The dot plots below display the pre- and post-test math scores for students in of Mr. Perez's
math classes.
The mean for the Pre-Test scores is 4.
The mean for the Post-Test scores is 10.
The mean absolute deviation of both tests is 2.
Describe the difference between the means as a multiple of the MAD.

Answer:

9. A = Length by Width

Length = x

Width = 12x - 6y

A = x(12x - 6y)

A = 12x² - 6xy

10. A = ½bh

h = 2ab

A = ½(b)(2ab)

A = ab²

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

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:

1/59

Step-by-step explanation:

Answer:

1/59

think of it dude

Answer:

2x+156=4x+192

192-156=-4x+2x

36=-2x

x=-18

Step-by-step explanation:

Answer:

The number 3.97 is very close to the whole number 4. Therefore, the difference of 4.3 - 3.97 is about 0.33. So, the difference of 4.3 - 3.97 is less than 1.

Remember: The farther the number is to the right, the smaller it becomes.

Ex. 0.10 is greater than 0.100 since the number is shorter and closer to the ones/whole number spot.

:)

Answer:

34

Step-by-step explanation:

omg please don't listen to the other person it's 34 bc if you look at the angle under 2 it's 34 so that's your answer for one

Answer:

I pretty sure its A

Step-by-step explanation:

Answer:

The answer on the top, 32 * __ = 3616

Step-by-step explanation:

3616/32 = __

multiply by 32

3616 = 32 * __ or 32 * __ = 3616

Answer:

x=30

HOPE THIS HELPS

-Todo <3

Step-by-step explanation:

60=2x

/2   /2

30=x

Answer:

your answer will be 70 have a nice day:)

Step-by-step explanation:

43+27=70

Answer: 18

Step-by-step explanation:

           To answer this question you have to add all the number and however many over 100 there is that how many like both of the teams so 27 + 48 + 43 = 118

then you take 100 away from 118 and you get 18

Answer:

Polygon. A closed plane figure for which all sides are line segments. The name of a polygon describes the number of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon.

Answer:

7

Step-by-step explanation:

Because half of 40% is 20%

So 14%2 = 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.

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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Answer:

C

Step-by-step explanation:

The probability is 1/3

Answer:

5.2m

Step-by-step explanation:

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∘ )

The amount of interest charged at the end of the term is approximately $644.75.

To calculate the amount of interest charged at the end of the term, we can use the simple interest formula:

Interest = Principal * Rate * Time

Principal = $6,250

Rate = 4.12% = 0.0412 (decimal form)

Time = 2 years + 6 months = 2.5 years

Plugging in these values into the formula, we have:

Interest = $6,250 * 0.0412 * 2.5

Calculating this expression:

Interest = $6,250 * 0.0412 * 2.5 = $644.75

Therefore, the amount of interest charged at the end of the term is $644.75 (rounded to the nearest cent).

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Answer:

(10n + 19) (12n - 4)º ... The midsegment of a trapezoid is parallel to each base and its measure is one half the ...

Missing: pointsR( ‎S

Step-by-step explanation:

The given series is an alternating series with a pattern of adding and subtracting consecutive terms. To determine Sn, we need to find the sum of the first n terms of the series. Therefore, the sum of the series is -13,365.

In the given series, each term is obtained by adding 11 to the previous term and then changing its sign. We can observe that the first term is positive (45), the second term is negative (-56), the third term is positive (67), and so on.

To find Sn, we need to determine the number of terms in the series and then calculate the sum. The series ends with -342, so we need to find the position of -342 in the series.

To do this, we can subtract 45 from -342 and divide the result by 11 to find the number of terms. (-342 - 45) / 11 = -297 / 11 = -27. Therefore, the series consists of 27 terms.

To find the sum of the first 27 terms, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.

Using the formula, we can calculate Sn as follows: Sn = (27/2)(45 - 342) = (27/2)(-297) = -13,365.

Therefore, the sum of the series is -13,365.

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Answer:

bhjtijo3

Step-by-step explanation:

Answer:

Step-by-step explanation:

D. 14

The equation "6x + y = 29" is not a result of solving the given system of equations by addition.

To solve a system of equations by addition, we aim to eliminate one variable by adding the equations together. Let's analyze the given system of equations:

Equation 1: 5x + 2y = 5

Equation 2: 3x - y = 14

To eliminate the y variable, we can multiply Equation 2 by 2 and add it to Equation 1:

2(3x - y) = 2(14)

6x - 2y = 28

Adding this modified Equation 2 to Equation 1, we get:

(5x + 2y) + (6x - 2y) = 5 + 28

11x = 33

x = 3

Substituting the value of x into either of the original equations, we find that y = -1. Therefore, the solution to the system of equations is x = 3 and y = -1.

Now, let's verify the options to see which equation is not a result of solving the system by addition:

A) 11x = 33 - This equation is derived from adding the two equations together.

B) 6x + y = 29 - This equation is derived from substituting the values of x and y into one of the original equations.

C) 2y = 2 - This equation is derived from isolating the variable y in Equation 1.

D) x = 3 - This equation is derived from solving for x.

Thus, the equation "6x + y = 29" is not a result of solving the system of equations by addition.

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Answer:

4 − 3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.