Tony rents a bike that costs $4 per hour and $10 for the lock. He has $32 to spend. How long can he rent the bike? Write an equation that represents this situation. Be sure to explain how you got your equation and specify what the variables represent.

The laplace transform of f(t) is

F (s) =  2/s³ - 2e^{-2s}/s³ + e^{-2s}/s²  + 2e^{-2s}/s  -  3e^{-3s}/s²  + 7e^{-3s}/s

Since f(t) = t² 0 < t < 2,

= t - 1 for 2 < t < 3 and

= 7 for t > 3

Since f(t) has discontinuities at t = 0, t = 2, t = 3, expressing f(t) in terms of unit step, we have

t² = t²u(t) - t²u(t - 2)

t - 1 = (t - 1)u(t - 2) - (t - 1)u(t - 3)

=  (t - 1 + 1 - 1)u(t - 2) - [(t - 1 + 3 - 3)u(t - 3)]

=  (t - 2 + 1)u(t - 2) - [(t - 3 + 2)u(t - 3)]

= (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) + 2u(t - 3)

f(t) = 7 = 7u(t - 3)

So, f(t) =  t²u(t) - t²u(t - 2) + (t - 2)u(t - 2) + u(t - 2) - (t - 3)u(t - 3) - 2u(t - 3) +  7u(t - 3)

\(L[u(t - c)f(t - c)}] = e^{-cs} F(s)\)

and \(L[t^{n}] = \frac{n!}{s^{n + 1} }\)

Taking the laplace transform, we have

L{f(t)} = L{t²u(t)} - L{t²u(t - 2)} + L{(t - 2)u(t - 2)} + L{u(t - 2)} - L{(t - 3)u(t - 3)} - L{2u(t - 3)} +  L{7u(t - 3)}

\(F(s) = \frac{2!}{s^{3} } - \frac{e^{-2s} 2!}{s^{3} } + \frac{e^{-2s} 1!}{s^{2} } + \frac{e^{-2s} 1!}{s } - \frac{e^{-3s} 1!}{s^{2} } - \frac{2e^{-3s} 1!}{s^{2} } + \frac{7e^{-3s} 1!}{s} \\= \frac{2!}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

\(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{e^{-3s}}{s^{2} } - \frac{2e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

So, the laplace transform of f(t) is \(F (s) = \frac{2}{s^{3} } - \frac{2e^{-2s}}{s^{3} } + \frac{e^{-2s} }{s^{2} } + \frac{2e^{-2s}}{s} - \frac{3e^{-3s}}{s^{2} } + \frac{7e^{-3s}}{s}\\\)

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Step-by-step explanation:

everything can be found in the picture

Mean (X + Y) = Mean (X) + Mean (Y).

The above statement is false.

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Probability Distributions of Discrete Random Variables:

Probability distributions of discrete random variables list the probabilities associated with each possible outcome. Also called probability function or probability mass function.

The probability of a discrete random variable is between 0 and 1. Also, the sum of the probabilities of a discrete random variable is equal to 1. The probability distribution of discrete random variables resembles the normal distribution.

Example:

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X goes from result 1 + 1 = 2 to 2 and the maximum value goes from result 6 + 6 = 12 to 12. Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

Discrete random variables should not be confused with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. However, a discrete random variable can have a range of possible values ​​that result from experimentation.

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Answer:

one option could be for the first box 5 and 9 and in the next box 15 and 27 bc u can scale factor it by 3

Step-by-step explanation:

Answer:

- 5/4

Step-by-step explanation:

5/6  /  (-2/3)       to divide by a fration, flip it and MULTIPLY

= 5/6 * - 3/2 = -15/12  =  - 5/4

Answer:

- 5/4

Step-by-step explanation:

took the test

Answer:

C. The solution t = 5 is the only valid solution to this system since time cannot be negative.

Step-by-step explanation:

Given

\(h(t) = -16t^2 + 48t + 210\)

\(h(t) = 50\)

Required

Determine which of the options is true

After solving

\(h(t) = -16t^2 + 48t + 210\)

for

\(h(t) = 50\)

We have that

\(t = -2\) and \(t = 5\)

Because time can't be negative, we have to eliminate \(t = -2\)

So, we're left with

\(t = 5\)

Because of this singular reason, we can conclude that option c answers the question

The statement that are consistent with the guidelines for hitching trailers are:

A. Trailers must be connected to the tow vehicle before loading.

D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.

Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.

Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.

Therefore the correct option is A and D.

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Based on the given information, the graph of the function will shift 6 units up from the parent graph, f(x).

A function is a mathematical rule that relates one input value to one output value. The parent graph of a function is the simplest form of the graph that shows the basic behavior of the function.

In this case, the function is being shifted vertically by 6 units. This means that all points on the graph will be shifted upward by 6 units compared to the parent graph.

The shape of the graph will remain the same, but its position will change. Understanding how functions are transformed is important in mathematics and can be used to model a wide range of real-world phenomena.

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Answer:

\(z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17\)  

The p value for this case would be given by:

\(p_v =P(z>3.17)=0.00076\)  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

\(\hat p=\frac{59}{400}=0.1475\) estimated proportion of defectives from the company B  

\(p_o=0.1\) is the value to verify

\(\alpha=0.05\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:\(p \leq 0.1\)  

Alternative hypothesis:\(p > 0.1\)  

The statistic would be given by:

\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)  

Replacing the info given we got:

\(z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17\)  

The p value for this case would be given by:

\(p_v =P(z>3.17)=0.00076\)  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Answer:

The market closed with a rating of 2773 points on Wednesday.

