Yes, the inverse of the matrix exist and a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.
The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.
According to the question,
The matrix given is [tex]\left[\begin{array}{cc}2&5\\5&13\end{array}\right][/tex]
Let Matrix be A
To check if its inverse exist , We have to find out the determinant
|A| = 13(2) - 5(5)
=> 26 - 25
=> 1
Determinant is non zero
Hence , Inverse exist
(b) To find the inverse , we have to find the adjoint of A
adj A = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
Inverse is ratio of adj A and determinant A
A⁻¹ = adj A / |A|
=> [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex] / 1
=> A⁻¹ = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
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Solve the system of equations.
Y=2x+7
Y=-x-8
Select all the expressions that are equal to
2/3 to power of 2
4/9 , 4/3, 1/9 x 4 , 1/3 x 1/3, 2/3 x 2/3
Answer to the problem:
4/9, 1/3 x 1/3, 2/3 x 2/3
Find the value of x and y .
x°=__
y°=___
In triangle PQR , the value of x and y is equal to 90° and 85° respectively.
As given in the question,
In the given triangle PQR,
Measure of ∠R = 5°
From the diagram,
PQ ≅ QR
⇒ ∠P ≅ ∠R
⇒m ∠P = m ∠R
⇒m ∠P = 5°
In ΔPQR,
∠P + ∠Q + ∠R = 180°
⇒ 5° + ∠Q + 5° = 180°
⇒ ∠Q = 170°
From the diagram,
y° = (1/2) ( ∠Q)
= 170°/2
= 85°
∠P + y° + x° = 180°
⇒ 5° + 85° + x° = 180°
⇒ x° = 180° - 90°
⇒ x° = 90°
Therefore, in triangle PQR the measure of x° and y° is equal to 90° and 85° respectively.
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help i suck at math!!!!
Answer:
146
Step-by-step explanation:
the sides of a triangle always equal 180, so just subtract those numbers from 180
Find the vector v with an initial point at (5, 7) and a terminal point at (2, 10). write your answer in component form. then write the vector v as a linear combination of the unit vectors i and j. finally, find the length of the vector.
The length of the vector v is approximately 4.24. A vector is a mathematical object that has both magnitude and direction
Vectors are commonly used in physics, engineering, and other fields to represent quantities that have both magnitude and direction, such as velocity, acceleration, and force. They are also important in linear algebra, where they can be used to represent lines and planes in space, and to solve systems of linear equations.
The vector v can be expressed in component form as v = <2-5, 10-7> = <-3, 3>.
To express the vector v as a linear combination of the unit vectors i and j, we can write it as v = (-3)i + 3j.
To find the length of the vector, we can use the Pythagorean theorem:
length of v = sqrt((-3)^2 + 3^2) = sqrt(9 + 9) = sqrt(18) = 3*sqrt(2) = 4.24
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To test if an observed frequency distribution with five classes is normally distributed, we need to find _____.a. The t-statisticb. The expected, normally distributed class frequenciesc. The class marksd. The class relative frequencies
Finding the t statistic is necessary to check the normality of a five-class observed frequency distribution.
what the T statistic means?The t-value gauges the magnitude of the difference in relation to the range of your sample's data. Or to put it another way, T is just the calculated difference shown in units of standard error. The evidence is stronger against the null hypothesis the larger the value of T.
Which T statistic value is optimal?In general, t-values that are more than +2 or less than -2 are acceptable. We are more confident in the coefficient's ability to predict outcomes the higher the t-value. Low t-values are a sign of the predictability of that coefficient's coefficient being unreliable.
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Find all the real and complex eigenvalues of the following real matrices. Then, diagonalize them over C
, if possible. A=[0 2;-2 0]; B= [0-1 0; 1 0 0;0 0 1]
The eigenvalues of A are the complex numbers +2i and -2i.The diagonalized form of the matrix B is [1 0 0; 0 1 0; 0 0 -1]
A. A matrix A can be written in the form of
A = [a b; c d]
The eigenvalues λ of A can be calculated using the following formula:
λ = (a+d ± √(a+d)^2 -4(ad-bc))/2
Substituting the values of A gives
λ = (0 + 0 ± √(0)^2 - 4(-2))/2
λ = 2i and -2i
Since the eigenvalues are complex, the matrix cannot be diagonalized over C.
