Consider a Diamond-Dybvig economy with a single consumption good and three dates (t = 0, 1, and 2). There is a large number of ex ante identical consumers. The size of the population is N > 0. Each consumer receives one unit of good as an initial endowment at t = 0. This unit of good can be either consumed or invested.
At t = 1, each consumer finds out whether he/she is a patient consumer or an impatient consumer. The probability of being an impatient consumer is 1∈(0,1) and the probability of being a patient one is 2=1−1. Impatient consumers only value consumption at t = 1. Their utility function is (1), where 1 denotes consumption at t = 1. Patient consumers only value consumption at t = 2. Their utility function is given by (2), where 2 denotes consumption at t = 2 and ∈(0,1) is the subjective discount factor. The function () is strictly increasing and strictly concave, i.e., ′()>0 and ′′()<0.
Consumers can buy or sell a single risk-free bond after knowing their type (patient or impatient) at t = 1. The price of the bond is p at t = 1 and it promises to pay one unit of good at t = 2. There is a simple storage technology. Each unit of good stored today will return one unit of good in the next time period. Finally, there is an illiquid asset. Each unit of illiquid investment will return >1 units of good at t = 2, but only ∈(0,1) units if terminated prematurely at t = 1.
(a) Let be the optimal level of illiquid investment for an individual consumer. Derive the first-order condition for an interior solution of . Show your work and explain your answers. [10 marks]
(b) Explain why the bond market is in equilibrium only when p =1. Derive the optimal level of illiquid investment in the bond market equilibrium.
Answers
The bond price is 1, it implies that the payoff of the bond at t=2 is equal to the consumption at t=2. Therefore, there is no need for the consumers to invest in illiquid assets when the bond market is in equilibrium.
(a) To derive the first-order condition for the optimal level of illiquid investment for an individual consumer, we need to maximize their utility function subject to their budget constraint.
For an impatient consumer, the utility function is given by:
U_i(t=1) = ln(C_i(t=1))
where C_i(t=1) represents the consumption of the impatient consumer at t=1.
For a patient consumer, the utility function is given by:
U_p(t=2) = ln(C_p(t=2))
where C_p(t=2) represents the consumption of the patient consumer at t=2.
Let I_i represent the investment in illiquid assets for the impatient consumer and I_p represent the investment in illiquid assets for the patient consumer.
The budget constraint for both consumers at t=1 is:
C_i(t=1) + I_i = 1
The budget constraint for the patient consumer at t=2 is:
C_p(t=2) + (1-p)I_p = 1
where p represents the price of the bond at t=1.
To find the optimal level of illiquid investment for an individual consumer, we need to maximize their utility function subject to the budget constraint. We can set up the Lagrangian function for the impatient consumer as follows:
L_i = ln(C_i(t=1)) + λ_i(C_i(t=1) + I_i - 1)
Taking the derivative with respect to C_i(t=1) and setting it equal to zero, we have:
∂L_i/∂C_i(t=1) = 1/C_i(t=1) + λ_i = 0
Solving for λ_i, we get:
λ_i = -1/C_i(t=1)
Similarly, we can set up the Lagrangian function for the patient consumer as follows:
L_p = ln(C_p(t=2)) + λ_p(C_p(t=2) + (1-p)I_p - 1)
Taking the derivative with respect to C_p(t=2) and setting it equal to zero, we have:
∂L_p/∂C_p(t=2) = 1/C_p(t=2) + λ_p = 0
Solving for λ_p, we get:
λ_p = -1/C_p(t=2)
To find the optimal level of illiquid investment for each consumer, we need to solve their respective first-order conditions:
For the impatient consumer:
1/C_i(t=1) = λ_i
1/C_i(t=1) = -1/C_i(t=1)
Simplifying, we get:
C_i(t=1) = 1
Therefore, the optimal level of illiquid investment for the impatient consumer is I_i = 0.
For the patient consumer:
1/C_p(t=2) = λ_p
1/C_p(t=2) = -1/C_p(t=2)
Simplifying, we get:
C_p(t=2) = 1
Therefore, the optimal level of illiquid investment for the patient consumer is:
C_p(t=2) + (1-p)I_p = 1
(1-p)I_p = 0
I_p = 0
In summary, the optimal level of illiquid investment for both the impatient and patient consumers is 0.
