Express y in terms of x in the equation ax + by = c where b ≠ 0.
Answers
The equation of y in terms of x is y =(c/b) - (a/b)x
What is an Equation ?An Equation is a mathematical statement formed when two algebraic expressions are equated with an equal sign.
The equation given in the question is
ax + by = c , b ≠ 0.
Express y in terms of x in the equation
by = c - ax
y = (c/b) - (a/b)x
Therefore the equation of y in terms of x is y =(c/b) - (a/b)x
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Related Questions
Which panda was heavier when born
Answers
Answer: The one on the left.
Step-by-step explanation:
There is no file, but the panda on the left is bigger.
The formula for the surface area of a cylinder is A-2πr^2+2πrh. Mr. Sanders asks his students to rewrite the formula solved for h. The table shows the responses of four students.
Which student solves for h correctly?
Answers
Answer:
Renee
Step-by-step explanation:
We have the formula for total surface area of a cylinder as
\(A = 2 \pi r^2 + 2 \pi rh\)
First switch sides so the h term is on the left side:
\(2 \pi r^2 + 2 \pi rh = A\)
Subtract \(2\pi r^2\) from both sidess:
\(2 \pi rh = A - 2 \pi r^2\)
Divide both sides by \(2 \pi rh\):
\(h = \dfrac{A-2\pi r^2}{2\pi r}\)
This corresponds to Renee's answer so Renee is correct
What is the image point of (0,1)after a translation right 5 units and up 5 units?
Answers
Answer:
6,5
Step-by-step explanation:
(x,y)
X: 0 + 5 right = 5,*
Y: 1 + 5 up = *,6
6,5
Solve for fff:
f+\dfrac{1}{4}=-\dfrac{7}{2}f+
4
1
=−
2
7
Answers
Subtract 4 from both sides of the equation, then subtract f from both sides and divide both sides by -7/2 to solve for f.
In order to solve for f, the equation must be manipulated to isolate it on one side of the equation. To do this, the equation must be manipulated algebraically. First, subtract 4 from both sides of the equation. This will move the constant part to the other side of the equation, leaving only the f on the left side. Then, subtract f from both sides, which will move the f to the other side and leave only the constant on the left side. Finally, divide both sides of the equation by -7/2. This will move the coefficient of f to the other side and will leave only f on one side of the equation, thus isolating it. The resulting answer is f=1. This process of manipulating the equation algebraically is called solving the equation for f.
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Let Y1,…,Yn be independent Pois (μ) random variables. Sample data, y1,…,yn , assumed to be generated from this probability model, are used to estimate μ via Bayes' Rule. The prior uncertainty about μ is represented by the random variable M with distribution p
M (μ), taken to be Gamma(ν,λ). 1. By completing the following steps, show that the Bayesian posterior distribution of M over values μ is a gamma distribution with the parameters ν and λ in the prior replaced by ν+∑ i=1-n yi and λ+n, respectively. (a) Write down the prior distribution of M. (b) Write down and simplify the joint likelihood. Explain clearly any results or assumptions you are using. (c) Derive the claimed posterior distribution. Again, make clear any results or assumptions you are using. 2. Take λ→0 and ν→0 in the prior for M. (a) Write down a formula for the posterior expectation of M. (b) Write down a formula for the posterior variance of M. (c) Briefly comment on any connections between the Bayesian posterior distribution of M and the ML estimator of μ, namely μ~ = Yˉ (d) Suppose you have the numeric values n=40 and ∑ i=1-n yi =10. Use R to find a 2-sided 95% Bayesian credible interval of μ values. (The quiz asked for a description of how to use R to find the interval.)
Answers
Bayesian Posterior Distribution with Poisson Likelihood and Gamma Prior Bayesian analysis is a statistical inference method that calculates the probability of a parameter being accurate based on the prior probabilities and a new set of data. Here, we consider a Poisson likelihood and gamma prior as our probability model.
