You have 6/7 cup of frosting to frost the cupcakes you made. If each cupcake requires 1/14 frosting ,how many cupcakes do you frost?

Answer:

-3

Step-by-step explanation:

find absolute values.

-7 + 4

-3

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Answer: The answer is -3

Answer:

3     : 1

Step-by-step explanation:

1 girl for 3 boys

We want the ratio of boys to girls

boys: girls

3     : 1

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

slope = 1/2

Step-by-step explanation:

slope = y2-y1 / x2-x1

1 - -2 / 4 - -2 = 3/6 = 1/2

or think of it this way. for every 1 step up you take 2 steps to the right to stay on the line. 1/2

The required center of the circle's equation is (h, k) = (-4, 1), and the radius, r = 7.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

To convert the equation to standard form, we complete the square for both x and y. To do this, we add and subtract the square of half the coefficient of the x term and the y term, respectively:

x² + 8x + (8/2)² - 2y + 2(8/2)(1/2)y - 2y + (2/2)² = 32

Simplifying, we get:

x² + 8x + 16 - 2y + y + 1 = 32

Now we can combine like terms:

x² + 8x + 16 + y - 2y + 1 = 32

x² + 8x + y + 17 = 32 + 17

x² + 8x + y = 49

Now we have the equation in standard form:

(x + 4)² + (y - 1)² = 49

The center of the equation is (h, k) = (-4, 1), and the radius, r = 7.

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The solution to the system of equations in parameterized form is:

x = (6/13)z - 4/13

y = (10/13)z + 1/13

z = t (where t is a parameter representing the free variable)

To solve the system of equations:

x = 2z - 4y

4x + 3y = -2z + 1

We can use the method of substitution or elimination. Let's use the method of substitution.

From the first equation, we can express x in terms of y and z:

x = 2z - 4y

Now, we substitute this expression for x into the second equation:

4(2z - 4y) + 3y = -2z + 1

Simplifying the equation:

8z - 16y + 3y = -2z + 1

Combining like terms:

8z - 13y = -2z + 1

Isolating the variable y:

13y = 10z + 1

Dividing both sides by 13:

y = (10/13)z + 1/13

Now, we can express x in terms of z and y:

x = 2z - 4y

Substituting the expression for y:

x = 2z - 4[(10/13)z + 1/13]

Simplifying:

x = 2z - (40/13)z - 4/13

Combining like terms:

x = (6/13)z - 4/13

Therefore, the solution to the system of equations in parameterized form is:

x = (6/13)z - 4/13

y = (10/13)z + 1/13

z = t (where t is a parameter representing the free variable)

In this form, the values of x, y, and z can be determined for any given value of t.

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Answer:

D. undefined

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

A horizontal line has a slope of 0.

A vertical line has a undefined slope.

Any other line will have a slope of some number.

Answer:

D

Step-by-step explanation:

The slope of a line represents  the number of units a line rises or falls vertically for each unit of horizontal change from left to right.

1) A line with positive slope (m > 0) rises from left to right.

2) A line with negative slope (m < 0) falls from left to right.

3) A line with zero slope is horizontal (parallel to x-axis).

4) A line with undefined slope is vertical (parallel to y-axis).

Ans: The line is parallel to y-axis. So, the slope is undefined

Answer:

26

Step-by-step explanation:

just add a few points

The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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Answer:

x = 7

Step-by-step explanation:

Given:

∠DEF = 117°

∠DEG = (12x + 1)°

∠GEF = (5x - 3)°

Find:

value of x

Computation:

∠DEF = ∠DEG + ∠GEF

117° = (12x + 1)° + (5x - 3)°

117° = 17 x - 2

x = 7

Answer:

m = 8.2 × 10³ grams

Step-by-step explanation:

Given that,

The weight of a monkey = 8.2 kilograms.

We need to convert its mass from kilograms to grams.

We know that,

1 kg = 1000 grams

or

1 kg = 10³ grams

In 8.2 kg,

8.2 kg = 8.2 × 10³ grams

Hence, the weight of the monkey is equal to 8.2 × 10³ grams.

this integral does not have a simple closed-form expression, and you may need to use numerical methods or special functions to evaluate it.

