8.547 Rounded to tbe nearest hundredth​

The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

What is Linear algebra?

The study of vector spaces and linear transformations is the focus of the mathematical field known as linear algebra. It includes the geometric and algebraic characteristics of matrices and vectors.

Vectors are used in linear algebra to describe quantities that have both a magnitude and a direction. They can be multiplied by one another, scaled using scalars, and put through a variety of procedures. Contrarily, matrices are rectangular arrays of numbers that can be used to represent a variety of mathematical structures, including systems of equations and linear transformations.

Let's begin by reformatting the system of equations into a matrix form in order to get the general solution:

\(\[x' = \begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix} x\]\)

where x is the (x, y) column vector.

We can determine the eigenvalues and eigenvectors of the coefficient matrix (5 1; -26 -5) to solve this system.

We begin by computing the eigenvalues by resolving the defining equation:

\(\[\det(A - \lambda I) = 0\]\)

where A is the matrix of coefficients and I is the matrix of identities.

The characteristic equation is \(\(\begin{pmatrix} 5 & 1 \\ -26 & -5 \end{pmatrix}\)\) using the coefficient matrix.

\(\[\begin{vmatrix} 5 - \lambda & 1 \\ -26 & -5 - \lambda \end{vmatrix} = 0\]\)

Increasing the determinant's scope:

\(\((5 - \lambda)(-5 - \lambda) - (-26)(1) = 0\)\)

Simplifying:

\(\((\lambda - 5)(\lambda + 5) - 26 = 0\)\(\lambda^2 - 25 - 26 = 0\)\(\lambda^2 - 51 = 0\)\)

We obtain two eigenvalues after solving for :

\(\(\lambda_1 = \sqrt{51}\)\(\lambda_2 = -\sqrt{51}\)\)

Then, for each eigenvalue, we identify the matching eigenvectors.

If \(\(\lambda_1 = \sqrt{51}\):\((A - \lambda_1 I)v_1 = 0\)\)

Changing the values:

\(\((5 - \sqrt{51})v_1 + v_2 = 0\)\(-26v_1 + (-5 - \sqrt{51})v_2 = 0\)\)

We can use the free variable v_1 = 1 to solve these equations:

\(\(v_2 = \sqrt{51} - 5\)\)

As a result,\(\(v_1 = \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to _1 = sqrt(51).

In the same way, for \(\(\lambda_2 = -\sqrt{51}\):\((A - \lambda_2 I)v_2 = 0\)\)

Changing the values:

\(\((5 + \sqrt{51})v_3 + v_4 = 0\)\(-26v_3 + (-5 + \sqrt{51})v_4 = 0\)\)

We can use the free variable\(\(v_3 = 1\)\) to solve these equations:

\(\(v_4 = -\sqrt{51} - 5\)\)

As a result, \(\(v_2 = \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\).\) is the eigenvector corresponding to\(\(\lambda_2 = -\sqrt{51}\)\)

The system of equations general solution is denoted by the following notation:

\(\[x = c_1 \cdot e^{\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ \sqrt{51} - 5 \end{pmatrix} + c_2 \cdot e^{-\sqrt{51}t} \cdot \begin{pmatrix} 1 \\ -\sqrt{51} - 5 \end{pmatrix}\]\)

where t stands for the independent variable (time) and c_1 and c_2 are arbitrary constants.

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The measure of ∠B = 50°.

We have two angles ∠A and ∠B which are supplementary to each other.

Two angles are said to be supplementary if their sum is equal to 180°.

Mathematically -   x + y = 180°

According to the question -

∠A = (5x + 30)° and

∠B= (x +30)°,

Now, ∠A and ∠B are supplementary angles. Therefore -

∠A + ∠B = 180°

(5x+30)+(x+30) = 180

5x+30+x+30=180

6x+60=180

6x=180-60

6x = 120

x = 120/6

x = 20

Now measure of ∠B = x+30

∠B = 20+30

∠B = 50°

and ∠A = 5x+30

∠A = 5(20)+30

∠A = 100+30

∠A = 130°

Hence we get the measure of the ∠A and ∠B as 130° and 50°

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The graph is in the attached image.

The closure of b, denoted by b+, is the set of all elements that can be reached from b through one or more transitions in the set F. Starting with b, we see that the transition b+c is in F, which means we can add c to our set. Then, the transition c→{de} is also in F, so we can add d and e to our set. Therefore, the closure of b is b+ = {b, c, d, e}.

Given the set F = {a+b, b+c, c→de}, the closure of b refers to the smallest set that contains b and is closed under the operations in F. In this case, the closure of b would be {b, a+b, b+c}. This is because the set includes b and is closed under the addition operation with a and c, as specified in F.

