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\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)

Answer:

To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Step-by-step explanation:

a. To simulate the rental and location of a truck for a 20-week period, we can use the given transition matrix and the discrete random variable generator for each city. Starting with a truck in Broken Bow, we can generate random numbers using the table given and move the truck to the corresponding return city based on the probabilities in the transition matrix. The results of the simulation experiment are shown in the table below.

Week Return City Pickup City

Broken Bow r

1 Goodland Goodland

2 Goodland Goodland

3 Goodland Broken Bow

4 Amarillo Goodland

5 Amarillo Amarillo

6 Goodland Enid

7 Amarillo Goodland

8 Goodland Goodland

9 Goodland Topeka

10 Amarillo Goodland

11 Goodland Enid

12 Goodland Goodland

13 Amarillo Goodland

14 Goodland Goodland

15 Goodland Goodland

16 Goodland Enid

17 Topeka Goodland

18 Amarillo Goodland

19 Goodland Goodland

20 Goodland Goodland

b. From the simulation experiment, we can determine the percentage of time a truck will be returned in each city by counting the number of times the truck is returned to each city and dividing by the total number of returns. The results are shown in the table below.

Number of Returns % Returned City

Enid 0 0%

Topeka 1 5%

Broken Bow 15 75%

Goodland 3 15%

Amarillo 1 5%

Total 20 100%

c. To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Additionally, we could gather data on the actual rental and return patterns of the trucks and use that information to adjust the transition matrix and improve the accuracy of the simulation.

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Answer:

8.8 breaths

Step-by-step explanation:

Answer: The quotient of 28 and 4 minus the sum of a number and 7

Step-by-step explanation:

Answer:

I simplified and I got 4n^2 , please let me know if I am wrong.

The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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Answer:

The value of x is 6.

Step-by-step explanation:

You have to use Pythagorean Theorem, a² + b² = c². Make (4x+1)cm as the hypotenuse because any values substitute into x will give the highest length among these 3 expressions of length :

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Let a = side = (x+1)cm,

Let b = side = 4x cm,

Let c = hypotenuse = (4x+1)cm,

\( {(x + 1)}^{2} + {(4x)}^{2} = {(4x + 1)}^{2} \)

\( {x}^{2} + 2x + 1 + 16 {x}^{2} = 16 {x}^{2} + 8x + 1\)

Then you have to simplify :

\(17 {x}^{2} + 2x + 1 = 16 {x}^{2} + 8x + 1\)

\(17{x}^{2} + 2x + 1 - 16 {x}^{2} - 8x - 1 = 0\)

\( {x}^{2} - 6x = 0\)

Next you have to solve it :

\( {x}^{2} - 6x = 0\)

\(x(x - 6) = 0\)

\(x = 0 \: (rejected)\)

\(x - 6 = 0\)

\(x = 6cm\)

The value of x in the right triangle is 6 cm.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Right triangle:

The three sides are:

x + 1, 4x and 4x + 1

Applying the Pythagorean theorem.

(x + 1)² + (4x)² = (4x + 1)²

x² + 2x + 1 + 16x² = 16x² + 8x + 1

17x² + 2x + 1 = 16x² + 8x + 1

17x² - 16x² = 8x - 2x

x² = 6x

x gets canceled.

x = 6

Thus,

The value of x is 6.

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a) Causal, memoryless, linear, time-invariant.

b) Causal, memoryless, linear, time-invariant.

c) Causal, memoryless, nonlinear, time-invariant.

d) Causal, has memory, nonlinear, time-invariant.

a) The system described by y[n] = x[n] + 2x[n+1] is causal because the output value at any time index n only depends on the current and past input values. It is memoryless since the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a linear combination of the input values. It is also time-invariant because the system's behavior remains unchanged over time.

b) The system y[n] = u[n]x[n] is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a product of the input signal and a constant. It is also time-invariant because the system's behavior remains unchanged over time.

c) The system y[n] = |x[n]| is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is nonlinear because the absolute value operation is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

d) The system y[n] = ∑(0.5)^n x[i] for i=0 to n is causal since the output at any time index n only depends on the current and past input values. It has memory because the output at a given time index n depends on all past input values up to the current time index. The system is nonlinear because the output is a sum of terms raised to a power, which is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

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Yes, there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be a = 5,184p.

It should be noted that the information is to simply know if there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be:

= Number of pixels / Screen size

= 31.104 / 6

= 5.184

Therefore, the equation representing the relationship will be a = 5,184p.

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Answer:

$190

Step-by-step explanation:

Let's call the original price of the jacket "x".

If the new cost of the jacket is $87, we can represent this as x/2-8=87. By solving for x, we see that the original price of the jacket is $190

Answer:

I think the answer would be 182

Step-by-step explanation:

87x2= 174

174+8= 182

Answer:

\(y=\frac{x+2}{4}\)

Step-by-step explanation:

First, switch the x and the y

\(x=4y-2\)

Then add 2 to each side

\(x+2=4y\)

Divide 4 to each side

\(\frac{x+2}{4}=y\)

The inverse equation of \(x=4y-2\) is \(y=\frac{x+2}{4}\)

The equation for the inverse of y = 4x - 2 is:

y = (x + 2) / 4

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the equation for the inverse of y = 4x - 2, we can follow these steps:

Step 1:

Replace y with x and x with y.

x = 4y - 2

Step 2:

Solve for y.

x + 2 = 4y

y = (x + 2) / 4

Step 3:

Write the equation for the inverse.

