Solve the following PDE (Partial
Differential Equation) for when t > 0. Express the final answer
in terms of the error function when it applies.
Answers
Main Answer: The solution of the differential equation of y''(t) + 2y'(t) + y(t) = f(t) for t > 0 in terms of the error function is y(t) = f(t) * erf((t-sqrt(2t))/sqrt(2)) * e^-t - sqrt(2/π) * ∫0t [f(τ) * e^(-(t-τ)) * e^((τ-sqrt(2τ))/sqrt(2))] dτ.
Supporting Explanation:
The differential equation of y''(t) + 2y'(t) + y(t) = f(t) for t > 0 is a second-order linear ordinary differential equation with constant coefficients, where f(t) is the forcing function. To solve the equation, the homogeneous solution can be found by assuming that y(t) = e^rt. Substituting this into the differential equation and solving for the roots of the characteristic equation, gives the general solution of the homogeneous equation as y_h(t) = c_1e^(-t) + c_2te^(-t), where c1 and c2 are arbitrary constants.
To find the particular solution of the non-homogeneous equation, the method of undetermined coefficients can be used. However, if the forcing function is in the form of a Gaussian function, then it is more convenient to use the error function. The error function is defined as erf(x) = (2/√π) ∫0x e^(-t^2) dt, which has the properties of erf(-x) = -erf(x) and erf(x) = 1 - erf(-x).
The particular solution of the non-homogeneous equation can then be written as y_p(t) = f(t) * erf((t-sqrt(2t))/sqrt(2)) * e^-t. The complementary solution and the particular solution are added together to obtain the general solution of the non-homogeneous equation. However, due to the exponential function in the particular solution, the superposition principle does not apply and the integral of the product of f(τ) and the exponential function needs to be evaluated. This gives the complete solution of y(t) = y_h(t) + y_p(t) = c_1e^(-t) + c_2te^(-t) + y_p(t) = f(t) * erf((t-sqrt(2t))/sqrt(2)) * e^-t - sqrt(2/π) * ∫0t [f(τ) * e^(-(t-τ)) * e^((τ-sqrt(2τ))/sqrt(2))] dτ.
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Related Questions
.Find the amount of each payment to be made into a sinking fund earning 8% compounded monthly to accumulate $57,000 over 8 years. Payments are made at the end of each period. The payment size is $ (Do not round until the final answer. Then round to the nearest cent.)
Answers
The amount of each payment to be made into a sinking fund earning 8% compounded monthly to accumulate $57,000 over 8 years is $505.45.
A sinking fund is a fund that an organization or a government sets up to help repay its debts or cover its planned expenditures. It is also referred to as a reserve fund. The purpose of a sinking fund is to make payments towards a debt, such as a bond issue when it becomes due. A sinking fund helps reduce the risks associated with default. Sinking funds are used to pay off debts, replace assets, or fund upcoming capital projects.
What is Compounded Monthly?
Compounded Monthly is when interest is paid on the original principal as well as on the accrued interest. In simple terms, Compound interest is the interest that is earned not only on the original deposit but also on any interest that has already been earned. The monthly compounding formula is calculated using this method.
What is the amount of each payment to be made into a sinking fund earning 8% compounded monthly to accumulate $57,000 over 8 years?
To find the amount of each payment to be made into a sinking fund earning 8% compounded monthly to accumulate $57,000 over 8 years, we use the formula:
PMT = FV([i/12]) / [(1 + [i/12])^(n*12) - 1]
where,
PMT = Paymenti = Interest rateFV
= Future value of the investment = number of years.
In this case, the amount of the payment that needs to be made into a sinking fund can be calculated as follows: Let's first convert the interest rate to
monthly interest rates = 8% / 12 = 0.6667%
FV = $57,000n = 8 years
PMT = 57000 / [(1 + 0.6667%)^(8*12) - 1]/ [0.6667%(1 + 0.6667%)^(8*12)]
PMT = $505.45
Hence, the amount of each payment to be made into a sinking fund earning 8% compounded monthly to accumulate $57,000 over 8 years is $505.45.