Assumptions:The prior uncertainty about μ is represented by the random variable M with distribution pM(μ), taken to be Gamma(ν,λ).Let Y1,…,Yn be independent Pois(μ) random variables. Sample data, y1,…,yn, are assumed to be generated from this probability model, and the aim is to estimate μ via Bayes' Rule.1) To show that the Bayesian posterior distribution of M over values μ is a gamma distribution with the parameters ν and λ in the prior replaced by ν+∑i=1-nyi and λ+n, respectively.
By completing the following steps.(a) Prior distribution of M:M ~ Ga(ν,λ)∴ pm(m) = (λ^(ν)m^(ν-1)e^(-λm))/(Γ(ν))(b) Likelihood:Here, we have Poisson likelihood. Therefore, the joint probability of observed samples Y1, Y2, …Yn isP(Y1, Y2, …, Yn | m,μ) = [Π i=1-n (e^(-μ)μ^Yi)/Yi! ]The likelihood is L(m,μ) = P(Y1, Y2, …, Yn | m,μ) = [Π i=1-n (e^(-μ)μ^Yi)/Yi! ] * pm(m)(c) Posterior distribution:Using Bayes' rule, the posterior distribution of m is obtained as shown below.
π(m|Y) = P(Y | m) π(m) / P(Y), where π(m|Y) is the posterior distribution of m.π(m|Y) = L(m,μ) π(m) / ∫ L(m,μ) π(m) dmWe know that L(m,μ) = [Π i=1-n (e^(-μ)μ^Yi)/Yi! ] * pm(m)π(m) = (λ^(ν)m^(ν-1)e^(-λm))/(Γ(ν))π(m|Y) ∝ [Π i=1-n (e^(-μ)μ^Yi)/Yi! ] (λ^(ν)m^(ν-1)e^(-λ+m))So, the posterior distribution of m isπ(m|Y) = [λ^(ν+m) * m^(∑ Yi +ν-1) * e^(-λ-nm)]/Γ(∑ Yi+ν).We can conclude that the posterior distribution of M is a gamma distribution with the parameters ν and λ in the prior replaced by ν+∑i=1-nyi and λ+n, respectively.2) Here, we have λ → 0 and ν → 0 in the prior for M.
The posterior distribution is derived asπ(m|Y) ∝ [Π i=1-n (e^(-μ)μ^Yi)/Yi! ] (m^(ν-1)e^(-m))π(m) = m^(ν-1)e^(-m)The posterior distribution is Gamma(ν + ∑ Yi, n), with E(M|Y) = (ν + ∑ Yi)/n and Var(M|Y) = (ν + ∑ Yi)/n^2.The connection between the Bayesian posterior distribution of M and the maximum likelihood (ML) estimator of μ is that as the sample size (n) gets larger, the posterior distribution becomes more and more concentrated around the maximum likelihood estimate of μ, namely, μ ~ Y-bar.Using R to find a 2-sided 95% Bayesian credible interval of μ values:Here, we have n = 40 and ∑ i=1-nyi = 10.
The 2-sided 95% Bayesian credible interval of μ values is calculated in the following steps.Step 1: Enter the data into R by writing the following command in R:y <- c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3)Step 2: Find the 2-sided 95% Bayesian credible interval of μ values by writing the following command in R:t <- qgamma(c(0.025, 0.975), sum(y) + 1, 41) / (sum(y) + n)The 2-sided 95% Bayesian credible interval of μ values is (0.0233, 0.3161).
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GIVING BRAINLIEST! what is the slope and the y-intercept of the line on the graph below?
Answers
Answer:
Your answer is C. the y intercept is 1 and the slope is -1/4. Hope this helped!
Step-by-step explanation:
Compute the flux of the vector field through the surface S. F = −xz i − yz j + z2k and S is the cone z= sqrt(x^2+y^2) for 0 ≤ z ≤ 9, oriented upward.
