Estimate the total shaded area below, list all that are correct: A. 14/28 B. 2 1/10 C. 2 100/200 D. 5/2

The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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Answer: The answer is 0.

Step-by-step explanation:

2(3x-1) = 4x

6x-2 = 4x

-2 = -2x

0 = x

Answer:

(3,1) is a solution to this equation

Answer:

yes

Step-by-step explanation:

(3,1); x + 3y = 6  4x - 5y = 7

(3,1)=(x,y)

3 + 3(1) = 6   4(3) - 5(1) =7

3 + 3 = 6        12 - 5 = 7

6=6                 7=7

Therefore, (3,1) is a solution to the two equations x + 3y = 6 and 4x - 5y = 7

Answer:

D 50 minutes

Step-by-step explanation:

If the customer is the fifth car in line then x = 5, so

f(5) = 7(5) + 15

f(5) = 35 +15

f(5) = 50

Answer:

The first graph

Step-by-step explanation:

the dots go down

The first graph is showing a negative correlation so option (A) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

A negative correlation means the value of the function is decreasing as an independent variable is increasing.

So the slope of the negative correlation graph is always negative.

Hence "The first graph is showing a negative correlation".

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Answer:

x= -9/4 or -3

second one is x=5/6 or -8

Answer:

see explanation

Step-by-step explanation:

Given

4x² + 21x + 27 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × 27 = 108 and sum = 21

The factors are 12 and 9

Use the factors to split the x- term

4x² + 12x + 9x + 27 = 0 ( factor the first/second and third/fourth terms )

4x(x + 3) + 9(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(4x + 9) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

4x + 9 = 0 ⇒ 4x = - 9 ⇒ x = - 2.25

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

Following the same method as the previous question

Given

6x² + 43x - 40 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × - 40 = - 240 and sum = + 43

The factors are + 48 and - 5, thus

6x² + 48x - 5x - 40 = 0

6x(x + 8) - 5(x + 8) = 0

(x + 8)(6x - 5) = 0

x + 8 = 0 ⇒ x = - 8

6x - 5 = 0 ⇒ 6x = 5 ⇒ x = \(\frac{5}{6}\)

Answer:

the answer is either 35 or 35.45

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

I just took the test. Front-end estimation is always a whole number.

The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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The behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros is as follows:

At x ≈ -4.919 and x ≈ -0.488, there are local minima.

At x ≈ 1.752, there is a local maximum.

Let's analyze the behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros in more detail.

To find the zeros of the function, we need to solve the equation -x^3 - 5x^2 - 3x + 9 = 0.

To simplify the calculations, let's use a numerical method like the Newton-Raphson method to approximate the zeros. We'll start with initial guesses and iteratively refine them to improve the accuracy of the solutions.

Initial guess: x_0 ≈ -5

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

where f(x) = -x^3 - 5x^2 - 3x + 9

f'(x) = -3x^2 - 10x - 3 (derivative of f(x))

x_1 = -5 - (-5^3 - 5(-5)^2 - 3(-5) + 9) / (-3(-5)^2 - 10(-5) - 3)

≈ -4.919

Initial guess: x_0 ≈ -1

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

x_1 = -1 - (-1^3 - 5(-1)^2 - 3(-1) + 9) / (-3(-1)^2 - 10(-1) - 3)

≈ -0.488

Initial guess: x_0 ≈ 2

Applying the Newton-Raphson method:

x_1 = x_0 - f(x_0) / f'(x_0)

x_1 = 2 - (2^3 - 5(2)^2 - 3(2) + 9) / (-3(2)^2 - 10(2) - 3)

≈ 1.752

After iterating through the Newton-Raphson method, we approximate the zeros as follows:

x ≈ -4.919

x ≈ -0.488

x ≈ 1.752

Now, let's analyze the behavior of the graph at each zero:

x ≈ -4.919:

