The discrete-time system is described by yik-11 + 2y[k] = Fiki, with fiki = [k] and y(0) = 0. Solve the above equation iteratively to determine yll] and y[2] values.

Car insurance for an 18-year-old typically ranges from $200 to $400 per month.

The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.

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What is the average monthly cost of car insurance for an 18-year-old?

Answer:

Step-by-step explanation:

These are independent events, so we will just multiply the two probabilities together.

1/6 x 1/6 = 1/36

I'm always happy to help :)

The probability should be \(1\div 36\).

Since You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six.

So here the probability should be

\(= 1\div 6 \times 1\div 6 = 1\div 36\)

Hence, we can conclude that The probability should be \(1\div 36\).

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The individual counted a higher ratio of cars to trucks  at the second rest stop, since 17/22 was larger than 3/4.

At the first rest stop, the ratio of cars to trucks was 15:20 or 3:4. At the second rest stop, the ratio of cars to trucks was 17:22 or 17/22. Since 17/22 is larger than 3/4, the individual counted a higher ratio of cars to trucks at the second rest stop. To illustrate this using formulas, we can divide the number of cars by the number of trucks at each rest stop. This gives us 15/20 = 0.75 for the first rest stop and 17/22 = 0.77 for the second rest stop. Since 0.77 is greater than 0.75, the individual counted a higher ratio of cars to trucks at the second rest stop.

At the second rest stop, the individual counted a higher ratio of cars to trucks.The individual counted a higher ratio of cars to trucks  at the second rest stop, since 17/22 was larger than 3/4.

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Answer:

See attached

Step-by-step explanation:

The proof is in the attached picture.

The graph of y = f(x) can have at most one horizontal asymptote.

A horizontal asymptote is a horizontal line that the curve of the function approaches as x approaches positive or negative infinity. The number of horizontal asymptotes that a function can have depends on the behavior of the function as x approaches infinity and negative infinity.

If the function approaches a single horizontal line as x approaches positive or negative infinity, then that line is the horizontal asymptote. If the function approaches different horizontal lines as x approaches infinity and negative infinity, or if it does not approach any horizontal line, then it does not have a horizontal asymptote.

Therefore, the graph of y = f(x) can have at most one horizontal asymptote, which it approaches as x approaches positive or negative infinity.

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To find only one fake coin from 8 coins can be done in two weighings.

Divide the coins into three groups, A, B, and C, each consisting of three coins.

A and B are first weighed against one another. If the balancing scale is straight, fake coins belong in group C; otherwise, they belong in A or B, depending on which side of the scale is up.

Finding the lighter fake coin requires a second weighing if the first weighing indicates that the fake coins are in group C. Weigh any two phony coins from the group if A/B. The third coin is phony if the scale is balanced; else, choose the coin that is lighter.

For 3 weighing, make pair of 4 and followed by pair of 2 for the lighter group. At last, compare the last 2 coins to find the lighter coins.

8 → 4 →2 →1

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The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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Answer:

1=1

Step-by-step explanation:

expand (cost - sint)²= cost² - 2costsint +sint²

(cost +sin t)² = cost² + 2sintcost+sint²

simplifying these = 2(cost²+sint²)= 2

2 will divide with 2 giving 1

çost²+sint²=1

substituting cost²= 1-sint² in above equation

1-sint²+sint²=1

giving us 1=1

Answer:

26.3 hours

Step-by-step explanation:

We need to divide 250 by 9.50, therefore we get the answer ≈ 26.3

Answer:

b

Step-by-step explanation:

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

The solution of the function g(x) is (-1/7)x² + (4/7)x + (6/7).

We know that g(f(x)) = 4x² + 4x + 3. This means that the input of g is actually the output of f.

To find g(x), we need to undo the composition of functions and get g(x) in terms of x. We can do this by working backwards. Let's start by finding f(g(x)):

f(g(x)) = 2g(x) + 1

Now, we know that g(f(x)) = 4x² + 4x + 3, which means that:

g(f(x)) = ag(x)² + bg(x) + c

Substituting f(x) = 2x + 1, we get:

g(2x + 1) = a(2g(x) + 1)² + b(2g(x) + 1) + c

Expanding the right-hand side, we get:

g(2x + 1) = 4ag(x)² + (4a + 2b)g(x) + (a + b + c)

We can now compare this equation with the one we got for g(f(x)):

g(f(x)) = ag(x)² + bg(x) + c

Comparing the coefficients of g(x) in both equations, we get:

4a + 2b = b => 4a = -b

Comparing the constant terms in both equations, we get:

a + b + c = 3

We now have two equations with three unknowns (a, b, and c). However, we can use the equation 4a = -b to eliminate one of the unknowns. Substituting -4a for b in the equation a + b + c = 3, we get:

a - 4a + c = 3 => -3a + c = 3 => c = 3 + 3a

We now have expressions for b and c in terms of a. Substituting these expressions into the equation 4a = -b, we get:

4a = -(-4a - 3a - 3) => 4a = 7a + 3 => a = -1/7

Substituting this value of a into our expressions for b and c, we get:

b = -4a = 4/7 c = 3 + 3a = 6/7

Therefore, g(x) = ax² + bx + c = (-1/7)x² + (4/7)x + (6/7).

