Jada walks up to a tank of water than can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When
Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
How many minutes before Jada arrived was the water tank completely full?

There are 2 of each angles

BX cable is a type of metal-clad cable that is primarily used in indoor electrical wiring in commercial and industrial buildings.The total length of BX cable required is 259.125 feet.

To calculate how many feet of BX cable is required for the job, we need to add up the total lengths of the cable needed

Eight pieces of BX cable each 23 feet long equal

8 x 23 = 184 feet of cable needed.

Seven pieces of BX cable each 18 inches long equals 7 x 1.5 = 10.5

feet of cable needed.

Twelve pieces of BX cable each 24 inches long equals

12 x 2 = 24 feet of cable needed.

Twenty-five pieces of BX cable each 19.5 inches long equals

25 x 1.625 = 40.625 feet of cable needed.

To find the total length of BX cable required, we need to add up all these values:

184 + 10.5 + 24 + 40.625 = 259.125 feet of BX cable needed.

Therefore, the total length of BX cable required is 259.125 feet.

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Answer:

\(\sqrt{16}\sqrt{11}\)

Step-by-step explanation:

\(\sqrt{176}\implies \sqrt{16\cdot 11}\implies \sqrt{4^2\cdot 11}\implies 4\sqrt{11}\)

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Answer:

Step-by-step explanation:

The final volume is 0.1296  \(m^{3}\)

Let the length of the box, l = x

Therefore, according to the question, width, w = length/2 = x/2.

Height, h = 0.5 m (given in the question)

First, we have to calculate the area of the sides.

There are 6 sides in a cuboid (given that base is a rectangle)

Therefore,

Area, A = lw + wh + lh + lw + wh + lh = 2(lw + wh + lh)

Calculating,

A = 2(\(0.5x^{2}\) + 0.25x + 0.5x) = \(x^{2}\) + 1.5x

Given, Area of the 6 sides - Area of the base = 1.08m

 \(x^{2}\) + 1.5x - \(x^{2}\) = 1.08

1.5x = 1.08

x = 0.72

Therefore,

Volume = lwh = 0.5 * 0.72 * 0.72/2 = 0.1296 \(m^{3}\)

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

The Greatest common factor of 28 is 4.

Greatest Common Factor:

The largest number that is a factor of two or more numbers is called the greatest common divisor (GCF). The largest number (factor) by which it is divided, resulting in a natural number. Once all factors of the number are found, there are very few factors common to both. The largest number found with common divisors is called the greatest common divisor. GCF is also known as Highest Common Divisor (HCF).

The greatest common divisor of 28 is 4. The greatest common divisor of two numbers is the largest number that can be multiplied to get both numbers.

Factors of 28 - 1, 2, 4, 7, 14, 28

We can use division of both numbers by 4 to see if the answers have something in common. If so, we should check if a larger factor could have been used.

                             28/4 = 7

This was correct because 7  have no common divisors other than 1. The greatest common divisor of 28 is 4.

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Answer:

D

Step-by-step explanation:

it's D I don't have a full step by step

Answer: 4⋅(2+5) = 4 * (2+5) = 4 * 7 = 28

Step-by-step explanation:

Line 1 shows the original expression and Line 2 shows the expression is simplified by using the distributive property.

4⋅2 + 4⋅5 = 8+20 = 28

So the final result is 28.

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Answer: See graph below!

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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The graph of the given equation is attached to the solution.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given is an equation, 1.5x+2y = 3 we need to graph it,

So, first finding the coordinates,

1.5x+2y = 3,

Put x = 0

y = 1.5 [0, 1.5]

Put y = 0

x = 2 [2, 0]

Putting the coordinates on the graph and connect them, the line obtained will be the graph of the equation,

Since, the equation is linear the graph will be a straight line,

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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A percentage is a way to describe a part of a whole.  The most improbable simulation for this coin is heads are 9.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The most improbable simulation for this coin for heads is the frequency of heads coming up out of 20 which is far from the estimated frequency. Since out of these 20 times 75% of the times the head will come up. Therefore, the number of times the head will come up can be written as,

\(75\%\ of\ 20\\\\= \dfrac{75}{100} \times 20\\\\= 15\)

Now it is estimated that at least 15 times out of 20, the head will come up. Thus, the most improbable simulation for this coin is heads are 9.

