please help, tysm if you do :D

For the given system of initial value problem,

A₁ = 7,

A₂ = -1, and

y = 2exp(-t),

To solve the given system of initial value problem (IVP) with the matrix equation x' = Ax, where A is the given matrix and x(0) = [10, -4, 21], we can use the eigenvalue-eigenvector method.

The matrix A is given as:

A = | 4 -2 0 |

| 3 -1 0 |

| 1 7 2 |

Let's find the eigenvalues and eigenvectors of matrix A.

To find the eigenvalues, we solve the characteristic equation:

det(A - λI) = 0

Substituting the values, we get:

| 4-λ -2 0 |

| 3 -1-λ 0 |

| 1 7 2-λ |

Expanding the determinant, we have:

(4-λ)[(-1-λ)(2-λ)] + 2[3(2-λ) - (-1-λ)7] = 0

Simplifying and solving the equation, we find the eigenvalues:

λ₁ = -1

λ₂ = 2

λ₃ = 2

Next, let's find the corresponding eigenvectors.

For λ₁ = -1:

(A + I)v₁ = 0

| 5 -2 0 | | v₁₁ | | 0 |

| 3 -1 0 | * | v₁₂ | = | 0 |

| 1 7 1 | | v₁₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₁:

v₁ = | 2 |

| 5 |

|-1 |

For λ₂ = 2:

(A - 2I)v₂ = 0

| 2 -2 0 | | v₂₁ | | 0 |

| 3 -3 0 | * | v₂₂ | = | 0 |

| 1 7 0 | | v₂₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₂:

v₂ = | 1 |

| 1 |

|-1 |

For λ₃ = 2:

(A - 2I)v₃ = 0

| 2 -2 0 | | v₃₁ | | 0 |

| 3 -3 0 | * | v₃₂ | = | 0 |

| 1 7 0 | | v₃₃ | | 0 |

Solving the system of equations, we find the eigenvector corresponding to λ₃:

v₃ = | 2 |

| 3 |

| 1 |

Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:

x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂ + c₃ * exp(λ₃ * t) * v₃

Substituting the given initial condition x(0) = [10, -4, 21], we can find the specific solution by solving the following system of equations:

c₁ * v₁ + c₂ * v₂ + c₃ * v₃ = x(0)

Substituting the values of the eigenvectors and the initial condition, we get:

2c₁ + c₂ + 2c₃ = 10 (Equation 1)

5c₁ + c₂ + 3c₃ = -4 (Equation 2)

-c₁ - c₂ + c₃ = 21 (Equation 3)

Solving this system of equations will give us the values of c₁, c₂, and c₃, which will determine the specific solution.

By solving Equations 1, 2, and 3, we find:

c₁ = 1

c₂ = -5

c₃ = -3

Therefore, the specific solution to the initial value problem is:

x(t) = exp(-t) * | 2 | + exp(2t) * | 1 | + exp(2t) * |-3 |

| 5 | | 1 |

|-1 | | 1 |

Simplifying this expression, we get:

x(t) = | 2exp(-t) + 5exp(2t) - 3exp(2t) |

| 5exp(-t) + exp(2t) + exp(2t) |

|-exp(-t) + exp(2t) + exp(2t) |

Finally, we can rewrite the solution in the given form (7) - ₁ (1) ¹²+₂ (1) ¹:

x(t) = 7 * | 2exp(-t) | + (-1) * | 5exp(-t) |

| 5exp(-t) | | -exp(-t) |

Therefore, A₁ = 7, A₂ = -1, and y = 2exp(-t).

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Answer:

a) 64° each

b) 15.78 cm

c) 51.78 cm

Step-by-step explanation:

a) (180 - 52)/2 = 64°

b) cos 64 = x/18, x = 7.89, 2x = 15.78 cm

c) 18 + 18 + 15.78 = 51.78 cm

Answer: 120

Step-by-step explanation:

Answer: Cup-$14, Saucer-$6.5

Step-by-step explanation:

Given

Cup and saucer costs $20.5

A cup and two saucer costs $27

Assume the price of cup and saucer are x and y

So, we can write

[tex]\Rightarrow x+y=20.5\quad \ldots(i)\\\\\Rightarrow x+2y=27\quad \ldots(ii)[/tex]

Solving [tex](i)\ \text{and}\ (ii)[/tex] we get

[tex]x=\$\ 14, y=\$\ 6.5[/tex]

Thus, the cost of the cup is $14 and that of the saucer is $6.5

Answer:

5.2m

Step-by-step explanation:

Answer:

x= 64° y= 18° z= 98°

Step-by-step explanation:

x= 64°

y = 18°

z = 180° - x - y

z = 180° - 64° - 18°

z= 98°

We can see here that when the ladybird is rotated:

This ladybird made a 90° turn clockwise.

