At McDonald's it costs $1.59 for medium-size fries and $3.29 for a cheeseburger

A. Write an expression for the total cost of f fries and c cheeseburgers


B. You have $20 to spend. If you purchase 3 orders of fries and also want to buy a drink for $1.99, how many cheeseburgers can you buy?

The arclength of the curve (e* +e-*) from -1 to 1 is 2(2 arccosh(2) - √3).

The problem requires finding the arclength of the curve (e* +e-*) from -1 to 1.

The arclength of the curve is given by the formula:

L = ∫√(1+(dy/dx)²) dx

To find dy/dx, we differentiate the curve (e* +e-*) with respect to x:

dy/dx = d/dx(e* +e-*) = e^x - e^(-x)

Now, we substitute this into the arclength formula and integrate from -1 to 1:

L = ∫(-1)^1 √(1+(e^x - e^(-x))²) dx

We can simplify the integrand using the identity (a-b)² = a² - 2ab + b²:

L = ∫(-1)^1 √(2 + 2e^(2x) - 2e^(-2x)) dx

= ∫(-1)^1 √(4(e^(2x) + e^(-2x)) - 4) dx

= 2 ∫0^1 √(e^(2x) + e^(-2x) - 1) dx

Next, we make the substitution u = e^x + e^(-x), du/dx = e^x - e^(-x), and simplify:

L = 2 ∫2^2 √(u² - 1) du/u

= 2 ∫arccosh(u) du

= 2(u arccosh(u) - √(u² - 1))|2^2

= 2(2 arccosh(2) - √3)

Therefore, the arclength of the curve (e* +e-*) from -1 to 1 is 2(2 arccosh(2) - √3).

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The solution of the given equation; tan 23 = 22 / x for the variable x as required is; 52.07.

It follows from the task content that the value of x in the given equation is to be determined.

Since the given equation is; tan (23) = 22 / x;

By multiplying both sides by; x / tan (23); we have that;

x = 22 / tan (23)

x = 22 / 0.4225

x = 52.07.

Ultimately, the solution of the equation for x is; 52.07.

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Answer:

degree 4

terms 2 and 4

Step-by-step explanation:

Answer:

Formula

Probability=Number of favorable outcomes/Number of of total outcomes

1. Probabily of spinning yellow is

The number of favorable outocme is 1 case

The number of total outcomes is 5 cases

P=1/5=20%

2.Probabily of spinning yellow is

The number of favorable outcomes is 2 case

The number of of total outcomes is 5 cases

P=2/5=40%

Answer:

0.5

Step-by-step explanation:

The formula a(7) * 1.01 represents an exponential growth model, where a(7) is the area covered by mold at week 7, and 1.01 represents a growth rate of 1% per week.

The exponential growth model is represented by the formula a(7) * 1.01, where a(7) is the area covered by mould at week 7, and 1.01 indicates a weekly growth rate of 1%.

By multiplying the area at week 7 by 1.01, we can approximate the area covered by mold at week 8.

However, it's important to note that this model assumes that the growth rate remains constant and does not account for any limiting factors such as availability of food or changes in environmental conditions.

Additionally, this model may not accurately represent the actual growth of mold, as mold growth can be complex and affected by many variables.

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Answer:

Interest earned after 12 years is $48,000.

Step-by-step explanation:

The first step is to find 4% of 10,000

10,000 times .4 equals to 4,000

4% of 10,000 is 4,000

So each year, $4,000 is added

Times $4,000 by 12 years and you will have the total interest earned.

In case you need to know, the total amount of the bank account should be $58,000.

I hope this helps! :)

It would take Patricia and Denise working together approximately 72/17 hours to complete the job. This fraction cannot be simplified further, so the answer is expressed as 72/17 hours.

To determine how many hours it would take Patricia and Denise to paint the living room together, we can use the concept of their individual rates of work.

Let's assume the total work of painting the living room is represented by 1 (the whole job). Therefore, Patricia's individual rate of work would be 1/8 of the job per hour, and Denise's individual rate of work would be 1/9 of the job per hour.

When they work together, their rates of work add up. Therefore, we can add their individual rates to find their combined rate of work:

Combined rate = Patricia's rate + Denise's rate

Combined rate = 1/8 + 1/9

To add the fractions, we need a common denominator, which in this case is 72. So, let's convert the fractions to have the same denominator:

Combined rate = 9/72 + 8/72

Combined rate = 17/72

This means that together, Patricia and Denise can complete 17/72 of the job per hour.