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The area of the region pictured below that is bounded by the functions f(x) = x² − 7x + 12 and g(x) = the x-axis when integrating with respect to y is 2√41 − 50.

To use the disk method, we need to integrate the area of each circular cross section of the solid of revolution as we rotate R around the x-axis. Each cross section will have radius f(x) and thickness dx.

So, the volume V of the solid is given by:

V = ∫[1,3] π[f(x)]^2 dx

Substituting f(x) = x^2 + 2 gives:

V = ∫[1,3] π(x^2 + 2)^2 dx

Expanding the square and integrating term by term, we get:

V = ∫[1,3] π(x^4 + 4x^2 + 4) dx

= π[(1/5)x^5 + (4/3)x^3 + 4x)]|[1,3]

= π[(243/5) + (108/3) + 12 - (1/5) - (4/3) - 4]

= π(484/15)

Therefore, the volume of the solid of revolution when R is rotated around the x-axis is (484/15)π.

To find the area of the region bounded by the functions f(x) = x² − 7x + 12 and g(x) = the x-axis when integrating with respect to y, we need to first solve for x in terms of y.

Starting with f(x) = x² − 7x + 12, we have:

x² − 7x + 12 = y

Rearranging, we get:

x² − 7x + (12 − y) = 0

Using the quadratic formula, we get:

x = (7 ± sqrt(49 − 4(12 − y)))/2

Simplifying, we get:

x = (7 ± sqrt(25 + 4y))/2

Since we are integrating with respect to y, we need to express the limits of integration in terms of y.

The region is bounded by the x-axis, so the lower limit of integration is g(x) = 0, or y = 0. The upper limit is given by the intersection of f(x) and g(x), which occurs when:

x² − 7x + 12 = 0

Factoring, we get:

(x − 3)(x − 4) = 0

So the solutions are x = 3 and x = 4. We can use these values to find the upper limit of integration:

f(3) = 0, f(4) = 4

Therefore, the limits of integration are y = 0 to y = 4.

The area A of the region is given by:

A = ∫[0,4] (x_max − x_min) dy

where x_max and x_min are the maximum and minimum values of x for a given value of y.

We found that:

x_max = (7 + sqrt(25 + 4y))/2

x_min = (7 - sqrt(25 + 4y))/2

Substituting these expressions into the integral, we get:

A = ∫[0,4] [(7 + sqrt(25 + 4y))/2 − (7 - sqrt(25 + 4y))/2] dy

Simplifying, we get:

A = ∫[0,4] sqrt(25 + 4y) dy

Making the substitution u = 25 + 4y, we get:

A = (1/2)∫[25,41] sqrt(u) du

= (1/2)[(2/3)u^(3/2)]|[25,41]

= (1/2)[(2/3)(41^(3/2) − 25^(3/2))]

= 2√41 − 5√25

= 2√41 − 50

Therefore, the area of the region pictured below that is bounded by the functions f(x) = x² − 7x + 12 and g(x) = the x-axis when integrating with respect to y is 2√41 − 50.

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Answer:

q1 3 x ^2 − 5 x + 10

q2 1 − y^ 4

q3 exact form: x = − 5 /6

decimal form : 0.83r

q4 1 /2 z^ 2 + 1

Step-by-step explanation:

hope it correct please mark as brainliest if correct

thank you

Answer:

0.68

Step-by-step explanation:

We can use long division to find the decimal equivalent of \(\frac{13}{19}\) since a fraction is just another way of writing a division statement.

\(19\overline{\smash{)}#13}\\\\0.\\19\overline{\smash{)}#130}\\\\0.6\\19\overline{\smash{)}#130-114=16}\\\\0.6\\19\overline{\smash{)}#160}\\\\0.68\\19\overline{\smash{)}#160-152 = 8}\\\\0.68\\19\overline{\smash{)}#80}\\\\0.684\\19\overline{\smash{)}#80}\)

0.684 to the nearest hundredth is 0.68.

Hope this helped!

Answer: 61.58

Step-by-step explanation:

C = 2 π r = 2 · π · 9.8

π = pi

radius times pi (3.14) times 2 (because two radius makes the diameter)

9.8 times 3.14 times 2 = 61.57522in

Now we round.. 61.58

:) I hope this helps!  

Answer:

Team A catches up to B in 2 hours, at the 11 mile mark

Step-by-step explanation:

(5.5 mi/hr)(x) = (4 mi/hr)(x) + 3 mi

(1.5 mi/hr)(x) = 3 mi

x = 3/1.5 = 2 hours

In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

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The inequality which allow able for width x is 0 ≤ x ≤ 10.

