Answers
Answer:
x = 12
Side length = \(2\sqrt{3}\) in
Step-by-step explanation:
Area of the given hexagon = 6 × (Area of the triangular section)
Area of the triangular section = \(\frac{1}{2}(\text{Base})(\text{Height})\)
= \(\frac{1}{2}(2)(\sqrt{3})^{\frac{x}{12}}(\sqrt{3})^{\frac{x}{6}}\)
= \((\sqrt{3})^{\frac{x}{12}}[(\sqrt{3})^2]^{\frac{x}{12}}\)
= \((\sqrt{3})^{\frac{x}{12}}(3)^{\frac{x}{12}}\)
= \((3\sqrt{3})^{\frac{x}{12}}\)
Now area of the given hexagon = \(6(3\sqrt{3})^{\frac{x}{12}}\)
Since, area of the hexagon is = \(18\sqrt{3}\) in²
\(6(3\sqrt{3})^{\frac{x}{12}}=18\sqrt{3}\)
\((3\sqrt{3})^{\frac{x}{12}}=(3\sqrt{3})^1\)
\(\frac{x}{12}=1\)
x = 12
Therefore, side length = \(2(\sqrt{3})^{\frac{x}{12}}\)
= \((2\sqrt{3})^{\frac{12}{12}}\)
= \(2\sqrt{3}\) in.
Related Questions
The figure represents a traffic island that has angles measuring 60°, 20°, and 100°. Enter each angle next to its correct measure.
PLZZ HELPPPP
Answers
Answer:
possblie awnser is 1:Possible answer for Triangle 1: m∠A = 70°; m∠B = ∠55°; m∠C = 55°.
The compass marks equal lengths on both sides of ∠A; therefore, AB
Step-by-step explanation:
Answer:
m<M =100 M<N=60 m<p=20
Step-by-step explanation:
The value of a new car depreciates (loses value) in many ways. First, a new car can depreciate in value once it is purchased and driven off the car lot. After that the value of a car depreciates each year because it is one year older. Let's consider two different cars:
Car A Car B
Purchase Price $30,000 and $25,000
Precent of Initial Depreciation
20% 10%
Yearly Depreciation $2,000 $1,500
Based on the data answered in the previous three questions, write an equation to predict the value of Car A and Car B at the end of t years.
Car A: V =
t +
Car B: V =
t +
Answers
Answer:
Your car's value decreases around 20% to 30% by the end of the first year. From years two to six, depreciation ranges from 15% to 18% per year, according to recent data from Black Book, which tracks used-car pricing. As a rule of thumb, in five years, cars lose 60% or more of their initial value.
Step-by-step explanation:
What is the derivative of infinity?
Answers
Answer:
The derivative of infinity is undefined. Infinity is not a number, but rather a concept that represents a quantity that is unbounded or limitless. The derivative of a function at a point is a measure of the rate of change of the function at that point. Since infinity itself does not have a numerical value or a well-defined location, it is not possible to take the derivative of infinity. This means that the concept of the derivative does not apply to infinity and the derivative of infinity is undefined.
n a certain region, the probability of selecting an adult over 40 years of age with a certain disease is . if the probability of correctly diagnosing a person with this disease as having the disease is and the probability of incorrectly diagnosing a person without the disease as having the disease is , what is the probability that an adult over 40 years of age is diagnosed with the disease? calculator
Answers
To calculate the probability that an adult over 40 years of age is diagnosed with the disease, we need to consider the given probabilities: the probability of selecting an adult over 40 with the disease,
the probability of correctly diagnosing a person with the disease, and the probability of incorrectly diagnosing a person without the disease. The probability can be calculated using the formula for conditional probability.
Let's denote the probability of selecting an adult over 40 with the disease as P(D), the probability of correctly diagnosing a person with the disease as P(C|D), and the probability of incorrectly diagnosing a person without the disease as having the disease as P(I|¬D).
The probability that an adult over 40 years of age is diagnosed with the disease can be calculated using the formula for conditional probability:
P(D|C) = (P(C|D) * P(D)) / (P(C|D) * P(D) + P(C|¬D) * P(¬D))
Given the probabilities:
P(D) = probability of selecting an adult over 40 with the disease,
P(C|D) = probability of correctly diagnosing a person with the disease,
P(I|¬D) = probability of incorrectly diagnosing a person without the disease as having the disease,
P(¬D) = probability of selecting an adult over 40 without the disease,
we can substitute these values into the formula to calculate the probability P(D|C).