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Answer:

A coin is biased to display heads 75% of the time. It is tossed 20 times, and the outcomes are recorded. The most improbable simulation for this coin is

9 heads.

Step-by-step explanation:

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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The coefficient of x^3 in the Taylor series for f about x = 0 is (C) -1/16.

To find the Taylor series for f, we can use the formula:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

First, we need to find the derivatives of f:

f(x) = 1/(2 + x)
f'(x) = -1/(2 + x)^2
f''(x) = 2/(2 + x)^3
f'''(x) = -6/(2 + x)^4

Next, we can plug in x = 0 to find the values of f and its derivatives at x = 0:

f(0) = 1/2
f'(0) = -1/4
f''(0) = 1/4
f'''(0) = -3/8

Now, we can plug these values into the Taylor series formula:

f(x) = 1/2 - 1/4x + 1/4x^2/2! - 3/8x^3/3! + ...

Simplifying the terms with factorials gives us:

f(x) = 1/2 - 1/4x + 1/8x^2 - 1/16x^3 + ...

Therefore, the coefficient of x^3 in the Taylor series for f about x = 0 is -1/16.

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\(x\\\)Answer:

\(x=-2\)

Step-by-step explanation:

\(x+4=2\)

we want to solve for \(x\) so we will let \(x\) alone and we will move \(4\) to the other side of the equation with an opposite sign ( if it was positive then it will move to the other side with a negative sign, and the opposite is correct ):

\(x=2-4\)

solve :

\(x=2-4 \\x=-2\)\(x=2-4\)

\(x=-2\)

now \(x\) is equal to \(-2\)

Answer:

x = -2

Step-by-step explanation:

x + 4 = 2

x + 4 - 4 = 2 - 4

x = - 2

A = PDP^T, where P is the orthogonal matrix and D is the diagonal matrix.

To find an orthogonal matrix P and a diagonal matrix D such that A = PDP^T for the given symmetric matrix A, we need to find the eigenvalues and eigenvectors of A.

First, let's find the eigenvalues by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.

A - λI = 211 - λ, 121, 112

121, 121 - λ, 112

112, 112, 112 - λ

Expanding the determinant, we get:

(211 - λ)((121 - λ)(112 - λ) - 112(112)) - 121(121(112 - λ) - 112(112)) + 112(121(112) - 112(121 - λ)) = 0

Simplifying the equation, we find that the eigenvalues are λ = 1, λ = 1, and λ = 333.

Next, we find the eigenvectors corresponding to each eigenvalue.

For λ = 1, the eigenvector is [-1, 2, -1].

For λ = 1, the eigenvector is [1, 0, -1].

For λ = 333, the eigenvector is [1, 4, 1].

Now, we can construct the orthogonal matrix P using the eigenvectors as its columns:

P = [[-1, 1, 1],

[2, 0, 4],

[-1, -1, 1]]

And the diagonal matrix D using the eigenvalues on the diagonal:

D = [[1, 0, 0],

[0, 1, 0],

[0, 0, 333]]

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For Samantha, 2 tick marks east is 120 units east because 1 tick is 60 units.

For Ryu, 8 tick marks west is 480 units west because 1 tick is 60 units.

They are walking to form a line. Just add their distances from 0.

120 + 480 = 600.

--------------------------0----------------------------

Ryu: 480                         Samantha: 120

         480              +             120           =    600.

600 units, or feet.

Répondre:

Benoit a 10 ans

Explication étape par étape :

Laisser :

Âge de Thomas = x

Benoit age = y

il y a 5 ans :

x - 5 = 5 (y - 5)

x - 5 = 5y - 25 - - (1)

Aujourd'hui :

x = 3y - - (2)

Mettez x = 3y dans (1)

3 ans - 5 = 5 ans - 25

Recueillir des termes similaires

3 ans - 5 ans = - 25 + 5

-2a = - 20

Diviser les deux côtés par - 2

y = 10

Answer: Undefined

Step-by-step explanation:

Sec 3\(\pi\)/2 = 1/Cos(3\(\pi\)/2) = 1/0 = Undefined

Answer:

