The rational functions with the given asymptotes are presented as follows:
1. y = 1/(x³ + x² - 6x).
2. y = 1.5x²/(x² + 0.5x - 0.5).
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
For item 1, due to the vertical asymptotes, the denominator is given as follows:
x(x + 3)(x - 2) = x(x² + x - 6) = x³ + x² - 6x.
As the horizontal asymptote is of zero, the numerator has a lower degree than the denominator, hence it can be constant, and the function is given as follows:
y = 1/(x³ + x² - 6x).
For item 2, the denominator is given as follows:
(x + 1)(x - 0.5) = x² + 0.5x - 0.5.
Due to the horizontal asymptote of 3/2, the degree of the numerator must be the same as the denomiator, with a coefficient 3/2 that of the denominator, hence the numerator is given as follows:
3x²/2 = 1.5x².
Meaning that the function is:
y = 1.5x²/(x² + 0.5x - 0.5).
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Suppose that y(t) solves the ordinary differential equation
dy/dt = (t*y^-.5)/3 y(0)=1. Find y(1)
The solution of dy/dt = (t*y^-.5)/3 with y(0)=1 is y(1) = 1.
The solution to the given differential equation is given by the following formula:
y(t) = [tex](3/t^2)^2/3 + C[/tex]
where C is the constant of integration.
To find the value of y(1), we need to substitute t = 1 in the above formula.
y(1) =[tex](3/1^2)^2/3 + C[/tex]
y(1) = 9 + C
Since y(0) = 1, we can find the value of C by substituting t = 0 in the above formula.
y(0) = ([tex]3/0^2)^2/3 + C[/tex]
y(0) = 9 + C
1 = 9 + C
C = -8
Substituting C = -8 in the formula for y(1),
y(1) = 9 + (-8) = 1
Therefore, y(1) = 1.
Thus, the solution of [tex]dy/dt = (t*y^-.5)/3 , y(0)=1[/tex] is y(1) = 1.
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A steady current I flows down a long cylindrical wire of radius a.
(a) Find the magnetic field, both inside and outside the wire, if all the current is uniformly distributed over the outside surface of the wire only. (b) Find the magnetic field, both inside and outside the wire, if the current is distributed in such a way that the current density J is proportional tos^2, where s is the distance from the axis.
(c) Show that your answers to (a) and (b) are consistent with the magnetostatic boundary conditions (Griffiths Eqn (5.76)) at the outside surface s = a.
(d) For the situation of part (a), determine the vector potential A everywhere.
For the situation in part (b), the boundary condition is given by B·n = μ_0J/2πa, where n is the unit normal vector to the surface of the wire and J is the current density. This is consistent with the magnetic
(a) The magnetic field outside the wire is given by B = μ_0I/2πs, where I is the current and s is the distance from the axis of the wire. The magnetic field inside the wire is zero.
(b) The magnetic field outside the wire is given by B = μ_0J/2πs, where J is the current density and s is the distance from the axis of the wire. The magnetic field inside the wire is given by B = μ_0J/2πa, where a is the radius of the wire.
(c) For the situation in part (a), the boundary condition is given by B·n = μ_0I/2πa, where n is the unit normal vector to the surface of the wire and I is the current. This is consistent with the magnetic field outside the wire, which is given by B = μ_0I/2πs.
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use Priya's method to calculate (0.0015) x (0.024)
Using Priya's method to calculate (0.0015) x (0.024) gives 0.0000360
How to multiply two decimals using Priya's method?
To multiply decimals using Priya's method, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Now, 15 × 24 = 360
0.0015 has 4 numbers after the decimal and 0.024 has 3 numbers after the decimal. The total is 7.
Moving the decimal point 7 spaces to the left, we get 0.0000360.
Thus, (0.0015) x (0.024) = 0.0000360
Note: 0.0000360 = 0.000036
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find the difference quotient of f; that is, find
The difference quotient of f; that is, [tex]\frac{f(x+h)-f(x)}{h}[/tex], h ≠ 0 for the function f(x) = x^2 - 9x + 6 is 2x - 9.
The function is f(x) = x^2 - 9x + 6.
We have to determine the differential equation; that is [tex]\frac{f(x+h)-f(x)}{h}[/tex].
