Complete the equivalent ratio. How many ounces are in 2 cups?

StartFraction 48 ounces Over 6 cups EndFraction = StartFraction question mark ounces Over 2 cups EndFraction

The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

According to the statement, we must find in what conditions a given expression may be a solution of an ordinary differential equation. Then, first and second derivatives of the equation are:

y' = α · cos x - β · sin x                 (1)

y'' = - α · sin x - β · cos x              (2)

Then, we substitute on the ordinary differential equation:

(- α · sin x - β · cos x) + (α · cos x - β · sin x) = 0

And by algebraic handling we simplify the resulting expression:

- (α + β) · sin x + (α - β) · cos x = 0

Where each coefficient represents a constant of a linear combination:

α + β = 0

α - β = 0

Then, the solution of the system of linear equations is (α, β) = (0, 0). The expression y = α · sin x + β · cos x is a solution of the ordinary differential equations if and only if (α, β) = (0, 0).

The statement is incomplete and complete form cannot be found, then we decided to create a new statement:

Please prove that y = α · sin x + β · cos x is the solution of the differential equation d²y / dx² + dy /dx = 0 where the following condition is observed, if and only if α = β = 0.

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The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Parent functions are the basic function that represents the entire family of that function family

The function is given as;

g(x) = 3cos (x + 180°) + 1

As a general rule, the parent function of any function is the basic equation of the function family

The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

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Answer:

2x+6-(x^2+6x+9)*pi

Step-by-step explanation:

2*(x+3) - (x+3)^2*pi

2x+6-(x^2+6x+9)*pi

um I think there are answer choices so I don't know if I have to keep going but that should be right

Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]

[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]

Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]

[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]

Answer:

.06

Step-by-step explanation:

add all the 4 values listed, plus the .06

divide by 5

you get -.01

:)

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

In this problem we need to find a sinusoidal expression that models the curve seen in the picture. The most typical sinusoidal model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

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The mean of the sample from number of patients treated at Dr. Frank's dentist office each day for ten days is 8.2

Given data:

13, 9, 7, 8, 2, 4, 22, 12, 5, 0.

Mean of the sample = Total number of patients treated / number of days

= (13 + 9 + 7 + 8 + 2 + 4 + 22 + 12 + 5 + 0) / 10

= 82/10

= 8.2

Therefore, the mean of the sample is 8.2

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The velocity vector of the given path  r(t) = (9cos2(t), 3t - t^3, 2t) is [tex]v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex].

According to the given question.

We have a path

r(t) = (9cos2(t), 3t - t^3, 2t)

So, the vector form of the above vector form can be written as

[tex]r(t) = 9cos2(t)\hat{i}+ (3t - t^{3} )\hat{j} + 2t\hat{k}[/tex]

As, we know that the rate of change of position of an object is called velocity vector.

Therefore, the velocity vector of the given path r(t) = (9cos2(t), 3t - t^3, 2t) is given by

[tex]v = \frac{d(r(t))}{dt}[/tex]

[tex]\implies v = \frac{d(9cost\hat{i}+(3t-t^{3})\hat{j}+2t\hat{k} }{dt}[/tex]

[tex]\implies v = \frac{d(9cost\hat{i})}{dt} +\frac{d(3t-t^{3})\hat{j} }{dt} +\frac{d(2t)}{d(t)}[/tex]

[tex]\implies v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex]

Hence, the velocity vector of the given path  r(t) = (9cos2(t), 3t - t^3, 2t) is [tex]v = 9sint\hat{i}+(3-3t^{2} )\hat{j} +2\hat{k}[/tex].

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Hi :)

We'll use sohcahtoa to solve this problem

[tex]\large\boxed{\boxed{\begin{tabular} {c|1} \sf{ Sohcahtoa} & \sf{Formulas} \\\cline{1-2} \\\ \sf{Soh} & \sf{Opp/hyp} \\\sf{Cah} & \sf{Adj/hyp} \\\sf{Toa} & \sf{Opp/adj} \end{tabular}}}}[/tex]

Thus

The function that equals [tex]\sf{\dfrac{7}{25}}[/tex] besides [tex]\sin B[/tex] is :

[tex]\tt{Learn\:More;Work\;Harder}[/tex]

:)

The element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

To find the element:

As we have given two matrices A and B:

Therefore, the element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.

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Answer:

4/3

Step-by-step explanation:

The slope is the change in y over the change in x.  