To evaluate the integral (x^2)/y^(4/3) ds along the curve C, where x=t^2 and y=t^3, for -3≤t≤3, follow these steps:
Parametrize the curve C
Given the curve x=t^2 and y=t^3, the parametric representation of the curve is R(t) = (t^2, t^3), where -3≤t≤3.
Calculate the derivative of R(t)
R'(t) = (2t, 3t^2).
Compute the magnitude of R'(t)
| R'(t) | = √( (2t)^2 + (3t^2)^2 ) = √( 4t^2 + 9t^4 ) = t√( 4 + 9t^2 ).
Substitute x and y in the integral
Given the integral (x^2)/y^(4/3) ds, substitute x=t^2 and y=t^3 to get the expression (t^2)^2/(t^3)^(4/3).
Simplify the expression
Simplify the expression to get (t^4)/(t^4) = 1.
Evaluate the integral
Now, evaluate the integral ∫(1 * |R'(t)|) dt from t=-3 to t=3:
∫[1 * t√( 4 + 9t^2 )] dt from t=-3 to t=3.

Solve the integral
Unfortunately, However, it's essential to follow these steps to set up the problem correctly and understand the process of evaluating an integral along a curve parametrized by a variable t.

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Answer:

A = 8 and B = -2 and the equation is:

8x - 2y = -24

Step-by-step explanation:

Line intercepts

Any non-horizontal and non-vertical line has two intercepts: The y-intercept is the point where the line crosses the y-axis, and the x-intercept is the point where the line crosses the x-axis, also called the zero or root.

We are given the equation:

Ax+By=-24

The x-intercept is (-3,0). Substituting the values of x and y:

A(-3)+B(0)=-24

Operating:

-3A = -24

Dividing by -3:

A = -24 / (-3) = 8

A = 8

The y-intercept is (0,12). Substituting and using the just-found value of A

8(0)+B(12)=-24

Operating:

12B = -24

Solving:

B = -2

Thus, A = 8 and B = -2 and the equation is:

8x - 2y = -24

The correct choice is (e) All of the above is a property for all LP problems.

All Linear Programming (LP) problems have a linear objective function that is to be maximized or minimized (property a), a set of linear constraints (property b), and decision variables (property c). Additionally, LP problems require variables that are all restricted to nonnegative values (property d). Therefore, all of the given properties are true for all LP problems, making option (e) the correct choice.

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Answer:

It would be 2. 6x - 1 = 1 + x

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

-2/25

Step-by-step explanation:

Use the slope formula: rise/run to find the slope

Answer:

slope = - \(\frac{2}{25}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 20, 18) and (x₂, y₂ ) = (30, 14)

m = \(\frac{14-18}{30-(-20)}\) = \(\frac{-4}{30+20}\) = \(\frac{-4}{50}\) = - \(\frac{2}{25}\)

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

The critical points are (2,1) and (0,0). Given, z = 3x² - xy + 2y² - 4x - 7y + 12.1. Find the critical points at which the function may be optimized.

To find the critical points, we need to solve the following system of equations: ∂z/∂x = 0, ∂z/∂y = 0∂z/∂x = 6x - y - 4 = 0∂z/∂y = -x + 4y - 7 = 0By solving these equations, we get two critical points: (2,1) and (0,0).2. Determine whether at the computed points, the function takes on its maximum or minimum value.

To determine whether each critical point is a maximum, minimum, or saddle point, we need to compute the second partial derivatives of z: ∂²z/∂x² = 6, ∂²z/∂y² = 4, ∂²z/∂x∂y = -1At the point (2,1), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.At the point (0,0), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.Therefore, the function z = 3x² - xy + 2y² - 4x - 7y + 12 is optimized at (2,1), where the minimum value is z = 3(2)² - (2)(1) + 2(1)² - 4(2) - 7(1) + 12 = -10.