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A and B are partners sharing profit and loss in the ratio of 3:2. A new partner C is admitted and 1/4 share off profit is given.what is the new profit sharing ratio ?
Answers
Answer:
Correct option is: 9:6:5
Step-by-step explanation:
I'm not sure but hope it helps.
And climate change that's how do you determine the circumference of a circle when you know the radius
Answers
In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
Answers
The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).
Sample size, n=400
Sample proportion, p = 40 / 400
= 0.1
We use normal approximation, for this, we check that both np and n(1-p) >5.
Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation = root( p * (1-p) /n )
= 0.015
For constructing Confidence interval,
Margin of Error (ME) = z x SD = 0.0294
95% confidence interval is given by Sample Mean +/- (Margin of Error)
0.1 +/- 0.0294 = (0.0706 , 0.1294)
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Fill in the blank so that products unloaded and time are in a proportional relationship.
A conveyer belt unloads 48 products in 6 minutes. The same conveyor belt unloads
⬜ products in 1 minute.
Answers
Answer: 8 products in 1 minute
Step-by-step explanation:
6 min=48 products
48/6=8
1 min= 8 products
If a=4, b=6, and sina=3/5 in triangle abc, then sin b eqauls
Answers
If in triangle ABC, where A = 4, B = 6, and sin A = 3/5, the value of sin B can be calculated. sin B is approximately equal to 0.104528.
In a triangle, the sum of all angles is 180 degrees. Using this information, we can find angle C by subtracting angles A and B from 180 degrees. Angle C = 180 - (A + B) = 180 - (4 + 6) = 180 - 10 = 170 degrees. Since sin A = 3/5, we can use the sine function to find sin B. sin B = sin (180 - (A + C)) = sin (180 - (4 + 170)) = sin 6 = 0.104528. Therefore, sin B is approximately equal to 0.104528.
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Carlisle Transport had $4,520 cash at the beginning of the period. During the period, the firm collected $1,654 in receivables, paid $1,961 to supplier, had credit sales of $6,916, and incurred cash expenses of $500. What was the cash balance at the end of the period?
Answers
To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.
Starting cash balance: $4,520
Cash inflows: $1,654 (receivables collected)
Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)
Total cash inflows: $1,654
Total cash outflows: $1,961 + $500 = $2,461
To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:
Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows
Cash balance at the end of the period = $4,520 + $1,654 - $2,461
Cash balance at the end of the period = $4,520 - $807
Cash balance at the end of the period = $3,713
Therefore, the cash balance at the end of the period is $3,713.
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Find the nth term of this number sequence
1, 7, 13, 19, ...
Answers
Answer:
6n-5
Step-by-step explanation:
Some different types of sequences
To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).
To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.
To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.
Finding the type of our sequence
Note the following:
19-13=6
13-7=6
7-1=6
So, to get each next term, add 6. However, what is the nth term?
Finding an expression for our sequence
You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on. This starting point shifts the "6n" piece of our expression so that it lines up on the sequence. I'm going to call this starting point "b" for the base that is supporting this sequence.
So the expression will look something like \(6n+b\)
Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".
\(6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5\)
So, the expression for the nth term of the sequence is \(6n-5\)
Verifying
To verify that the expression we found is right, we can test our expression for each of the terms we do know:
The first term (n=1) is 1
\(6n+b=n^{\text{th}} \text{ term}\\\)
\(6(1)-5 \overset{?}{=} (1)\)
\(6-5 \overset{?}{=} 1\)
\(1 \overset{\checkmark}{=} 1\)
The second term (n=2) is 7
\(6n+b=n^{\text{th}} \text{ term}\\\)
\(6(2)-5 \overset{?}{=} (7)\)
\(12-5 \overset{?}{=} 7\)
\(7 \overset{\checkmark}{=} 7\)
The third term (n=3) is 13
\(6n+b=n^{\text{th}} \text{ term}\\\)
\(6(3)-5 \overset{?}{=} (13)\)
\(18-5 \overset{?}{=} 13\)
\(13 \overset{\checkmark}{=} 13\)
The fourth term (n=4) is 19
\(6n+b=n^{\text{th}} \text{ term}\\\)
\(6(4)-5 \overset{?}{=} (19)\)
\(24-5 \overset{?}{=} 19\)
\(19 \overset{\checkmark}{=} 19\)
Solve for t 16−2t=t+9+4t
Answers
Answer:
Step-by-step explanation:
16-2t=t+9+4t
7=7t
t=1
The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from.