To find the value of f(x+h) substitute x+h in place of x the the function.
f(x+h) = (x+h)^2 - 9(x+h) + 6
Solving
F(x+h) = x^2 + 2xh + h^2 - 9x - 9h + 6
Now putting the value
[tex]\frac{f(x+h)-f(x)}{h} = \frac{(x^2 + 2xh + h^2 - 9x - 9h + 6)-(x^2 - 9x + 6)}{h}[/tex]
Simplify
[tex]\frac{f(x+h)-f(x)}{h} = \frac{x^2 + 2xh + h^2 - 9x - 9h + 6-x^2 + 9x - 6}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h} = \frac{2xh + h^2 - 9h}{h}[/tex]
Taking common h on both side, we get
[tex]\frac{f(x+h)-f(x)}{h} = \frac{h(2x + h - 9)}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex] = (2x + h - 9)
Now setting the limit h tends to 0
[tex]\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex] = [tex]\lim_{h\rightarrow 0}[/tex](2x + h - 9)
Now putting h = 0, we get
[tex]\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex] = 2x - 9
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The complete question is:
Find the difference quotient of f; that is, find [tex]\frac{f(x+h)-f(x)}{h}[/tex], h ≠ 0 for the following function. Be sure to simplify.
f(x) = x^2 - 9x + 6
Being in series means that for the system to operate, both components A and B must work. Assume the two components are independent. The probability A works is 0. 90 and the probability B functions is also 0. 90. What is the probability the system works under these conditions
The probability that the system works under these conditions is 0.81 (0.90 x 0.90 = 0.81).
What is the probability the system works ?This question uses the concept of independent probabilities, Independent probabilities refer to the likelihood of two or more events occurring independently of each other.
In other words, the probability of one event occurring does not influence the probability of another event occurring.
This means that if the probability of one event occurring is known, the probability of the other event occurring can be calculated independently.
given below
Step 1: Determine the probability that both components A and B will work.
Step 2: Multiply the probability that component A will work by the probability that component B will work.
Step 3: The result of Step 2 is the probability that the system will work under these conditions.
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A line has this equation: -4y = -24x - 32 Write an equation for the parallel line that goes through (-10, 6).
The equation for the line that goes through (-10, 6) is given as y = -4x - 34
How to solve for the equationA parallel line has the same slope as the original line, but a different y-intercept. So, we want to find an equation of the form y = mx + b where m = -4 (the slope of the original line) and b is the y-intercept that gives the desired point (-10, 6).
We can find b by plugging in the coordinates of the point (-10, 6) into the equation y = mx + b:
6 = -4 * (-10) + b
6 = 40 + b
Subtracting 40 from both sides, we get:
-34 = b
So, the equation for the parallel line that goes through (-10, 6) is:
y = -4x - 34
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Adrian measured a line to be 12.8 inches long. If the actual length of the line is 12.7 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The required percent error of the measurement is 0.8%.
What is Error bars?Error bar, are the line through a point on a graph, axes, which emphasizes the uncertainty or variation of the corresponding coordinate of the point.
The percent error of Adrian's measurement can be calculated as follows:
(|Measured value - Actual value| / Actual value) * 100
= (|12.8 - 12.7| / 12.7) * 100
= (0.1 / 12.7) * 100
= 0.786%
Rounded to the nearest tenth of a percent, the error is 0.8%.
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Answer:6.6%
Step-by-step explanation:
What is the probability of randomly drawing and immediately Eating 3 red m&ms in a row from a bag that contains 7 red m&ms out of 25 m&ms total
The probability of randomly drawing and immediately eating three red M&Ms in a row from a bag that contains 7 red M&Ms out of 25 M&Ms total is 1/280.
This can be calculated by using the formula for probability, which is n/(N), where n is the number of desired outcomes and N is the total number of outcomes. In this case, n is equal to 7 (the number of red M&Ms) and N is equal to 25 (the total number of M&Ms). Therefore, the probability is 7/25, which simplifies to 1/280.In this case, the probability of drawing three red M&Ms in a row is 3 out of 25, or 3/25.