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Used the given information to determine the probability below round solution with 3 decimal places
Answers
The conditional probability formula is
\(P(B|A)=\frac{P(B\cap A)}{P(A)}\)which gives
\(P(B\cap A)=P(A)\times P(B|A)\)Then, for the first question, we get
\(\begin{gathered} P(A\cap B)=P(B\cap A)=P(A)\times P(B|A) \\ P(A\cap B)=0.46\times0.05 \end{gathered}\)which gives
\(P(A\cap B)=0.023\)Now, for the second question, we know that, for independent events
\(P(A\cap B)=P(A)\times P(B)\)then, we have
\(P(A\cap B)=0.46\times0.28\)which gives
\(P(A\cap B)=0.129\)Now, for question 3, we know that, when the events are dependent and mutually non-exclusive
\(\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=P(A)+P(B)-P(A)\times P(B|A) \end{gathered}\)By substituting the given values, we have
\(\begin{gathered} P(A\cup B)=0.46+0.28-(0.46\times0.05) \\ P(A\cup B)=0.74+0.023 \\ P(A\cup B)=0.763 \end{gathered}\)Finally, for the 4th question, we have
\(P(A\cup B)=P(A)+P(B)\)which gives
\(\begin{gathered} P(A\cap B)=0.46+0.28 \\ P(A\cap B)=0.74 \end{gathered}\)In summary, the solutions are:
Question 1:
\(P(A\cap B)=0.46\times0.05=0.023\)Question 2:
\(P(A\cap B)=0.46\times0.28=0.129\)Question 3:
\(P(A\cup B)=0.46+0.28-(0.46\times0.05)=0.763\)Question 4:
\(P(A\cap B)=0.46+0.28=0.74\)25x2 - 64 = 0
I need help solving this using quadratic function.
Answers
Answer:
Step-by-step explanation:
25x^2-64=0
x=8/5, -8/5
Answer: x = 8/5, -8/5
Step-by-step explanation:
25x^2 -64 = 0
(5x+8)(5x-8) = 0
x = 8/5, -8/5
la suma de dos ángulos internos es siempre mayor que la medida del tercer ángulo
verdadero o falso y por que
Answers
Utilizando el triangulo rectangulo como contraejemplo, veremos que esto es falso.
¿Es la propicición verdadera o falsa?Primero, sabemos que para todo triangulo la suma de sus angulos internos es igual que 180°.
Ahora, vamos a el triangulo más comun. El triangulo rectangulo.
Este es el triangulo que tiene uno de sus angulos internos igual a 90°.
Digamos que los otros dos angulos internos son A y B, entonces tendriamos:
A + B + 90° = 180°
Despejando A + B obtenemos:
A + B = 180° - 90° = 90°
A + B = 90°
Entonces vemos que la suma de estos dos angulos internos es igual que el tercer angulo.
Encontramos un contraejemplo de la proposición, asi, concluimos que la proposición es falsa.
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Need help ASAP plz
What is the slope of (1,4) (7,2)
Answers
Answer:
3 or 3/1
Step-by-step explanation
the equation for finding the slope when given two coordinate pairs is (y₂ - y₁)/(x₂ - x₁), aka change in y over change in x.
pick one of your coordinate pairs to be y₂ and x₂. it doesn't matter which coordinate pair you choose. the remaining coordinate pair will be your y₁ and x₁.
for this example, i'll use the coordinate pair (7, 2) as my y₂ and x₂ and (1, 4) as my y₁ and x₁.
first, substitute the x-value and y-value from the first coordinate pair.
(y₂ - y₁)/(x₂ - x₁) ⇒ (7 - y₁)/(2 - x₂)
then substitute the y-value and x-value from the remaining coordinate pair.
(7 - y₁)/(2 - x₂) ⇒ (7 - 4)/(2 - 1)
subtract 7 - 4.
(7 - 4)/(2 - 1) ⇒ (3)/(2 - 1)
subtract 2 - 1.
(3)/(2 - 1) ⇒ (3)/(1) or 3/1
simplify.
3/1 ⇒ 3
i hope this helps! have a great day <3
Write the equation of the line in fully simplified slope-intercept form.
Answers
the -6 is the y intercept and -2/5 is the slope
Damian has a bag that contains pineapple chews, lemon chews, and watermelon chews. He performs an experiment. Damian randomly removes a chew from the bag, records the result, and returns the chew to the bag. Damian performs the experiment 68 times. The results are shown below:
A pineapple chew was selected 39 times.
A lemon chew was selected 24 times.
A watermelon chew was selected 5 times.
Based on these results, express the probability that the next chew Damian removes from the bag will be lemon chew as a decimal to the nearest hundredth.
Answers
There is a 0.35 percent chance that the next chew Damian takes out of the bag will be a lemon chew.
