Every 3 months a man deposits in this bank account savings of 8,000 in how many years would he have saved 288,000

The first-order optimality condition for convex optimization problems can be applied to characterize the optimal point, x* in the given optimization problem.

The first-order optimality condition states that if x* is an optimal point for the given convex optimization problem, then there exists a vector v* such that:

∇f(x*) + v* = 0

Here, ∇f(x*) is the gradient of the objective function f(x) evaluated at x*, and v* is the Lagrange multiplier associated with the constraint x ∈ C.

In the given optimization problem, the objective function is ∥a−x∥², and the constraint set is C.

To apply the first-order optimality condition, we need to find the gradient of the objective function. The gradient of ∥a−x∥² is given by:

∇f(x) = 2(x - a)

Now, let's apply the first-order optimality condition to the given problem:

∇f(x*) + v* = 0

Substituting the gradient expression:

2(x* - a) + v* = 0

Rearranging the equation:

x* = a - (v*/2)

This equation provides a characterization of the optimal point x* in terms of the Lagrange multiplier v*. By solving the equation, we can find the optimal point x*.

It's important to note that the Lagrange multiplier v* depends on the constraint set C. The specific form of v* will vary depending on the nature of the constraint set. In some cases, it may be necessary to further analyze the specific properties of the constraint set C to fully characterize the optimal point x*.

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Answer:

The y value of Function A when x = -4 is greater than the y value of Function B when x = -4.

Step-by-step explanation:

A.) y = 2(-4) + 5 = -8 + 5 = -3

B.) y = 2(-4) + 2 = -8 + 2 = -6

-3 is greater than - 6.

Answer:

Step-by-step explanation:

We are given two congruent sides.

The third side AB is common and therefore congruent to itself.

It gives us 3 congruent sides.

This is a side-side-side or SSS postulate.

Correct choice is B

Answer:(d)

Step-by-step explanation:

Given

AB=AC

\(\therefore\) We can write

\(\angle ABC=\angle ACB\ \quad \text{[angles corresponding to equal sides are equal]}\)

\(\angle ABC=\angle BCA=\angle ACB=65^{\circ}\)

In this problem the diagonal of the Tv is 19 and the hight is 11 so we can use the pythagorical theorem to find the width (w) so:

and we solve for w so

The equation for the probability that the student selects a movie ticket from the mystery bag, given that there are 175 total tickets, is approximately 0.25.

To calculate the probability of selecting a movie ticket from the mystery bag, we need to divide the number of movie tickets by the total number of tickets in the bag.

Let's denote the number of movie tickets as "x". Since we know that the movie tickets make up 25% of the total tickets, we can express it as:

x = 0.25 * 175

Simplifying the equation, we have:

x = 43.75

Therefore, the number of movie tickets in the bag is 43.75.

To calculate the probability of selecting a movie ticket, we divide the number of movie tickets by the total number of tickets:

Probability of selecting a movie ticket = x / Total tickets

Probability of selecting a movie ticket = 43.75 / 175

Probability of selecting a movie ticket ≈ 0.25

Hence, the equation for the probability that the student selects a movie ticket from the mystery bag, given that there are 175 total tickets, is approximately 0.25.

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Answer:

y - 3 = -4(x + 1).

Step-by-step explanation:

First,  calculate the slope (m) using the formula:

y - y1 = m(x - x1),

m = (y2 - y1) / (x2 - x1),

where (x1, y1) = (-1, 3)

(x2, y2) = (2, -9):

m = (-9 - 3) / (2 - (-1))

= (-12) / (3)

= -4.

Now substitute the values into the point-slope formula:

y - 3 = -4(x - (-1))

y - 3 = -4(x + 1).

The given polar equation is r = 9 sin θ, and we have to sketch its graph and find the tangent line(s) at the pole.Sketching the graph of the polar equation:For each θ, r = 9 sin θ is the polar equation.

It implies that when θ = 0°, r = 0, when θ = 90°, r = 9, and when θ = 180°, r = 0, etc.Therefore, we can take several values of θ and then the corresponding r value and plot the points, which in turn results in the following graph:figureAs shown in the figure, the graph consists of four petals.Find the tangent line(s) at the pole:When θ = 0, the given equation becomesr = 9 sin 0r = 0We have to find the equation of the tangent line at the pole.We know that the polar equation of a tangent line to a curve at (r, θ) is given byr = r cos (θ - α)where α is the angle between the positive x-axis and the tangent line at the point of tangency.So, the polar equation of the tangent line at

θ = 0° isr = r cos (θ - α)When θ = 0, r = 0Thus, the equation becomes0 = 0 cos (0 - α)0 = 0 cos α

We can see that α can be any angle, so we have an infinite number of tangent lines at the pole, i.e., θ = 0°.Therefore, the value of θ = 0° will be the answer:Sketch a graph of the polar equation. r = 9 sin θ:The polar equation of a curve describes the distance and the angle of each point in the plane from the pole and the positive x-axis, respectively.

