There are 17280 ways 5 letter words can be made from "math is fun" if each word must have 2 consonants and 3 vowels.
Permutation and Combination:
In mathematics, permutation refers to the process of putting all members of a set into a particular order or order. In other words, if the set is already ordered, the permutation of its elements is called permutation. Substitutions occur in more or less noticeable ways in almost every field of mathematics. They often occur when different orders are considered in a particular finite set.
Combining is a way of selecting items from a collection, and (unlike permutation) the order of selection does not matter. In smaller cases you can count the number of combinations. Combining refers to combining n things, taken k times at once, without repetition.
In the word " MATH IS FUN"
The number of Vowels = 03
The number of Consonant = 06
Total Number of words = 09
and, total number of words in even place = 04
The Number of ways = ⁴C₃ = 4 × 3 × 2 ×1/ 3×2×1
= 4
Now,
The vowels can be arranged among themselves in 3! = 6 ways and 5 consonants can fill the remaining 6 places in 5! ,
i.e., 6× 5 × 4× 3× 2× 1 = 720
Therefore,
Total Number of ways = 4 × 6× 720
= 17280 ways
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Examine the composite figure formed by placing a triangular prism on top of a rectangular prism. All of the measurements have centimeters as their units.
The triangular base has height 12, base 14 & 2 other sides 13 & 15. The prism height is 20. The rectangular prism is 8 by 14 by 20. The prisms share a face that is 14 by 20.
© 2018 StrongMind
To find the surface area, Brad splits the figure into two pieces, the rectangular prism and the triangular prism.
He finds the total surface area of the rectangular prism by finding the area of each face to get 1,104 cm2.
He then finds the total surface area of the triangular prism by finding the area of each face to get 1,008 cm2.
Finally, he adds the surface areas together to get 2,112 cm2.
Is Brad's solution correct? Why or why not?
Answer:
Step-by-step explanation:
Brad's solution to find the surface area of the composite figure is not correct.
In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,
but it's not taking into account that the two prisms share a face that is 14 by 20.
When finding the surface area of a composite figure, it's important to take into account any shared faces.
Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,
otherwise he will be counting it twice in the final result.
The correct method would be:
Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2
Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2
Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.
So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.
Answer:90x567
Step-by-step explanation:
a plant in alamo, tn, manufactures complex transformer components that must meet specific guidelines for safety. one such component is constructed to deliver 1,000 volts of electricity. a component creates a critical safety hazard if it absorbs humidity at a level above 3%. any components that absorb too much humidity will be destroyed. a quality control inspector uses a random sample of components to conduct a hypothesis test with h0: the humidity level absorbed is 3%, and ha: the humidity level absorbed is more than 3%. what is the consequence of a type ii error in this context?
A type II error in this context would be when the inspector incorrectly fails to reject the null hypothesis (H0), meaning they accept the null hypothesis that the humidity level absorbed is 3% when it is actually more than 3%.
What is hypothesis test?A hypothesis test is a statistical procedure used to evaluate a hypothesis by using sample data. Brainly experts can use hypothesis tests to verify the accuracy of their answers by collecting sample data, analyzing it and making a conclusion. Hypothesis testing involves formulating a null and alternate hypothesis, generating a test statistic, and using the test statistic to make a decision. Brainly experts can use hypothesis testing to check the validity of their answers and to ensure that they are providing accurate information to their users.
This type of error would result in potentially hazardous components being approved for use and could lead to catastrophic accidents. In other words, if the inspector fails to reject H0 when it is false, it could lead to unsafe components being used and put the health and safety of people in danger.
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let s denote the set of all (positive) divisors of 60^5 . the product of all the numbers in s equals 60^e for some integer e. what is the value of e?
As per the given divisor and product, the value of e is 5.
The term divisor in math is defined as a number which divides another number and it is a part of the division process.
Here we have given that let us consider that s denote the set of all positive divisors of 60⁵
Here we also know that the product of all the numbers in s equals 60ⁿ for some integer n.
As per the given condition, the terms are written as,
=> s = 60⁵
=> s = 60ⁿ
Here we have to compare the given values then we the expression like the following,
=> 60⁵ = 60ⁿ
As per the rule of exponent, the value of e = 5.
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Is 1over9 > or < 1over11
The fraction 1/9 is greater than the fraction 1/11.
How to compare fractions?Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.
To compare unlike fractions:
Step 1: Observe the denominators of the given fractions: .
Step 2: Now, let us convert them in such a way that the denominators become the same.
Step 3: Compare the fractions:
Step 4: The fraction with the larger numerator is the larger fraction.
The given fractions are 1/9 and 1/11.