Define ProbabilityThe possibility or chance of an event occurring is quantified by probability. A number between 0 and 1, with 0 signifying impossibility and 1 signifying certainty, is used to symbolize it.
probability of selecting a lemon chew = number of times a lemon chew was selected / total number of experiments
In this case, the number of times a lemon chew was selected is 24, and the total number of experiments is 68:
probability of selecting a lemon chew = 24 / 68
To express this probability as a decimal to the nearest hundredth, we can divide 24 by 68 using a calculator or by long division:
24 ÷ 68 = 0.35294117647...
Rounding this decimal to the nearest hundredth gives:
0.35
Therefore, the probability that the next chew Damian removes from the bag will be a lemon chew is approximately 0.35 or 35% to the nearest hundredth.
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Given line is parrel to M
Prove 1 is supplementary to 2
Answers
S1: m || n
S2: m∠2 ≅ m ∠3
R3: Corresponding angles postulate
R5: Linear pair angles are also supplementary angles
S7: m∠1 + m∠2 =180°
What is linear pair?
An angle pair that is linear is produced when two lines intersect at a single point. The terms "linear" and "rectangular" are used to describe angles that follow the intersection of two lines in a straight line. Total angles of a linear pair are always equal to 180°.
Given that line m and line n are parallel to each other.
Statement 1: m || n
Reason 1: Given
Corresponding angles postulate: When a transversal divides two parallel lines, the resulting angles are congruent.
Statement 2: m∠2 ≅ m ∠3
R2: Corresponding angles postulate
S3: m∠2 ≅ m ∠3
R3: Corresponding angles postulate
Statement 5: ∠1 is supplementary to ∠2.
Reason 5: The linear pair angles are also supplementary angles.
Statement 7: m∠1 + m∠2 = 180°
Reason 7: Substitution property of equality
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Landon is going to invest $3,400 and leave it in an account for 18 years. Assuming
the interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Landon to end up with $8,900?
Answers
Answer:
3,418
Step-by-step explanation:
new information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as . a. sample information b. population information c. conditional information d. sampling without replacement
Answers
Sampling without replacement is a process of collecting data from a population mean where each unit is selected only once.
To calculate sampling without replacement, first determine the size of the population you are sampling from. For example, if you are selecting 10 items from a population of 100, then the population size is 100. Next, calculate the number of possible combinations by using the mathematical formula nPr (n is population size, r is the number of items you are selecting). For our example, the formula would be 100P10, which would give us a result of 100!/(90!*10!) = 9,092,000 possible combinations. Finally, divide the number of possible combinations by the population size to determine the probability of selecting a specific combination. In our example, the probability would be 9,092,000/100 = 90,920.
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Angles A and B are the acute angles of a right triangle. If the tangent of A is 2.1445, the angle B measures
Answers
Answer:
Answer is 25°
Step-by-step explanation:
let me know if you got it correct
Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 3 7 2 -1 1372 -1 2 7 17 6 -1 0132 1 A = - 3 - 12 - 30 - 7 10 0001
Answers
The bases for ColA and NulA are {1,2,-1,3}, {1,0,-2,7,-23,6}. The dimension of the subspace ColA is 3 and the dimension of NulA is 3.
To find the bases for the subspaces of the matrix A, we first need to reduce it into echelon form.
This is shown below:
1 3 7 2 -1 1372 -1 2 7 17 6 -1 0 -3 -12 -30 -7 10 0 0 0 -34 -11 -9
The reduced matrix is in echelon form. We can now obtain the bases for the column space (ColA) and null space (NulA). The non-zero rows in the echelon form of A correspond to the leading entries in the columns of A. Hence, the leading entries in the first, second, and fourth columns of A are 1, 3, and -1, respectively.The bases for ColA are the columns of A that correspond to the leading entries in the echelon form of A. Therefore, the bases for ColA are {1, 2, -1, 3}.The bases for NulA are the special solutions to the homogeneous equation
Ax = 0.
We can obtain these special solutions by expressing the reduced matrix in parametric form, as shown below:
x1 = -3x2
= -10 - (11/34)x3
= 1/34x4 = 0x5
= 0x6
= 0
Therefore, a basis for NulA is {1, 0, -2, 7, -23, 6}. The dimension of ColA is 3 and the dimension of NulA is 3.
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24 divided by the ratio 3:4 please help please
Answers
green : black = 3 : 4
green = 24
black = 4/3 x 24 = 32
b= 34
This is the answers
g = green
b = black
The equation (x + 9)^2 + (y - 4)^2 = 81 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals. Hint: position is the center of the circle and range is the radius of the circle.