Answers
The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .
The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.
The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.
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UL.Z This question is designed to be answered with a calculator. A midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0 111. 0 120 O 132. O 160.
Answers
The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.
The width of each subinterval is (4 - 0) / 4 = 1.
Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.
The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.
Evaluating the function at these midpoints, we get:
f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6
f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54
f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54
f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6
Now, we calculate the sum of these values and multiply it by the width of the subinterval:
Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.
Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.
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Pls help i will mark brainliest
Answers
Answer: DE = 17
Step-by-step explanation:
You can solve by similar triangle ratios or by pythagorean theorem:
AB/CD = CD/x
54/76.5 = 12/x
Solve for x: 54x = 12(76.5) = 918
x = 918/54 = 17
Or, because CDE is a right triangle:
\(12^{2} + 12^{2} = x^{2}\)
\(x^{2} = 288\\\)
x = \(\sqrt{288} = 17\)
HURRY PLEASE!! I’ll mark you as brainliest!!
Solve the system: 3x + y = 10 and -4x - 2y = 2
Answers
Answer:
(11 , -23)
Step-by-step explanation:
i hope this is right
Answer:x=11 and y= −23 (11,-23)
given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. a. prediction value are meaningful for all x-values that are realistic in the context of the original data setb. prediction value are meaningful only for x-values that are not included in the original data setc. prediction value are meaningful only for x-values in (or close to) the range of the original data
Answers
Once the regression line has been constructed, it can be used to make predictions about the value of y for a given value of x. However, these predictions are only meaningful if the value of x is in or close to the range of the original data. This is because the regression line is constructed based on the data points, and therefore it only accurately models the relationship between x and y within the range of the data.
For example, if the original data points have x-values between 0 and 100, then the regression line will provide meaningful predictions for y only for x-values between 0 and 100, or close to this range. Predictions for x-values outside of this range may not be accurate, because the regression line may not accurately represent the relationship between x and y outside of the range of the data.
Therefore, in order for the prediction value to be meaningful, the value of x must be in or close to the range of the original data.
What is the answer!!!!!?
Answers
Answer:
<BYX = 74 degrees
Step-by-step explanation:
The sum of angles of the adjacent sides of the trapezoid is 180 degrees
Given
<A = 106 degrees
<A + <BYX = 180
106 + <BYX = 180
<BYX = 180-106
<BYX = 74 degrees
Do number 3 please
Answers
Answer:
EBC is 55 degrees :)
Step-by-step explanation:
Since ABD and EBC are congruent, it means that they share the same amount of degrees, and 150 - 40 is 110, which divided by two is 55, so both ABD and EBC are 55 degrees.
solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. y'' 2y' − 8y = 3e−3x − e−x
Answers
To solve the given differential equation y'' + 2y' - 8y = 3e^(-3x) - e^(-x) by variation of parameters, we first need to find the complementary solution to the homogeneous equation y'' + 2y' - 8y = 0.
The characteristic equation associated with the homogeneous equation is r^2 + 2r - 8 = 0, which factors as (r - 2)(r + 4) = 0. Therefore, the complementary solution is y_c = c1e^(-4x) + c2e^(2x).
Next, we can find the particular solution using the method of variation of parameters. We assume the particular solution has the form y_p = u1(x)e^(-4x) + u2(x)e^(2x). We then find the derivatives y_p' and y_p'' and substitute them into the original differential equation, which allows us to solve for u1'(x) and u2'(x).
After finding u1'(x) and u2'(x), we integrate them to obtain u1(x) and u2(x). Finally, we substitute these values back into the particular solution y_p = u1(x)e^(-4x) + u2(x)e^(2x) to obtain the complete solution to the nonhomogeneous differential equation.
The explanation paragraph would further detail the steps involved in finding the complementary solution, setting up the particular solution using variation of parameters, and solving for the unknown functions u1(x) and u2(x). It would explain how the initial conditions are applied to find the specific values of the constants in the general solution. The final result would be the complete solution to the given differential equation satisfying the initial conditions.
