A restaurant offers 3 starters, 5 mains and 4 desserts. How many possible combinations of 3 courses are there?​

Answer:

1) NOT Equivalent

2) Equivalent

3) NOT Equivalent

Step-by-step explanation:

1) 3(x+3)= 3x+9

2) 6(y+1)=6y+6

3)x(x+4)=x²+4x

The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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Answer:

c=3•6 between xy andxz is7•2

The standard form of 5004200 is \(5.0042\times10^6\).

The standard form of a number is a way of writing the numbers in a form that follows a certain rule.

According to the given question.

We have a number 5004200.

The standard form of 5004200 is given by

\(5.0042\times10^6\)

Hence, the standard form of 5004200 is \(5.0042\times10^6\).

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Answer:The standard from of a number is introduced to avoid the difficulity of reading the large number

Step-by-step explanation:The given number is 50042000

5 million,4 thousands and 2 hundred in the standard form 5,004,200

Answer:

3.5

Step-by-step explanation:

The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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384,000 bacteria would be present at the end of 7 hours if it doubles itself every hour.

Initial number of bacteria=3000

Number of bacteria at the end = initial number of bacteria * (base)ⁿ

where, n= number of hours

Number of bacteria at the end=3000*2⁷

                                                    =3000*128

                                                     =384,000

Therefore, there will be 384000 bacteria at the end of seven hour if the bacteria doubles itself every hour.

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Answer: the number of blues is 42.

the number of whites is 30.

Step-by-step explanation: Let there be 'x' blues and 'y' whites then

the ratio of blues to white is 7 to 5:

x : y = 7 : 5

the number of blues exceeds the number of whites by 12

x = 12 + y

the solutions of the system of equations

x/y = 7/5

x = 12 + y

are

x = 42 blues

y = 30 whites

Answer:

(2, 1) and (4, 2): \(\frac{1}{2}\)

(-4, 5) and (-3, -7): \(-12\)

Step-by-step explanation:

Hello! Let's help you with that problem there!

So we know that in a slope intercept form, it is depicted as \(y=mx+b\). There are two ways to essentially find m, which is slope in this case. The first method is the \(\frac{rise}{run}\) method. This is typically used when you have a graph to look off from and it's just a matter of counting the displacement from one point to another.

However, there is another way to find the slope given 2 points and that is what we are going to do here, since we have no graph to reference and have all the relevant information to find the slope using this formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

With this formula, we can plug in the coordinate values and solve for the slope!

(2, 1) and (4, 2):

\(m=\frac{2-1}{4-2}\)

\(m=\frac{1}{2}\)

Therefore, the slope of these points is \(m=\frac{1}{2}\)

(-4, 5) and (-3, -7):

\(m=\frac{-7-5}{-3-(-4)}\)

\(m=\frac{-12}{1}\)

\(m=-12\)

Therefore, the slope of these points is \(m=\frac{-12}{1}\) or \(m=-12\)

Answer:

12 cups

Step-by-step explanation:

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

3/4

Step-by-step explanation:

1 1/2 can be expressed as an improper fraction 3/2

hence

1 1/2 ÷ 2

= 3/2 ÷ 2

= 3/2 x 1/2

= 3/4

The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

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Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

push ups Step-by-step explanation:

Answer:

I answered

Step-by-step explanation:

SOLUTION:

Step 1:

In this question, we are given the following:

A pipefitter must connect a pipeline to a tank as shown in the figure.

The run from the pipeline to the tank is 64ft 6in., while the set (rise) is 35ft 9in.

Step 2:

A. How long is the connection?

Converting 64 feet 6 inches to inches, we have that:

Also, we have 35 feet 9 inches, we have that:

Using Pythagoras' Theorem, we have that:

The length of the connection = 73 feet 9 inches

Step 3:

Will the pipe fitter be able to use standard pipe fittings?

From the diagram, we can see that:

The width of a rectangular piece is 28 and the length is 58.

let us consider

w=width

w+30=length

After cutting:

w-12 =width

w + 30-12=length, or w + 18

Now to calculate the length and width consider the area of a rectangle:

Area of a rectangle=w*l

substitute the values in the above formula:

(w-12)(w+18)(6) = 2400

(w-12 )(w+18) = 400

w²+6w-216 = 400

w²+6w-616 = 0

(w + 28)(w - 22) = 0

The roots of the equation are {-22, 28}.

to find the length just substitute in the length formula:

length=28+30

length=58.

The width is 28 and the length is 58.

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Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:

no solutions

Step-by-step explanation:

-8x + x + 15 = -7x + 12

Combine terms

-8x + x + 15 = -7x + 12

-7x +15 = -7x +12

Add 7x to each side

15 = 12

This is never true so there are no solutions

Steps to solve:

-8x + x + 15 = -7x + 12

~Combine like terms

-7x + 15 = -7x + 12

~Add 7x to both sides

-7x + 7x + 15 = -7x + 7x + 12

~Simplify

15 = 12

There are no solutions.