Answers
Answer:
The position of the radio is (-9, 4).
The range of the radio is 9.
Step-by-step explanation:
The equation (x + 9)^2 + (y - 4)^2 = 81 is in the form of a circle, so we can use the standard equation for a circle to find the center and radius of the circle. The standard equation for a circle is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius of the circle
In the equation (x + 9)^2 + (y - 4)^2 = 81, we can see that:
h = -9 k = 4 r = 9Therefore, the center of the circle is at (-9, 4) and the radius of the circle is 9.
The position of the source of the radio signal is at the center of the circle, which is at (-9, 4). The range of the signal is the radius of the circle, which is 9. This means that the radio signal can be received by any device within a 9-unit radius of the source.
The source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.
The equation (x + 9)^2 + (y - 4)^2 = 81 represents the position and range of the source of a radio signal. By analyzing the equation, we can determine the position of the source and the range of the signals.
Position: The equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle. Comparing this with the given equation, we can see that the center of the circle is at (-9, 4). Therefore, the position of the source of the radio signal is at the coordinates (-9, 4).
Range: In the equation, the term 81 represents the radius of the circle, denoted as r. So, the range of the signals is equal to the radius, which in this case is √81 = 9 units. This means that the radio signals from the source can reach a maximum distance of 9 units from the center.
In summary, the source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.
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The function t=f(S) models the time, in hours, for a sample of water to evaporate as a function of the size S of the sample, measured in millimeters. What are the units for f’’(S)?
Answers
Given that,
The function is t = f(S).
To find,
The unit of f''(S).
Solution,
The given function shows the time for a sample of water to evaporate as a function of the size S of the sample, measured in millimeters.
f'(S) will be in hours per Mililiter
And
f''(S) will be in hours per Mililiter per Mililiter. Therefore, this is the required solution.
Solve for x in the equation x2-10x+25= 35-
X=5+2√ √5
O x=5± √√35
x=10+2√√/5
x = 10+ √√√35
0 0 0 0
Answers
The solution of the quadratic equation is x=5±√35 .
A quadratic equation is given by the equation which can be written in the form ax²+bx +c.
There are two solution of x for a quadratic equation. the graph of a quadratic equation is in the shape of a parabola in the cartesian plane.To solve a quadratic equation various methods are used:Completing of squaresMiddle term factorizationusing the quadratic formulathe given quadratic equation is :
x²-10x+25=35
Simplifying the equation we get:
or, x²-10x+25-35=0
or, x²-10x-10=0
Now we will solve the equation by completion squares method:
x²-10x-10=0
or, x²-2×x×5+5²-5²-10=0
or, (x-5)²=35
or, x-5=±√35
or, x= 5±√35
Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .
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n conducting a test on the hypotheses H0: µ = 50 and Ha: µ > 50, you find that the population mean is 55 when it is actually 50. This results in what type of error?
A. No error
B. Type I error
C. Type II error
D. Standard deviation of the mean
E. There is not enough information given
Answers
If n conducting a test on the hypotheses H0: µ = 50 and Ha: µ > 50, then the type of error is option (B) Type I error
The error that results from rejecting a true null hypothesis is known as a Type I error, while the error that results from failing to reject a false null hypothesis is known as a Type II error.
In this case, the null hypothesis is that the population mean is 50, and the alternative hypothesis is that the population mean is greater than 50. Since the sample mean is found to be 55, which is greater than 50, it would be tempting to reject the null hypothesis in favor of the alternative hypothesis. However, we cannot be certain that the population mean is truly greater than 50 based on the sample mean alone.
Therefore, the correct option is (B) Type I error
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Answer:
Type I error
Step-by-step explanation:
Got this right on the test. Good luck, my FLVS fellows!
consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?
Answers
Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.
Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.
First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.
Next, we can find the vertex using the formula:
Vertex = (-b/2a, f(-b/2a))
where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:
Vertex = (-b/2a, f(-b/2a))
= (-6/(2*-1), f(6/(2*-1)))
= (3, -14)
So the vertex of the parabola is at the point (3,-14).
Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.
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what is the slope of the line -7x+3y=24
Answers
Get in terms of y
-7x + 3y = 24
3y = 7x + 24
y = 7x/3 + 8
Notice this is in form y = mx + b
m is slope
7/3 is being multiplied by x, therefore that is the slope because this is in that form.