Here, LCM of denominator 9 and 11 is 99
Then, fractions becomes 11/99 and 9/99
11/99>9/99
1/9>1/11
Therefore, the fraction 1/9 is greater than the fraction 1/11.
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write the ratio in simplest form 1. 30 treadmills to 36 elliptical machines / 2. 180 red marbles to 145 blue marbles / 3. in the word flashlight what is the ratio of vowels to total letters? /
The ratio in simplest form in the three cases is 5 : 6, 36 : 29 and 1 : 5.
30 treadmills to 36 elliptical machines can be simplified to 5 treadmills to 6 elliptical machines. To simplify, you can divide both numbers by their greatest common factor, which in this case is 6.
30/6 = 5 and 36/6 = 6
So 30 : 36 = 5 : 6
180 red marbles to 145 blue marbles can be simplified to 12 red marbles to 11 blue marbles. To simplify, you can divide both numbers by their greatest common factor, which in this case is 5.
180/5 = 36 and 145/5 = 29
180 : 145 = 36 : 29
In the word "flashlight", the ratio of vowels to total letters is 2:8. The word "flashlight" has 2 vowels (a,i) and 10 total letters. To simplify divide by 2.
2 : 10 = 1 : 5
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Please help me with this problem!!
Check the picture below.
What type of chart can graph 2 different types of data?
A combination chart can be made up of the area, bar, column, dot, and line charts.
Bar charts are one of the most common data visualizations. Each data series can be represented by a different type of chart. They are all then displayed simultaneously on the same chart.
Adding a chart type that displays over another chart type can give you an immediate comparison of two or more data series over a dimension such as time.
Combination charts enable you to compare different series of data through different types of charts on the same axes simultaneously. This is useful for visualizing large quantities of data in varied formats.
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What does it mean by included or not includee points in plotting points on quadratic inequality?
When plotting points on a quadratic inequality, the "included" points refer to the points that satisfy the inequality, and the "not included" points refer to the points that do not satisfy the inequality.
What is quadratic inequality?Generally, A quadratic inequality is an inequality that can be written in the form of
ax^2 + bx + c > 0 or ax^2 + bx + c < 0,
where a, b, and c are constants and x is a variable.
These types of inequalities can be solved using the same methods as solving quadratic equations, with the added step of testing the solutions in the original inequality to determine whether they are valid solutions.
Simply put, an equation of the kind with the greatest degree two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is to solve quadratic inequalities.
For example, if the inequality is "y > x^2," the points that are above the parabola y = x^2 would be included, and the points that are below the parabola would be not included.
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer:
Sin A / A = Sin B / B Law of Sines
Sin 73 / X = Sin 59 / 18 Application of Law of Sines
X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1
GH is tangent to both circle A and circle E. Determine the length of HE.1) 27 units2) 3 units3) 1.8 units4) 4 units
The length of HE is 4 units.
Given that GH is tangent to both circle A and circle E, we can use the property of tangents that states that a tangent line to a circle is perpendicular to the radius drawn to the point of tangency.
If we let r be the radius of circle A and circle E, and let HE be the length of the line segment from the center of the circles to the point of tangency, we can use the Pythagorean Theorem to determine the length of HE.
The Pythagorean theorem is a fundamental result in mathematics that states that in a right 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 lengths of the other two sides.
Since GH is tangent to both circles, it is perpendicular to the radius of both circles and we can create a right triangle with legs HE and r. We can use the Pythagorean theorem to find the length of HE
HE^2 + r^2 = GH^2
We can use the information given to find the value of GH, then we can solve for HE using the equation above.
We know that GH is tangent to both circles, which means that GH is equal to the diameter of both circles. So GH = 2r
Substituting this value into the equation above:
HE^2 + r^2 = (2r)^2
HE^2 = 2r^2 - r^2 = r^2
HE = √(r^2) = r
Given that HE = r and r = radius of circle A and Circle E, HE = radius of Circle A = radius of Circle E.
Therefore, the length of HE = radius of Circle A or Circle E = 4 units.
So, the length of HE is 4 units.
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Please the inverse of this function!!
Answer:
[tex]\frac{5x-3}{4}[/tex]
Step-by-step explanation:
[tex]x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y[/tex]
A certain infinite geometric series has first term 7 and sum 4. What is the result when the third term is divided by the second term
The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.
A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.
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An ellipse has a vertex at (3, 0), a co-vertex at (0, −1), and a center at the origin. Which is the equation of the ellipse in standard form?
HELP!!!!
Answer:
First and last one
Step-by-step explanation:first and last one
Help me please this is my math assignment I got to skipped my math class and now I am confused .-.