The given polar equation is r = 9 sin θ.It means that when the value of θ is substituted in the equation, the corresponding distance from the origin can be found. For instance, when θ = 0°, r = 0; when θ = 90°, r = 9, and when θ = 180°, r = 0, etc.We can take different values of θ and then the corresponding r values to plot the graph of the given polar equation. We know that θ lies between -π and π.Therefore, let’s take the following values of θ:θ = -π, -π/2, 0, π/2, πWe will find the corresponding r values using the given polar equation r = 9 sin θ, and then we will plot these points, which will give the polar curve.θ = -π:r = 9 sin (-π)r = 0θ = -π/2:r = 9

sin (-π/2)r = -9θ = 0:r = 9 sin (0)r = 0θ = π/2:r = 9 sin (π/2)r = 9θ = π:r = 9 sin (π)r = 0

Now, we can plot these points on the polar plane and get the polar curve as shown below:figureAs shown in the figure, the given polar equation r = 9 sin θ represents four petals.Find the tangent line(s) at the pole:When θ = 0, the given equation becomesr = 9 sin 0r = 0We have to find the equation of the tangent line at the pole.We know that the polar equation of a tangent line to a curve at (r, θ) is given byr = r cos (θ - α)where α is the angle between the positive x-axis and the tangent line at the point of tangency.So, the polar equation of the tangent line at θ = 0° isr = r cos (θ - α)When θ = 0, r = 0Thus, the equation becomes0 = 0 cos (0 - α)0 = 0 cos αWe can see that α can be any angle, so we have an infinite number of tangent lines at the pole,

i.e., θ = 0°.Therefore, the value of θ = 0° will be the answer.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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The perimeter of the shaded part is: 25.1 cm.

The area of the shaded part is: 36.6 cm².

Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).

Parameters given are:

Plug in the values into the equation

Area = 8² - 2(8² - 1/4π(8²)).

Area = 64 - 2(64 - 50.3)

Area = 36.6 cm²

Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm

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Answer:

(a)  Proof below.

\(\begin{aligned}\textsf{(b)} \quad x_1&=-6.75308642\\x_2&=-6.561443673\\x_3&=-6.535451368\end{aligned}\)

(c)  Approximations to the location of one of the roots of the equation given in part (a).  

Step-by-step explanation:

Given equation:

\(20-x^3-7x^2=0\)

Add x³ to both sides of the equation:

\(\implies 20-x^3-7x^2+x^3=0+x^3\)

\(\implies 20-7x^2=x^3\)

Divide both sides of the equation by x²:

\(\implies \dfrac{20}{x^2} -\dfrac{7x^2}{x^2} =\dfrac{x^3}{x^2}\)

\(\implies \dfrac{20}{x^2} -7 =x\)

Given recursive rule:

\(\begin{cases}x_{n+1}=\dfrac{20}{x_n{^2}}-7\\x_0=-9\end{cases}\)

Therefore:

\(\begin{aligned}\implies x_1&=\dfrac{20}{x_0{^2}}-7\\\\&=\dfrac{20}{(-9)^2}-7\\\\&=\dfrac{20}{81}-7\\\\&=\dfrac{20}{81}-\dfrac{567}{81}\\\\&=\dfrac{20-567}{81}\\\\&=-\dfrac{547}{81}\\\\&=-6.75308642\end{aligned}\)

\(\begin{aligned}\implies x_2&=\dfrac{20}{x_1{^2}}-7\\\\&=\dfrac{20}{\left(-\dfrac{547}{81}\right)^2}-7\\\\&=\dfrac{20}{\left(\dfrac{299209}{6561}\right)}-7\\\\&=\dfrac{131220}{299209}-7\\\\&=\dfrac{131220}{299209}-\dfrac{2094463}{299209}\\\\&=-\dfrac{1963243}{299209}\\\\&=-6.561443673\end{aligned}\)

\(\begin{aligned}\implies x_3&=\dfrac{20}{x_2{^2}}-7\\\\&=\dfrac{20}{\left(-6.561443673\right)^2}-7\\\\&=\dfrac{20}{\left(43.05254308\right)}-7\\\\&=0.4645486322-7\\\\&=-6.535451368\end{aligned}\)

The values x₁, x₂ and x₃ are approximations to the location of one of the roots (zeros) of the equation given in part (a).

Each iteration gives a slightly more accurate value of a root x.

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

m<1=50

m<2=130

m<3=50

m<4=130

m<5=40

m<6=40

m<7=90

m<8=140

Step-by-step explanation:

The value of g in the intersected lines is 28 degrees.

When lines intersect, angle relationships are formed such as linear angles, adjacent angle, vertically opposite angles. Therefore, let's find the angle g in the intersected lines as follows:

Therefore,

g + 43 = 71

subtract 43 from both sides of the equation'

g + 43 - 43 = 71 - 43

g = 28

Therefore,

g = 28 degrees

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Step-by-step explanation:

A has no solution.

