The cost of making a phone call is $0.40 plus $0.07 for each additional
minute. Find the number of minutes you can talk for closest to $2.00.

Answer:

Revenue = 1.25x * (45-5x)

Revenue = 56.25x - 6.25x^2

Therefore, the answer is A) 56.25x - 6.25x^2.

To convert the FSM (Finite State Machine) to a controller using a state register and logic gates, follow these steps:
1. Identify the states of the FSM: Review the FSM you created for exercise 3.30 and list down all the states it contains.

2. Design the state register: Create a state register that can store the different states of the FSM. You can use flip-flops or any other suitable storage device.

3. Implement the logic gates: Use logic gates (such as AND, OR, and NOT gates) to implement the transitions between different states. Connect the outputs of the logic gates to the inputs of the state register.

4. Connect the state register to the FSM: Connect the outputs of the state register to the inputs of the FSM to control its behavior based on the current state.

5. Test and verify: Test the controller by simulating different inputs and checking if it transitions between the states correctly according to the desired behavior of the original FSM.

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Answer:

1) f(x) = 500·(1.1)ˣ

2) f(x) = 500·(0.9)ˣ

Step-by-step explanation:

1) The given values in the table are;

x; 0, 1, 2, 3

f(x); 500, 550, 605, 665.5

By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;

550/500 = 11/10 = 1.1 = 605/550 = 665.5/605

From which we have;

The values of f(x) are in a geometric progression

The nth of a geometric progression = a·rⁿ

The common ratio, r = 1.1

The first term, a = 500

The number of terms, n = x

Therefore, xth term, f(x) = a×(r)ˣ

Substituting the values gives;

The equation for the data shown in the table is f(x) = 500·(1.1)ˣ

2) The given table of values is presented as follows;

x; 0, 1, 2, 3

f(x); 500, 450, 405, 364.5

The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405

The terms of f(x) are in a geometric progression

The first term. a = 500

The common ratio, r = 9/10 = 0.9

The nth term of a geometric progression, G.P. = a·rⁿ

By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;

The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.

Answer:

0

Step-by-step explanation:

Since 6x - 44 and 88 degrees are the same (exterior angles), we can start off with the first equation, 6x - 44 = 88

6x - 44 = 88

    +44    +44

6x      =   132

÷6         ÷6

x  = 22

same with the second problem (exterior angles are equal):

equation:

15x + 6 = 9x + 54

       -6              -6

15x    = 9x + 48

-9x      -9x

6x   =    48

÷6         ÷6

x   =   8

Hope this helped! :D

Answer:

1. x=22

2. x=8

Step-by-step explanation:

1. Opposite exterior angles are congruent, so 6x-44=88. You would add 44 to both sides, making the equation 6x=132, and then divide both sides by 6 to get your answer of x=22.

2. Again, opposite exterior angles are congruent, so 15x+6=9x+54. You would subtract 9x from both sides, making the equation 6x+6=54, then subtract 6 from both sides, making the equation 6x=48, and then divide both sides by 6 to get your answer of x=8.

(hope this helps!)

The chain rule for the function: dh/dx = df/dx * du/dx * dv/dx, where df/dx, du/dx and dv/dx are the derivatives of f, u and v with respect to x.

The chain rule is a rule used to calculate the derivative of a composite function. It states that the derivative of the composite function is equal to the product of the derivatives of each of its component functions. In the case of the function dh/dx, where h(x) = f(x, u(x), v(x)), the chain rule can be written as:

dh/dx = df/dx * du/dx * dv/dx

This means that the derivative of h with respect to x is equal to the product of the derivatives of f with respect to x, u with respect to x, and v with respect to x. This can be broken down further, where df/dx is the derivative of f with respect to x, du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.