The equation for situation 1 is y = 3.5x
The equation for situation 2 is y = 3x
The equation for situation 3 is y = (5/2)x
The equation for situation 4 is (1/2)x = y
How to match each equation to the situation it describes?The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k. That is k = y/x
Situation1
A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.
k = y/x = 70/20 = 3.5
For every 70 square feet of dirt, there are 2 loads.
y = kx
y = 3.5x
Situation 2
I am making a water and salt mixture that has 2 cups of salt for every 6 cups.
k = 6/2 = 3
This means in every 3 cups there is 1 cup of salt
y = 3x
Situation 3
A store has a "4 for $10" sale on hats.
k = 10/4 = 5/2
This means $5 for 2 hats.
y = (5/2)x
Situation 4
For every 48 cookies I bake, my students get 24.
k = 24/48 = 1/2
This means 1 student gets 2 cookies
y = (1/2)x or (1/2)x = y
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A rectangle ha a perimeter of 42 centimeter. What are whole number dimenion of the rectangle with thi perimeter that would have the mallet area?
The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of rectangle will be in meters, centimeters, inches, feet, etc.
Perimeter of rectangle = 42 cm.
2 × (l + b) = 42
l + b = 21
So l + b = 2 + 19 ; 3+ 18; 4+17; 5+16; 6+ 15 ; 7+14 ; 8+13 ; 9+12; 10 +11:
Area for l × b = 2× 19= 38 sq.cm
Area for second case = 3* 18=54sq.cm
Area for third case = 4* 17=68sq.cm
Area for fourth case = 5* 16=80sq.cm
Area for fifth case = 6* 15=90sq.cm
Area for sixth case =7* 14=98sq.cm
Area for seventh case =8* 13=104sq.cm
Area for eighth case =9* 12=108sq.cm
Area for ninth case =10* 11=110sq.cm
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a pair of dice are tossed. what is the probability that doubles are rolled, given that the sum on the two dice is less than 7?
Answer:
To solve this problem, we will use the following steps:
Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).
Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.
Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.
Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.
Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.
Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.
Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.
Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.
5/18 = 0.278
Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.
a right rectangular prism 3 in by 4.25 in by 18.25 in what is the total surface area of the prism
The total surface area of the prism will be 290.125 Square units.
What is a surface area of a rectangular prism?The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.
The surface area of a rectangular prism is given by:
SA = 2 (lh +wh + lw )
where
l = 3
w = 4.25
h = 18.25
SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)
SA = 2 (54.75 + 77.5625 + 12.75)
SA = 2 (146.0625)
SA = 290.125 square units
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Factoriser -
D = (2x + 3)² + (x-2)(2x + 3)
Answer:
Step-by-step explanation:
Answer:
D = (2x + 3)² + (x-2)(2x + 3)
Factoring D, we get:
D = (2x + 3)² + (x-2)(2x + 3)
= (2x + 3)(2x + 3 + x-2)
= (2x + 3)(3x - 2)
si A/4 = B/9 y A + B = 169; halle el valor de "A"
El número A = 52 es una solución del sistema de ecuaciones lineales.
¿Cómo resolver un sistema de ecuaciones lineales mediante métodos algebraicos?
En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:
A / 4 = B / 9
A + B = 169
Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:
B = 169 - A
Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:
A / 4 = (169 - A) / 9
9 · A = 4 · (169 - A)
9 · A = 676 - 4 · A
13 · A = 676
A = 52
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Find the value of x.
Answers to all the questions form 1 to 10 are illustrated below.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know the angle formed at the center of a circle is twice the angle formed at the circumference.
Answering each one in short.
1. x = 136/2 = 68°.
2. x = 146/2 = 73°.
3. x = 2×49 = 98°.
4. x = 2×62° = 124°.
5. As m∠O = 100°, x = 100/2 = 50°.
6. m∠O = 360 - 100 - 150 = 110°, x = 110/2 = 55°.
We know the angle formed by the same chords at the circumference is equal in measure.
7 . x = 18°.
8. x = 27°.
9. x = 180 - 55 - 90 = 35°.
10. x = 180 - 12 - 91 = 77°.
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if the nth term of an ap is 4n+1,then it's 3''' term is
We have,
nth term = 4n+1
Putting n = 3, we have the 3rd term, i.e.,
4(3) + 1 = 12 + 1 = 13
Answer:
13
four horizontal lines and four vertical lines are drawn in a plane. in how many ways can four lines be chosen such that a rectangular region is enclosed?
Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.
The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as
4C2 = 4!/ (2!×2!)
4C2 = 6
The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.
