A large grocery store has 300 cases of canned vegetables in the storeroom. During the past month, the store removed 86 cases, 51 cases, 54 cases, and 78 cases to put on the shelves. Also, the store received two lots of 59 cases each. How many cases are in the storeroom now?

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:

P (3, - 2 )

Step-by-step explanation:

Solve the equations simultaneously for point of intersection P

5x + 3y = 9 → (1)

7x - 2y = 25 → (2)

Multiplying (1) by 2 and (2) by 3 and adding will eliminate the y- term

10x + 6y = 18 → (3)

21x - 6y = 75 → (4)

add (3) and (4) term by term to eliminate y

31x + 0 = 93

31x = 93 ( divide both sides by 31 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for x

Substituting into (1)

5(3) + 3y = 9

15 + 3y = 9 ( subtract 15 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

Then P = (3, - 2 )

Answer: Same Side Interior Angles

Step-by-step explanation:

Imma help you eliminate the options.

-These angles are inside the parallel lines, meaning that they have to be interior angles. That eliminates any answers involving exterior angles. Next, simply by definition, it wouldn't be corresponding. Finally, alternate interior angles is eliminated because the angles are on the SAME SIDE of the transversal, meaning that Same-Side interior angles is the answer.

Answer:

The approximate angle of \(\vec u = \frac{1}{2}\cdot \vec v\), where \(\vec v = \langle 10, 15\rangle\), is 56º.

Step-by-step explanation:

Let \(\vec v = \langle 10, 15\rangle\) and \(\vec u = \frac{1}{2}\cdot \vec v\), then the resulting vector is described below:

\(\vec u = \frac{1}{2}\cdot \langle 10,15\rangle\)

\(\vec u = \left\langle 5,\frac{15}{2} \right\rangle\)

From Trigonometry, we find that direction angle of this vector is defined by the following inverse trigonometric expression:

\(\theta = \tan^{-1}\left(\frac{u_{y}}{u_{x}} \right)\) (1)

Where:

\(u_{x}\) - x-Component of \(\vec u\), dimensionless.

\(u_{y}\) - y-Component of \(\vec u\), dimensionless.

If we know that \(u_{x} = 5\) and \(u_{y} = \frac{15}{2}\), then the direction angle of the vector is:

\(\theta = \tan^{-1}\left(\frac{\frac{15}{2}}{5} \right)\)

\(\theta =\tan^{-1} \frac{15}{10}\)

\(\theta = \tan^{-1} \frac{3}{2}\)

\(\theta \approx 56.310^{\circ}\)

The approximate angle of \(\vec u = \frac{1}{2}\cdot \vec v\), where \(\vec v = \langle 10, 15\rangle\), is 56º.

Answer:

C. 124

Step-by-step explanation:

#4: The transformation can be represented by (x, y - 8).

Step-by-step explanation:

1/4 divided by 4 = 1/4 x 1/4 = 1/16

8 divided by 1/3=8 x 3 = 24

Step-by-step explanation:

1/4 divided by 4 = 1/4 x 1/4 = 1/16

8 divided by 1/3=8 x 3 = 24

y=-2x(squared)+3x-7

the 2x is squared

hope that helped

An observation that causes the values of the slope and the intercept in the line of best fit to be considerably different from what they would be if the observation were removed from the data set is said to be an outlier.

An outlier is an observation that is significantly different from other observations in a dataset. It is a data point that is located far away from the other data points, and it may have a disproportionate influence on the analysis and conclusions drawn from the data.

what is slope?

Slope is a measure of the steepness of a line. It is calculated as the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) between two points on the line. The slope represents the rate at which the line is rising or falling.

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Answer:$181.81

Step-by-step explanation:300/198

=1.5151515….multiple by 120

=181.818181

Answer:

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink

Step-by-step explanation:

From the question we have;

The charges of the roller skating rink = A skate rental fee + An hourly rate

The total cost to skate for 2 hours = $9.50

The total cost to skate for 5 hours = $18.50

The relationship between the total cost of skating and the duration in hours = Linear relationship

Let 'x' represent the number of hours skating and let 'y' represent the total cost, we have;

The form of the equation is y = m·x + b

Where;

m = The rate of change of the linear relationship

b = The initial value (y-intercept)

When x = 2, y = 9.50

Therefore, we can write;

9.50 = 2·m + b...(1)

When x = 5, y = 18.50

Therefore, we can write;

18.50 = 5·m + b...(2)

Subtracting equation (1) from equation (2) gives;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

The rate of change, m = 3.0

Similarly, we have;

From equation (1), we get;

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The initial value = 3.50

Therefore, the initial value, b = $3.50 is the skate rental fee while rate of change m = $3.0 is the hourly rate the rate.

