The correct statement is:
Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.
Given,
Four statements regarding p value and null hypothesis.
Now,
Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.Hence the correct statement for this problem is given by:
Given a p-value of 0.02 and a significance level of 3%, you should reject the null hypothesis.
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Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 18 feet long and Ariadne's shadow is 15 feet long. If Dixon is 6 feet tall, how tall is Ariadne?
Clear
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your cursor is over the target before releasing. The target will highlight or the cursor will change. Need help? Watch this video.
==============================================
Explanation:
We have a proportion in the form:
A/B = C/D
where,
A = length of Dixon's shadowB = Dixon's heightC = length of Ariadne's shadowD = Ariadne's heightEach is measured in feet.
In this case,
A = 18B = 6C = 15D = unknownLet's solve for D.
A/B = C/D
18/6 = 15/D
3 = 15/D
3D = 15
D = 15/3
D = 5
Ariadne is 5 feet tall.
the ... of a positive integer is negative.
Answer:
Multiplying
Step-by-step explanation:
The Multiplying of a positive integer is negative.
4x-5y≥-35 (y>-x-2 please help
The common region to the graph of both inequality represents the possible solution sets to the inequality.
What is inequality? What are algebraic expressions?An inequality is used to make unequal comparisons between two expressions.
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is a system of inequality as -
4x - 5y ≥ -35
y > - x - 2
Refer to the graph attached. The common region to the graph of both inequality represents the possible solution set to the inequality.
Therefore, the common region to the graph of both inequality represents the possible solution sets to the inequality.
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80 POINTS AND BRAINLIEST IF THIS IS ANSWERED (WITH STEPS PLS)
The total surface area of the prism is 204 cm²
what is a prism in math?Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases.
Given here: A prism with triangular base with three of its faces as rectangle and its bases triangles.
Thus total surface area is the sum of areas of all these 5 faces
TSA= Sum of the area of the two slanted rectangles + Sum of the two bases + the sum of the rectangle the prism is resting on in the figure
Now dimensions of the slanted rectangles are given by length =12 and breadth =5 and the dimensions of the last rectangle are length =12 and breadth = 6
∴ TSA= 2×12×5 +1/2 ×6×4 +12×6
= 120+12+72
=204 cm²
Hence, The total surface area of the prism is 204 cm²
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A monument is made up of 50,123 sandstone blocks and 100,001 limestone ones. How many blocks make up the monument?
The monument is made up of 150,124 blocks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monument:
50,123 sandstone blocks
100,001 limestone blocks.
Now,
The total number of blocks.
= 50,123 + 100,001
= 150124
Thus,
150,124 blocks.
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2. If you have cardboard pieces of 3ft, 3ft, 6ft ,9 ft and want to make a kite shape. What are the
possible dimensions that you can choose to make the kite shape. Draw the shape and explain.
To make a kite shape, we need two pairs of equal length sticks and a diagonal connecting the midpoints of each pair.
We can choose the following pairs of equal length sticks from the given pieces of cardboard: (3 ft, 3 ft), (6 ft, 6 ft), or (9 ft, 9 ft).
For the diagonal stick, we can choose the longest piece of cardboard, which is 9 ft.
Therefore, we can make a kite shape with dimensions (3 ft, 3 ft, 9 ft) or (6 ft, 6 ft, 9 ft) or (9 ft, 9 ft, 9 ft).
The resulting shape will have two sticks of equal length forming the top and bottom of the kite, and the longest stick forming the diagonal.
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From the cardboard pieces provided, we can select the following sets of equal-length sticks: (3 ft, 3 ft), (6 ft, 6 ft), or (9 ft, 9 ft).
We can use the longest 9-foot length of cardboard as the diagonal stick.
So, using the measurements (3 feet, 3 feet, 9 feet), (6 feet, 6 feet, 9 feet), or (9 ft, 9 ft, 9 ft).
Two sticks of equal length will form the top and bottom of the resulting shape, with the longest stick making the diagonal.
PLEASE HELP!!!
Pls, answer need it NOW :(((
Answer:
using the random numbers, we can determine that 5 servers will be correct.
Step-by-step explanation:
(this may be incorrect, but the if their success rate is 60% then it should be 7.2, but this is not what the question is asking)
classify each quantity as a vector, a scalar, or it cannot be determined. in the figure, arrow a has a magnitude of 13.0 and makes an angle =30.6∘ with the horizontal.
The speed describes as : A scalar quantity with magnitude only.
What is speed?
Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
Some more information about speed:
When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed.
When an object travels a different distance at regular intervals, it is said to have variable speed.
Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.
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Find values of the constants A, B, C, and D that make the following equation an identity (i.e., true for all values of x). 3x³+4x²-6x/(x²+2x+2)(x²-1) = Ax+B/x²+2x+2 + C/x-1 + D/x+1
By Solving the given identity equation we get A = 32/5, B = 36/5, C = 1/10 and D = -7/2.
Given (3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = (Ax + B)/(x² + 2x + 2) + C/(x - 1) + D/(x + 1)
Taking LCM in RHS
(3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = ((Ax + B)(x² - 1) + C(x² + 2x + 2)(x + 1)+ D(x² + 2x + 2)(x - 1))/(x² + 2x + 2)(x² - 1)
3x³ + 4x² - 6x = Ax³ - Ax+ Bx² - B + C(x³ + 3x² + 4x + 2)+ D(x³ + x² -2)
3x³ + 4x² - 6x = (A + C + D)x³ + (B + 3C + D)x² +(-A + 4C)x - B + 2C -2D
Comparing coefficients of RHS with LHS
So, A + C + D = 3 --(1)
B + 3C + D = 4 --(2)
- A + 4C = -6 --(3)
- B + 2C -2D = 0 --(4)
We have 4 variables and 4 equations. Solving them, we get
A = 32/5, B = 36/5, C = 1/10 and D = -7/2
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Determine the following limits, using [infinity] or −[infinity] whenappropriate, or state that they do not exist. a. limx→5+ 1/x−5 b. limx→5− 1/x−5 c. limx→5 1/x−5
The following limits a) the limit does not exist. b) the limit does not exist and c) the limit does not exist.
a) limx→5+ 1/x−5 = 1/0 which is undefined. Therefore, the limit does not exist.
b) limx→5− 1/x−5 = −1/0 which is undefined. Therefore, the limit does not exist.
c) The two-sided limit of 1/x−5 as x approaches 5 from both the left and the right side is undefined. Therefore, the limit does not exist.
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis both rely heavily on limits, which are also needed to describe concepts like continuity, derivatives, and integrals.
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A utility company charges $0. 12 per kilowatt-hour for energy a customer uses. They give a credit of $0. 0025 for every kilowatt-hour of electricity a customer with a solar panel generates that they don't use themselves. A customer has a charge of $82. 04 and a credit of -$4. 10 on this mouth bill. How many kilowatt-hour did they generate that they didn't use themselves?
The 683.67 kilowatt-hour was charged while 1640 kilowatt-hour generated the credit by not being used.
The amount of electricity consumed will be calculated by the formula -
Amount of electricity consumed = total charged amount ÷ amount of unit electricity consumed
The amount of electricity that earned the credit will be calculated by the formula -
Amount of electricity that earned the credit = total reduction amount ÷ credit on unit electricity
Keep the values in formula
Amount of electricity consumed = 82.04/0.12
Performing division on Right Hand Side of the equation
Amount of electricity consumed = 683.67
Amount of electricity that earned the credit = 4.10/0.0025
Performing division on Right Hand Side of the equation
Amount of electricity that earned the credit = 1640
Thus, the amount of electricity consumed is 683.67 units and unused electricity is 1640 units.
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Kate and Jamal are racing their robots across the school gym. Kate's robot gets an 8-foot head start and travels 2 feet per second. Jamal's robot travels 3 feet per second. How long will it take for Jamal's robot to catch up to Kate's robot?
It will take Jamal's robot 8 seconds to catch up to Kate's robot.
How long will it take for Jamal's robot to catch up to Kate's robot?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let's t represent the time it takes for Jamal's robot to catch up to Kate's robot (in seconds).
During this time, Kate's robot will have traveled a distance of 2t + 8 feet.
Jamal's robot will have traveled a distance of 3t feet.
When Jamal's robot catches up to Kate's robot, these two distances will be equal:
2t + 8 = 3t
Solving for t:
3t -2t = 8
t = 8 seconds.
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in how many ways can 8 questions true and false examination be answered if he answers half the questions true and half false
Answer:
Hence the correct answer is 256
the lines containing the altitudes of a triangle are concurrent, and the point of concurrency is called the of the triangle.
The point of concurrency for the lines containing the altitudes of a triangle is called the orthocenter of the triangle.
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
The orthocenter for a triangle with an acute angle is located within the triangle.For the obtuse angle triangle, the orthocenter lies outside the triangle.The vertex of the right angle is where the orthocenter for a right triangle is located.The place where the altitudes connecting the triangle's vertices to its opposite sides intersect is known as the orthocenter.It is located inside the triangle in an acute triangle. For an obtuse triangle, it lies outside of the triangle. For a right-angled triangle, it lies on the vertex of the right angle.