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The derivative of k(x) is:

\(k'(x) = e^{ (-3/5*x^{-3/5} + 2*x^{-3/4})}*( (9/25)*x^{-8/5} + (-3/2)*x^{-7/4}})\)

Remember the chain rule, if:

h(x) = f( g(x)), then:

h'(x) = f'( g(x))*g'(x)

Here we have the function:

\(k(x) = e^{ (-3/5*x^{-3/5} + 2*x^{-3/4})}\)

The derivate of the exponential is itself, then we will get:

\(k'(x) = e^{ (-3/5*x^{-3/5} + 2*x^{-3/4})}*( (-3/5)*(-3/5)*x^{-3/5 - 1} + 2*(-3/4)*x^{-3/4 - 1}})\\\\k'(x) = e^{ (-3/5*x^{-3/5} + 2*x^{-3/4})}*( (9/25)*x^{-8/5} + (-3/2)*x^{-7/4}})\)

That is the derivate of k(x).

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New function that is a horizontal stretch of F(x)=\((x+2)^{3} + 5\) is F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)

The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).

F(x)=\((x+2)^{3} + 5\)

F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)ch visit :
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Considering the piece-wise function described, the catering cost for a dinner with 40 guests is of $600.

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, considering between 0 and 40 guests, the definition is the open circle at (0, 100) and goes up to a closed circle at (40, 600), hence the catering cost for a dinner with 40 guests is of $600.

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Answer:

600

Step-by-step explanation:

edge

Answer:

There will be sufficient evidence to conclude. A further explanation is provided below.

Step-by-step explanation:

The given values are:

\(\sigma=1.8\)

\(\alpha=0.05\)

\(n=10\)

As we know,

\(\bar{x}=\frac{\Sigma x_i}{n}\)

  \(=\frac{71.5}{10}\)

  \(=7.15\)

The standard deviation will be:

⇒  \(s=\sqrt{\frac{1}{n-1} \Sigma(x_i- \bar{x})^2 }\)

On substituting the values, we get

⇒     \(=\sqrt{\frac{1}{10-1} [(6.5-7.15)^2+...(7.7-7.15)^2]}\)

⇒     \(=\sqrt{\frac{1}{9} [(6.5-7.15)^2+...(7.7-7.15)^2]}\)

⇒     \(=0.477\)

According to the question,

Hypotheses:

\(H_o: \sigma=1.8\)

\(H_a: \sigma<1.8\)

The test statistic will be:

⇒ \(X^2=\frac{(n-1)s^2}{\sigma^2}\)

⇒       \(=\frac{(10-1)\times 0.477^2}{1.8^2}\)

⇒       \(=\frac{2.0477}{3.24}\)

⇒       \(=0.632\)

Thus the above is the correct response.

Answer:

2,400

Step-by-step explanation:

The email with an open rate of 9.6% was opened by 2400 people.

The open rate of email campaigns = 9.6%

number of emails = 25000

The percentage is the value per hundred.

For example, A students got 800 marks out of 1000 marks. So, his percentage will be 800/1000 *100 = 80%

So, 9.6% of 25000 = 9.6*25000/100

9.6% of 25000 = 9.6*250

9.6% of 25000 = 2400

So, the email was opened by 2400 people.

Therefore, the email was opened by 2400 people.

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(i) The dual of the given LP problem can be found by following these steps:

1. For each constraint in the primal problem, create a dual variable. In this case, we have three constraints, so we'll have three dual variables: y1, y2, and y3.
2. The objective function of the dual problem will be the sum of the products of the primal variables and their corresponding dual variables. So, the dual objective function is:
  Maximize w = 3y1 + 2y2 + y3.
3. For each primal variable x, create a constraint in the dual problem with the coefficient of the corresponding dual variable equal to the coefficient of x in the primal objective function. So, the dual constraints are:
  y1 + 2y2 - y3 ≤ -2
  y1 + y2 + y3 ≤ -1
  y1, y2, y3 ≥ 0.

(ii) To find the optimal solution to the dual problem, we need to solve the optimal tableau of the dual problem. From the given information, we know that Row 0 of the optimal tableau is:
  w = 4x1 + e2 + (M-1)a2 + (M+2)a3 = 0.
 