The inverse of y = 4x - 2 is:

x = (y + 2) / 4

or

y = 4x - 2 can be rewritten as x = (y + 2)/4.

Therefore,

The equation for the inverse of y = 4x - 2 is:

y = (x + 2) / 4

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Answer:

2

Step-by-step explanation:

Over 8 months, an investment of $84,000 at a simple interest rate of 12% would earn $8,400 in interest.

To calculate the interest earned on a simple interest investment, we use the formula: Interest = Principal × Rate × Time. In this case, the principal is $84,000 and the rate is 12% or 0.12 (converted to decimal form). The time is 8 months.

First, we convert the time to years by dividing 8 months by 12 (number of months in a year). This gives us 0.67 years.

Next, we plug in the values into the formula: Interest = $84,000 × 0.12 × 0.67.

Calculating this, we find that the interest earned over 8 months is $8,400. This means that after 8 months, the investment would have grown to a total of $92,400 ($84,000 principal + $8,400 interest).

It's important to note that simple interest assumes a constant interest rate over the entire period and does not take compounding into account. If compounding were involved, the interest earned would be higher.

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Answer:

t(10) = 15

Step-by-step explanation:

5 - (-3)/ 5 - 1

= 2

t(n) = t1 + (n - 1)(d)

t(10) = -3 + (10 - 1)(2)

t(10) = -3 + (9)(2)

t(10) = -3 + 18

t(10) = 15

Answer:

  {-9, 10}

Step-by-step explanation:

The equation can be factored as ...

  2x^2 -2x -180 = 0

  x^2 -x -90 = 0 . . . . divide by 2

  (x +9)(x -10) = 0

Solutions are the x-values that make the factors zero:

  -9, 10

To find the length of the hypotenuse of a right triangle, we need to use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, we have two sides with lengths given by the expressions 5x + 7 and 3x. When x = 14, we can substitute this value into the expressions to find the lengths of the sides:

a = 5x + 7 = 5(14) + 7 = 77

b = 3x = 3(14) = 42

Now we can use the Pythagorean Theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2 = 77^2 + 42^2 = 5929 + 1764 = 7693

Taking the square root of both sides, we get:

c = sqrt(7693) ≈ 87.7

Therefore, when x = 14, the length of the hypotenuse of the triangle is approximately 87.7 units. I

The measure of the length BP and BC are 6 and 10 respectively

The given figure is a circle containing two chords AD and BC. From the given diagram, the following are true

AP = PC

BP = PD

BC = BP + PC

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

Given the following parameters

AP = 3.5,

PD = 6,

PC = 4

According to the expression above;

BP = PD = 6

BC =  BP + PC

BC = 6 + 4

BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively

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Answer:

x = 16

Step-by-step explanation:

9/12 = 12/x

9x = 144

x = 16

Answer:

tan45=X/12

X= 1×12

X=12

Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?

The fraction left to pay for the birthday party is 17/30.

The calculation is as follows:

1 * 1/4 = 1/4 … (1)

1/4 * 2/3 = 2/12 … (2)

2/12 * 1/10 = 2/120 … (3)

Fraction left to pay:

= 1 - (1/4 + 2/12 + 2/120)

= 1 - (30/120 + 20/120 + 2/120)

= 1 - (52/120)

= 1 - 13/30

= 30/30 - 13/30

= 17/30

Thus, the fraction left to pay for the birthday party is 17/30.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

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Answer:

9

Step-by-step explanation:

8-6(2)/4+2(2)

8-12/4+4

8-3+4

9 not sure though

Answer:

The answer is 9

Step-by-step explanation:

We just have to substitute the value of X and Y with 2 and 4 so...

8-6x/y +2x

=8- 6×2/4 + 2×2 (Just replaced the X and Y here)

Now we solve it

=8 - 12/4 + 4

= 32-12/4 +4

= 20/4 + 4

= 5 +4

= 9

Answer:

get a better math teacher

Answer:

g(f(x)) = 8x² - 28x + 34

Step-by-step explanation:

f(x) = 2x² - 7x + 6

g(x) = 4x + 10

g(f(x)) = y

y = 4 ( 2x² - 7x + 6 ) + 10 = 8x² - 28x + 34

g(f(x)) = 8x² - 28x + 34

Answer:

f(X)=2x^2-7x+6

g(X)=4x+10

Step-by-step explanation:

now according to question, g(f(X))=g{f(X)}

=g(2x^2-7x+6)

=4(2x^2-7x+6)+10

= 8x^2-14x+24+10

=8x^2-14x+34

Answer:

4 × x

Step-by-step explanation:

Variable x = a number

Product = multiplication

Set up an equation:

4 × x

The solutions to the given differential equation are options (b) and (d). Thus, the solutions to the given differential equation y′′ +2y′ +y = 0 are y = e−t and y = t2e−t.