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5/7 of 56 is 40
which of these calculations is also true
option 1: 56 x 5/7 = 40
option 2: 5/7 x 40 = 56
option 3: 56 ➗ 40 = 5/7
option 4: 56 ➗ 5/7 = 40
Answer:
Option 1 is correct
Step-by-step explanation:
two linear equations in two variables have no solution. the equations are
When two linear equations in two variables have no solution, it means that the equations are not compatible. This means that the equations cannot be solved simultaneously, as there is no set of values that can satisfy both equations. This can be seen by graphing the equations on a coordinate plane. If the two lines are parallel, then they will never intersect, and thus, there is no solution. If the two lines are the same line, then they will intersect at every point, and thus, any point on the line is a solution.
In the case of two linear equations in two variables, if the equations are not parallel and not the same line, then the equations will intersect at one point. This point is the solution to the two equations. If the equations are not parallel and not the same line, but do not intersect, then there is no solution. This means that the equations are incompatible and cannot be solved simultaneously.
In summary, two linear equations in two variables have no solution when the equations are incompatible. This means that the equations are either parallel or the same line, but do not intersect. In this case, there is no set of values that can satisfy both equations, and thus, there is no solution.
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Two linear equations in two variables have no solution if and only if the lines represented by the equations are parallel and do not intersect.
In other words, the lines do not have a common point, which means that there is no pair of values for the variables that satisfy both equations simultaneously.
Here's an example:
y = 2x + 1
y = 2x + 3
In this case, the lines represented by the equations are parallel and do not intersect, so there is no solution for the system of equations.
You can see this graphically by plotting the lines on a coordinate plane: the lines are close to each other, but they never intersect, so there is no common point that satisfies both equations.
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Naomi wants to save $100 000, so she makes quarterly payments of$1500 into an account that earns 4.4%/a compounded quarterly. How long will it take her to reach her goal?
It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.
How to calculate?To find the number of quarters required to reach $100,000 with a quarterly payment of $1500 and an interest rate of 4.4% compounded quarterly, we will use the formula below:
N = log((A / P) + 1) / log(1 + r)
Where:
N = number of quarters
A = target amount ($100,000)
P = payment per quarter ($1500)
r = interest rate per quarter (4.4%/4 = 1.1%)
Substituting the values, we have that
N = log((100,000 / 1500) + 1) / log(1 + 0.011)
N = log(66.67) / log(1.011)
N = 4.67 quarters
In conclusion, It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.
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This shape is made up of one half-circle attached to an equilateral triangle with side lengths 19 inches. You can use 3.14 as an approximation for π. What is the approximate perimeter of the entire shape? Solve on paper, and enter your answer on Zearn. You can use your Zearn calculator to help you solve.
The perimeter of the entire shape that is made up of a semi circle and an equilateral triangle would be = 116.66in
What is a perimeter of a shape?The perimeter of a shape is defined as the total area of all the sides surrounding that shape.
The perimeter of the object can be calculated by the addition of the perimeter of the triangle and the circle.
The perimeter of the triangle = a+b+c = 19+19+19 = 57in
The perimeter of the circle = 2πr
where π = 3.14
r = 19/2 = 9.5 in
perimeter = 2×3.14×9.5 = 59.66in
The perimeter of the whole object = 57+59.66 = 116.66in.
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Conider the expreion\[x^2 18x \boxed{\phantom{00}}. \]
Find all poible value for the miing number that make thi expreion the quare of a binomial. If you find more than one, then lit the value eparated by comma. Pleae help aap
If the expression is the square of a binomial, then it must have the form [tex]$(ax + b)^2 = a^2x^2 + 2abx + b^2$[/tex].
Comparing the coefficients of like terms, we have:
[tex]a^2 = x^2$, so $a = x[/tex]
[tex]2ab = 18x$, so $b = 9[/tex]
Therefore, the missing number is [tex]$\boxed{9}$[/tex].
Missing Number Square of BinomialThe missing number was found by using the fact that the expression must have the form [tex]$(ax + b)^2 = a^2x^2 + 2abx + b^2$[/tex] if it is the square of a binomial.
By comparing the coefficients of like terms in this equation and in the expression given, [tex]$x^2 18x \boxed{\phantom{00}}$[/tex], we were able to solve for the values of [tex]$a$[/tex] and [tex]$b$[/tex] as follows:
[tex]$a^2 = x^2 \Rightarrow a = x$[/tex]
[tex]$2ab = 18x \Rightarrow b = 9$[/tex]
Finally, we see that the coefficient of the [tex]$x$[/tex] term in the expression is [tex]$2ab = 2 \cdot x \cdot 9 = 18x$[/tex], which matches the given expression. Hence, the missing number is [tex]$\boxed{9}$[/tex].