The equivalent for all three perpendiculars is the product of the sections into which the orthocenter divides an altitude.Therefore, the point of concurrency for the lines containing the altitudes of a triangle is called the orthocenter of the triangle.
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Evaluate the expression using a calculator. Round your answer to two decimal places when appropriate.
Square root 5^32,768 =
The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The radical expression is given below.
[tex]\rightarrow \sqrt[5]{32,768}[/tex]
The number 32,768 can be written as,
32,768 = 8 x 8 x 8 x 8 x 8
32,768 = 8⁵
Then the value of the expression is given as,
[tex]\rightarrow \sqrt[5]{32,768}\\\\\rightarrow \sqrt[5]{(8)^5}[/tex]
→ 8
The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.
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calculate the integral, assuming that ∫10()=−4, ∫20()=5, ∫41()=10.
The definite integral [tex]\int_{10}^{41}[/tex] f(x)dx = 14.
To calculate the definite integral of a function, we can use the Fundamental Theorem of Calculus, which states that the definite integral of a function is equal to the difference between the antiderivative of the function evaluated at the upper and lower limits of the integration interval. In this case, the definite integral is given as [tex]\int_{10}^{41}[/tex] f(x)dx.
Given that F(10) = -4, F(20) = 5, and F(41) = 10, where F(x) is the antiderivative of f(x), we can calculate the definite integral as follows:
[tex]\int_{10}^{41}[/tex] f(x)dx = F(41) - F(10) = 10 - (-4) = 14.
The Fundamental Theorem of Calculus (FTC) is a theorem in mathematics that establishes the connection between differentiation and integration.
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can anyone answer -13b = 793
How are coefficient estimates from WLS (weighted least squares) interpreted?Select one:a. They should only be used for hypothesis testing. Coefficient estimates from the un-weighted, original model should be used for prediction.b. There is no difference in interpretation since each observation is scaled by the same divisor.c. Take the inverse of the natural logarithm of the coefficient to find marginal effects.d. They must be scaled up by the weight used in order to calculate marginal effects.
Coefficient estimates from WLS (weighted least squares) are interpreted in a similar manner to those from an un-weighted, original model. The main difference is the weights used to scale the observations.
Therefore, correct answer will be:- Coefficient estimates from the un-weighted, original model should be used for prediction
This can cause estimates to differ depending on the weight chosen. When interpreting the coefficient estimates, it is important to consider the weights used when calculating the model. This is because they can affect the magnitude of the coefficient estimates.
Additionally, the weights should be taken into account when calculating the marginal effects of the coefficients. This can be done by scaling up the coefficients by the weight used. Ultimately, the interpretation of coefficient estimates from WLS should be done in the same manner as those from an un-weighted model, but the weights should be taken into account when considering their magnitude and when calculating marginal effects.
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at rush hour, two people per second step onto an escalator. the escalator takes 20 seconds to bring a person from the bottom to the top. how many people are on the escalator during rush hour? (round to the nearest integer)
The number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.
At rush hour, two people per second step onto the escalator, so in one second, 2 people get on the escalator.
The escalator takes 20 seconds to bring a person from the bottom to the top, so for every 20 seconds, 2 people get on the escalator and 2 people get off the escalator.
To find the number of people on the escalator during rush hour, we need to determine the number of people on the escalator after a certain amount of time, say t.
The number of people on the escalator at time t can be calculated as follows:
people on the escalator at time t = 2 * t - 2 * floor(t / 20)
where floor(t / 20) represents the number of complete cycles (20 seconds each) that have occurred.
For example, if t = 40 seconds, then floor(t / 20) = 2, so the number of people on the escalator would be:
people on the escalator at time 40 = 2 * 40 - 2 * 2 = 76
The number of people on the escalator will continue to increase as long as rush hour continues, so it is not possible to give a single answer to the question "how many people are on the escalator during rush hour?" without more information.
In general, the number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.
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The number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.
At rush hour, two people per second step onto the escalator, so in one second, 2 people get on the escalator.
The escalator takes 20 seconds to bring a person from the bottom to the top, so for every 20 seconds, 2 people get on the escalator and 2 people get off the escalator.
To find the number of people on the escalator during rush hour, we need to determine the number of people on the escalator after a certain amount of time, say t.
The number of people on the escalator at time t can be calculated as follows:
people on the escalator at time t = 2 * t - 2 * floor(t / 20)
where floor(t / 20) represents the number of complete cycles (20 seconds each) that have occurred.