When x is close to -4.919, y is close to zero. Since the coefficient of the leading term (-x^3) is negative, as x approaches -4.919 from the left side, the graph of the function will be decreasing. As x approaches -4.919 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -4.919 is a local minimum.

x ≈ -0.488:

When x is close to -0.488, y is close to zero. Similarly, as x approaches -0.488 from the left side, the graph will be decreasing, and as x approaches -0.488 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -0.488 is also a local minimum.

x ≈ 1.752:

When x is close to 1.752, y is close to zero. In this case, as x approaches 1.752 from the left side, the graph will be increasing, and as x approaches 1.752 from the right side, the graph will be decreasing. Therefore, the behavior of the graph near x ≈ 1.752 is a local maximum.

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Answer:

  1435.5 m²

Step-by-step explanation:

You want the area of the triangular prism with base side lengths 12 m, 33 m, and 35 m, and height 13 m. The altitude of the base triangle is given as 11.3 m from the longest side.

The area of each triangular base is ...

  A = 1/2bh

  A = 1/2(35 m)(11.3 m) = 197.75 m²

The area of the three rectangular faces will be ...

  LA = (12 m)(13 m) +(33 m)(13 m) +(35 m)(13 m)

  = (13 m)(12 +33 +35 m) = (13 m)(80 m) = 1040 m²

The total area is the sum of the lateral area and the areas of the two bases:

  A = 1040 m² +2(197.75 m²) = 1435.5 m²

The surface area of the triangular prism is about 1435.5 m².

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The Miller index notation for the (100) plane in an FCC crystal structure is [100].

Miller indices are a way to describe crystal planes and directions in a standardized manner. In the case of FCC crystal structure, the (100) plane is parallel to the x-y plane and intersects the x-axis, y-axis, and z-axis at points where the Miller indices are (1,0,0), (0,1,0), and (0,0,1), respectively.

However, to express the (100) plane in a concise and standardized manner, we can use the Miller index notation, which involves taking the reciprocals of the intercepts of the plane with the crystallographic axes and then reducing them to the smallest integer values. In the case of the (100) plane in FCC, all of the intercepts are 1, so the Miller indices are [100].

the pd expression for the (100) plane in FCC crystal structure is [100].

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Answer:

where is the options? or is any given.

Step-by-step explanation:

Answer:

y = 110

z = 70

Step-by-step explanation:

Answer:

12.0

Step-by-step explanation:

Answer:

452.4

Step-by-step explanation:

I'm pretty sure it's water bro

Answer:

{1, 2, 3}

Step-by-step explanation:

As we know that n divided by 3 must have a remainder of either 1, 2, or 0 (none).

Thus, it is {1, 2, 0}

Or we can write F = {0, 1, 2}

I hope this helps you :)

To calculate the effective annual cost of not taking the discount and paying on day 40, we need to determine the cost of financing the purchase over 40 days.

First, we can calculate the cost of not taking the discount:

Discount = 3%

Days to Pay = 40

Effective Interest Rate = (Discount % / (100% - Discount %)) x (365 / (Days to Pay - Discount Period))

Effective Interest Rate = (3% / (100% - 3%)) x (365 / (40 - 20))

Effective Interest Rate = 0.03109 or 3.109%

This means that if Wyatt Oil does not take the discount and pays on day 40, they will effectively be paying an annual interest rate of 3.109% to finance the purchase.

Therefore, the closest answer to the effective annual cost is 3.109%, which is option B: 18%.

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Answer:

Area = 50 cm²

Step-by-step explanation:

Area of a trapezium ABDE = ½(a + b)h

where,

a = BD = 2.5 cm

b = AE = 7.5 cm

h = DE = ?

We need to find DE ti be able to calculate the area.

