients are not ALL zero.
Hence,
It is True that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
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Andrew collects stamps. he collected a total of 150 stamps. is 84% of the stamps he collected were foreign, how many other stamps did he collect?
Answer:
24
Step-by-step explanation:
If 84% of the stamps he collected were foreign, that means he collected 150 * 0.84 = 126 foreign stamps.
So, he collected 150 - 126 = 24 stamps that were not foreign.
Let Si and S2 be subsets of a vector space V. Prove that span(Si n S2) C span(S1) nspan(S2). Give an example in which span(S1nS2) and span(Si)nspan(S2) are equal and one in which they are unequal.
Let S₁ and S₂ be subsets of a vector space V. So, proves are shown as well.
What is vector space?A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.
Let, S₁ and S₂ be subsets of vector space V
Now, S₁ ⊆ V, S₂ ⊆ V
(S₁ ∩ S₂) ⊆ V
Let, x ⊆ span (S₁ ∩ S₂)
x ∈ span (S₁) and x ∈ span (S₂)
x ∈ span (S₁ ∩ S₂)
∴ span (S₁ ∩ S₂) ⊆ span (S₁) ∩ span (S₂)
span (S₁ ∩ S₂) = span (S₁) ∩ span (S₂)
where either S₁ ⊆ S₂ or, S₂ ⊆ S₁
span (S₁ ∩ S₂) ≠ span (S₁) ∩ span (S₂)
where, (S₁ ⊆ S₂) = ∅ but span (S₁) ∩ span (S₂)
(S₁ ∩ S₂) = ∅ i.e. span (S₁ ∩ S₂)
but span (S₁) = R₁²
span (S₂) = R₁²
Thus, span (S₁) ∩ span (S₂) = R₁²
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Which of the following tables represents a relation that is a function?
x y
−5 −3
−2 3
−1 1
3 4
3 −1
x y
−5 4
−2 4
0 −4
0 4
3 4
x y
−4 0
−2 2
0 3
2 0
3 4
x y
1 −4
1 −2
1 0
1 2
1 4
A shop tech earns a base pay of $18.48 per hour, plus "time-and-a-half for overtime (time exceeding 40 hours). If he works 44.5 hours during a particular week, what
is his gross pay?
The gross pay is $
Answer: Gross pay = $733.04
Step-by-step explanation:
If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 65 °F to 104 °F?
Express your answer to two significant figures and include the appropriate units.
HÅ
Value
20
Provide Feedback
Units
Submit Request Answer
?
P Pearson
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So, using a heater with a heating output of 5900 kJ/min, it will take roughly 9.05 hours to heat the water in the hot tub from 65°F to 104°F.
What kind of energy does heating use?When the temperature rises, atoms and molecules move faster and collide, creating thermal energy (also known as heat energy). Thermal energy is the energy that results from the heated substance's temperature.
How do you calculate kW for heating?Calculate the square footage or square metres of your room. The room's dimensions are then multiplied by its width, height, and length. Then double this amount by 6. For BTUs or 0.0606 for kW, respectively.
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the number of marbles peter had to be the number of marbles ravi had was in the ratio 8:5. after giving 18 marbles to his friends, peter had the same number of marbles as ravi. how many marbles did ravi have?
Answer:
30
Step-by-step explanation:
before
p:r
=8:5
after
p:r
=5:5
3 units=18
1 unit=6
no. of marbles Ravi has=5 units=6×5=30
A mechanic charger a flat rate of $30 per hour. You have already bought all the parts needed and only have $120 to fix your car. How many hours can the machine work on your car? Find the y-intercept and slope
Answer: 4 hours
Step-by-step explanation: y int = 120, slope = 30
Which pair of transformations could map ABC to A’B’C’, such that the triangles are similar but not congruent?
The pair of transformations that could map ABC to A’B’C’, such that the triangles are similar but not congruent are dilation and rotation
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ΔABC
Let the dilated triangle be represented as ΔA'B'C'
Let the dilation scale factor be represented as k
Now , when a triangle is dilated by a scale factor of k , there is a change in the shape of the triangle
After a dilation , the triangle will enlarge or compress by a factor k , but it will be similar to the parent triangle
Now , when the triangle is rotated , it only changes the initial coordinates of A , B and C
Hence , the transformations are dilation and rotation
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The absolute value of the sum of two Integers does not exceed the sum of the absolute values of these integers. əziou? aydunu le O V x Vy( ]z +y] 5 [+/+ 1y1) (18) + (0) 5126+2EXE O (18) + |3| 5] +31 ANEXE 0 (IAI + 3 + x| -) AXA
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
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The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
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pls help it’d overdue!!