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How To Convert Mcg To Mg Manually?
To Convert Mcg To Mg, divide your mcg figure by 1000
How To Convert Mcg To Mg?
1 milligram (mg) = 1000 micrograms (mg)
1 microgram (mcg) = 1/1000
=0.001 milligrams (mg)
Input:
Choose "mcg to mg conversion" or "mg to mcg conversion" from the top drop-down list, respectively.After that, note the number that needs to be transformed.At last. By pressing calculate, you can quickly convert between mcg and mg.To learn more about mcg to mg conversion refer to:
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Divide the number of mcg by 1000 to convert it to mg .A microgram is equal to 0.000001 g in micrograms because the prefix "micro-" in this context stands for 10-6.
How is mcg to mg converted? Divide the number of mcg by 1000 to convert it to mg.A microgram is equal to 0.000001 g in micrograms because the prefix "micro-" in this context stands for 10-6.Consequently, we set 1,000 mcg as the same as 1 mg.The mass in milligrams is multiplied by 1,000 to convert to micrograms, and the number of milligrams is divided by 0.001 to convert to micrograms for the conversion of mcg to mg units.Thousandth of a gram and 1,000 micrograms make up a milligram.Typically, the letter "mg" stands in for a milligram.The unit of measurement for a microgram is one millionth of a gram and one thousandth of a milligram.mcg or ug is the most common abbreviation.
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The total urface area of right Circular cone i 90π cm2. If the radiu of the bae of cone i 5 cm, find the hight of cone
The height of the cone is - 3.4 centimeters.
What is the total surface area of cone?The combined curvature of the surface and the cone's base area make up a cone's total surface area. TSA of cone = πr2 + πrl = πr(l+r) square units. is the formula to determine the cone's total surface area.Cones have a single face and a base that resembles a cylinder. V=13r2h, where r is the radius of the cone's base and h is its slant height, can be used to calculate a cone's volume. A=πr(r+l) gives the cone's total surface area.The total surface area of a cone is the combination of the curved surface as well as the base area of a cone.Given data :
The total surface area of the cone is calculated by the formula -
Total surface area = πrl² + πr²
Keep the values in the formula to find the value of length or hypotenuse.
90π = πr(l² + r)
90 = 5(l² + 5)
18 = l² + 5
l² = 13
Now, find the height of the cone.
length² = perpendicular² + base²
13 = perpendicular² + 5²
Perpendicular² = 25 - 13
Perpendicular² = 12
Perpendicular = 3.4 centimeters.
Thus, the height of the cone is 3.4 centimeters
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A simple random sample of size n=14 is obtained from a population with μ=64 and σ=19.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of overbarx.
(b) Assuming the normal model can be used, determineP(overbar x < 68.2).
(c) Assuming the normal model can be used, determineP(overbar x ≥ 65.6).
Part a) A. The population must be normally distributed
Part b) P(overbar x < 68.2) = 0.7967
Part c)P(overbar x ≥ 65.6)= 0.3745
Define the term normally distributed?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward any extreme. The distribution's mean is another name for the center of the range.a) Population is normally distributed -
mean (μ) = 64 and a standard deviation (s) = σ /√n = 19/√14b) P(overbar x < 68.2)
Estimate the z score (z).
z = (x - μ) / s
z = (68.2 - 64) / 19/√14
z = 0.83
Use z table,
P(overbar x < 68.2) = P(z < 0.83)
P(overbar x < 68.2) = 0.7967
c) P(overbar X ≥ 65.6)
Estimate the z score (z).
z = (x - μ) / s
z = (65.6 - 64) / 19/√14
z = 0.32
Use z table,
P(overbar x ≥ 65.6) = P(z ≥ 0.32)
= 1 - P(z < 0.32)
= 1 - 0.6255
= 0.3745
P(overbar x ≥ 65.6) = 0.3745
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A regular pentagon, a regular octagon, and SBY meet at a point. What is the mSBY ?
The mSBY is the measure of the interior angle formed when three lines meet at a point. In this case, the three lines are a regular pentagon, a regular octagon, and SBY.