Answer:

La ecuación de la recta es \(y = -6\cdot x +23\).

Step-by-step explanation:

Para construir la ecuación de la recta podemos utilizar un punto contenido en la recta y su pendiente. En primer punto, hallamos el punto con la resolución del siguiente sistema de ecuaciones lineales:

\(x+4\cdot y = 0\) (1)

\(x-3\cdot y = 7\) (2)

La solución del sistema de ecuaciones es \((x,y) = (4,-1)\).

Por Geometría Analítica, sabemos que la Ecuación de la Recta en su forma explícita es:

\(y = m\cdot x + b\) (3)

Donde:

\(x\) - Variable independiente.

\(y\) - Variable dependiente.

\(m\) - Pendiente.

\(b\) - Intercepto.

Si sabemos que \((x,y) = (4,-1)\) y \(m = -6\), entonces el intercepto de la recta es:

\(b = y-m\cdot x\)

\(b = 23\)

Ahora, la ecuación de la recta es \(y = -6\cdot x +23\).

The particular solution of the given differential equation is;\(z_p(x, y)\) = (-1/2)sin(x - y)

Given the differential equation as below

(Dx² − 2DxDy)z = sin(x − y)

The characteristic equation is given as;

(m - Dx)² = 0

Solve the above equation by considering the value of m as the repeated root;

m - Dx = 0m = Dx. So, the characteristic equation is

(m - Dx)² = 0

or (Dx - m)² = 0

(Dx - m)² = 0Dx - m = 0

or Dx = mD²x - Dm/Dx

= 0D²x - mDx

= 0Dx(D - m)

= 0

Therefore, the general solution of the given differential equation

z(x, y) = C₁x + C₂y + (1/2)sin(x-y)

For the particular solution,

\(z_p(x, y) = Asin(x - y)\)

By substituting the value of \(z_p(x, y)\) in the differential equation;

Dx² - 2DxDy(Asin(x - y)) = sin(x - y)

Differentiate\(z_p(x, y)\) with respect to x and y separately,

\(Dz_p/dx = Acos(x - y)Dz_p/dy = -Acos(x - y)\)

Substitute the above values in the given differential equation;

Dx²(Asin(x - y)) - 2DxDy(Acos(x - y)) - sin(x - y)

= 0A{Dx²sin(x - y) - 2DxDy(cos(x - y))}

= sin(x - y)2DxDy(cos(x - y)) - Dx²sin(x - y)

= -sin(x - y)

Therefore, A = -1/2

Substitute the value of A in the value of \(z_p(x, y);\)

\(z_p(x, y)\) = (-1/2)sin(x - y)

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To find the ratio in the lowest term, we have to simplify it.

We divide each part by 6.

Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.

Answer:

a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation:

Answer:

66-3i

Step-by-step explanation:

(4-3i)-(9-71)

(4-3i)-(-62)

(4-3i)-62

66-3i

0.35 is the probability of getting C i.e. P(C) = 0.35

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Considering the tree:

P(C) = P(AC) + P(BC)

P(C) = (0.5×0.4) + (0.5×0.3)

P(C) = 0.2 +  0.15

P(C) = 0.35

Therefore, the probability of getting C, P(C) is 0.35

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Answer:

Mac is 19 years old, Joe is 11 years old

Step-by-step explanation:

2J - 3 = M

J + M = 30

M = 30 - J

2J - 3 = 30 - J

3J = 33

J = 11

M = 30 - 11

M = 19

Answer:

9.2

Step-by-step explanation:

The directional derivative of the given function f(x,y) = 2xy² - x³y at point (1,1) in the direction that makes an angle of 60° with the positive direction of the x-axis is (2 - 3√3) units.

Given function f(x,y) = 2xy² - x³yThe direction of the derivative is the angle which is made by the line passing through a point where the derivative is to be found and the gradient of the function at that point.

As we know that direction is specified by angles, so the direction of the derivative at a point will be given by the angle that the line makes with the x-axis.

Given a point (1,1) in the direction that makes an angle of 60° with the positive direction of the x-axis. We need to find the directional derivative of the given function at the point (1,1) in the direction that makes an angle of 60° with the positive direction of the x-axis.

We know that the direction of the gradient vector at any point is always perpendicular to the level surface passing through that point.

Therefore, The gradient vector of the given function at the point (1,1) can be calculated as:∇f(x, y) = [∂f/∂x, ∂f/∂y]∇f(1,1) = [4, -3].