Which is different?
O Solve
3
==
X
O Solve
O Find x so that 3:x and 12:8 are equivalent.
O
Find x so that 3:12 and x:8 are equivalent.
12
8
12 3
X
8
=
Find "both" answers
The answer to the "different" question is x =
The answer to the "same" questions is x =
D
The answer to the "different" question is: 32
The answer to the "same" question is: 2
Translate into a proportion: What number is 63% of 107? Let n= the number.
Answer:
look at the picture.......................
A tank originally holds 10 grams of salt, mixed into 100 gallons of water. Water containing 1.5 g of salt/gallon
is entering at the rate of 5 gallons/minute. I water is exiting the tank at the same rate, find the amount of salt Q in
the tank after time t.
Reflect the point in the x-axis followed by the y-axis.
Answer:
(3, - 4 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
(- 3, 4 ) → (- 3, - 4 )
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 3, - 4 ) → (3, - 4 )
For each of the following quadratic equations, find the discriminant and draw its sign diagram: Hence find values of m for which the equation has: (i) A repeated root (ii) two distinct real roots (iii) no real roots (a) x^2 − 4x + m = 0 (b) mx^2 + 3x + 2 = 0 (c) x^2 - mx + 1 = 0
a) For two distinct real roots: x > 0 or x > m
b) For two distinct real roots: x > 0 or x > 2m
c) For two distinct real roots: x > 0 or x > 4
This is based on the quadratic equation.
What is a quadratic equation?Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.
a) Quadratic equation: x² - 4x + m = 0
The discriminant: Δ = b² - 4ac
Δ = (2x)² - 4.x.(m)
Δ = 4x² - 4mx
Δ = 4x (x - m)
For two distinct real roots: Δ > 0
4x (x - m) > 0
x > 0 or x > m
For two real roots: Δ ≥ 0
4x (x - m) ≥ 0
x ≥ 0 or x ≥ m
For a repeated root: Δ = 0
4x (x - m) = 0
x = 0 or x = m
(b) Quadratic equation: mx² + 3x + 2 = 0
The discriminant: Δ = b² - 4ac
Δ = (3x)² - 4.mx.(2)
Δ = 4x² - 8mx
Δ = 4x (x - 2m)
For two distinct real roots: Δ > 0
4x (x - 2m) > 0
x > 0 or x > 2m
For two real roots: Δ ≥ 0
4x (x - 2m) ≥ 0
x ≥ 0 or x ≥ 2m
For a repeated root: Δ = 0
4x (x - 2m) = 0
x = 0 or x = 2m
(c) Quadratic equation: x² - mx + 1 = 0
The discriminant: Δ = b² - 4ac
Δ = (x)² - 4.x.(1)
Δ = x² - 4x
Δ = x (x - 4)
For two distinct real roots: Δ > 0
x (x - 4) > 0
x > 0 or x > 4
For two real roots: Δ ≥ 0
x (x - 4) ≥ 0
x ≥ 0 or x ≥ 4
For a repeated root: Δ = 0
x (x - 4) = 0
x = 0 or x = 4
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A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate to the nearest degree the angle of the sector.
Answer:
177°
Step-by-step explanation:
A sector is the area between two radi.
We are given the perimeter of the sector as 21.4cm and the radius 4.2cm. Subtracting two radi from the perimeter will give us the arc of the sector as 13.
As we know, the formula for the length of an arc is: length of arc = ∅/360 × πd. Diameter is double the radius so in this case it's 8.4; so filling in the blanks our new formula is: 13 = ∅/360 × 8.4π.
We are trying to find ∅ which is the degree of the sector. So from this formula we can rearrange it by dividing 8.4π on both sides of the equation giving ¹³/8.4π = ∅/360; from here we multiply 360 on both sides and therefore getting ∅ on its own therefore allowing us to equate it.
Plug that all into a calculator and you get 177.3440794 so you can round it down to 177°
I saw this question a few minutes ago but spent a bit of time calculating it...sorry :)