It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).
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One of the solutions to the equation 5x^2+bx+12=0 is -4/5. Find the value of b.
Answer:
19
Step-by-step explanation:
Substitute x = -4/5 and solve for b.
5x² + bx + 12 = 0
5(-4/5)² + b(-4/5) + 12 = 0
16/5 − 4/5 b + 12 = 0
16 − 4b + 60 = 0
4b = 76
b = 19
Answer:
Step-by-step explanation:
Given rectangle MNOP below, NQ = 65. If MO = -6x+10, solve for x.
Answer:
x= -9.17
Step-by-step explanation:
To solve for x, we can use the information provided about the rectangle to set up an equation. Since opposite sides of a rectangle are congruent (have the same length), we know that MO = NP.
Therefore, we can set up the equation:
-6x + 10 = 65
To solve for x, we can subtract 10 from both sides:
-6x = 55
And then divide both sides by -6:
x = -9.17
evaluate the indefinite integral as an infinite series. integral cos(x) − 1/ x dx
∑[infinity]n=1+C
The infinite series for the given indefinite integral will be as [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex].
We know that the infinite series also called as Maclaurin series
the Maclaurin series for cos(x)
cos(x) = Σ[infinity]n=0 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]
cos(x) = [tex]1 - \frac{x^2}{2!} + \frac{x^4}{4!} - .. + (-1)^n \frac{x^{2n}}{(2n)!}[/tex]
cos(x) - 1 = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]
Now, divide both sides by x
cos(x) -1/x = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!}[/tex]
[tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] [tex]\int { } \,[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!} dx[/tex]
or [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]
Therefore, [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]
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the length of a rectangle is increasing at a constant rate of 3 cm/s, and its width is increasing at a constant rate of 0.5 cm/s. at the time the length is 5 cm and the width is 1.2 cm, how fast is the area of the rectangle increasing?
The area of a rectangle is increasing at a constant rate of 3.5 cm²/s when the length is increasing at a constant rate of 3 cm/s and the width is increasing at a constant rate of 0.5 cm/s.
The area of a rectangle is calculated as length multiplied by width (A = L x W). At the given time, the length is 5 cm and the width is 1.2 cm, so the area is 6 cm². When the length is increasing at a constant rate of 3 cm/s, and the width is increasing at a constant rate of 0.5 cm/s, then the area is increasing at a rate of 3.5 cm²/s. This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5). This is the rate of increase of the area and is expressed as 3.5 cm²/s This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5).
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a square pavement has a side length of 50 m. how many square tiles, each of side length 5 m, are needed to tile the pavement?
The required number of tiles required is 100
as per detail stated above,
the length of the side of the square tile is (s) = 5m
the length of the side of the square pavement (S) is 50m
the area of square tile whose side length is 5 m is
area = side (s) times side (s)
area = 5 x 5
area = 25
now the second area
the area of the square pavement whose side length is 50m is
area = side (s) times side (s)
area = 50 x 50
area = 2500[tex]m^2[/tex]
now to find
the required number of tiles = area of the square pavement by the area of the square tile
therefore
the required number of tiles are =
=> 2500/25
=> 100
therefore the required number of tiles are 100.
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What is the total displacement of the car after 5 h? question 8 options: 0 km 15 km 20 km 40 km.
The total displacement of the car after 5hrs is 0km.
Displacement is a vector quantity that refers to the object's overall change in position.changing in final position from its initial positioncalculating the distance between an object's initial position and its final position.In physics terms, displacement is referred to as the variables. The displacement formula is as follows:s =sf– si
where, s = displacement.
In the given graph, there is the change in distance covered with the time that is:
after two hours car reaches 15 km away from the initial pointafter 4 hours it reaches 20 km away from the initial pointAfter 5 hours car returns back to the initial point.Thus, the displacement will be 0 km as the final point and initial point are the same.
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calculate the double integral. 3xy2 x2 + 1 da, r = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} r
The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).
[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]
3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)
8㏑(2)
A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.
The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.
The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.
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Right triangles 1,2, and 3 are given with all their angle measures and approximate side
lengths.
One of the right triangles that are given which can be used to approximate PQ of the given triangle above is triangle labelled 3 and it's value = 9.5.
What is a right triangle?A right triangle is defined as the triangle that is has one of its angle equal to 90 degrees.
Therefore, the value of the side of the triangle PQ can be obtained using the Pythagorean formula;
c² = a² + b²
c² = PR = 7²
a² = 6.4²
b² = PQ = ?
b² = c² - a²
b² = 49+40.96
b² = 89.96
b= √ 89.96
b = 9.5.
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