In your solution, you must write your answers in exact form and not as decimal approximations. Consider the function
f(x) = e²²³, x ER. (a) Determine the fourth order Maclaurin polynomial P₁(x) for f. (b) Using P(x), approximate es. (c) Using Taylor's theorem, find a rational upper bound for the error in the approximation in part (b). (d) Using P₁(x), approximate the definite integral fe³d.r. 2 (e) Using the MATLAB applet Taylortool: i. Sketch the tenth order Maclaurin polynomial for f in the interval −3 < x < 3. ii. Find the lowest degree of the Maclaurin polynomial such that no difference between the Maclaurin polynomial and f(x) is visible on Taylortool for x € (−3, 3). Include a sketch of this polynomial.

The correct answer is as follows:

A. Ageing population

b. Higher life expectancy and best medical facilities.

c. yes less children in 1991.

The data points are ordered, and the center one is chosen by doing so (or if there are two middle numbers, taking the mean of those two numbers).

Once all of the individual values have been added up, the total is divided by the total number of observations to arrive at the average. Taken as the value for which half of the observations are larger and half are less, the "middle" value is used to compute the median.

Given In 1980, the average age of Americans was 30.0 years old. The median age in 1991 was 33.1 years old.

A. The population's aging, which has caused the mean to climb.

B. As technology has advanced over time, people are living longer and expecting better medical care.

C. Yes, in order for the median age to increase, there must be fewer children overall in 1991 than there were in 1980. If there are more kids, the median age might actually decrease.

The complete question is;

The median age of the U.S. population in 1980 was 30.0 years. In 1991, the median age was 33.1 years.

a. What does it mean for the median age to rise?

b. Give two reasons why the median age could rise.

c. For the median age to rise, is the actual number of children less in 1991 than it was in 1980? Why or why not?

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Answer:

612 /1 or 6120/10

Step-by-step explanation:

factor the numerator and denominator and cancel common factors

Answer:

612 there is no fraction solution.....well i dont think so...

Step-by-step explanation:

convert 1/4 into a decimal: 1/4 = .25

                                                         DIVIDE

153 / .25 = 612

                                                        ANSWER

612

if there was a fraction solution it'll probably be 2448/4 = 612

2448/4 would be the fraction solution...

Step-by-step explanation:

is it helpful or not,? don't forget to thank

Answer:

\(x = \frac{13}{4} \)

Step-by-step explanation:

\(4(x + 5) = 6(2x - 1)\)

Expand the terms in the bracket

That's

\(4x + 20 = 12x - 6\)

Subtract 12x from both sides of the equation

\(4x - 12x + 20 = 12x - 12x - 6 \\ - 8x + 20 = - 6\)

Subtract 20 from both sides

\( - 8x + 20 - 20 = - 6 - 20 \\ - 8x = - 26\)

Divide both sides by - 8

\( \frac{ - 8x}{ - 8} = \frac{ - 26}{ - 8} \\ x = \frac{26}{8} \)

We have the final answer as

\(x = \frac{13}{4} \)

Hope this helps you

Answer:

50.24

Step-by-step explanation:

equation A=pi R^2

r^2 = 4^2 = 16

16*3.14 = 50.24

Answer: 50.24

Step-by-step explanation:

A vector space is an abstract mathematical concept that is used to describe a collection of elements, known as vectors.

Vector is a mathematical object that has both magnitude and direction. It can be represented graphically by a line segment with a starting point and an endpoint. Vectors are used in physics, engineering, and mathematics to represent physical quantities such as force, velocity, and acceleration. They can also be used to represent geometric figures such as lines, points, and planes. Vectors are important in many applications, such as navigation, graphics, and robotics.

It is an important concept in linear algebra, and is used to describe the behavior of linear equations and systems.

A vector space is made up of a set of vectors, which can be seen as elements of the space. Each vector is a combination of scalar numbers, called components, and the space is made up of all possible combinations of these components. The components can be real numbers, complex numbers, or even functions.