  However, the given information does not provide any details about the values of x1, e2, a2, or a3. Therefore, without this information, we cannot determine the specific optimal solution to the dual problem.

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Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant \(b^2-4ac\) applies to quadratic equations when they are organised in standard form: \(ax^2+bx+c=0\).

All quadratic equations can be solved with the quadratic formula: \(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\).

When \(b^2-4ac\) is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

\(0=-2x^2+3\)

We are given above equation. Notice how there are values for a and c but none for b, as there is no bx term. This means that the value of b is 0. We can rewrite the equation so it shows this:

\(0=-2x^2+0x+3\)

Now that we have the values of a, b and c, we can plug them into the discriminant:

\(D=0^2-4(-2)(3)\\D=-4(-2)(3)\\D=-4(-6)\\D=24\)

Because 24 is positive, there are two real, distinct solutions for this equation.

I hope this helps!

Answer:

3 gallons, i think

Step-by-step explanation:

1+1=2

1/4+3/4=4/4

2 4/4= 3

Answer:

16.66

Step-by-step explanation:

It says round to the nearest hundredth, not the nearest tenth

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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It would take approximately 19 years for the value of the account to reach $2,590.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.2/100

r = 0.022 per year.

Plug the given values into the above formula and solve for time t.

A = P( 1 + r/n )^( n × t )

t = In(A/P) / n[ In( 1 + r/n ) ]

t = In( $2,590/$1,700 ) / ( 12[ In( 1 + 0.022/12 ) ] )

t = 19.155 years

t = 19 years

Therefore, the time taken is approximately 19 years.

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Answer: y= 3/5x+1

Step-by-step explanation: if you want to check if its perpendicular go on Desmos graphing calculator on goolge and plug both equations:)

(5x² - 13x -28)/(x-4) = (x-4)(5x+7) so x = -7/5  and x = 4 are the two factors of the given polynomial.

The factors of a polynomial are those values of x for which the given polynomial satisfies.

According to the given question we have to divide a polynomial            (5x² - 13x -28) by (x - 4).

(5x² - 13x -28)/(x-4) = (x-4)(5x) + (7x - 28).

(5x² - 13x -28)/(x-4) = (x-4)(5x+7).

So, the obtained factor is (5x+7) = 0.

∴ 5x + 7 = 0

5x = -7

x = -7/5 is a factor of the given polynomial and by substituting these value in x.

(5x² - 13x -28)

5(-7/5)² - 13(-7/5) - 28 = 0

5(49/25) + 91/5 - 28 = 0

49/5 + 91/5 - 28 = 0

140/5 - 28 = 0.

28 - 28 = 0

0 = 0     ( hence satisfied that -7/5 is a factor of the given polynomial ).

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Answer:

16^10, 4^20 y 2^40

Step-by-step explanation:

Para expresar el producto

16^7 ×16^3  16 ^7 ×16^3

como una potencia de 16, podemos sumar los exponentes y mantener la base:

16^7 × 16^3 = 16^7 + 3=16^10  16^7 ×16^3  =16^7+3  =16 ^10

Para expresar el resultado como una potencia de 4, podemos utilizar la relación

16

=

4

2

16=4

2

:

1

6

10

=

(

4

2

)

10

=

4

2

×

10

=

4

20

16

10

=(4

2

)

10

=4

2×10

=4

20

Finalmente, para expresar el resultado como una potencia de 2, utilizamos la relación

4

=

2

2

4=2

2

:

4

20

=

(

2

2

)

20

=

2

2

×

20

=

2

40

4

20

=(2

2

)

20

=2

2×20

=2

40

Por lo tanto, el producto

1

6

7

×

1

6

3

16

7

×16

3

 puede ser expresado como

1

6

10

16

10

,

4

20

4

20

 y

2

40

2

40

.