Answers
The flux of the vector field F = -xz i - yz j + z² k through the surface S, which is the cone z = √(x² + y²) for 0 ≤ z ≤ 9, oriented upward, can be computed by evaluating the double integral:
Flux = ∫[0,2π]∫[0,9] (r² cos(u) + r² sin(u) + r³) r dr du.
To compute the flux of the vector field F = -xz i - yz j + z² k through the surface S, which is the cone
z = √(x² + y²) for 0 ≤ z ≤ 9, oriented upward, we can use the surface integral formula:
Flux = ∬S F · dS
where F is the vector field, dS is the outward-pointing unit normal vector to the surface S, and ∬S represents the surface integral over S.
To proceed with the calculation, we first need to parameterize the surface S in terms of two variables, typically denoted as u and v. In this case, we can use cylindrical coordinates:
x = r cos(u)
y = r sin(u)
z = r
where r is the radius, and u varies from 0 to 2π.
Next, we calculate the partial derivatives of x, y, and z with respect to u and v:
∂x/∂u = -r sin(u)
∂y/∂u = r cos(u)
∂z/∂u = 0
∂x/∂v = 0
∂y/∂v = 0
∂z/∂v = 1
Now, we can calculate the cross product of the partial derivatives ∂r/∂u and ∂r/∂v:
∂r/∂u x ∂r/∂v = (-r sin(u) i + r cos(u) j) x k
= -r sin(u) i x k + r cos(u) j x k
= -r cos(u) i - r sin(u) j
The magnitude of this cross product is √(r² cos²(u) + r² sin²(u)) = r.
Now, we calculate the dot product F · (∂r/∂u x ∂r/∂v):
F · (∂r/∂u x ∂r/∂v) = (-xz i - yz j + z² k) · (-r cos(u) i - r sin(u) j)
= xr cos(u) + yr sin(u) + z² r
Since z = r, we can simplify further:
Flux = ∬S F · dS = ∬S xr cos(u) + yr sin(u) + r³ dA
To evaluate this integral, we integrate over the surface S with respect to the parameters u and r:
Flux = ∫[0,2π]∫[0,9] (r² cos(u) + r² sin(u) + r³) r dr du
Integrating this expression will yield the flux of the vector field F through the surface S.
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Select the TWO distinct equations used to solve |4x-7|=5 for x
a) 4x+7= 5
b) 4x+7= -5
c) 4x-7= 5
d) 4x-7= -5
Answers
Answer:
\( |4x - 7| = 5 \\ \\ 4x + 7 = - 5\)
b is the answer
Rewrite the following in ascending order.
9/25, 2/5, 14/-75, -19/10, 8/15
Answers
Step-by-step explanation:
Given numbers are 9/25 ,2/5, 14/-75, -19/10, 8/15
The denominators = 25 , 5, 75, 10, 15
LCM of the denominators = 150
9/25 = (9/25)×(6/6) = 54/150
2/5 = (2/5)×(30/30) = 60/150
14/-75 =(-14/75)×(2/2) = -28/150
-19/10 = (-19/10)×(15/15) = -285/150
8/15 = (8/15)×(10/10) = 80/150
Ascending order of the numbers
= -285/150, -28/150, 54/150, 60/150, 80/150
-19/10, 14/-75, 9/25, 2/5, 8/15
Harry takes medicine every day. If the dosage is 0.2 of a gram per day, what is the total amount of medicine he consumes in a week?
Answers
Answer:
1.4 grams of medison for thr whole week combinded
Answer:
1.4 g
Step-by-step explanation:
0.2 gram per day x 7 days = 1.4 g total consumed in a week
There are five activities on the critical path, and they have standard deviations of 1, 3, 1, 4, and 3 days. The standard deviation of the critical path is: Multiple Choice A 6 B.5. C/3. D. 4
Answers
The standard deviation of the critical path is 6.
To calculate the standard deviation of the critical path, we need to use the concept of variance and consider the activities on the critical path.
The variance of a project or critical path is the sum of the variances of the activities on that path.