B. The eigenvalues of B can be calculated using the same formula as above
λ = (a+d ± √(a+d)^2 -4(ad-bc))/2
Substituting the values of B gives
λ = (0 + 1 ± √(1)^2 - 4(0))/2
λ = 1, 0, -1
To diagonalize the matrix, we must find the eigenvectors associated with each eigenvalue. The eigenvectors of B can be calculated using the following formula:
v = (a - λI)x
Substituting the values of B and the eigenvalues gives:
v1 = (0 - 1I)x
v2 = (0 - 0I)x
v3 = (0 - (-1I))x
The eigenvectors are
v1 = [1 0 0]
v2 = [1 0 0]
v3 = [0 1 0]
The diagonalized form of the matrix B is
[1 0 0; 0 1 0; 0 0 -1]
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if the correlation coefficient is .4, the percentage of variation in the dependent variable explained by the estimated regression equation is .
If the correlation coefficient is 4, the percentage of variation in the dependent variable explained by the estimated regression equation is 16%.
The correlation coefficient is a measure of linear association between two variables, usually denoted by r. A correlation coefficient of 4 indicates a strong positive linear relationship between the two variables.
A correlation coefficient of 4 does not give any indication as to the percentage of variation in the dependent variable explained by the estimated regression equation. To find this percentage, we must use the coefficient of determination, denoted by r2.
The coefficient of determination is the square of the correlation coefficient and can be interpreted as the percentage of the variance in the dependent variable that is explained by the estimated regression equation.
Hence, in this case, r2 would be 16, indicating that the estimated regression equation explains 16% of the variance in the dependent variable.
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Given: AB AC and DA bisects /BAC.
Prove: ZDBC ZDCB.
Step
Statement
AB AC
DA bisects BAC
AD AD
ZBAD ZDAC
A
Reason.
Given
Reflexive Property
Select a Resison
B
Solve for proof
Use photo to understand better PLEASE HELP
The correct option is C ie 3.
D is the midpoint of BC.
What is Congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
What are the congruency properties of a triangle?
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
RHS (Right angle-Hypotenuse-Side)
In triangles BAD and CAD,
(i) AD=AD (common)
(ii)∠DAB=∠CAD (Given, AD bisects ∠BAC)
(iii)AB = AC (given)
Thus, by SAS property both the triangles BAD and CAD are congruent .
By cpct , ∠ADB=∠ADC = x (let)
Since ∠ADB and ∠ADC lies in a straight line
So by the property of straight lines the sum is 180°.
Now ∠ADB+∠ADC= 180°
⇒x+x= 180°
⇒2x= 180°
⇒x=90°
∴AD ⊥ BC
By cpct ,BD=DC
So D is the midpoint of BC.
Hence option C that is 3 is the right answer.
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1. A taxi service charges a $ 1.95 flat rate plus $ 0.55 per mile. Jason only has $ 12 to spend on a ride. Which graph best represents the number of miles Jason can afford to travel?
Answer:
B
Step-by-step explanation:
Subtract $1.95 from $12 to account for the flat rate that Jason must pay, then divide that by 0.55, or the per mile charge. The answer, or the highest amount of miles he can go with $12, is 18.27272727. The answer that best represents the number of miles he can go is B because he can go up to 18 miles, including 18 miles, hence the closed circle.
5. Simplify -2 + 6.45z - 6 + (-3.25z).
[tex]-2 + 6.45z - 6 + (-3.25z)[/tex]
Combine Like Terms:
[tex](6.45z+-3.25z)+(-2+-6)[/tex]
[tex]\fbox{3.2z - 8}[/tex]
write an indirect proof in paragraph form. given: triangle rvt and svt are equilateral. triangle rvs is not equilateral
The indirect proof that defines triangle RVS is not equilateral is explained below.
How triangle look like?
In math, A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices and also a polygon.
Here we need to find the indirect proof for the triangle RVS which is not equilateral.
Here we know that, We need to write an indirect proof in paragraph proof.
For, the given statement, △RVT and SVT are equilateral;
And △RVS is not equilateral.
Then the explanation for this one is written as,
Let us assume temporarily that △RST is equilateral.
And we have given that △RVT and SVT are equilateral, then the sides of △RVT, SVT, and RST are congruent.