Best of Luck!

The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.

If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.

As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.

Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.

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The equivalent function to the expression (5x - 4 + 2x + 8) is 7x + 4.

An expression in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). For example -

f(x) = 4x + 6

Given is the function -

5x - 4 + 2x + 8

We have -

5x - 4 + 2x + 8

Solving, we get -

7x - 4 + 8

7x + 4

Therefore, the equivalent function to the expression (5x - 4 + 2x + 8) is 7x + 4.

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The area of the rectangle is (343/48)sqrt(3), or approximately 6.177 square inches.

To solve this problem, we first need to draw a diagram. Let ABC be the triangle, with altitude AD of length 7 inches. Let EF be the rectangle inscribed in the triangle, with one side on AB. Let G be the point where EF meets AD. Let AG have length x, and GD have length y.

Since EF is a rectangle, its opposite sides are parallel. Therefore, EF is parallel to BC. Furthermore, EF and BC have the same length, since EF is inscribed in the triangle. Let the length of EF (and BC) be z.

Since AG and GD are the two parts of AD that EF intersects, we have x+y=7.

Since EF is half the length of BC, we have z=0.5(AB).

The area of the rectangle is zy. Using similar triangles, we can see that (x/z) = (y/(7-z)). Solving this equation for y, we get y=(7z)/(2z+x). Substituting this expression for y into the expression for the area of the rectangle, we get:

Area of rectangle = zy =

\((7z^2)/(2z+x)\)

To find the value of z, we use the fact that z=0.5(AB). Using the Pythagorean theorem in triangle ABC, we have:

\(AB^2 = AD^2 + BD^2 = 7^2 + (2z)^2 \)

\(= 49 + 4z^2\)

Using the fact that z=0.5(AB), we can solve for z:

\(z^2 = (AB^2)/16\)

\(

= [(49 + 4z^2)/16]\)

Multiplying both sides by 16 and rearranging, we get:

\(12z^2 = 49\)

\(z^2 = 49/12\)

\(z = (7/2) \sqrt{} (3)/2\)

Now we can substitute this value of z into the expression for the area of the rectangle:

Area of rectangle =

\([(7/2) \sqrt{} (3)/2][(49/3+4(49/48))]\)

\( = (343/48) \sqrt{} (3)\)

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A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless.

The therapeutic response that the nurse should identify in the client after a back massage includes relaxing of facial muscles and the pulse remaining within the expected range.
Massage is a fundamental nursing measure that is often utilized as part of palliative care for patients. The purpose of back massage is to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nursing assessment of the patient before and after the massage is essential to determine its effectiveness as a therapeutic intervention for the patient.
When providing back massage as a palliative care measure to an unconscious, grimacing, and restless client, the nurse should identify several therapeutic responses as follows;
The shoulders droop: The nurse should expect the shoulders of the client to relax during massage therapy. If this occurs, it is a sign that the patient is experiencing relaxation and tension relief.
The facial muscles relax: Relaxation of the facial muscles is a common therapeutic response during back massage. The nurse should observe the patient's face for any signs of relaxation, which may include softening of facial lines, eyelids drooping, or a general expression of peacefulness.
The respiratory rate (RR) decreases: The nurse should expect the client's respiratory rate to decrease during a back massage. This is because relaxation stimulates the parasympathetic nervous system, resulting in decreased respiratory rate, heart rate, and blood pressure.
The pulse is within the expected range: The nurse should expect the client's pulse to remain within the expected range during a back massage. A normal pulse rate is between 60-100 beats per minute for adults. If the pulse remains within this range, it is a sign that the patient is responding positively to the massage therapy.

In conclusion, providing back massage as a palliative care measure to an unconscious, grimacing, and restless client can help to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nurse should identify therapeutic responses in the patient during the massage therapy, which may include relaxation of the shoulders, facial muscles, decreased respiratory rate, and pulse remaining within the expected range.

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Answer:

The median is 13!

Step-by-step explanation:

14

you write the numbers in numerical order, then count inwards.

Answer:

B

Step-by-step explanation:

36 ÷ 3 = 12 is basically the division version of the original equation. None of the other equations equal the same answer so B is the correct option.

36 ÷ 3 = 12 is equivalent to 3 • 12 = 36

The solution to the expression ⁴√(-15/16) is (-15/16)^1/4

From the question, we have the following parameters that can be used in our computation:

⁴√(-15/16)

The above expression means that we calculate the 4th root of -15/16

-15 and 16 do not have perfect fourth roots

This means that the expression can only be rewritten as

(-15/16)^1/4

It cannot be evaluated

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