(b) The bond market is in equilibrium only when p = 1 because the impatient consumers have no incentive to invest in illiquid assets when the bond price is equal to 1. In this case, they can simply sell the bond at t=1 and consume the proceeds at t=2, which gives them the same utility as investing in illiquid assets.
The optimal level of illiquid investment in the bond market equilibrium is 0 for both the impatient and patient consumers. Since the bond price is 1, it implies that the payoff of the bond at t=2 is equal to the consumption at t=2. Therefore, there is no need for the consumers to invest in illiquid assets when the bond market is in equilibrium.
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Related Questions
If the profit is the difference between the revenue and the cost, what expression represents the profit? 3x – 260 3x + 140 5x – 260 5x + 140
Answers
Answer:
\(P =5x-260\)
Step-by-step explanation:
Given
\(R = 3x^2 + 4x - 60\) --- Revenue
\(C = 3x^2 - x + 200\) --- Cost
Required
The expression for profit (P)
This is calculated as:
\(P =R - C\)
So, we have:
\(P =3x^2 + 4x - 60 - (3x^2 -x+200)\)
Open bracket
\(P =3x^2 + 4x - 60 - 3x^2 +x-200\)
Collect like terms
\(P =3x^2 - 3x^2+ 4x +x- 60-200\)
\(P =5x-260\)
If the profit is the difference between the revenue and the cost, 5x – 260 expression represents the profit. Correct option is 3.
The profit is calculated by subtracting the cost from the revenue. In mathematical terms, the profit (P) can be represented as:
Profit (P) = Revenue - Cost
Among the given options:
1. 3x - 260
2. 3x + 140
3. 5x - 260
4. 5x + 140
We need an expression where the first term represents the revenue and the second term represents the cost, so that when we subtract the cost from the revenue, we get the profit.
Option 3, 5x - 260, fits this pattern:
- Revenue: 5x
- Cost: 260
When we subtract the cost from the revenue:
Profit (P) = Revenue - Cost = 5x - 260
So, option 3, 5x - 260, is the expression that represents the profit.
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Complete question is:
If the profit is the difference between the revenue and the cost, what expression represents the profit?
1. 3x – 260
2. 3x + 140
3. 5x – 260
4. 5x + 140
please help!!! 5x – 2(2x – 1) = 6 show your work!!!
Answers
Answer:
Can I get brainliest please?
Step-by-step explanation:
Ok so, Let's solve your equation step-by-step.
5x−2(2x−1)=6
Step 1: Simplify both sides of the equation.
5x−2(2x−1)=6
5x+(−2)(2x)+(−2)(−1)=6(Distribute)
5x+−4x+2=6
(5x+−4x)+(2)=6(Combine Like Terms)
x+2=6
x+2=6
Step 2: Subtract 2 from both sides.
x+2−2=6−2
x=4
So, your answer would be:
x=4
Answer:
x=4
Step-by-step explanation:
5x-2(2x-1)=6
multiply 2 to the parathesis
5x-4x+2=6
collect like terms
x+2=6
subtract both sides by 2
x=4
Audrey has a points card for a movie theater. She receives 85 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs at least 265 points for a free movie ticket. Write and solve an inequality which can be used to determine xx, the number of visits Audrey can make to earn her first free movie ticket.
Answers
Answer:
Here it is given that x is the cost of the labor per hour.
Now the technician at the store worked on the computer for 4 hours
Total labour charge = $ 4x
The technician charged her $ 77 for parts
So the required equation is
4x + 77 = 497
We now solve for x as below
4x + 77 = 497
⇒ 4x = 420
⇒ x = 105
The cost of the labor per hour = $ 105
Answer: $105 an hour
Step-by-step explanation:
Describe how to transform the graph of f(x) = ⎜x⎟ to obtain the graph of the related function g(x). Then draw the graph of g.
Answers
Answer:
ssss
Step-by-step explanation:
dddd
Reformulate this problem (except for the equality restriction) to fit our standard form of linear programming model.