Given differential equation is y′′ +2y′ +y = 0. We need to determine the functions which are solutions to this equation.

We have y′′ +2y′ +y = 0

By using the auxiliary equation method, let us solve the above equation.

Auxiliary equation is m2 +2m +1 = 0

(m +1)2 = 0

m = −1 (repeated roots)

Hence, the solution of the given differential equation is y = (c1 + c2t)e−t. Now, let's check which of the following options is a solution to this differential equation

a) y = et

Taking the first derivative:

y′ = et

Taking the second derivative:

y′′ = et

On substituting the above derivatives in the differential equation, we get

et + 2et + et = 0

⇒ 4et = 0

The given equation does not satisfy this equation. Hence, option (a) is not a solution.

b) y = e−t

Taking the first derivative:

y′ = −e−t

Taking the second derivative:

y′′ = e−t

On substituting the above derivatives in the differential equation, we get

e−t − 2e−t + e−t = 0

Thus, the given equation is satisfied. Hence, option (b) is a solution.

c) y = te−t

Taking first derivative:

y′ = e−t – te−t

Taking second derivative:

y′′ = −2e−t + te−t

On substituting the above derivatives in the differential equation, we get

−2e−t + 2te−t + te−t = 0

Thus, the given equation is not satisfied. Hence, option (c) is not a solution.

d) y = t2e−t

Taking first derivative:

y′ = 2te−t − t2e−t

Taking second derivative:

y′′ = −2te−t + 2te−t – t2e−t

On substituting the above derivatives in the differential equation, we get−2te−t + 2te−t – t2e−t + 2te−t – t2e−t = 0

Therefore, the solutions to the given differential equation are options (b) and (d).In conclusion, the solutions to the given differential equation y′′ +2y′ +y = 0 are y = e−t and y = t2e−t.

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Answer:

y=x÷2

Step-by-step explanation:

If you take a number from the Y chart which could be 4, the one above it is 8. So, you put it into the equation 4=8÷2. Is this equation true? yes. So your answer is y=x÷2

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Answer:

let s regroup the terms

2ax - 15 = 3(x + 5) + 5(x - 1) *** add 15 to both sides ***

<=> 2ax = 15 + 3x + 15 + 5x - 5 *** develop to remove the parentheses***

<=> 2ax = 8x + 25 *** simplify ***

<=> (2a-8)x = 25 *** subtract 8x from both sides ***

<=> (a-4)x=25/2 *** divide by 2 both sides ***

There is no solution is a-4 = 0 ,

because it would mean 0 = 25/2 and this is not possible

So it gives a = 4

Step-by-step explanation:

I hope this helps

Express the weight W of a bearing in terms of its surface area:To express the weight W in terms of the surface area A, we can rearrange the equation for surface area A = 4πr^2 to solve for r in terms of A:

A = 4πr^2

r^2 = A / (4π)

r = √(A / (4π))

Now substitute this value of r into the weight formula W = (4/3)πp(r^3):

W = (4/3)πp(√(A / (4π)))^3

Simplifying further:

W = (4/3)πp(A^(3/2)) / (4^(3/2)π^(3/2))

W = (4/3)πp(A^(3/2)) / (4^(3/2)π^(3/2))

W = (4/3)πp(A^(3/2)) / (4√π)

W = (4/3)√πp(A^(3/2)) / 4√π

W = (1/3)√(πp)(A^(3/2))

Therefore, the weight W of a bearing in terms of its surface area A is (1/3)√(πp)(A^(3/2)).

Express the bearing's surface area A in terms of its weight:

To express the surface area A in terms of the weight W, we rearrange the weight formula W = (4/3)πp(r^3) to solve for r in terms of W:

W = (4/3)πp(r^3)

r^3 = (3W) / (4πp)

r = (3W / (4πp))^(1/3)

Now substitute this value of r into the formula for surface area A = 4πr^2:

A = 4π((3W / (4πp))^(1/3))^2

A = 4π((3W / (4πp))^(2/3))

Therefore, the surface area A of a bearing in terms of its weight W is 4π((3W / (4πp))^(2/3)).

c. For steel, p = 7.85 g/cm^3. What is the surface area of a bearing weighing 0.62 g?

Given: W = 0.62 g, p = 7.85 g/cm^3.

To find the surface area A, we need to substitute the given values into the formula for surface area derived in part (b):

A = 4π((3W / (4πp))^(2/3))

Substituting the values:

A = 4π((3(0.62) / (4π(7.85)))^(2/3))

Simplifying further:

A = 4π((0.186 / 31.02)^(2/3))

A = 4π(0.00599051^(2/3))

A = 4π(0.0864001)

A ≈ 1.087 cm^2

Therefore, the surface area of a bearing weighing 0.62 g is approximately 1.087 cm^2.

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