Therefore, RV≅VSRS which follows that △RVS is equilateral.
In contradicts the given that △RVS is not equilateral, then the temporary assumption must be false. It follows that △RST is not equilateral.
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PLEASE ANSWER FAST THIS IS TIMED
The graph of the linear inequation [tex]y \leq \frac{1}{2}x -5[/tex] has been described below
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by
[tex]> , < , \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
The given linear inequation is
[tex]y \leq \frac{1}{2}x -5[/tex]
Here equality is maintained. So the line is a solid line
Now, (0, 0) does not satisfy the inequality.
So the solution is below the line
When graphing the inequality above, we will draw a solid line and the solution lies below the line
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Consider the leaking bucket example from the lecture notes. The derivation for the governing equation assumed proportional relationship between the fluid exit velocity and the height of the water (i.e , Qout Kh(t)) . Another cOmmon assumption of this relationship (called the Toricelli model) assumes the relationship to be Qout Kvhc) Using built-in MATLAB solver; solve both differential equations below and plot the height of the water for 120 seconds where . 30 in" . K = 1.4.and h(O) 10 cm antor nro (t) dhpror Khpropt (t) = 0 What t0 turn in: a) A printout of each of your function files b) Publish your script file in which You use your functions
function dhdt = propt(t,h) %propt calculates the rate of change of the height of the liquid in the bucket given , %Define the initial condition h0 = 10; %Define the time span tspan = 0:120 with height of the water.
Function file 1:
function dhdt = propt(t,h) %propt calculates the rate of change of the height of the liquid in the bucket given by dhdt = -1.4h %Inputs: %t = time %h = height of the liquid in the bucket %Output: %dhdt = rate of change of the height of the liquid in the bucket dhdt = -1.4*h; end
Function file 2:
function dhdt = toricelli(t,h) %toricelli calculates the rate of change of the height of the liquid in the bucket given by dhdt = -K*sqrt(h) %Inputs: %t = time %h = height of the liquid in the bucket %Output: %dhdt = rate of change of the height of the liquid in the bucket K = 1.4; dhdt = -K*sqrt(h); end
Script file:
clear; close all; clc; %Define the initial condition h0 = 10; %Define the time span tspan = 0:120;
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A random sample of 16 pharmacy customers showed the waiting times below (in minutes).
20 27 24 23 19 21 18 17
22 15 18 32 16 20 19 19
Find a 90 percent confidence interval for μ, assuming that the sample is from a normal population.
The 90% confidence interval for the population mean is given as follows:
(18.75, 22.51).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.
From the sample given in this problem, the parameters are as follows:
[tex]\overline{x} = 20.63, s = 4.3, n = 16[/tex]
Then the lower bound of the interval is given as follows:
20.63 - 1.7531 x 4.3/4 = 18.75.
The upper bound of the interval is of:
20.63 + 1.7531 x 4.3/4 = 22.51.
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would you expect the proportion of stay-at-home residents to be higher in virginia than in arkansas? support your conclusion with the results obtained in parts (b) and (c). from the results obtained in parts (b) and (c), we would expect the number of stay-at-home residents to be higher correct: your answer is correct. in arkansas than virginia. the sample results show that, rounded to two decimal places, the estimated percentage of arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of virginia residents who were born there is %.
As per the estimated percentage, the test statistic is 0.6167 or 61.67%
The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have given that in Arkansas than Virginia. the sample results show that, rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.
And we need to find the test statistics.
While we looking into the given situation we have identified the following values,
=> H0 : p = 0.577
=> Ha : p ≠ 0.577
Now, we have estimate the proportion of stay-at-home residents in Arkansas is calculated as,
Here the Proportion of stay-at-home residents in Arkansas is written as,
=> p = 74/120 = 0.6167
Therefore, the test statistics is 0.6167.
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The sketch shows a curve with equation y = ab* where a and b are constants and b>0 The curve passes through the points (0,5) and (2,45) Calculate the value of a and b.
NEED PROPER ANSWER AND WORKING OUT
WILL MARK BRAINLIEST
Round 10.29 to the nearest tenth
Answer:
10.3
Step-by-step explanation:
10.29 rounded to the nearest tenth is 10.3.
Find the length and width of a rectangle that has the given area and a minimum perimeter.