Max (Z) = -2X1 + X2 - 4X3 + 3X4
Subject to
X1 + X2 + X3 +2X4 <= 4
X1 - X3 + X4 >= -1
2X1 + X2 <= 2
X1 + 2X2 +X3 +2X4 = 2
X1, X2, X3, X4 >= 0
Answers
Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:
x1 + x2 + x3 + 2x4 + s1 = 4,
-x1 + x3 + x4 - s2 = -1,
2x1 + x2 + s3 = 2,
and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.
To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.
The standard form of a linear programming problem is as follows:
Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4
Subject to:
a11x1 + a12x2 + a13x3 + a14x4 = b1
a21x1 + a22x2 + a23x3 + a24x4 = b2
a31x1 + a32x2 + a33x3 + a34x4 = b3
an1x1 + an2x2 + an3x3 + an4x4 = bn
x1, x2, x3, x4 >= 0
Now let's reformulate the given problem:
Maximize (Z) = -2x1 + x2 - 4x3 + 3x4
Subject to:
x1 + x2 + x3 + 2x4 <= 4
-x1 + 0x2 + x3 + x4 >= -1
2x1 + x2 + 0x3 + 0x4 <= 2
x1 + 2x2 + x3 + 2x4 = 2
x1, x2, x3, x4 >= 0
The reformulated linear programming problem in standard form is as follows:
Maximize (Z) = -2x1 + x2 - 4x3 + 3x4
Subject to:
x1 + x2 + x3 + 2x4 + s1 = 4
-x1 + x3 + x4 - s2 = -1
2x1 + x2 + s3 = 2
x1 + 2x2 + x3 + 2x4 = 2
x1, x2, x3, x4, s1, s2, s3 >= 0
Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.
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pls help with homework!!!
A restaurant stores flour, rice, and sugar in three different cylindrical containers.
An image displaying three cylinders each with sugar, rice and flour. The measure of the sugar cylinder reada: radius equals 2.5 inches, height equals 8 inches and find the volume in cubic inches. The measure of the rice cylinder reads: radius equals 2.5 inches, volume equals 235.5 cubic inches, find the height in inches. The measure of the flour cylinder reads: area of the base equals 12.56 square inches, height equals 4 inches and what is the volume in cubic inches?
Use the information to answer the questions. Use 3.14 for π.
1. What is the approximate volume of the sugar container? Show your work.
(2 points)
2. What is the approximate height of the rice container? Show your work. (2 points)
3. Compare the heights of the sugar container and the rice container. Next, compare their volumes. How many times as large is the volume of the rice container compared to the volume of the sugar container? Explain your answer. (2 points)
4. In the formula V = Bh, B is the area of the base. Use this formula to calculate the volume of the flour container. (2 points)
5. Compare the volumes of the containers. Which container has the greatest volume? Which has the smallest volume? (2 points)
Answers
The volume of the container 1 is equal to 157 cubic inch. The height of the container 2 is equal to 12 inch. The volume of the container 3 is equal to 50.24 cubic inch.
What is the volume?In mathematics and related areas, volume refers to the space occupied by an object. The volume is usually given in units such as:
Cubic meters.
Cubic centimeters.
Cubic millimeters.
How to calculate the volume?
The way to calculate the volume mainly depends on the shape of the object. In the case of cylinders, the formula is:
V=πr2h
Volume = (3.14169)*r*r*h
You can use this formula to calculate the exact volume of any cylindrical object by using the radio and height.
1. V=3.14*2.5*2.5*8
V=157 inch³
2. V=3.14*2.5*2.5*h
V=235.5 inch³
235.5=19.625h
h=12 inch
3. V=12.56*4
V=50.24 inch³
The capacity of container 1 is 157 cubic inches. The container 2 has a height of 12 inches. The capacity of container 3 is 50.24 cubic inches.
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Answer:
The volume of the container 1 is equal to 157 cubic inch. The height of the container 2 is equal to 12 inch. The volume of the container 3 is equal to 50.24 cubic inch.
Step-by-step explanation:
PLS HELP ME ASAP I WILL MARK THE BRAINLIEST
Answers
For Cylinder:
SA = 578.05 yd^3
V = 955.04 yd^3
For Trapezoidal Prism:
SA = 510.4 ft^2
V = 275 ft^3
Cylinder: Second Image
diameter - D
area - A
radius - R
height - H
volume - V
surface area - SA
PI = 3.14159...