Your y's from the point given is -2, and 2.

Your x's from the point given is -1, and 2.  Since we want to know how much they have changed, we subtract these numbers to find the change.

Change in y's?  -2 - 2 or -4

Change in x's  -1 - 2 or -3

This gives me a slope of -4/-3  and a negative divided by a positive is a positive.

I could have found the change by going the opposite direction

Change in y's ? 2 - (-2) or 4

Change in x's? 2 - (-1) or 3

This gives me the same slope 4/3

Answer:

z = [tex]3\sqrt{13}[/tex]

Step-by-step explanation:

To find the measure of z we can use the Euclidian Theorem:

[tex]z^{2}[/tex] = 9(9+4) do the multiplication

[tex]z^{2}[/tex] = 117 find the root of both sides

z = [tex]3\sqrt{13}[/tex]

Condition (A) P(B/A) = y is true.

To find the true condition:

If two events are independent, then:

Use formulas for conditional probabilities:

For independent events these formulas will be:

Now in your case, Pr(A) = x and Pr(B) = y.

Therefore, condition (A) P(B/A) = y is true.

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The complete question is given below:

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?

a. P(B|A) = y

b. P(A|B) = y

c. P(B|A) = x

d. P(A and B) = x + y

e. P(A and B) = x/y

The total number of common tangents that can be drawn to the circles is 2.

A tangent serves as  line that touches the circle at a single point  whereby the  point where tangent meets the circle is the tangency.

A tangent to a circle can be described as the straight line  that touches the circle at only one point.

Therefore, from the definition, The total number of common tangents that can be drawn to the circles is 2.

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Type of model best fits the given situation linear.  Since it has a constant of +3 everyday.

What is a linear equation in math?

the membership of the local pta increases by 3 members a day for each day during the month of September.

Since it has a constant of +3 everyday.

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Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

Answer: B

Step-by-step explanation:

First, find the sum of the bottles, which is 6,235,168,989 which is not an estimate.

Rounding it to the nearest billion, the answer is 6,000,000,000 or B)

The smaller number is 28.

Answer:

Solution Given:

let the smaller number be a.

and larger number be a+4.

By question

a+(a+4)=60

a+a+4=60

2a=60-4

2a=56

a=[tex] \frac{56}{2} [/tex]

a=28

Answer:

y = 28

Step-by-step explanation:

Given variables:

Create two equations with the given information.

Equation 1

If one number is 4 more than another, then:

⇒ x = y + 4

(Remembering that x is the larger number and y is the smaller number).

Equation 2

If their sum is 60, then:

⇒ x + y = 60

Substitute Equation 1 into Equation 2 and solve for y:

⇒ (y + 4) + y = 60

⇒ 2y + 4 = 60

⇒ 2y + 4 -4 = 60 - 4

⇒ 2y ÷ 2 = 56 ÷ 2

⇒ y = 28

Therefore, the value of the smaller number (y) is 28.

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The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

The quadratic equation is given as:

y = -x^2 + 4x - 1

Differentiate the above quadratic equation.

This is done with respect to x by first derivative

So, we have:

y' = -2x + 4

Set the derivative to 0

-2x + 4 = 0

Subtract 4 from both sides of the equation

-2x + 4 - 4 = 0 - 4

Evaluate the difference in the above equation

-2x = -4

Divide both sides of the above equation by -2

x = 2

Rewrite as

h = 2

Substitute 2 for x in the equation y = -x^2 + 4x - 1

y = -2^2 + 4 *2 - 1

Evaluate the equation

y = 3

Rewrite as:

k = 3

A quadratic equation in vertex form is represented as:

y = a(x - h)^2 + k

So, we have:

y = a(x - 2)^2 + 3

In the equation y = -x^2 + 4x - 1, a = -1

So, we have:

y = -(x - 2)^2 + 3

Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3

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Answer:

Step-by-step explanation:

This is a question about naming parts of a polynomial. The attached image has more on the subject.

The word "degree" refers to the number of times a variable is a factor in a term. When there is only one variable, the degree of the term is the exponent of the variable. A missing exponent is understood to be 1. A missing variable is understood to have a degree of 0.

When there are two or more variables, the degree of the term is the sum of their exponents.

In some cases, we're only interested in the degree associated with a particular variable. For example, 7x²y³ is a 5th-degree term that is 2nd degree in x and 3rd degree in y.