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Answer:

it would be 3/7

Step-by-step explanation:

3+4=7 3 cousins out of the seven are girls

Answer:it would be 3/7

Step-by-step explanation:

Answer:

2.64cm

Step-by-step explanation:

A = π r^2

5.5 = π r^2

1.75 = r^2

r = 1.32

Diameter is then 2(1.32) = 2.64

Answer:

2.65 cm to the nearest hundredth

Step-by-step explanation:

A = πr^2 = 5.5

r^2 = 5.5/ π = 1.5707

r = 1.3231

Diameter = 2 * r

= 2.6462.

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

the mode number of hours is 4 because is the hour spent mostly on the computer

therefore the mode number of hours is 4 hours

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

-6 is the y intercept

7 is the slope

y=mx+b

The wavelength of an atom is 3.28× 10−11 m when it is travelling at its root-mean-square speed at 20 °C. Decide on the atom. Consequently, M = 2 and the gas's molar mass is 2 kgmol−1 .

Radio waves, light waves, and infrared (heat) waves are examples of electromagnetic radiation that flow through space in distinct patterns. Every wave is a specific size and shape.

calculation

urms=  \(\sqrt{\frac{3RT}{M} }\)

and

λ=h/murms

⟹urms=h/mλ⟹

 \(\sqrt{\frac{3RT}{M} }\)=h/mλ

72.2 = 148.17 / M

M = 148.17/72 ≈ 2

Consequently, M = 2 and the gas's molar mass is 2  kgmol−1. A gas with a molecular mass of 2 kgmol-1, however, does not exist.

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Answer:

20. from y-axis,

(0,3)

from x-axis,

(8,0)

from, m = (y-y1) /(x-x1)

m = (0-3)/(8-0)

m = -3/8

y-y1 = m(x-x1)

y-0 = -3/8(x-8)

y = -3/8x + 3

21. from x-axis,

x = -2

x = k

where, k is any real number.

equation of the line is x = -2.

22. from y-axis,

y = -3

y = k

equation of the line is y = -3.

To find the probability of picking 3 queens from the stack, we need to first find the total number of ways to pick 3 cards from the stack of 12. This is represented by the combination formula:

nCr = n! / (r! * (n-r)!)
where n is the total number of cards in the stack (12) and r is the number of cards we want to pick (3).
nCr = 12! / (3! * (12-3)!) = 220
So, there are 220 possible ways to pick 3 cards from the stack.
Now, we need to find the number of ways to pick 3 queens from the stack. Since there are 4 queens in the stack, we can use the combination formula again:
nCr = n! / (r! * (n-r)!)

where n is the number of queens in the stack (4) and r is the number of queens we want to pick (3).
nCr = 4! / (3! * (4-3)!) = 4
So, there are 4 possible ways to pick 3 queens from the stack.
Finally, we can find the probability of picking 3 queens by dividing the number of ways to pick 3 queens by the total number of ways to pick 3 cards:

P(3 queens) = 4 / 220 = 0.018 or approximately 1.8%.
To answer your question, let's calculate the probability of picking 3 queens from the stack of 12 cards containing 4 aces, 4 kings, and 4 queens.
The total number of ways to pick 3 cards from the stack of 12 cards is represented by the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of cards and k is the number of cards chosen. In this case, n=12 and k=3.

C(12, 3) = 12! / (3!(12-3)!) = 12! / (3!9!) = (12 × 11 × 10) / (3 × 2 × 1) = 220

calculate the number of ways to pick 3 queens from the 4 queens available:
C(4, 3) = 4! / (3!(4-3)!) = 4! / (3!1!) = (4 × 3 × 2) / (3 × 2 × 1) = 4
Finally, divide the number of ways to pick 3 queens by the total number of ways to pick 3 cards to find the probability:
Probability = (Number of ways to pick 3 queens) / (Total number of ways to pick 3 cards) = 4 / 220 = 1/55 ≈ 0.0182
So, the probability of picking 3 queens from the stack is approximately 0.0182 or 1/55.

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Answer:

y = 1.4m + 7.4

Step-by-step explanation:

no.......................

Answer:

25 ft

Step-by-step explanation:

8 yd = 24 ft

11 in < 1 ft

8 yd < 25 ft

Answer:

$0.52 or 52 cents

Step-by-step explanation:

Ratios:

\(\frac{25}{13} =\frac{1}{x} \\\\25x=13\\x=0.52\)