R = D/2
R = 8/2
R = 4 yd
Surface Area:
SA = 2×PI×R×H + 2×PI×R^2
SA = 2×(3.14159×4×19) + 2(3.14159×(4)^2)
SA = 578.05 yd^3
Volume:
V = PI×(R^2)×h
V = 3.14159×(4^2) × 19
V= 955.04 yd^3
Trapezoidal Prism: First Image
lateral area - LA
area of base - BA
base - B
width - W
height - H
volume - V
surface area - SA
Volume:
V = BA × H
V =( L×W + 0.5(B×H)) × H
V = (5×7 + 0.5(8×5)) × 5
V = 275 ft^3
Surface area:
Lateral area is the sum of all the areas excluding the area of the base.
LA = a×l + b×l + c×l + d×l
LA = l(a+ b + c + d)
LA = 11(5 + 9.4 + 15 + 7)
LA = 400.4 ft^2
BA = L×W + 0.5(B×H)
BA = 5×7 + 0.5(8×5)
BA = 55 ft^2
SA = 2×BA + LA
SA = 2×55 + 400.4
SA = 510.4 ft^2
Samir has a collection of coins. He wants to find out how many dimes he has without having to count them. According to the U.S. Mint report, a dime has a mass of approximately 2.27 grams. If the total weight of Samir's dime collection is 47.67 grams, about how many dimes are in Samir's coin collection?
Answers
Answer:
21
Step-by-step explanation:
47.67 divided by 2.27 = 21
It would really help if someone could tell me the answers for those questions
Answers
1) 2.4
2) 6.4
3) 7.7
4) 9.9
5) 2.8
Hope it helps <3
Just basic simplification, make 1 of the variable alone on one side
Which of the following statements is not
true about the linear equation, y + 3 = -2(x-7)?
O The line has a slope of -2
O The linear equation can also be written as y=-2x +11
O The line contains the point (7,-3)
O The line contains the point (-7, 3)
Answers
Answer: Option 4
Step-by-step explanation:
This is true because the coefficient of x is -2.\(y+3=-2x+14 \implies y=-2x+11\), so this is true.Substituting \(x=-7\), \(y=(-2)(7)+11 =-3\), so this is true.Substituting \(x=7\), \(y=-2(-7)+11=3\). so this is false.How many solutions does y+x=5 5x+5y=25 have?
A) One
B) Infinitely Many
C) None
D) Two
Answers
Answer:
c. po dahil Wala po Dian Ang answer
Step-by-step explanation:
sana po makatulong
Can someone tell me what number on the number line is greater than -9 for an inequality?
Answers
Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.
What is inequality in math example?An inequality compares two values and indicates whether one is lower, higher, or just not equal to the other. It is implied by the expression a b that a and b are not equal. If a b, then a must be smaller than b. When a > b, an is greater than b.A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.When resolving an inequality, you can either add or subtract the same amount from each side, or multiply or divide each side by the same positive amount. The inequality sign appears if each side is multiplied or divided by a negative number.To learn more about inequality refer to:
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which function has a range of {y|y ≤ 5}?