The vector space is defined by certain operations, called vector addition and scalar multiplication. Vector addition is the process of adding two vectors together, and scalar multiplication is a process of multiplying a vector by a scalar number. Using these operations, the vector space can be used to solve linear equations and systems of equations.

The vector space is also used to describe the geometry of the space. It is used to describe dimensions, angles, and distances between vectors. It is also used to describe shapes and objects within the space, and to describe how they interact with each other.

Finally, the vector space is used to represent linear transformations, which are important in physics and engineering. A linear transformation is a process of mapping a vector to another vector, and is used to describe the behavior of physical systems. This can be used to solve complicated equations and systems of equations.

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Answer:

       7 \(\frac{7}{8}\)

Step-by-step explanation:

Multiply 3 1/2 by 2 1/4

Convert to improper fraction to make it simpler:

7/2 times 9/4 = 7 7/8 square millimeters.

Hope this helps :)

Answer:

Step-by-step explanation:

3.5 x 2.25 = 7.875 or 7 and 7/8

The option that represents the answers for 6, 8, 10, and 14 is the second option-   31, 41, 51, 71

From the question, we are to determine the option that represents the answer for pictures 6, 8, 10, and 14

In the given diagram,

The first picture requires 6 matches

The 2nd picture requires additional 5 matches

the 3rd  picture requires additional 5 matches

and so on

That is

1 → 6

2 → 6 + 5 = 11

3 → 11 + 5 = 16

4 → 16 + 5 = 21

5 → 21 + 5 = 26

6 → 26 + 5 = 31

7 → 31 + 5 = 36

8 → 36 + 5 = 41

9 → 41 + 5 = 46

10 → 46 + 5 = 51

11 → 51 + 5 = 56

12 → 56 + 5 = 61

13 → 61 + 5 = 66

14 → 66 + 5 = 71

Hence, the option that represents the answers for 6, 8, 10, and 14 is the second option-   31, 41, 51, 71

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Answer:

a

Step-by-step explanation:

\(\frac{3x}{x-1}\) + \(\frac{8}{x-1}\)

These fractions have a common denominator and so do not require to be altered.

The numerators can be added to simplify, that is

= \(\frac{3x+8}{x-1}\)

The remaining fractions have different denominators and would require to be altered before they could be added.

Answer:

The value of the tangent is \(-\frac{4}{5}\).

Step-by-step explanation:

Let be \(A(x,y) = (-10, 8)\) on the terminal side of an angle in standard position and let be \(O(x,y)\) the origin of the angle and the origin of the Cartesian plane. By definition of tangent, we make use of the following expression:

\(\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}\) (1)

Where:

\(x_{A}, x_{O}\) - x-Coordinates of point A and point O.

\(y_{A}, y_{O}\) - y-Coordinates of point A and point O.

If we know that \(x_{A} = -10, x_{O} = 0\), \(y_{A} = 8\) and \(y_{O} = 0\), then the value of the tangent is:

\(\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}\)

\(\tan \theta = \frac{8-0}{-10-0}\)

\(\tan \theta = -\frac{4}{5}\)

Answer:

Step-by-step explanation:

In geometry, a "pyramid" is a polyhedron formed by connecting the vertices of the bases to a point called the apex. Most of the historical pyramids can be in Egypt and it has square bases.

Answer:

N=+24,-24

Step-by-step explanation:

Well this is a quadratic equation and we can make further deductions using it's discriminant

b²-4ac=0

N²-4(1×144)=0

N²-576=0

N²=576

N=√576

N=+24,-24

The possible values of N are +24, and -24 if both roots of x² + Nx + 144 are equal to each other.

Any equation of the form \(\rm ax^2+bx+c=0\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

x² + Nx + 144 = 0

Discriminant will be zero:

D = 0

b²-4ac=0

N²-4(1×144)=0

N²=576

N=√576

N=+24,-24

Thus, the possible values of N are +24, and -24 if both roots of x² + Nx + 144 are equal to each other.