Area: 5A square cm
Find length and width of a rectangle with minimum perimeter that has an area of 5A square cm
length=
width=
By taking minimum perimeter the value of length and width will both be [tex]\sqrt{5A}[/tex].
What is perimeter?Perimeter is basically the sum of all sides of a figure.
How to calculate perimeter of rectangle?The perimeter of a rectangle is 2l + 2w where l = length and w = width of rectangle.
Since the perimeter needed in this question is minimum, the figure must be a square and not a rectangle. For a square, area = a^2
5A = a^2
a = l = w = [tex]\sqrt{5A}[/tex]
Hence, both the length and width are equal to [tex]\sqrt{5A}[/tex].
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root of 63x to the power of 11 yz to the power of 10
The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
Root of 63x to the power of 11 yz to the power of 10
The value of root of 63x = [tex]\sqrt{63x}[/tex]
Now , the value of root of 63x to the power of 11 yz is
The value of root of 63x to the power of 11 yz = [tex](\sqrt{63x}^{(11yz)[/tex]
And ,
The value of root of 63x to the power of 11 yz to the power of 10 is
Value of root of 63x to the power of 11 yz to the power of 10 is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]
Therefore , the value of A is [tex](\sqrt{63x}^{(11yz)^1^0}[/tex]
Hence , The value of the equation is [tex]A = (\sqrt{63x}^{(11yz)^1^0}[/tex]
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The accompanying data file shows the midterm and final scores for 32 students in a statistics course Click here for the Excel Data File
a. Estimate a students final score as a function of hiss/her midterm score. (Round your answers t decimal places.) Final27.5818+ 0.6774 Midterm b. Find the standard error of the estimate. (Round your answer to 2 decimal places.) 14.947 c. Interpret the coefficient of determination. (Round your answer to 2 decimal places.) R means that % of the sample Variation â–¼ | in Final grades is explained by the sample regression equation
In this case, the coefficient of determination is 0.5297, which means that 53% of the sample variation in Final grades is explained by the sample regression equation.
The data file contains the midterm and final scores of 32 students in a statistics course. To estimate a student's final score as a function of their midterm score, we used a regression analysis. The regression equation was Final = 27.5818 + 0.6774 Midterm. This equation can be used to predict the final score of a student based on their midterm score. The standard error of the estimate was 14.947. This indicates the accuracy of the estimated final score. The coefficient of determination was 0.5297, which means that 53% of the sample variation in final grades is explained by the regression equation. This tells us that the regression equation is a relatively good predictor of a student's final score.
Given:
Midterm Score = x
Final Score = y
Regression Equation: y = 27.5818 + 0.6774x
Standard Error of the Estimate = 14.947
Coefficient of Determination = 0.5297
Calculating Final Score:
y = 27.5818 + 0.6774x
y = 27.5818 + 0.6774(x)
y = 27.5818 + 0.6774(x)
y = 27.5818 + 0.6774(x)
y = 27.5818 + 0.6774x
Final Score = 27.5818 + 0.6774(Midterm Score)
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suppose that there are 5 children in a gymnastics class. one day, they count the number of steps each persontakes while walking on their hands until they lose balance and come down. the results are: ashley (20),brittany (8), carol (22), darla (26), and erica (24).the mean number of steps these children took whilewalking on their hands is 20 steps.
The population is the number of children in gymnastic class = 5.
A parameter is the mean number of steps taken by the 5 children.
What is a parameter?
Four parameters, referred to as hybrid or h Parameters, can be used to assess any linear circuit with input and output terminals. These parameters are one measured in ohm, one in mho, and two dimensionless. Hybrid is short for "mixed." These parameters are referred to as hybrid parameters since they have dual dimensions
Here, we have
Given that,
Suppose that there are 5 children in a gymnastics class.
One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.
The mean number of steps these children took while walking on their hands is 20 steps.
We have to find the population and parameters.
The area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class make up the population.
Population = number of children in gymnastic class = 5.
Parameter = mean number of steps taken by the 5 children.
Hence, Population is the number of children in gymnastic class = 5.
A parameter is the mean number of steps taken by the 5 children.
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Give two ways to write K-6 in algebbraic expression
What is K in algebraic?
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra.
What does K mean in mathematics?