DE = CE - CD

DE = CE - 5

Since ∆ACE is similar to ∆BCD, therefore:

AE/BD = CE/CD

Plug in the values

7.5/2.5 = CE/5

Cross multiply

CE*2.5 = 7.5*5

CE*2.5 = 37.5

Divide both side any 2.5

CE = 37.5/2.5

CE = 15

Thus, DE = CE - 5 = 15 - 5

DE = 10

✅Area of trapezium = ½(BD + AE)DE

= ½(2.5 + 7.5)*10

= ½(10)10

= 50 cm²

324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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To determine if a high school's claim of having unusually high math SAT scores is justified, we can compare the sample mean with the population mean using a z-score.

The average math SAT score is given as 514 with a standard deviation of 113. A random sample of 60 students from the high school yielded a sample mean of 531. By calculating the z-score and comparing it to the range of usual events, we can assess the validity of the high school's claim. To determine if the high school's claim is justified, we calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n))

Where:
x is the sample mean (531),
μ is the population mean (514),
σ is the population standard deviation (113),
and n is the sample size (60).

Substituting the values into the formula: z = (531 - 514) / (113 / sqrt(60))
Calculating the z-score gives us a value. By comparing the z-score to the range of usual events, we can determine if the high school's claim is justified. The range of usual events is typically within ±2 standard deviations from the mean. If the z-score falls within this range, it suggests that the sample mean is not significantly different from the population mean, and the claim of unusually high scores may not be justified.

Please note that the provided explanation assumes a normal distribution and the use of a one-sample z-test.

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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As per the given standard deviation, the mean scores difference between online and paper tests is 2.9 and the p value of the test is 0.2999

Standard deviation:

In statistics, standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.

Given,

A college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68.4 with a standard deviation of 12.1. Those who took the test online had an average score of 71.3 with a standard deviation of 14.2.

Here we need to find the mean scores difference between online and paper tests and the p value of the test.

While we looking into the given question we have identified the following values,

Test on paper:

Average score = 68.4

Standard deviation = 12.1

Online test

Average score = 71.3

Standard deviation = 14.2

Total number of students = 45

So, the difference between the mean scores differ between online and paper tests is calculated as,

=> 71.3 - 68.4 = 2.9

And the p -  value is 0.2999.

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The cpk for this process is 0.5.

To calculate the cpk for this process, we first need to calculate the process capability index (cp) using the formula:
cp = (USL - LSL) / (6 × sigma)
where USL is the upper specification limit (48), LSL is the lower specification limit (30), and sigma is the process standard deviation (4).
cp = (48 - 30) / (6 × 4)
cp = 18 / 24
cp = 0.75
Next, we can calculate the cpk using the formula:
cpk = min[(USL - mean) / (3 × sigma), (mean - LSL) / (3 × sigma)]
cpk = min[(48 - 42) / (3 × 4), (42 - 30) / (3 × 4)]
cpk = min[6 / 12, 12 / 12]
cpk = min[0.5, 1]
cpk = 0.5

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*the box plots are shown in the attachment below.

Answer:

The median hours spent in the weight room for school 1 is less than the median for school 2 and the interquartile ranges for both.

Step-by-step explanation:

Median on a box plot is depicted by the vertical line that divides the rectangular box into 2.

The median hours for school 1 = 8

The median hours for school = 9

Interquartile range on a box plot is the range of the rectangular box.

Interquartile range for school 1 = 10 - 4 = 6

Interquartile range for school 2 = 12 - 6 = 6

Therefore, it is true that the median hours spent by school 1 (8 hrs) is less than the median hours spent by school 2 (9 hours).

It is also true that the jnterquartile range for school 1 and school tok are also equal (6).

(a) The number of ways to choose 5 colors without replacement from 15 distinct colors, where the order of the choices is not relevant, is given by the combination formula. This is denoted as "15 choose 5," or 15C5, which is equal to 3,003.

(b) If the order of the choices is relevant, then the number of ways to choose 5 colors without replacement from 15 distinct colors is given by the permutation formula. This is denoted as "15 permute 5," or 15P5, which is equal to 3,003,600.