For example, if t = 40 seconds, then floor(t / 20) = 2, so the number of people on the escalator would be:
people on the escalator at time 40 = 2 * 40 - 2 * 2 = 76
The number of people on the escalator will continue to increase as long as rush hour continues, so it is not possible to give a single answer to the question "how many people are on the escalator during rush hour?" without more information.
In general, the number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.
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How do you convert 125 Kilogram (kg) to Pound (lb)?
Answer:
275.5
Step-by-step explanation:
In order to convert.
It is fairly simple, follow my directions and next time when you have a question similar to this you’ll know what to do!
1 kg = 2.2 lb. It is as simple as that!
So your question,
“ Convert 125 kilograms to pounds “
125x2.2 = 275 .
Our answer is very close to the verified one, so now you know how to convert kilograms to pounds!.
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56.69904625 kg in 125 lbs. Likewise the question how many pound in 125 kilogram has the answer of 275.577827731 lbs in 125 kg.
What is the pound equivalent of 125 kilograms?125 kg*2.2046226218 lbs/1kg = 275.577827731 lbs
The weight of 125 kilograms is equivalent to 275.577827731 pounds (125kg = 275.577827731lbs). It is simple to convert 125 kg to lb. Simply use our calculator above or the method to convert 125 kg to pounds. To convert 125 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 125 kilograms to pounds is [lb] = 125 * 2.2046226218. Thus, 125 kilos is 275.577827731 pounds.
One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.
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8. 6- 4x = 6x - 8x + 2
Answer: x=5.3
Solution:
6x−8x−2=8.6−4x
−2x−2=8.6−4x
2x−2=8.6
2x=10.6
x=5.3
This graph shows the line `3x+2y=18`. Select all of the points that are on this line.
Answer:
(6,0), (0,9), (2,6)
Step-by-step explanation:
If a point is on a line, then the equation should be true when you plug in the x and y values.
(0,6): 3*0+2*6 = 18 -> 12 = 18, false
(6,0): 3*6+2*0 = 18 -> 18 = 18, true
(0,9): 3*0+2*9 = 18 -> 18 = 18, true
(9,0): 3*9+2*0 = 18 -> 27 = 18, false
(2,6): 3*2+2*6 = 18 -> 18 = 18, true
a typical rectangle is shown in the diagram located at position x. what is the height of this rectangle, in terms of ?
The height of the rectangle is equal to -2x² - 3x + 35.
The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.
We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.
To find the height, we subtract y2 from y1:
y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35
So, the height of the rectangle is equal to -2x² - 3x + 35.
It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.
Complete Question:
The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?
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The height of the rectangle is equal to -2x² - 3x + 35.
The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.
We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.
To find the height, we subtract y2 from y1:
y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35
So, the height of the rectangle is equal to -2x² - 3x + 35.
It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.
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Complete Question:
The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?
find the solution of the initial value problem y'' - 2y' - 3y = 6te^2t, y(0) = 1, y'(0)=0
The complete solution of the given initial value problem can be given by,
y(t) = [tex]\frac{7}{4} e^{3t} +\frac{7}{12} e^{-t} + -2te^{2t} -\frac{4}{3} e^{2t}[/tex]
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.
Therefore, the complete solution of the given initial value problem can be given by,
y(t) = [tex]\frac{7}{4} e^{3t} +\frac{7}{12} e^{-t} + -2te^{2t} -\frac{4}{3} e^{2t}[/tex]
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The full solution to the initial value problem can be provided by,
y(t) = 7/4e^3t + 7/12 e^ -t - 2e^2t- 4/3e^2t
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.
As a result, the full solution to the initial value problem can be provided by, y(t) = 7/4e^3t + 7/12 e^ -t - 2e^2t- 4/3e^2t
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Consider the problem of evaluating the function sin(x), in particular, the propagated data error, i. E. , the error in the function value due to a perturbation h in the argument x. (?) Estimate the absolute error in evaluating sin (x). (b) Estimate the relative error in evaluating sin(x). (c) Estimate the condition number for this problem. (d) For what values of the argument x is this problem highly sensitive?
The absolute error in evaluating sinx is [tex]cos x \triangle x[/tex].
(a)Consider the problem of evaluating the value of sin x.
The objective is to estimate the absolute error in sin x.
Assume r = sin x
The absolute error formula gives that:
[tex]\triangle r = \frac{\delta r}{\delta x} \triangle x[/tex]
[tex]= \frac{\delta sin x}{\delta x} \triangle x[/tex]
[tex]= cos x \triangle x[/tex]
(b) The objective is to estimate the relative error in sin x.