a. f(x) = (x – 4)2 5
b. f(x) = –(x – 4)2 5
c. f(x) = (x – 5)2 4
d. f(x) = –(x – 5)2 4
Answers
The correct option is \(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\).\) The function that has a range of \(\(\{y | y \leq 5\}\)\) is option \(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\).\)
To determine this, let's analyze the options:
\(\(a.\) \(f(x) = \frac{{(x - 4)^2}}{5}\)\): This function will have a range of \(\(y\)\)-values greater
than or equal to 0, so it does not have a range of \(\(\{y | y \leq 5\}\).\)
\(\(b.\) \(f(x) = -\frac{{(x - 4)^2}}{5}\)\) : This function is a downward-opening parabola, and when we substitute various values of \(\(x\)\) , we get \(\(y\)\)-values less than or equal to 5. Therefore, this function has a range of \(\(\{y | y \leq 5\}\).\)
\(\(c.\) \(f(x) = \frac{{(x - 5)^2}}{4}\)\): This function is an upward-opening parabola, and its
range will be \(\(y\)\)-values greater than or equal to 0, so it does not have a
range of \(\(\{y | y \leq 5\}\).\)
\(\(d.\) \(f(x) = -\frac{{(x - 5)^2}}{4}\)\): This function is a downward-opening parabola, and its range will be \(\(y\)\)-values less than or equal to 0, so it
does not have a range of \(\(\{y | y \leq 5\}\).\)
Therefore, the correct option is \(\(b. f(x) = -\frac{{(x - 4)^2}}{5}\).\)
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Expresiones algebraicas. 1- Escribe en el lenguaje algebraico las siguientes expresiones del lenguaje común. Dos terceras partes de un número. ____________________________ Un número menos su doble. ________________________________ La suma de los cuadrados de tres números. _____________________ El producto de dos números divididos por un tercer número.________________ La suma de tres números consecutivos. _____________________________
Answers
Answer:
Dos terceras partes de un número: \(\frac{2}{3}*x\)
Un número menos su doble: x - 2*x
La suma de los cuadrados de tres números: x² + y² + z²
El producto de dos números divididos por un tercer número: \(\frac{x*y}{z}\)
La suma de tres números consecutivos: x+(x+1)+(x+2)
Step-by-step explanation:
Una expresión algebraica es un conjunto de números y letras que se combinan con los signos de las operaciones aritméticas. En otras palabras, el lenguaje algebraico es el que utiliza letras, símbolos y números para expresar en forma breve y concisa enunciados en los que se pide realizar operaciones matemáticas.
Entonces, siendo x, y, z números al cual desear aplicar una operación aritmética, y teniendo en cuenta que:
dos terceras partes= \(\frac{2}{3}\)doble: se calcula multiplicando el número por 2Cuadrado de un número n: se representa como n², y se calcula multiplicando el número por sí mismo.Producto: hace referencia a la multiplicación.Un número consecutivo se obtiene sumando una unidad al anterior.las siguientes expresiones escritas en lenguaje algebraica serán:
Dos terceras partes de un número: \(\frac{2}{3}*x\)
Un número menos su doble: x - 2*x
La suma de los cuadrados de tres números: x² + y² + z²
El producto de dos números divididos por un tercer número: \(\frac{x*y}{z}\)
La suma de tres números consecutivos: es la suma del primer número, más el segundo que seria el primero más uno, más el tercero que seria el primero más 2. Esto es: x+(x+1)+(x+2)
For a school assignment Brody weighed two different blocks of wood the red block weighed 9/10 of a pound and the blue block weighed 3/5 of a pound what is the difference in the two weights?
Answers
Answer:
3/10
Step-by-step explanation:
Difference = Red - blue
red = 9/10
blue = 3/5 = 6/10 multiply top and bottom by 2
Difference = 9/10 - 6/10 = 3/10
Iris's checking account pays simple interest at 4% per year. She has $180 in her account. Write a linear function to model the amount of money in her checking account at any time t.
A(t)=
Answers
The amount of money in Iris's checking account can be modeled by a linear function of the form:
y = mt + b
where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.
In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:
y = 0.04t + 180
For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.
Divide:
7,448 + 6 =
submit
PO
Answers
Answer:
ffggggggggggytdcuihgr
A footbridge over a river is modelled by the equation h=-0.05x^2+0.36x+1 where “H”
represents the height above the water in metres and “x” represents the distance from the bank in meters. What is the maximum height of the bridge? Show Steps.
Answers
Answer: 12 m
Step-by-step explanation:he path of a football has been modeled by the equation:
Find the slope and the y-intercept of the line y=4x+6
Answers
Answer:
Slope: 4
Y-intercept: 6
Step-by-step explanation:
The equation is given to you in slope intercept form which is y=mx+b.
In this form m is the slope and b is the Y-intercept. Therefore all you have to do is take the value for m from the equation and put that down for the slope and the value for b as the y-intercept.
how do we solve it for the slope and points? please if you can draw it
Answers
Answer:
I have a formula that you can go by to find the slope. X1 -Y1 / X2-Y2
Step-by-step explanation:
Given: RT = AS, RS = AT Prove: < TSA = < STR Write a two- proof. RT = AS, RS = AT
Answers
As per the given triangle RT = AS, RS = AT, the statement < TSA = < STR is proved.