To calculate the mSBY, we must first calculate the measure of each of the other two angles. A regular pentagon has five sides, and each angle measures 108°. A regular octagon has eight sides, and each angle measures 135°. To calculate the mSBY, we must use the formula mSBY = 180° - (mP + mO). Using this formula, we can calculate that the mSBY is 37°: 180° - (108° + 135°) = 37°.
To visualize this, imagine three lines coming together at a point, forming an interior angle. The measure of the interior angle is the mSBY. The measure of the regular pentagon angle is 108°, and the measure of the regular octagon angle is 135°. When these two angles are added together, they equal 243°. Since the sum of the interior angles of a triangle is 180°, the measure of the interior angle must be 180° - 243°, which is 37°.
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A runner is training for a half marathon. On Wednesday, she ran 6 miles in 50 minutes. On Thursday, she ran 4 miles in 32 minutes. Assume she ran at a constant rate each day. On which day did she run faster? By how much faster did she run?
The day she runs faster is Wednesday.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
On Wednesday:
She ran 6 miles in 50 minutes.
Unit rate:
= 6/50
= 0.12 miles per minute _____(1)
On Thursday:
She ran 4 miles in 32 minutes.
Unit rate:
= 4/32
= 0.125 miles per minute _______(2)
From (1) and (2),
0.12 > 0.125
Thus,
On Wednesday she runs faster.
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Type the correct anwer in the box. Ue numeral intead of word. If neceary, ue / for the fraction bar. Clara ha a package of ix cookie he want to hare equally among her friend. A brown circle cookie. A brown circle cookie. A brown circle cookie. A brown circle cookie. A brown circle cookie. A brown circle cookie. If Clara make ure that each piece of cookie will be
3
5
of a cookie, he can hare her cookie among
We get to the conclusion that the response is 10x after examining the two sides.
What is meant by factor?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.The exact divisors of a given number are known as factors. Factors are also the numbers that can be combined in the right ways to multiply to get the original number. The sides of every scaled copy are a specific number of times longer than their corresponding sides in the original. This figure is known as the scaling factor. The size of the copy is influenced by the scale factor. A replica that has a scale factor greater than 1 is bigger than the original.The above equation's roots are 5 + 3i and 5 - 3i.
This indicates that x - (5+3i) and x - are the two factors of the provided polynomial (5 - 3i). The original statement must be the sum of the elements. We can thus write:
x² - (answer) + 34 = (x - 5 -3i)(x - 5 + 3i).........(1)
Simplifying the right hand side:
[tex]& (x-5-3 i)(x-5+3 i) \\[/tex]
[tex]& =x^2-5 x+3 x i-5 x+25-15 i-3 x i+15 i-9 i^2 \\[/tex]
[tex]& =x^2-10 x+25-9 i^2 \\[/tex]
[tex]& =x^2-10 x+25-9(-1) \\[/tex]
[tex]& =x^2-10 x+25+9 \\[/tex]
[tex]& =x^2-10 x+34[/tex]
Thus, we can write the Equation 1 as:
[tex]x^2-\left(\text { answer) }+34=x^2-10 x+34\right.[/tex]
Our analysis of the two sides leads us to the conclusion that the response is 10x.
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Points P (−2, 1), R (−2, −5), and Q (−6, −5)...Points P (−2, 1), R (−2, −5), and Q (−6, −5) create triangle PQR, which is then translated 1 unit down and 3 units to the right.What is the new x-coordinate of R?
Due to the triangle being translated 1 unit down and 3 units to the right, the new x-coordinate of R is now -2+3 = 1.R's x-coordinate was 2, thus 2 Plus 3 equals 1.
Triangle PQR is formed by points P (2, 1), R (2, 5) and Q (6, 5) and is then translated 1 unit downward and 3 units to the right. This indicates that all three points move three units to the right and one unit down. We may utilise R's initial x-coordinate, which was -2, to determine its new x-coordinate. Then, as R is being translated three units to the right, we add three to it. Consequently, R's new x-coordinate is now -2 + 3 = 1. Triangle PQR has been translated one unit down and three units to the right, giving rise to a new x-coordinate of R of 1. We must first determine the coordinates of each of the three triangle's points in order to determine the new x-coordinate of R. Point P is situated at (2, 1), point R at (2, 5) and point Q at (6, 5) respectively.