To find how many hours it would take them to complete the entire job (1), we can set up the equation:

(17/72) * Hours = 1

To solve for Hours, we can multiply both sides of the equation by the reciprocal of 17/72, which is 72/17:

Hours = 1 * (72/17)

Hours = 72/17

Therefore, it would take Patricia and Denise working together approximately 72/17 hours to complete the job. This fraction cannot be simplified further, so the answer is expressed as 72/17 hours.

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Here are the requested sketches:

Cone:

3D Sketch:

          ^

        /   \

       /     \

      /       \

     /_________\

Cross Section:

        ____

      /     \

     /       \

Hemisphere:

3D Sketch:

              ____

         _,-""|`-,  

      ,-' ._  |    \

    ,'     `-.|     \

   /          ;      ;

  ;            \    /

  |              \,'

  \                 \

   `,                \

     \                 \

      `,                ;

        `-..__         ,'    

               ``--._ :            

                       `\          

                         \.        

                          `        

Cross Section:

                 ____

        _____,-'    `--.

     ,-'                  `--.

   ,'                         `.

  ;                              \

 ;                                 \

 ;                                  )

 \                                ,'

  `.                            ,-'

    `--.                     ,-'

         `--.__        __,--'

                 ``--''

Frustum:

3D Sketch:

          ^        /|

         / \      / |

        /   \    /  |

       /     \  /   |

      /_______\/____|

Cross Section:

        ______

      /       \

     /         \

Rectangular Pyramid:

3D Sketch:

            .                  

            |\                  A

            | \                 |\

            |  \                | \

            |   \               C--B

            |____\                    

           D      E              

Cross Section:

          ___

         /   \

        /     \

Rectangular Prism:

3D Sketch:

        G-----H

       /|    /|

      / |   / |

     C--|---D  |

     |  E---|--F

     | /    | /

     |/     |/

     A-----B

Cross Section:

        ____

      /    \

     /      \

Triangular Prism:

3D Sketch:

            D

           /\  

          /  \     B

         /    \   / \

        /______\/    \

       A       C------E

Cross Section:

         ___

       /    \

      /      \

Cylinder:

3D Sketch:

                 _______

             ,-'         `._

          ,-'                `.

        ,'                      `.

      ,'                           `.

     /                                \

    ;                                  ;

    |                                  |

    ;                                  ;

     \                                /

      `.                            ,'

        `.                        ,'

          `._                _.'

             `--.______,--'

Cross Section:

                 _______

             ,-'         `-,

          ,'                 ',

        ,'                     ',

      ,'                         ',

     /                             \

    ;                               ;

    |                               |

    ;                               ;

     \                             /

      `.                         ,'

        `.                     ,'

          `._             _,-'

             `--._____,--'

Prism with Octagonal Base:

3D Sketch:

                   G _______ H  

                  /|       /|

                 / |______/ |

                / /|     / /|

               / /_|____/ / |

              /___/_____/ /|F

              |   |      | |

              |   |      | |

              |   |______|_|

              |  / C     | /E

              | /        |/

              |/________/D

              A          B        

Cross Section:

                 ____

             ,-  /  \  -,

           ,'___/_____\___`,

          ;|   /\     /\   |;

          ||  /  \   /  \  ||

          ;; /    \ /    \ ;;

          `;`      V      `;`

           `'             `'

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Answer:

A.) As x increases, the rate of change of g exceeds the rate of change of f

Step-by-step explanation:

Let's take the options given and look at them to actually know which is true.

Option A

We notice that as x increase in value the rate of change of g starts exceeding the rate of change of f.

Then it's exceeds it from the value x = 5

Option B

At x= 4.39

F= 2616.689

G= 2606.657

They are different values

Option C

That's opposite of option A

But option A is true which signify option C to be false

Option D

Not true also.

We can see from x= 0 to 4 the rate of change of F exceeds that of G

The largest possible value of l_z for l = 3, in units of ℏ, is 3ℏ.

For a state with l = 3, the largest possible value of l_z (l_z represents the z-component of angular momentum) can be calculated using the formula:

l_z = mℏ,

where m represents the magnetic quantum number. The allowed values of m range from -l to l, so for l = 3, m can take values from -3 to 3.