The relative error is given by:
[tex]\frac{\triangle r}{r} = \frac{cos x \triangle x}{sin x}[/tex]
[tex]= cot x \triangle x[/tex]
(c) The objective is to estimate the condition number for this problem.
The formula of a function r = f(x), its condition is given by:
[tex]\frac{x f'(x)}{f(x)}[/tex], here r = sin x
The condition number at point x is:
[tex]\frac{x\frac{d(sin x)}{dx} }{sin x}[/tex]
[tex]= \frac{x cos x}{sin x}[/tex]
= x cot x
(d) The objective is to find for what values of argument x is the problem highly sensitive.
Here, condition number is xcot x.
The cot function is highly sensitive at x=0.
Hence, the argument x is highly sensitive for x=0.
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How to Find Order and Degree of Differential Equation?
To find the order and degree of a given differential equation, simply count the highest derivative and the highest power of the unknown function that appear in the equation.
What is a differential equation?
A differential equation is an equation that relates an unknown function and its derivatives to some given functions or constants.
The order of a differential equation is defined as the order of the highest derivative appearing in the equation. For example, if a differential equation contains only the first derivative of the unknown function, it is said to be a first-order differential equation. If it contains the second derivative, it is a second-order differential equation, and so on.
The degree of a differential equation is defined as the highest power of the unknown function in the equation. For example, if a differential equation is of the form y' + 2y = 0, the degree of the differential equation is 1 (the highest power of y is 1). If it is of the form y'' + 4y = 0, the degree of the differential equation is 2 (the highest power of y is y^2).
Hence, To find the order and degree of a given differential equation, simply count the highest derivative and the highest power of the unknown function that appear in the equation.
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PLEASE HELP ME
A circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. If all of the mulch is spread evenly on the bed, what is the mulch's depth to an appropriate number of significant digits? A. 0.249 foot B. 0.2 foot C. 0.25 foot D. 0.2487
PLEASE SHOW WORK!!!
The correct answer is C. 0.25 foot.
To find the depth of the mulch, we need to determine the volume of the circular mulch bed and divide it by the area. The volume of a cylinder can be calculated as:
V = πr^2h
where r is the radius and h is the height (or depth) of the cylinder.
For the circular mulch bed, the radius is 1.6 feet and we want to find the height (or depth), so we can set the volume equal to the volume of the mulch:
V = π * 1.6^2 * h
V = 2 cubic feet
Solving for h:
h = V / (π * r^2)
h = 2 / (π * 1.6^2)
Using the value of π = 3.14, we get:
h = 2 / (3.14 * 1.6^2)
h = 0.24 inches
Therefore, the depth of the mulch is approximately 0.24 inches to the nearest hundredth of an inch, which is the appropriate number of significant digits.
To convert inches to feet, divide the number of inches by 12:
0.24 inches / 12 inches/foot = 0.02 feet
Rounding to the nearest hundredth of a foot, we get 0.25 feet as the answer.
Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.
Answer:0.69
Step-by-step explanation:
Let z = e^(2x). Then your equation is
z^2 +3z -28 = 0
(z +7)(x -4) = 0
z = -7 or 4
Taking the log of our definition of z, we have
ln(z) = 2x
x = ln(z)/2
So, the one real solution is
x = ln(4)/2 = ln(√4)
x = ln(2)
The decimal approximation is
x ≈ 0.69
3/10 / p = 4/5 / 1/4
What is the value of people in this proportion?
The value of people in this proportion is equal to 165/10 or 10.67.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.
By applying direct proportion to the given information, we have the following mathematical expression:
3/10/p = 4/5/1/4
3/10 × p = 4/5 × 4
3p/10 = 16/5
Cross-multiplying, we have the following:
15p = 160
People, p = 160/15
People, p = 10.67
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Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
The quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.
What is rational expression?The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.
Polynomial expressions must be set equal to zero in order to find the root or zero. However, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.
The given rational expression is:
[tex]\frac{2x - 1}{x + 1}[/tex] ÷ [tex]\frac{3x^2}{x^2 + x}[/tex]
The rational expression can be written as follows:
[tex]\frac{2x - 1}{x + 1} * \frac{x^2 + x }{3x^2} \\\\\frac{2x - 1}{x + 1} * \frac{x (x+ 1) }{3x^2}\\\\\frac{2x - 1}{3x}[/tex]
Hence, the quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.
Learn more about rational expression here:
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