Julie is trying to lose weight. She now weighs 180 pounds. Every week for eight weeks, she was able to lose 2 pounds. a. List Julie's weight for each week. b. Write a recursive definition for this sequence.

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, [tex]W(t)=7e^{-3t}[/tex]. The general solution of the given system is written as [tex]x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right][/tex].

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is [tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x[/tex].

Let's differentiate x₁ concerning t, and we get,

[tex]\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}[/tex]

Now,

[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}[/tex]

From this, we can write,

[tex]x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1[/tex]

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

[tex]\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}[/tex]

Now,

[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}[/tex]

From this, we can write,

[tex]x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2[/tex]

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

[tex]\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}[/tex]

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

[tex]\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}[/tex]

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

[tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right][/tex]

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It can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.

The percentage of children and adolescents in the United States displaying serious psychological disturbances is calculated by dividing the number of children and adolescents with serious psychological disturbances by the total number of children and adolescents in the United States. This can be expressed mathematically as:

% = (Number of children and adolescents with serious psychological disturbances / Total number of children and adolescents in US) x 100

Using estimates from 2018, approximately 48.5 million children and adolescents in the United States, and 10.5 million of them displaying serious psychological disturbances, the percentage of children and adolescents in the United States displaying serious psychological disturbances in 2018 can be calculated as:

% = (10.5 million / 48.5 million) x 100 = 21.7%

Therefore, it can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.

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Answer:

12 times y = x

Step-by-step explanation:

I see on you paper you want to do intervals of 2 so just take 12 and multiply it by the desired number. Equation: 12 x # = the y axis point. This is where #=x-axis and plugging it in the equation gives you the y point.

The weight of the coalition P1, P2, P3 is 36

From the question, we have the following parameters that can be used in our computation:

weighted voting system [20: 9,7,5,3,1]

The variable P1, P2 and P3 are the first three values

So, we have

P1 = 20

P2 = 9

P3 = 7

The weight of the coalition P1, P2, P3 is the sum of the points

So, we have

Coalition = 20 + 9 + 7

Coalition = 36

Hence, the weight coalition is 36

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If cement costs $76 per cubic yard, the total cost of cement for a sidewalk with a volume of 480 inches³ is $1,013.

The total cost of cement for the sidewalk is determined using unit conversions and multiplication.

After determining the volume in inches and converting it to yards, the result is multiplied by the unit cost of cement per cubic yard.

Dimensions of the Sidewalk:

Length = 40 inches

Width = 3 inches

Thickness = 4 inches

Volume = 480 inches³ (40 x 3 x 4)

36 Inches = 1 Yard

480 cubic inches = 13.33 cubic yards

Cost of cement per cubic yard = $76

Cost of the sidewalk = $1,013 ($76 x 13.33)

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Answer: To make the piecewise function continuous for all x, we need to make sure that the function values and the function slopes at the boundaries (-1 and 2) are the same for each piece.

For x = -1:

F(-1) = -6 (from the first piece)

F(-1) = A(-1) + 2 = -A + 2 (from the second piece)

So, to make the function continuous at x = -1, we need to set -6 = -A + 2, which gives us A = -8.

For x = 2:

F(2) = -x^2 + Bx + 14 (from the third piece)

F(2) = A(2) + 2 = 2A + 2 (from the second piece)

So, to make the function continuous at x = 2, we need to set -4 + 2B + 14 = 2A + 2, which gives us B = -5.

Now we can write the function with the constants that we found :

F(x) = -6 if x < -1

-8x + 2 if -1 ≤ x ≤ 2

-x^2 - 5x + 14 if x > 2

This function is continuous for all x and the values and slopes match at x = -1 and x = 2.

Step-by-step explanation:

The measure of ∠P is 96°.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠P and ∠R are alternate angles.

Alternate angles are equal.

So,

∠P = ∠R

2x = x + 48

2x - x = 48

x = 48

Now,

∠P = x + 48

∠P = 48 + 48

∠P = 96

Tus,

The value of ∠P is 96°.

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The rational function in the simplest form of (f/g)(x)  is x / 5x - 2.

Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).

Therefore, let's solve the rational function in the simplest form.

Hence,

f(x) = -x

g(x) = -5x + 2

(f/g)(x) = f(x) / g(x)

Therefore,

(f/g)(x) = - x / -5x + 2

Hence,

(f/g)(x) = - x / - (5x - 2)

Finally,

(f/g)(x) = x / 5x - 2

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Answer:

78cm  78.125

Step-by-step explanation:

Answer: 78.13

Step-by-step explanation:

you start with 40cm and find 25% of that and add it to 40cm. Or you can do 1.25x40=50 That would be July, so repeat to get 50x1.25=62.5 to get august, then again to get 62.5x1.25=78.13

Qualitative data is data that cannot be counted easily using numbers is not have the correct definitions.