15x - 45 = 15x + 75

-45 = 75

is false for every value of x.

in other words, when you add to the same thing different amounts, the result cannot be identical ever.

B has a solution

-45x - 45 = -75x + 75

-120x = 120

-x = 1

x = -1

C has a solution

45x - 45 = -15x + 75

60x = 120

x = 2

D has a solution

15x - 45 = 75x + 75

-120 = 60x

-2 = x

Answer:

If(x>y and x<50): # add semicolon

print(a+10) # one close bracket

add " " double quotes inside print statements

print("a+10")

the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

To find the probability of receiving five calls on a given day at the emergency center, we need to use the Poisson distribution formula:

\(P(x = 5) = (e^{-4})*\frac{(4^5)}{(5!)}\)
Where:
- x = number of phone inquiries
- e = Euler's number (approximately 2.71828)

- ! = factorial (i.e. 5! = 5*4*3*2*1)

Given that the average number of phone inquiries per day is four, we can use that as our lambda (λ) value in the Poisson distribution formula, since lambda represents the mean number of events in a specific time interval:

λ = 4

Now we can substitute these values into the formula and solve:

P(x = 5) = (e^-4)*(4^5)/(5!) = (2.71828^-4)*(1024)/(120) ≈ 0.156

Therefore, the probability that the emergency center will receive five calls on a given day is approximately 0.156, or 15.6%.

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The probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

To find the probability that the emergency center will receive five calls on a given day, given that the average number of phone inquiries per day is four, we can use the Poisson distribution formula.

Identify the average rate (λ): In this case, λ = 4 calls per day.

Identify the desired number of events (k): In this case, k = 5 calls.

Use the Poisson distribution formula: \(P(X = k) = (e^(-λ) \times (λ^k)) / k!\)

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate

k is the desired number of events

k! is the factorial of k

Plug in the values and calculate the probability:

\(P(X = 5) = (e^{(-4)} \TIMES (4^5)) / 5!\)

\(P(X = 5) = (0.0183 \times 1024) / 120\)

P(X = 5) ≈ 0.1755

So, the probability that the emergency center will receive five calls on a given day is approximately 0.1755 or 17.55%.

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In insurance, in a 100/300 policy, it should be noted that up to $100,000 bodily injury per single person injured in the accident will be covered.

An insurance coverage simply means the amount of risk or liability for an individual.

In this case, in a 100/300 policy, up to $100,000 bodily injury per single person injured in the accident will be covered.

Also,an amount up to $300,000 in total will be for bodily injuries per accident. Finally, there's a $100,000 for damages to the property of others.

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Answer:

20.25

Step-by-step explanation:

Just multiply the base and height then divide the results in half.

Hope this helps!

\(y=-\frac{5}{4}x -5\)Answer:



Step-by-step explanation:

Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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The expected length of series of four coin flips is 1.

Given data:

To find the expected length of the longest run in a series of four coin flips, consider all possible outcomes and calculate their probabilities.

No runs: If all four coin flips result in alternating heads and tails, there are no runs.

The probability of this outcome is \((\frac{1}{2})^4 = \frac{1}{16}\)

One run of length 2: There are three positions where a run of length 2 can occur: HH, TT, or HT.

The probability of this outcome is \(3*(\frac{1}{2})^4 = \frac{1}{16}\)

One run of length 3: There are two positions where a run of length 3 can occur: HHH or TTT.

The probability of this outcome is \(2*(\frac{1}{2})^4 = \frac{1}{16}\)

One run of length 4: There is only one position where a run of length 4 can occur: HHHH or TTTT.

The probability of this outcome is \((\frac{1}{2})^4 = \frac{1}{16}\)

To find the expected length of the longest run, multiply the length of each possible run by its corresponding probability and sum them up:

Expected length of longest run = \((0 * \frac{1}{16}) + (2*\frac{3}{16}) + (3 * \frac{2}{16}) + (4 * \frac{1}{16})\)

= (0 + 6 + 6 + 4) / 16

= 16 / 16

= 1

Hence, the expected length of the longest run in a series of four coin flips is 1.

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The relationship between the heart beating and minutes passing is,

30x. It will beat 1800 times in 60 minutes.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

An elephant's heart beats an average of 30 beats every minute.

The relationship between the heart beating and minutes passing is,

30x.

Where x is the number of minutes.

So,

30(60) = 1800 beats in 60 minutes.

Therefore, 1800 beats in 60 minutes.

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Answer:

Point Form:

( − 41 /5 , 16 )

Equation Form:

x = − 41 /5 , y = 16

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Answer:

Hey! Answer: F

Step-by-step explanation:

13.5 ÷ 9= 1.5

18 ÷ 12 = 1.5

So our pattern is to enlarge/multiply it by 1.5

So 1.5 x 15 = 22.5

So F is our answer!

Answer:

\(126\frac{6}{19}\) £

Step-by-step explanation:

£1 = €1.14  /\(*\frac{144}{1.14}\)

£\(\frac{144}{1.14}\)=144€= \(126\frac{6}{19} \\\)£