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Una persona consume de promedio 250 m' de Coca Cola al día. Cuinto dinero en dólares gasta
anualmente en dicha bebida? (Suponer que llitro vale $0,75)
Calcula cuántos litros consumes al año
el consumo medio es de 250 cm³ en 1 día
Eso significa 1000 cm³ en 4 días. 1000 cm³ = 1 litro
Entonces 1 año = 365 días.
dividelo entre 4 dias
entonces cuantos litros se consumen al año
365 días * 1 Litro / 4 días = 91,25 Litros por año
si 1 litro cuesta 0.75$.
91,75 litros * $0,75 = $68.437.
redondeado a $68.44
About Sobre El Litro
El litro es una unidad de medida de volumen. Sin embargo, el litro no es una unidad estándar internacional, sino que se ha identificado como una de las "unidades no estándar aceptadas para su uso con Standard". La unidad estándar internacional de volumen es el metro cúbico (m³).
1L = 1dm³ = 1000 cm³ = 1000 cc
1 ml = 1 cm³ = 1 cc l
Un litro corresponde a:
0,001 metros cúbicos
1000 centímetros cúbicos
1 decímetro cúbico
Cubo de botones de 10 centímetros de lado.
Un metro cúbico (m³) contiene 1.000 litros. Entonces los litros también se pueden dividir en unidades más pequeñas.
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Which is an advantage of purchasing and owning a home?
A. Homeowners have less control and choice in their lodging than other housing options.
B. Owning a home provides a partial tax shelter for housing related expenses.
C. An individual assumes all responsibility for maintenance and repair of owned property.
D. Property taxes are an opportunity to grow equity
"Owning a home provides a partial tax shelter for housing-related expenses" the following is an advantage of purchasing and owning a home.
Hence, option (B) is correct choice.
The Benefits of Owning a Home:
Interest rates are low.
Creating equity: The difference between what you can sell the house for and what you owe is your equity. As you pay down your mortgage, your equity rises. Over time, more of your monthly payments will be applied to the loan balance rather than the interest, resulting in more equity.
Federal tax breaks: Mortgage interest is deductible on the first $750,000 of the house's purchase price, as are home equity loan interest, property taxes up to $10,000 if married ($5,000 if married filing separately), and various closing fees at the time of purchase.
Greater privacy: Because you own the property, you may renovate it to your desire, something tenants do not have.
Home office: The work-at-home craze may persist after the epidemic has passed, implying that more of us will require a home office. The appropriate configuration affects both comfort and productivity.
Monthly payments that are predictable: A fixed-rate mortgage requires you to pay the same amount each month for principle and interest until the loan is paid off. Rents are subject to rise with each annual lease renewal. Changes in property taxes or homeowner's insurance can affect monthly payments, although not as often as rent hikes.
Stability: People tend to stay in a house they own for a longer period of time, if only because purchasing, selling, and relocating is difficult.
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Answer:
B. Owning a home provides a partial tax shelter for housing related expenses
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The expression that is equivalent to x^(2/5) is
C. ⁵√x²How to determine the equivalent expressionInformation given in the problem
the expression x^(2/5)
This equation represents exponents in fraction form and the basics for the calculation is from
a^(b/c) =
[tex]\sqrt[c]{a^{b} }[/tex]
Rewriting the expression is done as below
x^(2/5)
= [tex]\sqrt[5]{x^{2} }[/tex]
comparing with [tex]\sqrt[c]{a^{b} }[/tex]
gives the following values
a will be equal to x
b will be equal to 2
c will be equal to 5
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Find the range for the measure of the third side of a triangle given that the measures of two sides are 13 and 27.
Based on the Triangle Inequality Theorem, the range is: 14 < third side < 40.
What is the Triangle Inequality Theorem?The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In other words, the length of any one side of a triangle must be less than the sum of the lengths of the other two sides.
This theorem is used to determine the possible range of lengths for the sides of a triangle and to test whether a set of given lengths can form a triangle.
So, the range for the measure of the third side of a triangle given that the measures of two sides are 13 and 27 is:
14 < third side < 40.