Hope this helps :)
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- Jeron
Find the 10th term of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.
f(1) = 8, f(n) = f(n − 1) + 15
The 10th term is
Answers
Answer:
\(87.\)
Step-by-step explanation:
\(f(1) = 8, f(n) = f(n − 1) + 15 \\ The \: 10th \: term \: is \: \\ 8(10 − 1) + 15 = 72 + 15 = 87.\)
A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
show your work
Answers
The width of the freezer is 2.25ft
Volume of a rectangular prismThe formula for calculating the volume of rectangular prism is expressed as:
V = lwh
Given the following
length l = 8feet
w is the width
height h = 3feet
Substitute
54 = 8*3w
54 = 24w
w = 54/24
w = 2.25ft
Hence the width of the freezer is 2.25ft
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9/4 ÷ 3/8
HELP ME PLS
Answers
Answer:
the answer is 6 u welcome
Let p(x) be a power series of the form p(x) = 1 + ª₂x² + ª₁x²¹ +ª6x® + ···= ¹ + Σª2-x²k, -Σ² k=1 in which the coefficients a2k are all positive. a) (1 point) Find an expression for a2k valid for every k N if it is given that p"(x) = p(x) for every x = [0, 1]. b) (1 point) Write fn for the (continuous) function defined by fn(2)=1+ay +ay tan trương n =1+ Zazzzk k=1 for all x € [0, 1]. Show that f, is a convergent sequence with respect to the maximum norm in C([0, 1]). Hint: you may use without proof that f(1) is a convergent sequence in IR if that is convenient.
Answers
(a) The expression for a2k in the power series p(x) = 1 + ª₂x² + ª₁x²¹ +ª6x® + ···, satisfying p"(x) = p(x) for every x ∈ [0, 1], is a2k = 1/(4^k * k!).
(a) To find the expression for a2k, we differentiate p(x) twice and equate it to p(x):
p'(x) = 2ª₂x + 21ª₁x²⁰ + 6ª₆x⁵ + ...
p''(x) = 2ª₂ + 21 * 20ª₁x¹⁹ + 6 * 5ª₆x⁴ + ...
Equating p''(x) to p(x) and comparing coefficients, we have:
2ª₂ = 1 (coefficient of 1 on the right side)
21 * 20ª₁ = 0 (no x²⁰ term on the right side)
6 * 5ª₆ = 0 (no x⁴ term on the right side)
From these equations, we find that a2k = 1/(4^k * k!) for every k ∈ N.
(b) The function fn(x) is defined as 1 + a^y + a^y * tanh(√n * x). To show that fn is a convergent sequence in C([0, 1]), we need to show that fn converges uniformly in [0, 1].
First, we observe that fn(2) = 1 + a^y + a^y * tanh(√n * 2) is a convergent sequence in IR (real numbers) as n → ∞.
To show uniform convergence, we consider the maximum norm ||fn - f|| = max|fn(x) - f(x)| for x ∈ [0, 1]. We want to show that ||fn - f|| approaches 0 as n → ∞.
Using the fact that tanh(x) is bounded by 1, we can bound the difference |fn(x) - f(x)| as follows:
|fn(x) - f(x)| ≤ 1 + a^y + a^y * tanh(√n * x) + 1 + a^y ≤ 2 + 2a^y,
where the last inequality holds for all x ∈ [0, 1].
Since 2 + 2a^y is a constant, independent of n, as n → ∞, ||fn - f|| approaches 0. Hence, fn converges uniformly in [0, 1], making it a convergent sequence with respect to the maximum norm in C([0, 1]).
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find the slope of the following ^ :))
|
Answers
Answer:
m [slope] = 0
Step-by-step explanation:
When the slope is 0, x cancels out so the y value will remain the same.
There are several methods to finding slope but the easiest way to do this is by dividing the second y value - first y value by the second x value - first x value.
m = ∆y/∆x = y2-y1/x2-x1
You y2 and x2 are interchangable with y and x, because y1, and x1 are part of the starting coordinate,.
The reason you subtract the second
value from the first is because in a directly proportional relationship, y increases as x increases so the next x values will have a greater y value, this is a measure of steepness.
So the slope is:
-1 - -1 / 3 - -2 = -1 + 1 / 3 + 2 = 0 / 5 = 0.
Answer:
heres what u need
Step-by-step explanation:
\(\frac{-1}{-2} \frac{-1}{3}\)
divide top from bottom
\(-2/-1=2\)
2 is your x
\(3/-1=-3\)
-3 is your y
so your slope is (2,-3)
At Health Hair, the cost of a children's haircut, x, is $4 and the cost of an adult haircut, y, is $14. The sales from Friday were $568. There were 42 haircuts in all.