Since the variances are given as the squares of the standard deviations, we can square the standard deviations of each activity and sum them to find the variance of the critical path. Finally, we take the square root of the variance to obtain the standard deviation.
Given the standard deviations of the activities on the critical path:
Activity 1: Standard deviation = 1 day
Activity 2: Standard deviation = 3 days
Activity 3: Standard deviation = 1 day
Activity 4: Standard deviation = 4 days
Activity 5: Standard deviation = 3 days
Calculating the variance of the critical path:
Variance = (1^2) + (3^2) + (1^2) + (4^2) + (3^2) = 1 + 9 + 1 + 16 + 9 = 36
Taking the square root of the variance, we find the standard deviation of the critical path:
Standard deviation = √(36) = 6
Therefore, the standard deviation of the critical path is 6.
The correct choice is A. 6.
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Price of good x - $12
Price of good y- $2
Availiable to spend $30
Function- 3x^2 + y
Find MU1, MU2, MRS, and find the optimal bundle.
Answers
The answers:
MU1 = 6x, MU2 = 1, MRS = 6x, and Optimal bundle: x = 2, y = 6
1. Calculate the marginal utility of good x (MU1):
MU1 = d(3x^2)/dx = 6x
2. Calculate the marginal utility of good y (MU2):
MU2 = d(y)/dy = 1
3. Calculate the marginal rate of substitution (MRS):
MRS = MU1/MU2 = (6x)/1 = 6x
4. Set the MRS equal to the price ratio to find the optimal bundle:
MRS = Px/Py
6x = 12/2
6x = 6
x = 1
5. Substitute the value of x back into the utility function to find the corresponding value of y:
3(1)^2 + y = 30
3 + y = 30
y = 27
6. The optimal bundle is x = 1 and y = 27.
Given the prices of goods x and y, and the budget of $30, we can determine the optimal consumption bundle by maximizing utility. The utility function is U(x, y) = 3x^2 + y.
To find the optimal bundle, we need to compare the marginal utilities of the goods and the marginal rate of substitution (MRS). The marginal utility of good x (MU1) is calculated as the derivative of the utility function with respect to x, which gives us 6x. The marginal utility of good y (MU2) is a constant value of 1.
The MRS is the ratio of the marginal utilities of the goods. In this case, MRS = MU1/MU2 = (6x)/1 = 6x. The MRS is also equal to the price ratio Px/Py. Since the price of x is $12 and the price of y is $2, we have 6x = 12/2.
Solving for x, we find x = 1. Substituting this value back into the utility function, we can solve for y. Hence, y = 27.
Therefore, the optimal bundle is x = 1 and y = 27, which maximizes Pam's utility given the prices and budget constraint.
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combine like terms -4a+8+3a-9
Answers
Answer: -a+1
Step-by-step explanation:
-4a+8+3a-9
=-4a+3a+8-9
=(-4a+3a)+(8-9)
=-a+1
Hope this helps!! :)
Answer: -a -1
Step-by-step explanation:
{(1,0) (2,1) (3,1) (4,0)} is a function.
True or false? Explain.
Answers
Answer:
true
Step-by-step explanation:
They all have a x and y value
If the width of the fridge is 4 inches and cost of one square inch is five dollars find the total cost of the blanket
Answers
Answer:
$20
Step-by-step explanation:
Find the value of t0.05 for a t-distribution with 9 degrees of freedom. round your answer to three decimal places, if necessary.
Answers
Answer:
Find the value of t0.05 for a t-distribution with 9 degrees of freedom. round your answer to three decimal places, if necessary.
Step-by-step explanation:
Find the value of t0.05 for a t-distribution with 9 degrees of freedom. round your answer to three decimal places, if necessary.
Order -8, 9, -3, 6, -10, and 2 from least to greatest.
Answers
Answer:
-10, -8, -3, 2,6,9
will you be my friend
Answer:
-10, -8, -3, 2, 6, 9
Step-by-step explanation:
Hope this helps!