Step-by-step explanation:

Lets start with what we know:

Monday at close it had a rating of 2760 points.

Tuesday it gained 45 points.

Wednesday it had lost 32 points.

Once written out it becomes less intimidating to answer.

Monday + Tuesday + Wednesday = Answer

2760 + 45 - 32

= 2805 - 32

= 2773

Step-by-step explanation:

Pick any point on the graph below for a solution:

172273-3-$=$==8399993939384888884-%"%/=%=%8%

Step-by-step explanation:

(x^2-3/4x+y^2)=(x-y)2

(x-3/4*1/2)2

(x-3/8)(x-3/8)

(x^2-3x/8-3x/8+9/64)

(x^2-6x/8+9/64)

(x-3/8)2

Answer:

a. 2/3 < 5/3

b. 2 1/2 > 9/4

c. 2/5 < 3/7

a. 5/3 > 1 1/3

b. 2 1/2 = 10/4

c. 3 5/6 < 21/4

Step-by-step explanation:

2/3 = 0.6667 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

2 1/2 = 2.5

9/4 = 2.25

2/5 = 0.4

3/7 = 0.4286 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

1 1/3 = 1.3334 (Rounded Answer)

2 1/2 = 2.5

10/4 = 2.5

3 5/6 = 3.8334  (Rounded Answer)

21/4 = 5.25

To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.

Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.

Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.

Hence, in this case, since there are 100 items, then there will be 100 numbers of values.

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Answer:

I can help you what you need help with

Step-by-step explanation:

The scale read will be 123.28kg weight,f the elevator accelerates upward at a rate.

Given information:

W = 800 N

a = 5 m/s^2

The mass of the man is calculated as -

m = W / g

m = 800 / 9.8

m = 81.63 kg

When the man is standing in an elevator accelerating upwards, effective acceleration acting on him is -

a' = a + g

a' = 5 + 9.8

a' = 14.8 m/s^2

So the scale reading of the weight of the man is -

W' = m × a'

W' = 81.63 × 14.8

W' = 1208 N

W' = 123.28 kg wt

Hence, his weight on the scale is 1208 N.

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Answer:

18000000

Step-by-step explanation:

2000 x 9000 = 18000000

9 x 2 = 18

there are 3 0's on the 2 and 3 0's on the 9 so we are going to add them together.

000 + 000 = 000000

put the two answer together and they equal...

18000000

Step-by-step explanation:

2000x9000=18000000is. your answer

Answer:

D. 52 cubic units

Step-by-step explanation:

Given info:- In triangle (∆)ABC , in which ∠A = 2x, ∠B = x+15° and ∠C = 2x + 10°. Then find the value of x , also find the measure of each angles of a triangle.

Explanation:-

Let the angles be 2x, x+15 and 2x+10 respectively.

∵ Sum of the three angles of a triangle is 180°

∴ ∠A + ∠B + ∠C = 180° [Sum of ∠s of a ∆=180°]

→2x + x+15 + 2x+10 = 180°

→ 2x + x + 2x + 15 + 10 = 180°

→ 3x + 2x + 15 + 10 = 180°

→ 5x + 15 + 10 = 180°

→ 5x + 25 = 180°

→ 5x = 180°-25

→ 5x = 155°

→ x = 155°÷5 = 155/5 = 31.

Now, finding the measure of each angles of a ∆ABC by putting the original value of “x”.

∴ ∠A = 2x = 2(31) = 62°

∠B = x+15 = 31 + 15 = 46°

∠C = 2x + 10 = 2(31) + 10 = 62 + 10 = 72°.

Step-by-step explanation:

Let the total number of boys be x.

We know that :-

\( \frac{1}{1} = 1\)

is the greatest fraction.

Now, considering the class AS whole, we can say that the value of class is 1.

According to Equation given:-

\( \dfrac{4}{5} + x = 1\)

\(x = \dfrac{1}{1} - \dfrac{4}{5} \)

Taking LCM,

\( \dfrac{5 - 4}{5} \)

\( = \dfrac{1}{5} \)

Fraction of the class are boys.

Hope it helps :D

The equations for the given graphs respectively are y = (-1/3)x + 3, y = (1/3)x + 1, y = -3x, and y = x + 3.

The line in the first graph passes through the points (0, 3) and (3, 2).

The equation of the line is :

(y - 3) = [(2 - 3)/(3 - 0)](x - 0)

y - 3 = (-1/3)x

y = (-1/3)x + 3

The line in the second graph passes through the points (0, 1) and (3, 2).

The equation of the line is :

(y - 1) = [(2 - 1)/(3 - 0)](x - 0)

y - 1 = (1/3)x

y = (1/3)x + 1

The line in the third graph passes through the points (0, 0) and (1, -3).

The equation of the line is :

(y - 0) = [(-3 - 0)/(1 - 0)](x - 0)

y = -3x

The line in the fourth graph passes through the points (-3, 0) and (0, 3).

The equation of the line is :

(y - 0) = [(3 - 0)/(0 - (-3))](x - (-3))

y = x + 3

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

I would use Pythagorean theorem To find the lengths and just plug in numbers from the answer choices.

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

1. greatest common factor is 6x

2.3v^2

Answer:

6x and 3v²

Step-by-step explanation:

The greatest common factor of 30x² and 24x is 6x, because 30x²+24x=6x(5x+4)

The greatest common factor of 15v² and 12v² is 3v²