This ladybird made a 180° anticlockwise.

In mathematics, rotation refers to a transformation that turns or rotates an object around a fixed point called the center of rotation. It is a fundamental concept in geometry and is used to describe the movement of points, shapes, or figures in the plane or in three-dimensional space.

A rotation involves specifying the center of rotation, the angle of rotation, and the direction of rotation (clockwise or counterclockwise).

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Answer:

Step-by-step explanation:

4x - 12 = 11 - 3x

Bringing like terms on one side

4x + 3x = 11 + 12

7x = 23

x = 23/7

Answer:

Arthur knows that there is a difference among the groups somewhere, but he does not know where

Step-by-step explanation:

An ANOVA test is a test to find out whether the results of an experiment or a survey are significant or not. ANOVA test helps the researcher or the experimenter to decide whether they reject the null hypothesis or accept the alternate hypothesis in the experiment. In ANOVA test, the experimenter wants to find if there is a difference between them or not.

In the context, Arthur is doing a study and he wishes to find out effect of a sleep deprivation on the number of the calories that people consumed. He collects some data from his subject group from the sleep lab and after running the ANOVA test, he finds out that he can reject the null hypothesis. So on this basis, Arthur knows that there is some basic difference among the members of the group somewhere, but he does not know where actually the difference is.

Answer:

30

Step-by-step explanation:

Well 42

        -

       12

       30

Answer:

Test statistic

Step-by-step explanation:

Answer:

2x+156=4x+192

192-156=-4x+2x

36=-2x

x=-18

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The probability is 1/3

Notice that the weird figure looks like a rectangle that is missing a piece.

In this case, find the area of the rectangle... then subtract the area of the missing piece from that area of the rectangle.

-----------------------------------------------------------------------

Area of rectangle: 4 x 5 = 20 sq. inches

-----------------------------------------------------------------------

How to find the area of the missing piece:

So, the area of the missing piece: A = lw = (1)(2) = 2 sq. inches

-----------------------------------------------------------------------

Now, subtract the area of the missing piece from the area of the rectangle:

20 - 2 = 18 sq. inches

-----------------------------------------------------------------------

Answer:

x = -1/3

Step-by-step explanation:

We have,

sin(x + 7) = cos(4x + 8)

We need to find the value of x.

We know that,

sin(90-x) = cosx

So,

sin(90-(x + 7)) = cos(4x + 8)

cos(x+7) = cos(4x + 8)

i.e.

(X+7) = (4x+8)

7-8 = 4x-x

-1 = 3x

x = -1/3

Answer:

sin(22 ∘ ) = cos(68∘ )

Step-by-step explanation:

Sin(x+7)=cos(4x+8)

(x+7) + (4x+8) =   90

x + 7 + 4x + 8 =  90

5x + 15 =  90

    −15 =  −15

5x/5 = 75/5

x = 15

Answer: sin(22 ∘ ) = cos(68∘ )

Answer:

La nota de Carolina es 15 puntos.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de ecuaciones lineales que tienen más de una incógnita, relacionadas mediante las ecuaciones.

En los sistemas de ecuaciones, se debe buscar los valores de las incógnitas.  Al reemplazar en las ecuaciones, deben dar la solución planteada.

En este caso se debe plantear un sistema de ecuaciones, donde las incógnitas son:

Ambas notas juntas es igual a 34 puntos. Expresado matemáticamente es:

x + y= 34

Se sabe que Carmen obtuvo 4 puntos más que Catalina. Esto es:

y= x + 4

Entonces el sistema de ecuaciones a resolver es:

[tex]\left \{ {{x+y=34} \atop {y=x+4}} \right.[/tex]

A través del método de sustitución debes despejar una de las incógnitas en una de las ecuaciones y sustituir su valor en la siguiente. En este caso, ya tienes despejada la incógnita y en la segunda ecuación. Por lo que sustituyes esta expresión en la primer ecuación:

x+ x+4=34

Resolviendo obtienes:

x + x= 34 - 4

2*x=30

x= 30÷ 2

x=15

Sustituyendo este valor en la segunda ecuación obtienes:

y= x+4

y= 15 +4

y= 19

Recordando que "x" representa la nota de Carolina e "y" la nota de Carmen, entonces la nota de Carolina es 15 puntos y la nota de Carmen es 19 puntos.