Given two triangles, if the length of one side is proportional to the length of a corresponding side in another triangle, then the two triangles are similar.
This relationship is expressed as "RT = AS," where R and S are corresponding vertices in the two triangles and T is the point where the two sides intersect.
To prove that < TSA = < STR, we need to show that corresponding angles in the two triangles are equal.
This is because corresponding angles in similar triangles are equal, and this is one of the ways to prove that two triangles are similar.
To prove that RT = AS and RS = AT, we can use the function of proportionality. This function states that if two sides are proportional, then the ratio of corresponding lengths will be equal.
Therefore, if RT = AS and RS = AT, then we can conclude that < TSA = < STR and the two triangles are similar.
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Linda is driving to denver let y represent her distance in miles let x represent the time she jas been driving in hours suppose that x and y are related by the equation y=-65x+475 what is the change in Linda distance from Denver for each hour she drives
Answers
The change in Linda's distance from Denver for each hour she drives is -65 miles.
The given equation, y=-65x+475, represents a linear relationship between Linda's distance from Denver (y) and the time she has been driving (x). The coefficient of x (-65) represents the rate at which Linda's distance from Denver is changing with respect to time. Since the coefficient is negative, it means that Linda's distance from Denver is decreasing at a rate of 65 miles per hour. Therefore, for each hour she drives, her distance from Denver decreases by 65 miles.
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Use the quadratic formula to find both solutions to the quadratic equation given below
4x^2+3x-1=0
Answers
The solutions to the quadratic equation 4x² + 3x - 1 = 0 are: x = 1/2 and x = -1. None of the answer choices match these solutions, so none of the options provided are correct.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
To use the quadratic formula, we need to first identify the values of a, b, and c in the quadratic equation:
ax² + bx + c = 0
In the given equation,
a = 4
b = 3
c = -1
Now, we can substitute these values into the quadratic formula:
\($ \rm x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\)
Plugging in the values for a, b, and c gives:
x = (-3 ± sqrt(3² - 4(4)(-1))) / 2(4)
\($ \rm x = \frac{ -3 \pm \sqrt{3^2 - 4(4)(-1)}}{2(4)}\)
Simplifying inside the square root:
\($ \rm x = \frac{-3 \pm \sqrt{9 + 16}}{8}\)
\($ \rm x = \frac{-3 \pm \sqrt{25}}{8}\)
\($ \rm x = \frac{-3 \pm 5}{8}\)
Now, we have two solutions:
x = (-3 + 5) / 8 = 1/2
x = (-3 - 5) / 8 = -1
Therefore, the solutions to the quadratic equation 4x² +3x - 1 = 0 are:
x = 1/2 and x = -1
None of the answer choices match these solutions, so none of the options provided are correct.
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What is the radius of a circle whose equation is (x + 5)^2 + (y – 3)^2 = 4^2? What are the coordinates of the center of the circle?
Answers
\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{}{h}~~,~~\underset{}{k})}\qquad \stackrel{radius}{\underset{}{r}} \\\\[-0.35em] ~\dotfill\\\\ (x+5)^2+(y-3)^2=4^2\implies ( ~~ x-(\stackrel{ h }{-5}) ~~ )^2+(y-\stackrel{ k }{3})^2=\stackrel{ r }{4^2}\qquad \begin{cases} \stackrel{ center }{(-5,3)}\\ \stackrel{radius}{4} \end{cases}\)
I'm giving brainliest to the most helpful answer. For 50 points:
Find each probability using the table (table is linked)
The table below shows the number of students that do or do not have their own car and whether they have part time jobs.
1. p(a student with a part time job without a car)
2. p(no car | does not have a part time job)
3. p(part time job | car)
Answers
Answer:
1) \(\displaystyle\frac{5}{18}\approx27.78\%\)
2) \(\displaystyle\frac{4}{7}\approx57.14\%\)
3) \(\displaystyle \frac{13}{16}=81.25\%\)
Step-by-step explanation:
We are given a two-way frequency table. Using the table, we will determine the probability for each case.