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question content area the complement of a. P(B | A)b. P(A | BC)c. P(AC | B)d. P(A I B)
a. independent event P(AuB)=P(A)+P(B) b. mutually exclusive event P(AuB) = P(A) + P(B) - P(AnB) c. independent event P(A and B) = P(A).P(B)
d. complement P(A') = 1 - P(A)
a. For two events A and B the union of the two sets is simply all the elements present in both set. This can be expressed as
P(AuB)=P(A)+P(B)
b. Two events are said to be mutually exclusive if they cannot occur at the same time. i.e no same element must be present in both events at a time. This can be expressed as
P(AuB) = P(A) + P(B) - P(AnB)
c. event A and event B are said to be independent if the incidence of event A does not affect the probability of the event B.
This can be expressed as
P(A and B) = P(A).P(B)
d. complement of an event are simply all the occurrence not in he set but in the universal set.
the complement of set A can be expressed as
P(A') = 1 - P(A)
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle?x < 12. 5, x > 18. 912. 5 < x < 18. 9x < 6, x > 266 < x < 26.
The range of possible values for the third side of the triangle is d)6 < x < 26.
The third side of an acute triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides. By using the Pythagorean Theorem, we can find the range of possible values for the third side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. So, for this triangle, we have 10^2 + 16^2 = x^2.
Solve for x: x^2 = 256, so x = √256 = 16.
The third side must be shorter than the sum of the other two sides. So, the maximum value for x is 16 + 10 = 26.
The third side must be longer than the difference of the other two sides. So, the minimum value for x is 16 - 10 = 6.
Therefore, the range of possible values for the third side of the triangle is 6 < x < 26.
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
2. 6. NS. 3. 5
Electrons and protons are particles in an
atom with equal but opposite charges.
Electrons have a negative charge and
protons have a positive charge. What is the
charge of an atom with 2 more electrons
than protons?
Protons are a type of subatomic particle with a positive charge. With more electrons than protons, the particle is negatively charged.
Is proton and electron are same?A subatomic particle with a negative charge is an electron. A subatomic particle having a positive charge is called a proton. The strong nuclear force holds protons together in the nucleus of an atom. A type of subatomic particle without charge is the neutron (they are neutral).The atomic number is equal to the number of protons in the atom's nucleus (Z). In a neutral atom, there are exactly as many electrons as protons. The total number of protons and neutrons in the atom's nucleus is equal to the mass number (M) of the atom.A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound).Learn more about proton and electron refer to :
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True or False, the standard deviation is the positive square root of the variance.
Since, the formula for variance is Variance = (σ)², where σ denotes standard deviation, the statement "the standard deviation is the positive square root of the variance" is false.
What is standard deviation?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
The dispersion of the set of data values is measured by the standard deviation. The sigma symbol (σ) serves as its symbol.
This indicates that the data values tend to be more dispersed over a greater range for a higher standard deviation. While a lower number of standard deviation results from data being closer to its mean.
Variance, which is the expectation of the squared standard deviation, is a measure of how widely distributed the data are with respect to their mean.
As a result, the relationship between standard deviation and variance can be expressed numerically as, Variance = (σ)².
Therefore, standard deviation is not square root of variance.
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Find a vector orthogonal to both 2, 2, 0 and to 0, 2, 5 of the form 1
The vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
What is an orthogonal vector?
An orthogonal vector is a vector that is perpendicular to another vector in a given space. In other words, two vectors are orthogonal if their dot product is equal to zero.
To find a vector orthogonal to both 2, 2, 0 and 0, 2, 5 of the form 1, we can take the cross product of the two vectors, which results in a vector that is orthogonal to both. The cross product of 2, 2, 0 and 0, 2, 5 is given by:
(2, 2, 0) x (0, 2, 5) = (20, -10, -4)
So, a vector orthogonal to both 2, 2, 0 and 0, 2, 5 is given by (20, -10, -4). We can normalize this vector by dividing it by its magnitude, which is equal to sqrt(20^2 + (-10)^2 + (-4)^2) = sqrt(444). The normalized vector will be of the form 1:
[tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])
Hence, the vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex]).
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Solve. -3r = 9
Quetion 1 option:
r = 3
r = 12
r = -3
r = -27
Answer:
r=-3
Step-by-step explanation:
divide both sides by -3
-3r/-3=9/-33
r=-3