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After combining like terms to create equivalent expression we get (-1.9 + 1.2) + (5.1 - 3.6)t. Simplifying further, we get: -0.7 + 1.5t.

To combine like terms, we add or subtract the coefficients of the same variables. In this case, the variables are t and the constant terms (without variables) are -3.6, -1.9, and 1.2.

So the equivalent expression after combining like terms is:

(-1.9 + 1.2) + (5.1 - 3.6)t

Simplifying further, we get:

-0.7 + 1.5t

A coefficient is a numerical factor that is multiplied by a variable in an algebraic expression. It tells you how many times the variable appears in the expression. For example, in the expression 3x + 2, the coefficient of x is 3. Variables are symbols used to represent unknown quantities in mathematical equations or expressions. They can take on different values, and their value can be solved for using algebraic techniques. Equivalent expressions are expressions that have the same value for all possible values of the variables involved. For example, 2x + 4 and 4 + 2x are equivalent expressions since they simplify to the same value. Equivalent expressions can be useful in simplifying and solving algebraic equations.

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Complete Question

Combine like terms to create an equivalent expression. −

3. 6−1. 9+1. 2+5. 1 −3. 6−1. 9t+1. 2+5.

Answer:

One big reason why a car’s total price won’t match the price on its window sticker relates to fees charged by a car dealership and the automaker. For example, although a car may cost $19,995 according to the window sticker, that figure might be the price before the addition of a destination charge, which is a pricy manufacturer’s fee that can add up to $1,000 to the price. A dealer may also charge a documentation fee to prepare the vehicle’s documents for sale, and this figure can sometimes cost as much as $500. There are mandatory government fees too, such as the cost to process the car’s title work or change the registration to your name.

Step-by-step explanation:

Dealer and manufacturer fees usually aren’t the biggest add-ons to a car’s purchase price. The priciest addition typically comes in the form of taxes, since most states levy a sales tax on the entire price of a new or used vehicle. Since sales taxes can range as high as 8-10 percent in some areas, this can easily add thousands of dollars to your vehicle’s purchase price. For example, a $20,000 car purchased in an area with a 7 percent sales tax will cost an extra $1,400 on top of the purchase price, while a $30,000 car bought in a place with a 9 percent sales tax will see a whopping $2,700 price boost before you can drive it home.

Answer:

\(Rx=1(p) = (4,7)\)

Step-by-step explanation:

he given point P has coordinates, \((-2,7)\)                                                           We want to find the image of this point, after a reflection in the line \(x=1\)

To determine the probability that it will not rain for the next two weeks, we can use the provided probability model. The probability that it will not rain for the next two weeks is 0.68 or 68%, expressed as a decimal precise to two decimal places.

First, let's break down the probabilities given:
Step:1. Probability of rain this week: 0.20
Step:2. Probability of no rain this week: 1 - 0.20 = 0.80
Step:3. Probability of rain next week if it rains this week: 0.31
Step:4. Probability of no rain next week if it rains this week: 1 - 0.31 = 0.69
Step:5. Probability of rain next week if it doesn't rain this week: 0.15
Step:6. Probability of no rain next week if it doesn't rain this week: 1 - 0.15 = 0.85
Now, we want to find the probability that it will not rain for the next two weeks. To do this, we will multiply the probability of no rain this week (0.80) by the probability of no rain next week if it doesn't rain this week (0.85).
Probability (No rain for the next two weeks) = 0.80 * 0.85 = 0.68
So, the probability that it will not rain for the next two weeks is 0.68 or 68%, expressed as a decimal precise to two decimal places.

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The average speed is 10.63 mi/hr. By MVT, the speed was exactly 10.63 mi/hr at least twice. By the intermediate value theorem, the speed between 0 and 0 mi/hr was constant. Therefore, the speed of 10 mi/hr was reached at least twice in the race. The correct answer is A.

The average speed is (6.2 mi)/(35/60 hr) = 10.63 mi/hr.

By the Mean Value Theorem (MVT), there must exist a time during the race when the runner's instantaneous speed was equal to the average speed, i.e., 10.63 mi/hr.

By the Intermediate Value Theorem (IVT), since the runner started at 0 mi/hr and finished at 0 mi/hr, there must be some continuous segment of the race where the runner's instantaneous speed was exactly 10 mi/hr. Since the average speed is greater than 10 mi/hr, this segment must occur at least twice.

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Answer:

28 is your area and it is a rational number it's never ending number

Step-by-step explanation:

The side length of the square is a rational.

What is the area of the basement?

Any lower storey of a structure that is partially or completely below the lowest contiguous proposed ground level is referred to as a basement floor, provided that the portion of the storey above ground level does not exceed 75 cm.

Given: Taylor uses tape to mark a square play area in the basement for her daughter.