A "quadratic" term is one that has degree 2, or one in which the variable of interest has degree 2.

In the given function definition, the term -3x² is the quadratic term.

A "linear" term is one that has degree 1.

In the given function definition, there is no linear term.

If you must identify one, it would be 0x, a degree-1 term with a coefficient of 0.

A "constant" term is one that has no variables, or no variables of interest. It has degree zero.

For example, in the expression x² +2ax +a², when we are concerned with the variable x, the a² term is called the "constant" term because it does not contain the variable x. The same expression could be considered as a quadratic in 'a', in which case the x² term would be the "constant term."

In the given function definition, the term 1 is the constant term.

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

[tex]f_x=8x[/tex]

[tex]f_y=4y[/tex]

[tex]g_x=3[/tex]

[tex]g_y=3[/tex]

Setting up the Lagrange multiplier equations:

[tex]f_x=\lambda g_x[/tex]

⇒ 8x = 3λ                                        .....................(1)

[tex]f_y=\lambda g_y[/tex]

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944                            ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

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Step-by-step explanation:

for TEXAS using permutation formula

we have:5!/1!1!1!1!1!=5!=120

for MEXICO using permutation formula

we have:6!/1!1!1!1!1!1!=6!=720

The inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.

Linear inequalities are inequalities that involves at least one linear algebraic expression, that is, a polynomial of degree 1.Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

Hence, the inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.

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Answer:

C

Step-by-step explanation:

answer is C

Answer: eleven equals five minus b

Step-by-step explanation:  11 = eleven. = equals equal. 5 = five.  - =  minus. b = b

Using the arrangements formula, it is found that there are 20,160 different groups of players of 2 players that the coach can make.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, all 8 players will play, hence considering the order, the number of ways is:

[tex]A_8 = 8! = 40320[/tex]

However, the position does not matter, as for example, João and Elisa would form the same pair as Elisa and João, hence the removing the order, the number of groups is:

40,320/2 = 20,160.

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Answer:

The answer is 28!!!

Step-by-step explanation:

Use the combinations formula:

[tex]C = \frac{n!}{r!(n-r)!}[/tex]

n = 8

r = 2

[tex]C = \frac{8!}{2!~*~6! } = 28\\[/tex]

I got it right! Look at the pic for proof.

Hope this helps!! :)

Using the combination formula, it is found that he can make 4 different stacks.

The order in which the balls are selected is not important, as stated in the problem. hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, he has four flavors, and will choose three of them for the stacks, hence the number of different stacks is given as follows:

[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]

He can make 4 different stacks.

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Answer:

Step-by-step explanation:

As per the same approach I answered in a similar problem:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate theRise/Run:

RISE = (-11 - 9) = -20

RUN = (3 - (-2)) = 5

Rise/Run, or slope, is = -20/5 or -4

I graphed this line and the two points (attached).

Answer:

-20/5 or -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

As per the same approach I answered in a similar problem:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate theRise/Run:

RISE = (-11 - 9) = -20

RUN = (3 - (-2)) = 5

Rise/Run, or slope, is = -20/5 or -4

Answer:

12.5< × < 18.9

Step-by-step explanation:

because you would use the pythagoras theorem which a² + b² = c² in this case c is the third side the unknown so to work this out do square root of ( 10² + 16²) which is 100 + 256 = 356 and the square root of 356 is 18.86 which rounds to 18.9 so the second answer is correct :)

i hope this helps pls ask if you need any more help :)

1) a) The volume of the sphere is 100 cubic centimeters.

b) The volume of the cylinder is 200 cubic centimeters.

2) The volume of the cone is 175 cubic centimeters.

Herein we have two case of submerging solids into recipients full of liquid, the volume of the objects is equal to the volume of the displaced liquid. Now we proceed to calculate the volume of each object:

Point 1 - Part A:

0.8 L - 0.5 L = 3 · x

0.3 = 3 · x

x = 0.1 L

x = 100 cm³

The volume of the sphere is 100 cubic centimeters.

Point 1 - Part B:

0.8 L - 0.5 L = x + y

0.3 = x + y

0.3 = 0.1 + y

y = 0.2 L

y = 200 cm³

The volume of the cylinder is 200 cubic centimeters.

Point 2:

350 mL = 2 · z

z = 175 mL

z = 175 cm³

The volume of the cone is 175 cubic centimeters.

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