Qualitative data is used to address the research questionnaire regarding whats and how many(s) or also for research procedures to quantify a problem. This data can be used to compare or count data on a numerical scale.

This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. This data is used for Qualitative research which is very helpful when understanding social reality and the attributes, beliefs, and motivations of people.

The main importance of this kind of project come into the limelight when someone is trying to understand the reason behind one's beliefs or behaviors.

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Internet of Things refers to the technology that allows data, collected from sensors in all types of machines, to be sent over the Internet to repositories where it can be stored and analyzed.

Internet of Things refers to the collective network of connected devices and the technology that facilitates communication between devices and the cloud, as well as between the devices themselves.

There are some Advantages of IOT:

It can assist in the smarter control of homes and cities via mobile phones. It enhances security and offers personal protection.

Automating activities saves us a lot of time. Information is easily accessible, even if we are far away from our actual location, and it is updated frequently in real time.

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As per the permutation method, the number of possible way for here travel is 5.

The term permutation in math is known as an arrangement of objects in a definite order and the members or elements of sets are arranged here in a sequence or linear order.

Here we have given that Amanda got a train ticket valid for the five cities listed below.

There are Amsterdam, brussels, Lille, Paris, Rotterdam.

So, the given number of ways is 5.

Then the value of n = 5 and the value of r = 1 because here we have given that she can choose to visit some or none of these cities which means that she must chose at least one city.

Then the number of ways is calculated as,

=> ⁵P₁ =  5!/ (5 - 1)!

=> ⁵P₁ = 5!/4!

=> ⁵P₁ = 5

Complete Question:

Let us consider that Amanda got a train ticket valid for the five cities listed below. she can choose to visit some or none of these cities. she doesn't have time to visit all of them.

They are Amsterdam, brussels, Lille, Paris, Rotterdam

Find out the number of ways to visit each cites using permutation method.

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The required expressions are ¬ ∃x(F(x, Ralph)), ∀xF(x, Fred), and  ∀x∃yF(x,y). Here, ¬ means negation, ∃ means existential quantifier, and ∀ means universal quantifier.

One or more variables that are defined on a particular domain are expressed by a predicate. By giving the variable a value or by quantifying it, it is possible to turn a predicate with variables into a proposition.

There are two quantifiers used in this they are (i) existential quantifier which is represented by ∃ and (ii) universal quantifier which is represented by ∀.

For, the proposition, "Nobody trusts Ralph", the quantifier is written as      ¬ ∃x(F(x, Ralph)).

For the proposition, "Everybody trusts Fred", the quantifier is written as ∀xF(x, Fred).

For the proposition, "Somebody trust everybody", the quantifier is written as ∀x∃yF(x,y).

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Answer:

A system of linear equations is a set of two or more equations containing two or more variables. The solution to a system of linear equations is the set of values for the variables that makes all the equations in the system true.

For example, a system of linear equations whose solution is (6,19) could be represented by the following equations:

x + 2y = 25

3x - 4y = 6

Solving this system would yield x = 6 and y = 19 as the solution.

When σ is known, hypothesis tests are performed for one population mean. The one-mean z-test, or simply z-test, is a hypothesis test carried out for a single population mean when the population standard deviation is known.

A data distribution's spread is measured by standard deviation. It calculates the average separation between each data point and the mean.

Whether we consider the data to be a population unto itself or a sample of a broader population affects the method we use to calculate standard deviation.

Statistics is the parent topic for the Population Mean notion. In a nutshell, statistics addresses the issues of gathering data as well as its analysis, interpretation, and presentation. The population mean formula calculates the average of all the values in the population or set of data.

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Answer:

Step-by-step explanation:

You want the number of calories in each dish if 1 portion of hamburger and fries with 2 portions of fettuccine Alfredo has 4240 calories, and 2 portions of hamburger and fries with 1 portion of fettuccine Alfredo has 3980 calories.

The equations describing the calories in each dish can be written using h and f for the calories in a portion of hamburger and in a portion of fettuccine, respectively:

  1h + 2f = 4240

  2h +1f = 3980

Subtracting the first equation from twice the second gives ...

  2(2h +f) -(h +2f) = 2(3980) -(4240)

  3h = 3710 . . . . . . . simplify

  h = 1240 . . . . . . . divide by 3

Then the calories in the fettuccine can be found from the second equation:

  f = 3980 -2h = 3980 -2480 = 1500

The actual number of calories in a portion of hamburger and fries is 1240.

The actual number of calories in a portion of fettuccine Alfredo is 1500.

__

Additional comment

The attachment shows a calculator solution using matrix methods.

The fact that some people who smoked never develop lung cancer does not disprove the evidence.

The fact that some people who have never smoked develop lung cancer does not disprove the evidence linking smoking to lung cancer.

Smoking is a major risk factor for lung cancer, and the overwhelming majority of people who are diagnosed with the disease are smokers or former smokers. However, it is important to note that other factors, such as exposure to radon and other pollutants, can also increase the risk of lung cancer, and that some people may be more genetically susceptible to the disease. So, it is possible for people who have never smoked to develop lung cancer as well.