The area measures 28 ft2.

We know that the area of square is side length square.

As the area measures 28 square feet, so the side length of the square is, 28 feet.

Since 28 is a rational number.

Therefore, the side length of the square is a rational.

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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Answer:

B

Step-by-step explanation:

cut tghe shape into one rectangle and a two cimi circles

area of a rect. is b x h --> 7x14 = 98ft^2

now make the two cimi circles a whoal and find the area of a circle

pie r^2 --> 3.14x3.5^2 = 38.48

add both getting about 136.48

Answer:

136.48 ft^2 (B)

Step-by-step explanation:

First, we need to find the area of a rectangle.

A(rectangle) = l * w

  = 14 ft * 7 ft

  = 98 ft^2

Next we need to find the area of the two semicircles.

A(semicircle) * 2 = πr^2/2 * 2

                           = π(3.5 ft)^2

                           = 12.25π ft^2

                           = 38.48 ft^2

Finally, you add the two areas:

98 ft^2 + 38.48 ft^2 = 136.48 ft^2

Hope this helps!

If no sheets of plywood are bought and 220 units of currency are available, it is possible to buy 44 sheets of drywall.

Two or more expressions with an Equal sign is called as Equation.

Given that the equation 5 x + 22y=220 represents the number of sheets of drywall x and sheets of plywood y that can be bought with 220

If no sheets of plywood are bought, the equation 5x + 22y = 220 simplifies to 5x = 220, since 22y = 0 when y = 0.

We can isolate x on one side of the equation by dividing both sides by 5:

5x = 220

Divide both sides by 5.

x = 220/5

Divide numerator and denominator by five.

x = 44

Therefore, if no sheets of plywood are bought and 220 units of currency are available, it is possible to buy 44 sheets of drywall.

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Answer:

2 1/5+6 4/5 =  9

6 5/12 -2 1/12 = 4 1/3

11 8/9+4 1/3 =16  2/9

7 1/6-5 3/4 = 1  5/12

11/18+ 6 1/10 = 6 64/90

15 1/3- 2 5/8 = 12  17/24

Step-by-step explanation:

Using the technique of mixed numbers to add the fractions

2 1/5+6 4/5

=2+6 + 1/5+4/5     add the whole numbers separately and then the fractions

=8 5/5= 9

6 5/12 -2 1/12

=6-2 + 5-1/12

=4 4/12

= 4 1/3

11 8/9+4 1/3

=11+4 +8/9+1/3     adding the whole numbers separately

=15 + 8+3/9

= 15+11/9             adding the fractions separately

= 15+1+2/9

= 16+2/9

=16  2/9

7 1/6-5 3/4

= 7-5 +1/6 -3/4   subtracting the whole numbers separately

= 2+ 2-9/12   subtracting the fractions separately

= 2-7/12  

= 24-7/12

= 17/12

=1  5/12

11/18+ 6 1/10

= 11/18 + 61/10

= 110 +1098/180

= 1208/180

= 6 128/180

= 6 64/90

15 1/3- 2 5/8

=15- 2 + 1/3- 5/8

=13 + 8- 15/24

= 13 + -7/24

= 312-7/24

= 12 17/24

Answer: the average change in value of the car each year would be 720$

Step-by-step explanation: the over-all change in those 5 years was 3,600$ so we divide 3600$ into 5 to see how much the average change in value would be each year to get our final answer.

Hopefully this helped!

-Joshua

Based on the variable declarations and initializations you provided:
int a = 2; int b = 6; int c = 3;
An expression that evaluates to false would be one where the conditions are not met. For example:
(a + b == c)
This expression checks if the sum of a and b is equal to c. In this case, (2 + 6) is not equal to 3, so the expression evaluates to false.

One possible solution is:
The given variable declarations and initializations are:
int a = 2;
int b = 6;
int c = 3;

To evaluate which of the following expressions is false, we need to look at each expression and see if it produces a Boolean value of false.
a < b || c > b

This expression is true because 2 is less than 6 and 3 is greater than 6. Therefore, the OR operator (||) returns true because at least one of the operands is true.
a + b > c && c - a < b

This expression is true because 2 + 6 is greater than 3 and 3 - 2 is less than 6. Therefore, the AND operator (&&) returns true because both operands are true.
b % c == a || c * b < a

This expression is false because 6 % 3 is equal to 0, which is not equal to 2. Therefore, the equality operator (==) returns false. Moreover, 3 times 6 is 18, which is not less than 2. Therefore, the second operand is also false. Therefore, the OR operator (||) returns false because both operands are false.

Therefore, the expression "b % c == a || c * b < a" evaluates to false.