The joint and marginal pdf's of x = amount of almonds and Y = amount of cashews are
F(x,y) = fx(x) =
with fy(y) obtained by replacing x by y in fx(x). It is easily verified that Mu x = Mu y = A, and E(XY) = 2/ 5 Compute the correlation coefficient p for X and Y. P=
Answers
The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.
What is correlation coefficient?The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.
Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.
Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).
The correlation coefficient is computed as,
\($ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}\)
\($=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}\)
= -0.6675
Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.
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Using the distributive property, which of the following is the expanded form of −14(−8x+12y)
?
Answers
Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.
The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.
So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:
(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)
= (1/4) × 8x − (1/3) × 12y
= 2x − 3y
Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.
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Factor 1/3x - 1/3, if it cannot be factorized write cannot be factorized
Answers
Answer: \(1/3(x-1)\)
Step-by-step explanation: In this case, factoring cannot be done at a large scale because there is no degree higher than one on both terms. However, you can factor out the gcf on both terms which is one-half to make the equation in factorized form.
Please Mark Brainliest!
Answer:
Not sure what the expression actually is, but it is is either:
1.
\( \frac{1}{3x} - \frac{1}{3} \)
Then:
\( \frac{1}{3x} - \frac{1}{3} = \frac{1}{3} ( \frac{1}{x} - 1)\)
Or
2.
\( \frac{1}{3} x - \frac{1}{3} \)
Then:
\( \frac{1}{3} x - \frac{1}{3} = \frac{1}{3} (x - 1)\)
Write an algebraic expression for the statement: the income earned at $9.25 per hour for x hours
Answers
Answer:
9.25x
Step-by-step explanation:
Which of the right rectangular boxes shown has the greater volume?
Answers
Answer:
A
Step-by-step explanation:
I'm not sure 100% but i hope this still helps a little
Solve each system of linear equations using the elimination mehod
-8x + 10y = -22
8x - 15y = 17
Answers
Answer: y = 1 and x = 4
Step-by-step explanation:
-8x + 10y = -22
8x - 15y = 17
-----------------------
- 5y = -5 Add the two equations to eliminate x
y = 1 Solve for y
=====
8x - 15y = 17 (y = 1) Use y=1 in either equation
8x - 15 = 17
8x = 32
x = 4 Ta da
Answer:
solution: x = 4, y = 1 or (4, 1)
Step-by-step explanation:
To solve the system of linear equations using the elimination method, simply add both equations together (since the coefficeints of x have opposite signs):
-8x + 10y = -22
+ 8x - 15y = 17
- 5y = -5
Divide both sides by -5 to solve for y:
\(\frac{-5y}{-5} = \frac{-5}{-5}\)
y = 1
Next, substitute the value of y into one of the equations to solve for x:
-8x + 10y = -22
-8x + 10(1) = -22
-8x + 10 = -22
Subtract 10 from both sides
-8x + 10 - 10 = -22 - 10
-8x = -32
Divide both sides by -8 to solve for x:
\(\frac{-8x}{-8} = \frac{-32}{-8}\)
x = 4
Therefore, the solutions to the given systems of linear equations are: x = 4, y = 1 or (4, 1).
Complete the table.
f(x) = x2 + 5x + 4
+
f(x)
-4
-2
No
2
Answers
Step-by-step explanation:
f(x) = x2 + 5x + 4
+
f(x)
-4
-2
No
2
Yo can somebody please help me with this?
Answers
A sphere fits perfectly into the cylinder as shown, touching the top and bottom of the
cylinder. If the height of the cylinder is 32 inches, what is the approximate volume of
the sphere?
A 2,7317 cu in.
B 4,0961 cu in.
C 8,192n cu in.
D 5,4611 cu in.
Answers
Answer:
Step-by-step explanation:
we khow that the height of the cylinder is 32 inches
divide it by 2 to get the radius 32/2= 16
let V be the volume :
V= (4/3)*16³*π = 17157.28 in³ this really close to the volume of this sphereThe volume of the sphere will be 5461.3 π cubic inches. Then the correct option is D.