To find the largest possible value of l_z, we take the maximum value of m, which is 3. Therefore, the largest possible value of l_z for l = 3, in units of ℏ, is:

l_z = 3ℏ.

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Answer:

383ft

Step-by-step explanation:

Given parameters:

  Elevation = 240ft at the start

  Elevation at the end = -143ft

Unknown:

Change in elevation:

Solution:

The change in elevation is the difference between the two hiking milestone;

  change in elevation = Elevation at the start  - Elevation at the end

                                    = 240ft  - (-)143ft

                                   = 240 + 143

                                    = 383ft

Answer:

Step-by-step explanation:

Wheelbarrows  is 30/3 = 10

Pair of shoes is (18 - 10) /2 = 4 so one shoe is 2

2 Seed bags is 4 - 2 = 2 so one bag is 1

Answer is 1(seed baf) + 10(wheelbarrows X 2(shoe) = 21

Answer: He bought 5 sandwiches.

Step-by-step explanation:

We know that he purchased sandwiches (let's suppose that he bought X ) and one gallon of milk.

The cost of each sandwich is $8, then the cost of the X sandwiches will be X times $8, or: X*$8.

The cost of the gallon of milk is $4.

The total cost will be:

$4 + X*$8.

And we know that the total cost was $44, then we have the equation:

$4 + X*$8 = $44

We can solve this for X

X*$8 = $44 - $4

X*$8 = $40

X = $40/$8 = 5

This means that he bought 5 sandwiches

Answer:

When you graph it looks like this:

If each outcome in the sample space is equally likely, the probability that all three new employees will be a good fit is 1/8.

In this scenario, each new employee can either be a good fit (g) or a bad fit (b). Since each outcome is equally likely, we can determine the probability of all three employees being a good fit by considering the total number of equally likely outcomes.

For each employee, there are two possible outcomes (good fit or bad fit). Therefore, the total number of equally likely outcomes for three employees is 2 * 2 * 2 = 8.

Out of these 8 outcomes, we are interested in the specific outcome where all three employees are a good fit (g, g, g). There is only one such outcome.

Hence, the probability of all three new employees being a good fit is 1 out of 8 possible outcomes, which can be expressed as 1/8.

Therefore, if each outcome in the sample space is equally likely, the probability that all of the new employees will be a good fit is 1/8.

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After approximately 17.17 years, the amount due will reach $96,000 or more.

To determine the number of years it will take for the amount due to reach $96,000 or more, we can use the compound interest formula:

A = P(1 + r)^n

Where:

A is the final amount

P is the principal amount (loan)

r is the interest rate per period

n is the number of periods (years)

In this case, the principal amount is $42,000, the interest rate is 7.75% (or 0.0775 as a decimal), and we need to find the number of years, n, when the amount due reaches $96,000.

We can set up the equation as follows:

$96,000 = $42,000(1 + 0.0775)^n

Dividing both sides of the equation by $42,000:

1.0 = (1 + 0.0775)^n * ($96,000 / $42,000)

Simplifying:

1.0 = (1.0775)^n * 2.2857

To solve for n, we can take the logarithm of both sides of the equation:

log(1.0) = log((1.0775)^n * 2.2857)

Since log(1.0) is 0, we have:

0 = n * log(1.0775) + log(2.2857)

Solving for n:

n = -log(2.2857) / log(1.0775)

Using a calculator, we find:

n ≈ 17.17

Therefore, after approximately 17.17 years, the amount due will reach $96,000 or more.

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The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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The statement that in a group of 20 people and friendship is mutual, there must exist two people who have the same number of friends is, True.

A general rule, called the pigeonhole principle, is that if there are more pigeons than holes , there should be at least one hole with at least two pigeons. The pigeonhole principle guarantees what will happen in the worst case.

We have a group of 20 people , so N = 20

Each person can have 0 to 19 friends. But if someone has 0 friends, then no one can have 19 friends and similarly you cannot have 19 friends and no friends. So, there are only 19 options for the number of friends and 20 people. By the Pigeonhole Principle, our assumption that distinct friends is not true has been proven false, because according to the principle of withdrawal, there are at least two people who have the same number of friends as he, thus it must be indeed true. Hence, the number of possibilities for the number of friends the 20 people at the party have must be less than 20. Hence two people at the party have the same number of friends at the party.