K is derived from the Greek word kilo, which signifies 1,000. The Greeks similarly referred to a million as M, which stands for Mega. Therefore, if we adhere to the Greek abbreviations, billion would be represented by the letter G. (Giga).
Give some examples of what algebraic expressions are.
image outcome
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.
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a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) a window with the shape of a rectangle surmounted by a semicircle. the diameter of the semicircle is equal to the width of the rectangle. the rectangle has width x. if the perimeter of the window is 32 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
Answer:
The exact value of x so that the greatest possible amount of light is emitted is 8.96ft.
What is the perimeter of a semicircle?
The perimeter of a semicircle is half that of a circle, that is [tex]\pi r[/tex], where r is the radius of the circle.
Step-by-step explanation:
Given the width of the rectangle is x, let the height of the rectangle be y.
The radius of the semicircle is x/2.
The perimeter of the window is equal to [tex]2y+x+\pi \frac{x}{2} =32[/tex].
The area of the window is [tex]xy+\frac{1}{2}(\pi )(\frac{x}{2})^2=xy+\frac{\pi x^2}{8}[/tex].
We can insert into the formula for the area to obtain the area in terms of only x by solving the equation for the perimeter of y in terms of x.
[tex]2y=32-(1+\frac{\pi }{2} )x=32-(\frac{2+\pi }{2} )x\\y=16-(\frac{2+\pi }{4} )x[/tex].
Now the area of the window in terms of only x is:
Area=[tex]16x-(\frac{2+\pi }{4} )x^2+\frac{\pi x^2}{8}[/tex].
Since it is given in the question that maximum light should be admiitted, we will differentiate the Area and set it to 0.
[tex]16-2(\frac{2+\pi }{4} )x+\frac{\pi x}{4}=0\\ 16=x(1+\frac{\pi }{4})\\ x=\frac{16}{1+\frac{\pi }{4}} \\x=8.96ft[/tex].
Therefore the exact value of x is 8.96ft.
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Consider a particle in a rigid box of length L. For each of the states n = 1, n = 2 and n = 3:
a. Sketch graphs of ǀ (x) ǀ2. Label the points x = 0 and x = L.
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your ǀ (x) ǀ2 graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1 3. Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box.
For states, n = 1, 2, and 3 the probability of finding the particle at left 1/3rd of the box is P₁ = (3/4) * (2/L)² P₂ = (1/4) * (2/L)² and P₃ = (1/3) * (2/L)² respectively
a.
The wave function for the particle in a rigid box of length L for the state
n = 1, is given by:
|ψ₁(x)|² = (2/L)² * sin²(πx/L)
the wave function for the state n = 2, is given by:
|ψ₂(x)|² = (2/L)² * sin²(2πx/L)
And the wave function for the state n = 3, is given by:
|ψ₃(x)|² = (2/L)² * sin²(3πx/L)
The graphs of |ψ₁(x)|², |ψ₂(x)|², and |ψ₃(x)|² is attached.
b.
The points of maximum probability density, which occur at x = 0 and x = L for all three states are the positions at which the particle is most likely to be found.
c.
The points of minimum probability density, occur at x = L/2 for the state
n = 1, and at x = L/4 and x = 3L/4 for the state n = 2. For the state n = 3, the points of minimum probability density occur at x = L/3, x = 2L/3, and
x = L are the positions at which the particle is least likely to be found.
d.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 1 the probability of finding the particle in the left one-third of the box is greater than 1/3.
Since the probability density is highest at x = 0 and x = L, which are both outside the left one-third of the box for the state n = 2, the probability of finding the particle in the left one-third of the box is less than 1/3.
Since the probability density is highest at x = 0, which is in the left one-third of the box for the state n = 3, the probability of finding the particle in the left one-third of the box is equal to 1/3.
e.
We need to integrate the probability density over the region of interest to calculate the probability that the particle will be found in the left one-third of the box for each of the states n = 1, n = 2, and n = 3.
the probability for the state n = 1, is given by:
P₁ = ∫ |ψ₁(x)|² dx = (2/L)² * ∫ sin²(πx/L) dx
The probability for the state n = 2, is given by:
P₂ = ∫ |ψ_2(x)|² dx = (2/L)² * ∫ sin²(2πx/L) dx
The probability for the state n = 3, is given by:
P₃ = ∫ |ψ₃(x)|² dx = (2/L)² * ∫sin²(3πx/L) dx
Here all integrals have limits 0 and L/3
Solving these integrals gives:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
Thus, the probabilities that the particle will be found in the left one-third of the box are:
P₁ = (3/4) * (2/L)²
P₂ = (1/4) * (2/L)²
P₃ = (1/3) * (2/L)²
for the states n = 1, n = 2, and n = 3, respectively.