Answer:

I hope it will help you dear

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Step-by-step explanation:

hope this helps

After solving the given equation at g(x) = 3 the value obtained is 3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equation is,

g(x) = -2x + 9

Then,

g(3) = -2(3) + 9

= -6 + 9

g(3) = 3

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Your question seems incomplete, the complete question may be:

If g(x) = -2x + 9, what is the value of x

when g(x) = 3?

Answer:

\(x=\frac{1}{7}\)

Step-by-step explanation:

\(3x-4x-4-x+65=83x-8x+50\)

\(3x-4x-x-4+65=83x-8x+50\)

\(-2x-4+65=83x-8x+50\)

\(-2x+61=83x-8x+50\)

\(-2x+61=75x+50\)

\(-2x+61-61=75x+50-61\)

\(-2x=75x-11\)

\(-2x-75x=75x-11-75x\)

\(-77x=-11\)

\(\frac{-77x}{-77}=\frac{-11}{-77}\)

\(x=\frac{1}{7}\)

Answer:

x=1/7

Step-by-step explanation:

3x-4x-4-x+65=83x-8x+50

Solving the right side of equation we have;

83x-8x+50 = 75x +50

Solving the left side of the equation we have;

3x-4x-4-x+65= -2x +61

Equating left side and right side.

-2x +61= 75x +50

by grouping terms with x , we have :

-2x- 75x = -61+50

-77x= -11

x= -11/ -77 = 1/7

Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year.

**Answer: Tacoma's population in 2000 was around 200 thousand, and it has been growing at an annual rate of approximately 8% since then.**

The population of Tacoma, a city located in Washington state, was roughly 200 thousand in the year 2000. Over the years, the city has experienced steady growth in its population, with an average annual increase of approximately 8%. This growth rate signifies that each year, the population of Tacoma has been expanding by 8% of its previous year's population.

To better understand this growth pattern, let's consider an example. If we assume that the population of Tacoma in 2001 was 200,000 (the same as in 2000), the growth rate of 8% would lead to an increase of 16,000 individuals (8% of 200,000) in that year. Consequently, the population in 2001 would be 216,000 (200,000 + 16,000). In the following year, using the same growth rate of 8%, the population would increase by 17,280 (8% of 216,000), resulting in a population of approximately 233,280.

This growth trend continues each year, with the population of Tacoma increasing by approximately 8% of the previous year's population. It's important to note that these calculations are based on a consistent annual growth rate, and various factors such as migration, birth rates, and economic conditions can influence the actual population growth.

In summary, Tacoma's population in 2000 was around 200 thousand, and it has been growing at an annual rate of approximately 8%. This growth rate indicates that the city's population has been expanding by 8% of its previous year's population each year, contributing to its overall population growth over time.

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Answer:

B

Step-by-step explanation:

6 2/9 is 6.2, and sqrt 42 is 6.48

The product of (-8) and a number at most 50 will be

50 * (-8) = -400

Mathematicians use multiplication to calculate the sum of two or more numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

a mathematical operation that accepts two integers and outputs a result that is equal to the sum of a column that has one of the values repeated the same amount of times as the other number. Eight times three equals the total of eight times eight.

The product of (-8) and a number at most 50 will be

50 * (-8) = -400

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Therefore , the solution of the given problem of expressions function comes out to be 20x - 14 is a monomial expression.

Instead of generating estimates at random, variable it is better to use movable numbers, which can be growing, decreasing, or blocking. They could only help one another by sharing tools, information, or solutions to issues equation. An assertion of truth might include defenses, elements, and notations for mathematical operations like additional rejection, synthesis, and mixture.

Here,

Given :

4 expressions.

To find the monomial expression .

Thus , we do this

Hence , monomial expression has 1 power not more than that .

Here we can see,

=> 20x - 14 and 9/x

have power 1 in both of them.

But if we put 9x⁻¹ we get power as -1

.So, 20x - 14 is a monomial expression

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