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In this problem, the distributive property is very important, but there is another thing that we can look at to make this much easier. We notice that the terms on the left are being multiplied by 6. We can rewrite the right side so that it is also a multiple of 6:

6(3c - 5d + 6) = 6(1)

Now, we can divide both sides by 6, and we get:

6(3c - 5d + 6) = 6(1)

3c - 5d + 6 = 1

3c - 5d = -5

Hope this helps :)

Answers:

This can be found by using the combinations and permutations formulas.

Combinations being the C equation and Permutations being the P equation.

21: \(C_{6}(21) = \left[\begin{array}{ccc}21\\6\end{array}\right] =\frac{21!}{6!(21-6)!}=\frac{21*20*19*18*17*16}{6*5*4*3*2*1} = 54264\)

answer: 54264

22: \(C_{2}(n) = \left[\begin{array}{ccc}n\\2\end{array}\right] =\frac{n!}{2!(n-2)!}= answer\)

answers:

  Art: 15

  Writing: 21

  Technology:  28

23: \(P(n,r)=\frac{6!}{(6-6)!}=720\)

answer: 720

Explanation:

A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

Answer:

930 is equivalent to 310 because 9 x 10 = 30 x 3 = 90. 1240 is equivalent to 310 because 12 x 10 = 40 x 3 = 120.

It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.

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The Bode, amplitude, and phase diagrams for the transfer function H(s) = 100(1 + 100s) / [(1 + s*10^-1)(1 + 10s)] can be sketched.

The sketching of Bode, amplitude, and phase diagrams for a transfer function involves a systematic procedure. For the given transfer function H(s) = 100(1 + 100s) / [(1 + s*10^-1)(1 + 10s)], the following steps can be followed to construct the diagrams.

Determine the Break Frequencies: Find the poles and zeros of the transfer function. The break frequencies are the frequencies at which the poles and zeros have their maximum effect on the transfer function. In this case, there are two poles at 1 and 10, and no zeros. So, the break frequencies are ωb1 = 1 rad/s and ωb2 = 10 rad/s.

Calculate the Magnitude: Evaluate the magnitude of the transfer function at low and high frequencies, as well as at the break frequencies. At low frequencies (ω << ωb1), the transfer function approaches 100. At high frequencies (ω >> ωb2), the transfer function approaches 0. At the break frequencies, the magnitude can be calculated using the equation |H(jωb)| = |H(1)| / √2 = 100 / √2.

Plot the Amplitude Diagram: Sketch the amplitude diagram on a logarithmic scale. Start from the lowest frequency, and plot the magnitude at each frequency point using the calculated values. Connect the points smoothly. The diagram will show a flat response at low frequencies, a roll-off near the break frequencies, and a decreasing response at high frequencies.

Determine the Phase Shift: Evaluate the phase shift introduced by the transfer function at low and high frequencies, as well as at the break frequencies. At low frequencies, the phase shift is close to 0°. At high frequencies, the phase shift is close to -180°. At the break frequencies, the phase shift can be calculated using the equation arg(H(jωb)) = -45°.

Plot the Phase Diagram: Sketch the phase diagram on a logarithmic scale. Start from the lowest frequency, and plot the phase shift at each frequency point using the calculated values. Connect the points smoothly. The diagram will show a minimal phase shift at low frequencies, a sharp change near the break frequencies, and a phase shift of -180° at high frequencies.

By following these steps, the Bode, amplitude, and phase diagrams for the given transfer function can be accurately sketched, providing a visual representation of its frequency response characteristics.

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Answer:

9

Step-by-step explanation:

f(x)=2x+3

f(3) = 2(3) + 3

= 6 + 3 = 9

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

The coordinates of point A = (-5, -4),

The coordinates of the point B = (-3, 3)

Let the point at the distance 3/4 from A to B = P

The coordinates of point 3/4 from A to B = P

At the x-coordinate, the distance from B to A is =  -3-(-5) = 2 units.

At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.

Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)

                                            P = (-5 + (3/4×(2), -4 + 3/4×(7))

                                            P = (-3.5, 1.25)

Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).

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The complete question is -

What are the coordinates of the point 3/4 of the way from A to B?