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q1 signaling when education is productive i 6 points grading comment: a single worker incurs a cost of obtaining education of amount ee given by: c(e)=3⋅e 2 The worker's wage is based on how much education he obtains. If he receives education less than a threshold amount e, then he receives a wage that is proportional to his level of education: w(e)=5⋅e And if he receives education greater than or equal to the threshold eˉ, then his wage is proportional to the threshold: w(e)=12⋅ e ˉ So the utility that he receives when he chooses a level of education e is a piecewise function: u(e)={ 5⋅e−3⋅e 2 12⋅ e ˉ −3⋅e 2 e< eˉ e⩾ eˉ Answer the following. Round all numeric answers to at least three decimal places. Suppose that
eˉ=0.5
The worker's marginal cost of education when e=0.5 is 6.00. the derivative of the cost function with respect to the amount of education obtained.
The worker's marginal cost of education is the rate of change in the cost of obtaining education with respect to the amount of education obtained. In this case, the worker's cost of obtaining education is given by the equation c(e)=3e². At e=0.5, we can calculate the marginal cost of education by taking the derivative of the cost function with respect to the amount of education obtained. This gives us the equation c'(e)=6. Thus, the worker's marginal cost of education when e=0.5 is 6.00.
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Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3sin^2(t), y = 3cos^2(t), 0 = t = 5p
Find the length of the curve.
By The length of the curve can be found using the formula for the arc length of a parametric curve, the distance traveled by the particle is 30π.
The length of the curve can be found using the formula for the arc length of a parametric curve:
L = ∫0→5p √(dx/dt)2 + (dy/dt)2 dt
We can calculate dx/dt and dy/dt as follows:
dx/dt = 6sin(t)cos(t)
dy/dt = -6sin(t)cos(t)
Substituting these values into the formula for the arc length gives us:
L = ∫0→5p √[(6sin(t)cos(t))2 + (-6sin(t)cos(t))2] dt
= ∫0→5p 6√(sin2(t)cos2(t)) dt
= 6∫0→5p |sin(t)cos(t)| dt
= 6∫0→5p sin(t)cos(t) dt
= 6[(1/2)sin2(t) + (1/2)cos2(t)]5p
= 6[(1/2)(1) + (1/2)(1)]5p
= 6(1)5p
= 30π
Therefore, the distance traveled by the particle is 30π.
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Please Help
There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?
Assume that once each marble is chosen, it is not returned to the bag.
The probability is 2.54%.
What is probability?The formula of the favorable outcome over the total outcomes is used to describe probability.
given, There are several marbles of different colors in a bag in front of you. Your job is to select three marbles and record the color of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles, and 3 purple marbles.
The final probability if conditions are not dependent on each other is multiple possibilities of happening these events.
Probability of getting desired outcomes = (17 / 50) (8/49) ( 22/48)
Therefore the probability of selecting one red marble, one yellow marble, and a blue marble is 2.54%.
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What do I do now cause I’m stuck in the middle of the equation and not sure what else I may need to do besides make the x alone but I’m not sure how.
2x + 8 = 10
Answer:
x = 1
Step-by-step explanation:
2x + 8 = 10 Subtract 8 from both sides
2x + 8 - 8 = 10 - 8
2x = 2 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{2}{2}[/tex]
x = 1
Check:
2x + 8 = 10
2(1) + 8 = 10
2 + 8 = 10
10 = 10 checks.
Gabe is practicing for his upcoming track meet. One lap around the track is 1/4 of a mile. Gabe sets a goal to
run more than 2 miles today. How many laps should Gabe run to meet his goal?
Answer:
20=-7
Step-by-step explanation:
j
Answer:
8 Laps
Step-by-step explanation:
This is because one lap is 1/4 so it would take 4 laps to make it a whole, which would be a mile.
We could now times this by two, since 1 mile is half of 2 miles.
4 x 2 = 8
Which would make it 8