Now, the angle between the direction and x-axis is 60°So, the direction vector = [cos(60°), sin(60°)] = [1/2, √3/2].

Hence, the directional derivative of f(x,y) = 2xy² - x³y at point (1,1) in the direction that makes an angle of 60° with the positive direction of the x-axis is given by:∇f(1,1) . [cos(60°), sin(60°)] = [4, -3] . [1/2, √3/2]= (4 * 1/2) + (-3 * √3/2)= 2 - 3√3 units

The directional derivative of the given function f(x,y) = 2xy² - x³y at point (1,1) in the direction that makes an angle of 60° with the positive direction of the x-axis is (2 - 3√3) units.

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Natural numbers known as prime numbers can only be divided by one (1) and by the number itself.

In the given question we have to explain about the prime number.

Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.

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Answer:

number is 3

Step-by-step explanation:

let the number be n then the product of 3 and the number is 3n , so

16 = 7 + 3n ( subtract 7 from both sides )

9 = 3n ( divide both sides by 3 )

3 = n

That is the number is 3

Answer:

no because there is no relation between the temperature changes

Step-by-step explanation:

9514 1404 393

Answer:

  yes

Step-by-step explanation:

No domain value is repeated in Sam's ordered pairs, so the relation is a function.

The number of inflection points can a quadratic polynomial and a cubic polynomial have is zero and one respectively.

For the points of inflection,

We know that the roots of second derivatives give the inflection points of a function,

For inflection point , f(x)'' = 0

(a) For quadratic, there will be f(x)'' independent of x, So, there will be no point of inflection.

(b) For cubic, there is a second derivative have a linear function, So, only one point of inflection.

Any degree polynomial, it has (n-2) points of inflection, where n is the degree of the polynomial.

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The probability of rolling a number less than 12 can be calculated as follows: There are 12 possible outcomes when rolling a twelve-sided die with numbers labeled 1 through 12.

Since each number is equally likely to be rolled, the probability of rolling a number less than 12 is 11/12. This fraction can be simplified to 11/12, which is the answer.To calculate the probability of rolling a number less than 12, we must first understand the number of possible outcomes when rolling a twelve-sided die with numbers labeled 1 through 12. There are 12 possible outcomes, since each number has an equal chance of being rolled.Next, we must calculate the number of outcomes that are less than 12. Since all the numbers are less than 12, the number of outcomes that are less than 12 is 11.Finally, we must calculate the probability of rolling a number less than 12. This is done by dividing the number of outcomes that are less than 12 (11) by the total number of possible outcomes (12). 11/12 simplifies to 11/12, which is the probability of rolling a number less than 12.

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Venn diagram: Probability values :\(P(A) = 0.78P(B) = 0.54P(AUB) = 0.89a)\)The probability that ticket A will not drop in price \(P(A) = 0.78P(B) = 0.54P(AUB) = 0.89a)\)) The probability that only ticket B will drop in price is P(B)-P(A∩B) = 0.54-0.35 = 0.19c) The probability that at least one ticket will drop in price is\(P(AUB) = 0.89d) .\)

The probability that both tickets will not drop in price is \(1-P(AUB) = 1-0.89 = 0.11e)\)The probability that only one ticket will drop in price is \((P(A)-P(A∩B))+(P(B)-P(A∩B)) = (0.78-0.35)+(0.54-0.35) = 0.62f)\)The probability that no more than one ticket will drop in price is \(P(AUB)-P(A∩B) = 0.89-0.35 = 0.54e)\) The probability that ticket A will drop in price given that ticket B dropped in price i\(s P(A|B) = P(A∩B)/P(B) = 0.35/0.54 = 0.6481481481481481h\)) A and B are not mutually exclusive because P(A∩B) > 0. Answer: the probability that the ticket A will not drop in price is 0.22. Only the probability that ticket B will drop in price is 0.19. The probability that at least one ticket will drop in price is 0.89. The probability that both tickets will not drop in price is 0.11.

The probability that only one ticket will drop in price (not both) is 0.62. The probability that no more than one ticket will drop in price is 0.54. The probability that ticket A will drop in price given that ticket B dropped in price is 0.6481481481481481. A and B are not mutually exclusive because P(A∩B) > 0.

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Answer: i think its zero

Step-by-step explanation:

or u can just look it up on an sigma math calculator and that should give u the answer

Answer:

Step-by-step explanation:

A function is a relation in which each input has only one output

so a relation cannot have more than one output

Answer:

each input (x-value) only has one output (y-value)

Step-by-step explanation:

you can use the vertical line test; pretend to draw vertical lines and if there are two point on the graph where the vertical line touches, it cannot be considered function.