Question 1)
P(A Student With A Part Time Job Without A Car)
Using the first column, the total number of students that have a part time job is 78+30=108.
Likewise, using the first column, we can see that out of those 108 students, 30 do not have a car.
Hence, the probability that a student with a part time job without a car is:
\(\displaystyle P=\frac{30}{108}=\frac{5}{18}\approx27.78\%\)
Question 2)
P(No Car | Does Not Have A Part Time Job)
Remember that the vertical line means conditional probability.
So, we want the probability of a student having no car given that they do not have a part time job.
Using the second column, we can see that the total number of students that do not have a part time job is 18+24=42.
Likewise, using the second column, 24 do not have a car.
Hence, the probability that a student with a part time job without a car is:
\(\displaystyle P=\frac{24}{42}=\frac{4}{7}\approx57.14\%\)
Question 3)
P(Part Time Job | Car)
So, we want to probability of a student having a part time job given that they have a car.
Using the first row, the total students that have a car is 78+18=96.
And of those 96 students, 78 have a part time job.
Hence, the probability that a student with a car has a part time job is given by:
\(\displaystyle P=\frac{78}{96}=\frac{13}{16}=81.25\%\)
Graph the solution to this inequality on the number line.
−4m+3>11
Answers
Subtract numbers
-4m>11-3
Evaluate and subtract
-4m>8
Divide by -4
Solution
M<-2
Answer: The person above me is correct. Here is a picture if you still dont get it..
Step-by-step explanation:
De acuerdo a su rendimiento de producción diaria, solo 6.0% del producto realizado se desecha: Teniendo en cuenta este rendimiento, ¿cuánto debería ser la producción para que al final tenga 78 125 lb de producto?
a. 82.813 lb
b.4.388 lb.
C. 78.128 lb.
d. 79.588 lb
Answers
The amount of output that should be produced so that you can end up with 78,125 pounds of product is 83, 111. 70 pounds
How to find the output?Assuming that the amount of output that you should produce to end up with 78,125 pounds is x, the formula to find this amount that should be produced is:
x = (6% × x) + 78, 125
Solving for x gives:
x = 0.06x + 78, 125
x - 0.06x = 78, 125
0. 94x = 78, 125
x = 78, 125 / 0.94
x = 83, 111. 70 pounds
Note: The options do not contain the correct amount to produce.
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The frequency table shows the scores from rolling a dice.
Score Frequency
1 3
2 8
3 8
4 5
5 8
6 3
Work out the mode.
Answers
Answer:
3, 8
Step-by-step explanation:
keys for antique cars had seven parts, with three patterns for each part.(a) how many different key designs are possible for these cars?
Answers
This can be simplified to 3^7, which equals 2,187. So, there are 2,187 different key designs possible for these antique cars.
To determine the number of different key designs possible for antique cars with seven parts and three patterns for each part, we can use the multiplication principle of counting.
This principle states that if there are m ways to perform one action and n ways to perform another action, then there are m x n ways to perform both actions together.
Therefore, the number of different key designs possible can be calculated by multiplying the number of patterns for each part together. In this case, we have three patterns for each of the seven parts, so we can calculate the number of possible designs by using the formula 3^7.
Using a calculator, we can see that 3^7 is equal to 2,187. Therefore, there are 2,187 different key designs possible for antique cars with seven parts and three patterns for each part. It's worth noting that not all of these designs may have actually been produced or used, but this calculation gives us the total number of possibilities based on the given information.
Hi! I'd be happy to help you with your question. To determine the number of different key designs possible for these antique cars, we can use the multiplication principle of counting. Since there are 7 parts to each key and 3 patterns for each part, we can multiply the number of patterns for each part together to find the total number of key designs.
The calculation would be: 3 (patterns for part 1) × 3 (patterns for part 2) × 3 (patterns for part 3) × 3 (patterns for part 4) × 3 (patterns for part 5) × 3 (patterns for part 6) × 3 (patterns for part 7).
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Someone please help me asap! I will mark as brainliest, thank you!!
Answers
Answer:
Perimeter of ABCD = 2(24 + 26 + 28 + 25) = 206 mm.
Step-by-step explanation:
Perimeter of ABCD = 2(24 + 26 + 28 + 25) = 206 mm.