Answer:

B

Step-by-step explanation:

Answer:

402.1 in^2

Step-by-step explanation:

Find the area of the circle with the 18 in. radius first.

Formula for a circle is πr^2

So the area of the circle with the 8 in. radius is 1017.9 in^2

Now do the same for the 14 in. radius circle.

The area for the 14 in. radius circle is 615.8

Now subtract:

1017.9 - 615.8 =

402.1 in^2

hope this helped!

In the Capital Asset Pricing Model (CAPM), the coefficient of the market return is known as the stock’s beta. Beta measures the stock’s systematic risk, or its sensitivity to market movements.

A beta of 1 indicates that the stock’s return moves with the market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 indicates that the stock is less volatile than the market.

In this case, the estimated CAPM model for stock XYZ has a beta of 1.38. This means that stock XYZ is expected to be more volatile than the market. For every 1% increase in the market return, stock XYZ’s return is expected to increase by 1.38%. Conversely, for every 1% decrease in the market return, stock XYZ’s return is expected to decrease by 1.38%.

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There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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Answer:

8 m

Step-by-step explanation:

7.5 - 1.5 = 6

2 + 6 = 8

Answer: 45

Step-by-step explanation: 360-315=45

Answer:  (x - 2) (x - 1）

Step-by-step explanation:

x²-3x+2

= (x - 2) (x - 1）

The set of integers has the same cardinality as the countably infinite set A. The correct option is b.

A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers (integers starting from 1). This means that we can establish a one-to-one function (bijection) between the countably infinite set A and the set of integers.

Options a, c, and d are not necessarily true.

Option a: There is no guarantee that there is a one-to-one function from the set A to the set of rational numbers. The set of rational numbers, also known as Q, is uncountably infinite, while A is only countably infinite.

Option c: It is possible to have a surjective function (onto) from the set of rational numbers to a countably infinite set. For example, a function that maps every rational number to its numerator can be surjective onto the set of integers.

Option d: The open interval (0, 1) has a higher cardinality (uncountable) than a countably infinite set. The interval (0, 1) contains an uncountably infinite number of real numbers between 0 and 1, whereas A is countably infinite.

The correct option is b.

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Answer:

We have that y = 21 when x = 11.

Step-by-step explanation:

We solve this question by proportions, using a rule of three.

Since they vary inversely, we apply the inverse rule of three, that is, with lateral multiplication instead of diagonal.

33 - 7

y - 11

So

[tex]11y = 33*7[/tex]

Dividing both sides by 11

[tex]y = 3*7 = 21[/tex]

We have that y = 21 when x = 11.

Answer:

1/59

Step-by-step explanation:

Answer:

1/59

think of it dude

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis, the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.

(a) Null hypothesis: H0: β1 = 0 (The size of the home is not a significant predictor of the selling price of homes sold recently).

Alternative hypothesis: Ha: β1 ≠ 0 (The size of the home is a significant predictor of the selling price of homes sold recently).

(b) The t-test statistic: We can use the t-test statistic to test whether the slope (β1) of the regression line is significant at the 5% level.

t = (β1 - 0) / SE(β1)

  = 0.0643 / 0.01224

   = 5.25

(c) The degrees of freedom (df) for this t-test statistic will be n - 2, where n is the sample size.

Since the sample size is 48, the degrees of freedom will be 48 - 2 = 46.

(d) Final conclusion of this test: Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis.

Thus, we conclude that the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.

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Answer:

how many colors are there and how many of each color?

Step-by-step explanation:

Probability of an event is the measurement of its chance of occurrence.

Suppose that there are finite elementary events in the sample space of the considered random experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Percent counts the number compared to 100 whereas probability counts it compare to 1.

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:

For each 1, there are a/100 parts.

Thus, 50% = 50/100 = 0.50 (in probability)

The probability of selecting an orange candy depends on how many candies are there.

If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100% because then n(E) = 1 and n(S) = 1 where

Thus, the probability of selecting an orange candy depends on how many candies are there. If its the only candy, and at least one candy must be chosen, then its probability is 1 or say in percent it is 100%

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