What is the volume of the sphere?Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
A sphere fits perfectly into the cylinder as shown, touching the top and bottom of the cylinder.
If the height of the cylinder is 32 inches.
The height of the cylinder and sphere are same.
Then the radius of the sphere will be
r = 32 / 2
r = 16 inches
Then the volume of the sphere will be
V = 4/3 π(16)³ cubic units
V = 5461.3 π cubic inches
Then the correct option is D.
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Jason ate 2/3 of the pizza. What part of the pizza is left? (split in 6)
Answers
Answer:
4
Step-by-step explanation:
2/3 * 6/1 = 12/3
12/3 = 4/1
The part of the pizza that is left = 2 from the 2/3 pizza eaten by Jason.
What are word problems in mathematics?Word problems in mathematics are the use of arithmetic and mathematical operations to solve problems real-life problems.
From the given information, Let us assume that the total amount of the pizza is 1.
If Jason ate 2/3 of the pizza, then the part of the pizza that is left is:
\(\mathbf{=(1 - \dfrac{2}{3})}\)
\(\mathbf{=(\dfrac{3 -2}{3 })}\)
\(\mathbf{=\dfrac{1}{3 }}\)
Now, we are to split the remaining part of the pizza into 6 parts;
i.e.
\(\mathbf{=(\dfrac{\dfrac{1}{3}}{6})}\)
\(\mathbf{=(\dfrac{1}{3}}\times \dfrac{6}{1})}\)
= 2
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Find x when one arc measure is 59 and another arc is 2x and one anhle is 15
Answers
This value of x doesn't satisfy the Equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.
Let's start with the given information: we have two arc measures and an angle measure. We know that the sum of the arc measures is equal to the total circumference of the circle, which is 360 degrees. So, we can set up an equation:
59 + 2x = 360
Solving for x, we get:
2x = 301
x = 150.5
So, the value of x that makes one arc measure 2x and the other arc measure 59, and the angle measure 15, is 150.5.
Now, let's think about why this makes sense. The sum of the arc measures is equal to the total circumference of the circle, which means that the angle formed by those two arcs must be half of the central angle that intercepts them. In other words, the angle formed by the 59-degree arc and the 2x-degree arc is (59 + 2x)/2. We also know that the angle formed by the 15-degree angle and the same arc is equal to half of the angle formed by the two arcs. So:
(59 + 2x)/2 = (180 - 15)/2
59 + 2x = 165
2x = 106
x = 53
However, this value of x doesn't satisfy the equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.
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If I have $1900 dollars in my savings and my bank pays 5 percent simple interest on savings what is the total amount of money I will have in my account after 5 years?
Answers
The interest on a savings or loan at a particular rate for a period of time is calculated as
\(undefined\)Convert 7.34 X 10-3 kg to mg
Answers
Answer:
51380000 mg
Step-by-step explanation:
10 - 3 = 7
7.34 x 7 = 51.38
1 kg = 1000000 mg
51.38 x 1000000 = 51380000
When \(7.34 \times 10^{-3} kg\) is converted to milligrams the result is 7340 mg.
Given, that kilograms to be converted to milligrams.
Multiplication: It is the basic mathematical operation among subtraction, division and addition. Multiplication follows associative and distributive property.
Exponential multiplication:
a) \(10^{-3} = \frac{1}{1000}\)
b) \(10^3 = 1000\)
Conversion factors:
1 Kg = 1000 grams
1 Gram = 100 milligrams
1 kg = 1000000 mg
Apply unitary method to convert Kg to mg.
1 kg = 1000000 mg
Multiply both sides by \(7.34 \times 10^{-3} kg\)
\(7.34 \times 10^{-3} kg\) × 1 = \(7.34 \times 10^{-3} kg\) × 1000000
Here the kilograms is converted to equivalent milligrams.
\(7.34 \times 10^{-3} kg\) = 7340 milligrams
Thus the total milligrams in \(7.34 \times 10^{-3} kg\) are 7340 .
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