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Is (3, 0) a solution to the equation y = 5x + 3? *
1 point
Answers
Answer:
no
Step-by-step explanation:
Substitute x = 3 into the equation and if the result is 0 then it is a solution
y = 5(3) + 3 = 15 + 3 = 18 ≠ 0
Then (3, 0 ) is not a solution to the equation
Chau has ridden 22 miles of a bike course. The course is 44 miles long. What percentage of the course has Chau ridden so far?
Answers
Answer:50%
Step-by-step explanation:
50% brainliest pwease
in investigation 2, if you were to double the length of the paper strip you dropped through the tape timer, would the number of dots on the paper also double?
Answers
Yes, when the length of the paper strip doubles, so will the number of dots on it.
Yes, when the length of the paper strip doubles, so will the number of dots on it. This is the case because the dots are uniformly spaced apart, and the total number of spaces between the dots doubles as the length of the strip does. As a result, to occupy the same number of spaces as the strip's length, the number of dots must also double. The same rule holds true for every paper strip of any length; increasing the strip's length will result in doubling the number of dots on it. The quantity of dots on the paper strip is therefore directly proportional to the length.
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You find that statistical uncertainty is your largest measurement uncertainty and that the iv value is your largest propagated uncertainty. How can you try to improve both uncertainties in the simplest, but most effective way?.
Answers
The accuracy and reliability of measurements can be enhanced, leading to a reduction in uncertainties.
To improve both statistical uncertainty and the "iv" value, which represents the largest propagated uncertainty, there are some simple yet effective measures that can be taken:
Increase Sample Size: For statistical uncertainty, collecting a larger sample size can help reduce random errors and improve the precision of measurements. By increasing the number of data points, the statistical uncertainty, represented by quantities such as standard deviation or standard error, can be reduced. This allows for more reliable and accurate statistical analysis.
Refine Measurement Techniques: Evaluating and refining the measurement techniques can contribute to reducing both statistical and propagated uncertainties. Ensuring proper calibration and using more precise instruments can enhance measurement accuracy and minimize systematic errors. This step involves reviewing measurement procedures, identifying potential sources of error, and implementing improvements to minimize uncertainty.
Implement Quality Control Procedures: Introducing robust quality control procedures can help identify and address measurement uncertainties. Regularly monitoring and verifying the measurement process, including equipment calibration, can ensure consistency and accuracy. Implementing quality control measures provides confidence in the reliability and accuracy of the measurements, thus reducing uncertainties.
Repeat Measurements: Taking multiple measurements and calculating the average can help mitigate the effects of random errors and reduce statistical uncertainty. Repeating measurements under similar conditions and averaging the results can provide a more accurate representation of the true value and reduce the impact of individual measurement errors.
Analyze and Optimize Experimental Design: Analyzing the experimental design and optimizing it can contribute to reducing uncertainties. By carefully planning the experiment, considering factors such as controls, replication, and randomization, potential sources of uncertainty can be minimized. Optimizing the experimental design ensures that the measurements are conducted in the most efficient and accurate manner.
By implementing these steps, it is possible to improve both statistical uncertainty and the largest propagated uncertainty (iv value). These measures focus on refining measurement techniques, increasing sample size, implementing quality control, repeating measurements, and optimizing experimental design. By doing so, the overall accuracy and reliability of measurements can be enhanced, leading to a reduction in uncertainties.
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describe a rigid motion or a composition of rigid motions that can be used to make sure that ewach slice of quiche is the same size and shape as the first slice
Answers
The slice of quiche must be rotated 45° clockwise to ensure that each of the 8 slices are the same size and shape.
What is Rigid Motion?
A set can move in a rigid motion if the spacing between the points remains constant. A set is a collection of things or components in mathematics.
Explanation:
Given that each slice of quiche is the same size and shape as the first slice.The objective is to describe a rigid motions or composition of rigid motions.The rigid or composite of rigid motions can be described using the transformation of the rigid motions.Rotation:
A transformation about a point p, called the center of rotation.
Each point and its image are the same distance from p.
There are 8 slices so each central angle of a quiche must \(\frac{360}{8} =45\).