Write a system to represent the situation and solve the system and interpret the answer.
Answers
Answer:
x + y = 42
4x + 14y = 568
x = 2, y = 40
Step-by-step explanation:
x + y = 42
4x + 14y = 568
to solve, you can let 'x' = 42-y and substitute this expression for 'x' in the second equation to get:
4(42-y) + 14y = 568
168 - 4y + 14y = 568
168 + 10y = 568
10y = 400
y = 40
therefore, x = 2
check:
4(2) + 14(40) should equal 568
8 + 560 = 568
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 130 engines and the mean pressure was 5.9 lbs/square inch. assume the standard deviation is known to be 1 . if the valve was designed to produce a mean pressure of 5.8 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
Answers
Here the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
We have to evaluate null and alternative hypotheses for the scenario .
In this scenario, the null hypothesis is
H0: μ = 5.8
here
μ = true mean pressure produced by the valve.
Now for the alternative hypothesis is
HA: μ > 5.8
here
μ = true mean pressure produced by the valve.
Therefore to determine if there is sufficient observation at the 0.05 level that the valve performs above specifications,
Here we can utilize a one-tailed z-test with
α = 0.05
Then, test statistic can be evaluated as
z = (X' - μ) / (σ / √n)
where:
X' = sample mean
μ = hypothesized value concerning the population mean
σ = population standard deviation
n = sample size
Substituting in our values, we get:
z = (5.9 - 5.8) / (1 / √130) = 1.8856
Now utilizing a z-table we can evaluate that the p-value associated with this test statistic is approximately 0.0292.
Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
To learn more about null hypothesis
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Kelly was building a bed for her dollhouse. She used her bed, which is 4 feet × 6 feet, as a guide. She scaled down the dimensions of her bed by a factor 1 over 5 . What are the dimensions of the model bed she built?
0.8 foot × 1.2 feet
0.4 foot × 0.6 foot
0.08 foot × 0.12 foot
0.04 foot × 0.06 foot
Answers
Answer:
The first one
Step-by-step explanation:
1/5 =0.20
0.20 * 4 = 0.8 feet
0.20 * 6 = 1.2 feet
Determine the general solution for sin(x-30°) = cos 2 x
Answers
x-30=90-2x + 360k , where k= 0,1,2,3.......
3x= 120+360k
x= 40+120k
The quantity 1.0 mg/cm2 is the same as 1.0 x ________ kg/m2.
A. 10-4
B. 102
C. 106
D. 10-2
E. 104
Answers
The quantity 1.0 mg/cm2 is the same as 1.0 x 10-4 kg/m2.
To convert from milligrams per square centimeter (mg/cm2) to kilograms per square meter (kg/m2), we need to use conversion factors to adjust the units. The given options represent different powers of 10 that can be used as conversion factors.
We know that 1 kilogram (kg) is equal to 1,000,000 milligrams (mg), and 1 meter (m) is equal to 100 centimeters (cm). Therefore, we can express the conversion factors as follows:
1 kg = 1,000,000 mg (1)
1 m2 = 10,000 cm2 (2)
To convert from mg/cm2 to kg/m2, we can combine these conversion factors:
1 mg/cm2 = (1 mg / 1 cm2) x (1 kg / 1,000,000 mg) x (10,000 cm2 / 1 m2)
Simplifying the expression, we have:
1 mg/cm2 = (1 / 1,000,000) kg/m2 = 1 x 10-6 kg/m2
Therefore, the quantity 1.0 mg/cm2 is the same as 1.0 x 10-6 kg/m2.
Among the given options, the value that matches the conversion is option A: 10-4
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A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)
Answers
Answer:
A. Sample space = 6
B. 0.17
C. No
D. Yes
Step-by-step explanation:
A. The sample space of an experiment is the set of all possible outcomes of that experiment.
since there are three colours and 2 outcomes for a coin toss,
sample space = 3 * 2 = 6
B. Probability of picking a green first = 4/12 = 1/3
probability of a tail = 1/2
Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17
C. No.
Considering the two events;
A; green card is picked first
C ; a green or red card is picked
There is an intersection point for the two events. Therefore, they are not mutually exclusive.
D. Yes.
Considering the two events;
A; green card is picked first
B ; a blue or red card is picked
There is no intersection point for the two events. Therefore, they are mutually exclusive.