In part (a), we use the combination formula because we want to know the number of ways to choose 5 colors from 15 distinct colors without regard to the order of the choices. This formula is given by nCr = n!/(r!(n-r)!), where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15C5 = 15!/(5!(15-5)!) = 3,003.

In part (b), we use the permutation formula because we want to know the number of ways to choose 5 colors from 15 distinct colors, where the order of the choices matters. This formula is given by nPr = n!/(n-r)!, where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15P5 = 15!/10! = 3,003,600.

Overall, the key difference between part (a) and part (b) is whether or not the order of the choices matters. If the order doesn't matter, we use the combination formula (nCr), and if the order does matter, we use the permutation formula (nPr).

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Answer:

No solution

Step-by-step explanation:

I got it right on delta math, just dont write anything and turn that in and it should be correct.

Answer:

1. Putting  x = 0.5, y = -1/10 gives  0.44

2. Putting  x = -1, y = -3  gives 14

3. Putting x =3/4 , y = 2/5 gives 1.665

4. Putting  x = 0, y = 2.5 gives - 11.25

5.  Putting x = √2, y = √2 gives 17

6. Putting x = 2, y = -1  gives - 1

Step-by-step explanation:

-3x2 + 2y2 + 5xy - 2y + 5x2 - 3y2

1. Putting  x = 0.5, y = -1/10

-3(0.5)^2 + 2(-1/10)^2 + 5(-0.05) - 2(-1/10) + 5(0.5)^2 - 3(-1/10)^2

= -0.75 +0.02 - 0.25 +0.2 + 1.25- 0.03

= 0.44

2. Putting  x = -1, y = -3

-3(-1)^2 + 2(-3)^2 + 5(3) - 2(-3) + 5(-1)^2 - 3(-3)^2

= -3 +18 +15+6+5-27

= 14

3. Putting x =3/4 , y = 2/5

-3(3/4)^2 + 2(2/5)^2 + 5(6/20) - 2(2/5) + 5(3/4)^2 - 3(2/5)^2

=- 27/16 +8/25 +30/20 -4/5 +45/16 - 12/25

= 18/16 - 24/25 + 30/20

= 18/16 - 96+150/100

= 18/16 +54/100

= 1800+ 864/1600

= 2664/1600

=1.665

4. Putting  x = 0, y = 2.5

-3(0)^2 + 2(2.5)^2 + 5(0) - 2(2.5) + 5(0)^2 - 3(2.5)^2

= 12.5 - 5.0 - 18.75

= -11.25

5.  Putting x = √2, y = √2

-3(√2)^2 + 2(√2)^2 + 5(√2.√2) - 2(√2) + 5(√2)^2 - 3(√2)^2

= -6 +4+10-4+19-6

= 17

6. Putting x = 2, y = -1

-3(2)^2 + 2(-1)^2 + 5(-2) - 2(-1) + 5(2)^2 - 3(-1)^2

= -12+2 -10 +2 +20 -3

= -1

Answer:

\( = x_{1} = \frac{1 - \sqrt{65} }{4} . x_{2} = \frac{1 + \sqrt{65} }{4} \)

Step-by-step explanation:

\(2x ^{2} - x - 8 = 0\)

\(x = \frac{ - ( - 1)± \sqrt{( - 1 {)}^{2} } - 4 \times 2 \times ( - 8)}{2 \times 2} \)

\(x = \frac{1± \sqrt{1 + 64} }{4} \)

\(x = \frac{1± \sqrt{65} }{4} \)

\( = x_{1} = \frac{1 - \sqrt{65} }{4} . x_{2} = \frac{1 + \sqrt{65} }{4} \)

Answer:

\(x=\frac{-1+-\sqrt{65}}{4}\)

Step-by-step explanation:

Using the quadratic formula,

\(x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}\\x=\frac{-1+-\sqrt{-1^{2}+64}}{4}\\x=\frac{1+-\sqrt{65}}{4}\\\)