Hence, The slice of quiche must be rotated 45° clockwise to ensure that each of the 8 slices are the same size and shape.
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how do you solve 6-9(4p-3)= 2(6p+7)+3
Answers
Answer:
p= 1/3
=0.333
Step-by-step explanation:
Simplifying
6 + -9(4p + -3) = 2(6p + 7) + 3
Reorder the terms:
6 + -9(-3 + 4p) = 2(6p + 7) + 3
6 + (-3 * -9 + 4p * -9) = 2(6p + 7) + 3
6 + (27 + -36p) = 2(6p + 7) + 3
Combine like terms: 6 + 27 = 33
33 + -36p = 2(6p + 7) + 3
Reorder the terms:
33 + -36p = 2(7 + 6p) + 3
33 + -36p = (7 * 2 + 6p * 2) + 3
33 + -36p = (14 + 12p) + 3
Reorder the terms:
33 + -36p = 14 + 3 + 12p
Combine like terms: 14 + 3 = 17
33 + -36p = 17 + 12p
Solving
33 + -36p = 17 + 12p
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-12p' to each side of the equation.
33 + -36p + -12p = 17 + 12p + -12p
Combine like terms: -36p + -12p = -48p
33 + -48p = 17 + 12p + -12p
Combine like terms: 12p + -12p = 0
33 + -48p = 17 + 0
33 + -48p = 17
Add '-33' to each side of the equation.
33 + -33 + -48p = 17 + -33
Combine like terms: 33 + -33 = 0
0 + -48p = 17 + -33
-48p = 17 + -33
Combine like terms: 17 + -33 = -16
-48p = -16
Divide each side by '-48'.
p = 0.3333333333
Simplifying
p = 0.3333333333
Explanation: Different easier way.
6-9*(4*p-3)-(2*(6*p+7)+3)=0
(6-(9•(4p-3)))-(2•(6p+7)+3) = 0
(6 - 9 • (4p - 3)) - (12p + 17) = 0
16 - 48p = -16 • (3p - 1)
-16 • (3p - 1) = 0
-16 = 0
3p-1 = 0
3p = 1
p = 1/3 = 0.333
Amir notices that 3 out of every 50 cars that pass by his window
are green. If he observes 400 cars, what is the best estimate for how
many of them will be green?
Answers
Answer:
24 cars are green
Step-by-step explanation:
We know
Amir notices that 3 out of every 50 cars that pass by his window are green.
So, the ratio is 3:47
To get from 50 to 400, we time 8.
If he observes 400 cars, what is the best estimate of how many will be green?
We take
3 x 8 = 24 cars are green
So, there will be 24 cars that are green.
Select the slope-intercept form of an equation for a line with y-intercept –5 and slope 2.
Answers
Answer:
y = 2x - 5
Step-by-step explanation:
The format for slope intercept equation is:
y = mx + b
b is the y intercept and m is the slope, so plugging the numbers we have into the variables, we have:
y = 2x - 5
a total blood cholesterol level of 200 mg/dl or less is considered ideal by current medical standards. a nutritionist who believes the total cholesterol of women in her area is higher than this obtained the total cholesterol levels from 25 women and found that the average was 223 mg/dl, with a standard deviation of 30. what analysis should the nutritionist use?
Answers
The nutritionist should use a statistical hypothesis test to determine if the average total cholesterol level of the population is significantly higher than the ideal standard. The test will compare the average of the 25 women to the ideal standard
The nutritionist should use a statistical hypothesis test to compare the average cholesterol of the 25 women to the ideal standard of 200 mg/dl. To do this, the nutritionist will first determine the null hypothesis, which is that the average total cholesterol of the population of women in her area is not significantly different from the ideal standard. Then, the nutritionist will calculate the test statistic, which is the difference between the average cholesterol of the 25 women and the ideal standard, divided by the standard deviation of the sample population. This test statistic will be compared to a predetermined significance level and if it is greater than this level, it will be considered statistically significant. If the test statistic is found to be statistically significant, the nutritionist can conclude that the population has a higher average cholesterol than the ideal standard.
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Class A has 20 students, Class B has 15 students, if the average weight of the students of 2 classes is 34.2 kg and the ratio of the total weight of the students of class A to that of class B is 11:8, find the average weight of the students of class A
Answers
Answer:
the average weight of the students in Class A is 25.92 kg.