38

Step-by-step explanation:

Make a chart

20 =  4850

?   = 9215

9215 / 4850 = 1.9

20 x 1.9 = 38

I don't know it this is right but I hope it helps

Answer:

Equation: 20 / 4850 = x / 9215  Answer: 37.99 minutes

Step-by-step explanation:

(The backslashes are representing a divide symbol, not a fraction)

I don't know what kind of equation you need but the equation I wrote is the one I used to solve this. You must divide the amount of time it took to run the distance which is 20 minutes by the yards jogged which is 4850. That will give you the amount of time it took the athlete to jog one yard which you should then multiply by 9215 yards to find out how much time would be needed to cover that distance. In the equation, if you replace the "x" with the answer (37.99), the equations should be equal.

(I'm really sorry if this doesn't make sense or it's confusing but I hope it helped)

Answer:10 cashiers and 20 baggers

Step-by-step explanation:

1) We can visualize that regular octagon inscribed this way:

2) We can decompose that regular octagon as isosceles triangles since this the radius is known

But note that we only have the length of the radius:

3) So let's find the base of the triangle, note that the interior angle is:

Finding the height:

Now, let's find the area of one triangle and then multiply by 8 to get the area of the whole Octagon:

Answer:

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number)

The events are independent (the outcome of flipping thee coin has no effect on the outcome of rolling the die).⇒ P(head and an even number) = P(head) × P(even number)

P(even number)Assuming a fair coin and a fair die:

P(even number)Assuming a fair coin and a fair die:P(head)

P(even number)Assuming a fair coin and a fair die:P(head) =50%

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number)

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50%

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number)

P(even number)Assuming a fair coin and a fair die:P(head) =50%P(even number) =50% (since half the numbers on a die are even).P(head and even number) =50%×50%=25%

A. The given differential equation is an ODE (ordinary differential equation), as it contains only one independent variable, x.

C. The given differential equation is a first-order differential equation because it involves only the first derivative of the function y.

F. The given differential equation is a linear differential equation because the dependent variable y and its derivative appear only in the first degree, and no products or powers of y and its derivative appear.

G. The given differential equation is a candidate for integrating factors because it is a linear differential equation of first order.

H. The given differential equation is not separable, since it cannot be written in the form f(y)dy = g(x)dx.

I. The given differential equation is not homogeneous because it does not satisfy the condition of homogeneity, which requires that all terms of the equation have the same degree in y and its derivatives.

J. The given differential equation is not autonomous, as it explicitly depends on the independent variable x.

In summary, the given differential equation is a first-order linear ODE that is a candidate for integrating factors. It is not separable, not homogeneous, and not autonomous.

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according to the question the limit is 2i + 1.

We can use L'Hopital's rule to evaluate this limit:

lim t → 0 e^4ti sin(2t) / (2t e^(-3t))

Taking the derivative of the numerator and denominator with respect to t, we get:

lim t → 0 [4i e^4ti sin(2t) + 2 e^4ti cos(2t)] / (2 e^(-3t) - 3t e^(-3t))

Plugging in t = 0, we get:

[4i + 2] / 2 = 2i + 1

what is L'Hopital's rule?

L'Hopital's rule is a mathematical theorem that provides a method to evaluate limits of indeterminate forms, which are expressions that cannot be directly evaluated by substitution. The rule states that if the limit of a quotient of two functions is an indeterminate form of type 0/0 or ∞/∞, then under certain conditions, the limit of the quotient of the derivatives of the numerator and denominator as x approaches the limit point is equal to the original limit.

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Answer:

1=n

Step-by-step explanation:

Step 1- Distribute into the parenthesis.

7(3)+5(3)n= 6n+1(6)+4(6)n

Step 2- Multiply

21+15n= 6n+6+24n

Step 3- Add common variables to simplify.

21+15n= (24n+6n)+6

21+15n= 30n+6

Step 4- Subtract the smallest variable to both sides.

21+15n= 30n+6

   -15n  -15n

21= 15n+6

Step 5- Subtract 6 to both sides.

21= 15n+6

-6           -6

15= 15n

Step 6- Divide both sides by 15.

15= 15n

15   15

1=n