According to the given question.

The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.

Width

Let the length, and height of the box be l, and h respectively.

Therefore,

The perimeter of the base of box = 2(width + l) = 2(x + l)

Also, it is given that

l = 2.5x

So,

perimeter of the base = 2(x + 2.5x) = 2(3.5x)

Now, according to the given condition.

The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.So, the inequlaity which represent this scenario is

2(3.5x) + 60 ≤ 130

⇒ 7x ≤ 130-60

⇒ 7x ≤ 70

⇒ x ≤ 10  

Also, x is the width of the box, so it must have some measure and cant be negative therefore

0 ≤ x ≤ 10.

Hence, the inequality which allow able for width x is 0 ≤ x ≤ 10.

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Queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

The queueing system you have described can be modeled as an M/M/7 queue, where:

M represents that inter-arrival times and service times are exponentially distributed.

M represents that the arrival process is memoryless, meaning that the probability of a customer arriving at any given time does not depend on the previous arrival times or the state of the system.

7 represents the number of service channels, or lanes, available for customers to pay their toll.

The notation for this system is M/M/7, which indicates that it has an infinite queue capacity and that there is no limit to the number of customers that can be waiting in the queue.

In this queueing system, customers arrive randomly and independently, and they join the queue if all lanes are busy. They are served on a first-come, first-served basis, with the service times also being exponentially distributed.

This queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.

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Given:

a.) He has 12 1/2 cups of milk.

b.) The chef has 3 1/2 more cups of broth than milk.

Step 1: Since it is said that the chef has 3 1/2 more cups of broth than milk, and he has 12 1/2 cups of milk, we will be adding 3 1/2 and 12 1/2 to get the actual number of cups of broth.

We get,

In adding mixed numbers, we add separately the whole numbers and fractions and add them together later on.

Therefore, the chef has 16 cups of broth.

Step 2: Let's now determine the remaining cups of broth after using 14 1/2 cups to make soup. We will be subtracting the current 16 cups of broth by 14 1/2 cups for the soup.

We get,

Let's first convert them into similar fractions before subtracting.

Let's now proceed in subtracting them,

Therefore, the chef will have a remaining 1 1/2 cups of broths after using 14 1/2 cups for the soup.

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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y = -t is  parametric equation of the line passing through a and parallel to b

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

  and parallel to a vector <a, b, c> is given by :

  x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    

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The domain of the function A = 500 * e^(0.0425t) is t ≥ 0. This indicates that the function is defined for all non-negative values of t, representing the number of years.

To model the given situation, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A is the amount accumulated after t years,

P is the principal amount (initial deposit),

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

r is the annual interest rate (expressed as a decimal),

and t is the number of years.

In this case, Elaine deposited $500 at an interest rate of 4.25% compounded continuously. Substituting these values into the formula, we get:

A = 500 * e^(0.0425t)

The domain of this function is the set of all possible values for t. Since time cannot be negative, the domain will be t ≥ 0, meaning that the number of years must be non-negative.

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The value of side x is given by (C) 14.7 units approximately.

Given the triangle is a right angled triangle.

Now given also that, Height of triangle is = x units

Base of triangle is = 15 units

Hypotenuse of triangle is = 21 units

So by Pythagoras theorem, we get the sum of squares of base and height is equal to the square of hypotenuse. So,

\(x^2+15^2=21^2\\\Rightarrow x^2+225=441\\\Rightarrow x^2=441-225\\\Rightarrow x^2=216\\\Rightarrow x\approx14.7\)

So the value of x is 14.7 units approximately.

Hence the correct option is (C).

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Answer:

I believe that it is d. since the x values are increasing by 4 and the y values are decreasing by 1 each time, it has to be one of the -1/4 answers (rise/run) and the table starts at x=-8 so it must be d is my reasoning

Answer:

x=25

Step-by-step explanation:

2x+40=90

90-40=50

50 divided by 2 is 25

x=25

Answer:

60 cm³

Step-by-step explanation:

Step-by-step explanation:

=896000 is the answer

method -10x8x10x14x10x8

️️

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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The general solution of the differential equation is: y = ±√(7/6 eˣ + C)

To find the general solution of the differential equation 12yy' - 7eˣ = 0, we can use separation of variables.

First, we can divide both sides by 12y to get y' = 7eˣ/12y.

Next, we can multiply both sides by y and dx to separate the variables:

ydy = 7eˣ/12 dx

Integrating both sides, we get:

y²/2 = (7/12) eˣ + C

where C is the constant of integration.

Solving for y, we get:

y = ±√(7/6 eˣ+ C)

Therefore, the general solution of the differential equation is:

y = ±√(7/6 eˣ + C)

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