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Answer:first one Dependent 2 independed

Step-by-step explanation:

Step-by-step explanation:

Answer:

1)0

2)3/8

Step-by-step explanation:

2)total number of participants who are at least 20 years old = 3

Total number of participants= 8

Answer:

35

Step-by-step explanation:

m + f = 80, or f = 80 - m

2m = f + 25   Substitute

2m = (80 - m) + 25

2m = 105 - m

3m = 105

m = 35

The system of equations represents the number of male and female students are: M + F = 80  and F = 2M - 25 .

Out of total 80 students, there are 35 male students in the school band.

Let's use variables to represent the number of male and female students in the school band.

Let M represent the number of male students.

Let F represent the number of female students.

1. There are 80 students in the band:

M + F = 80

2. There are 25 fewer female students than twice the number of male students:

F = 2M - 25

So, the system of equations representing the number of male and female students in the school band is:

M + F &= 80

F &= 2M - 25

Now, solve this system of equations to find the number of male students ( M) in the band.

Substitute the second equation into the first equation:

M + (2M - 25) = 80

Combine like terms:

3M - 25 = 80

Add 25 to both sides:

3M = 105

Divide by 3:

M = 35

So, there are 35 male students in the school band.

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Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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Answer:

R60 is the answer to your question

The calculated z-value, rounded to the nearest hundredth, is -11.88 ,  there is enough evidence to reject the insurance company's claim

The automobile insurance company claims that it offers an average savings of $470 for teenage drivers compared to another company. To test this claim, we'll use the given data from the random sample of 30 customers with an average savings of $405 per year and a standard deviation of $30 per year.
To calculate the z-value, we'll use the formula:
z = (sample mean - population mean) / (standard deviation ÷ √sample size)
Here, the sample mean is $405, the population mean is $470, the standard deviation is $30, and the sample size is 30.
z = ($405 - $470) ÷ ($30 / √30)
z = (-$65) ÷ ($30 ÷ √30)
z = -65 ÷ (30 ÷ 5.48)
z = -65 ÷ 5.47
z ≈ -11.88
To determine whether there is enough evidence to reject the company's claim, we'll compare the z-value with the critical value, usually a 95% confidence interval (z = ±1.96). Since -11.88 is far outside this range.

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Answer: around 63.3

Step-by-step explanation: you need to find how much they traveled first (380) & then divided that by the other number (6). then you get somewhere around 63.3 . :))

Answer:

63.3

Step-by-step explanation:

Therefore, the student reads 2,436 pages on Thursday by the given equation.

According to the given information, the student reads three times as many pages on Thursday as on Wednesday. Let's say that the number of pages read on Wednesday is represented by the variable w. Then, we can write the equation:

Pages on Thursday = 3 * Pages on Wednesday

In this equation, we know that Pages on Wednesday = w. So we can substitute w into the equation and get:

Pages on Thursday = 3w

We are also given that on Wednesday, the student read 812 pages. So we can substitute 812 for w and get:

Pages on Thursday = 3 * 812

Simplifying, we get:

Pages on Thursday = 2,436

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Use the ^ symbol to indicate exponents. So for instance 4^2 = 4 squared.

A decrease of 19% means we have r = -0.19 and 1+r = 1+(-0.19) = 0.81 as the base of the exponent. A decrease of 19% means the population retains 81% each year.

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Answer: The bumblebee is visiting flowest at around .3 minutes faster

Explanation:

2.714 is the unit rate for bumblebee

3 is the unit rate for butterfly

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:

\({\dag{\underline{{\sf{\red{t {}^{2} = \: \dfrac{4.05}{5} \: = 0.81 \: , \: \: t = 0.9s}}}}}}\)

A - to reject a null hypothesis for the finger tapping technique example in the text, we would calculate the probability of that result if the null hypothesis were false. This involves conducting a statistical test to determine the likelihood that the observed results occurred due to chance if the null hypothesis (which states that there is no significant difference between the groups being compared) were false.

rejecting a null hypothesis means that we are concluding that there is a significant difference between the groups being compared. In order to make this conclusion, we need to determine the probability of observing the results we did if the null hypothesis were false. This is typically done by calculating a p-value, which is the probability of obtaining a result as extreme or more extreme than what was observed, assuming the null hypothesis were true. If the p-value is below a predetermined threshold (usually 0.05), we reject the null hypothesis and conclude that there is a significant difference between the groups being compared.

option A is the correct answer and involves calculating the probability of the observed results if the null hypothesis were false. This is done through statistical testing and is typically represented by a p-value.

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Answer:

For the outside square, the diagonal is 7√2, or about 9.9 units.

For the inside square, the diagonal is 5√2, or about 7.1 units.

Answer:

The answer is Y=3x

Step-by-step explanation:

Answer:

A and B are  the correct answers for the check all that apply

Step-by-step explanation:

Sorry if i'm to late