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The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.

The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:

|2x + y = 8 |

|3x - y = 7 |

This can be rewritten in matrix form as:

|2 1 | |x | | 8 |

|3 -1| |y | | 7 |

To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:

|2 1 | |x | | 8 |

|0 -2| |y | | 1 |

Then, we can divide the second row by -2 to get the coefficient of y to be 1:

|2 1 | |x | | 8 |

|0 1 | |y | |-1/2|

Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:

|2 0 | |x | | 8/2|

|0 1 | |y | |-1/2|

Therefore, the solution to the system of equations is x = 4 and y = -1/2.

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The factors and zeros of the function f(x)=x2-5x+6 are x-3, x-2 and 3 and 2 respectively

Given the quadratic function as;

f(x) = x² - 5x + 6

Using the factorization method of solving quadratic function, we have to multiply the coefficient of x² by the constant of the function

Then find the pair factors of the function that sums up to -5

The pair factors area -2 and -3

Substitute the values, we get;

x²- 2x - 3x + 6

Pair the expression

(x² -2x) - (3x + 6)

Factorize the value

x(x -2) -3(x - 2)

The zeros are;

x-3 = 0

x = 3

Then,

x -2 = 0

x =2

Hence, the values are 2 and 3

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Answer:

a.

b. 35/100 of 76 = 26 to 27 remained

c.
d. statistic

e. experiment

f. I don't think so

Step-by-step explanation:

The polynomial function with the given intercepts of the hirzontal axis can be written as:

p(x) = (x + 7)*(x - 8)*(x - 15)

We know that a polynomial of degree N whose leading coefficient is 1 and has the zeros {x₁, x₂, ...}

Then the polynomial can be written as:

p(x) = (x - x₁)*(x - x₂)*...

Here the zeros (also called intercepts of the horizontal axis, like on this case) are {-7, 8, 15}

Then wecan write the polynomial with these zeros as:

p(x) = (x - (-7))*(x - 8)*(x - 15)

p(x) = (x + 7)*(x - 8)*(x - 15)

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Answer:

Step-by-step explanation:

The top left angle = 52⁰ - also right angle = 52⁰.  ( alternate angles of parallel l;ines).

So, x = 180 - 2(52) = 180-104

= 76 degrees.

Answer: Quadrilateral

Step-by-step explanation:

hexagon: 6 sides

octagon: 8 sides

quadrilateral: 4 sides

triangle: 3 sides

The quadrilateral is the only one that makes sense.

The difference between 4.507 and 4.517 can be expressed as -0.010.

The concept that will be used here is substraction. The outcome of subtracting one integer from another is difference. While we frequently discuss differences in how objects appear, feel, or even taste, mathematics demonstrates how much two numbers vary from one another in terms of quantity. Difference is what is left behind after subtracting one number from another.

the outcome of subtraction of two numbers. the difference between two numbers. For instance: There is a 5 difference between 8 and 3.

We were to find the difference between 4.507 and 4.517 whichg implies the substraction between the values and can be done as

(4.507 - 4.517)= -0.010

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complete question:

What is the difference between 4.507 and 4.517

Answer: I think it is -7 I'm not exactly sure but that's what I think please take someone else's answer just in case.

Step-by-step explanation:

Circumference of circle = 7π yards

The correct option is B.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Given,

Segment drawn from one point on the circle through the center to another point = diameter of circle = 7 yards

Circumference of the circle = π × Diameter

                                              = 7π yards

Hence, 7π yards is the circumference of the circle

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Answer:

b

Step-by-step explanation:

If k is the number of classes and n is the number of observation then for class intervals, select the smallest k such that 2k >= n using statistics.

n = 36

2^5 = 32< 36

2^6 = 64 > 36

So k = 6

a) Frequency distribution: Answer A.

Class interval                 Frequency

0 to less than 1000        11

1000 to less than 2000        9

2000 to less than 3000 3

3000 to less than 4000 3

4000 to less than 5000 5

5000 to less than 6000 5

b) Relative frequency distribution: Answer B.

Class interval                        Relative frequency

0 to less than 1000            11 / 36 = 0.306

1000 to less than 2000            9 / 36 = 0.250

2000 to less than 3000    3 / 36 = 0.083

3000 to less than 4000     3 / 36 = 0.083

4000 to less than 5000     5 / 36 = 0.139

5000 to less than 6000     5 / 36 = 0.139

c) Cumulative relative frequency:

Class interval         Cumulative Frequency

less than 1000         11

less than 2000         20

less than 3000         23

less than 4000         26

less than 5000          31

less than 6000          36

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Answer:

f(-5) = 4

Step-by-step explanation:

[tex]f(x)=|x+1|\\f(-5)=|-5+1|=|-4|=4[/tex]