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The numbers in order from smallest to largest are:

0.39, 0.731, 0.773, 0.85

To arrange the numbers in order from smallest to largest, i.e. in ascending order, we compare them digit by digit starting from the left.

Comparing the first digit, we have 0.39, 0.731, 0.773, and 0.85. Since 0.39 is the smallest among the first digits, it comes first in the order.

Next, we compare the second digit of each number. We have 0.39, 0.731, 0.773, and 0.85. Among the second digits, 0.731 has the smallest value, so it comes next in the order.

Moving on to the third digit, we have 0.39, 0.731, 0.773, and 0.85. The third digit in all the numbers is different, so we compare them. The smallest third digit is in 0.39, so it comes before the other numbers.

Finally, we compare the fourth digit, but only the number 0.773 has a fourth digit. Since it is the only number with a fourth digit, it comes last in the order.

Putting it all together, the numbers in order from smallest to largest are: 0.39, 0.731, 0.773, and 0.85.

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Answer: 30 degrees

Step-by-step explanation: Vertical angles are always congruent. If Angle A and Angle B are vertical then they are equal to each other. They both will way thirty degrees.

a) Laplace transform :

1) 2s/(s² + 4)²

2)  1/s-2 + 2/(s-2)² + 4

b) Inverse laplace transform :

1)  \(e^{-3t}\)(1 + 2t)

2)  1/2(\(e^{3t} + e^{-3t}\))

Given,

Functions.

a)

1)

f(t) = tsintcost

L(tsintcost) = L(tsin2t/2)

= 1/2 L(tsin2t)

= 2s/(s² + 4)²

2)

f(t) =  \(e^{2t}\)  (sint + cost)²

L( \(e^{2t}\) (sint + cost)² ) = L( \(e^{2t}\) +  \(e^{2t}\)  sin2t)

= L( \(e^{2t}\) ) + L ( \(e^{2t}\) sin2t)

= 1/s-2 + 2/(s-2)² + 4

b)

1)

f(s) = s+5/s² + 6s + 9

f(s) = s+ 5 /(s+3)²

Take partial fraction,

= 1/s+3 + 2/(s+3)²

Take inverse of the f(s),

\(L^{-1}\) (f(s)) = \(L^{-1}\)( 1/s+3 + 2/(s+3)²)

f(t) = \(e^{-3t}\)(1 + 2t)

2)

f(s) = s/s² - 9

f(s) = s/(s+3)(s-3)

Taking partial fraction ,

f(s) = 1/2/s+3 + 1/2 /s-3

Taking inverse laplace of f(s),

\(L^{-1}\) (f(s))  =  \(L^{-1}\) ( 1/2/s+3 + 1/2 /s-3)

f(t) =  1/2(\(e^{3t} + e^{-3t}\))

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The two square roots of 25 are +5 and -5.

Explanation:

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of 25 is a number that, when multiplied by itself, gives 25.

The two square roots of 25 are +5 and -5, because:

+5 x +5 = 25

-5 x -5 = 25

Therefore, the two square roots of 25 are +5 and -5.

Answer:

parallel lines that never intersect.

Step-by-step explanation:

When dealing with two linear equations that have no solution, it means that they usually have two variables and are part of a system of equations. Such an example would be the following two equations

2x - y = 2

4x - 2y = 8

These two equations would be part of the same system and they have no solution because there is no pair of values that will give a valid solution to both for the variables x and y. In a graph these equations would appear as parallel lines that never intersect. This is why no solution is found, because there is no intersection.

Step-by-step explanation:

b = age of Bailey

c = age of Celine

b + c = x

c = b + 8

so, using that identity in the first equation

b + b + 8 = x

2b + 8 = x

or, to go "after" c (Celine) :

b = c - 8

c - 8 + c = x

2c - 8 = x

2c = x + 8

c = (x + 8)/2

in x years c will have increased to c+x, and b to b+x.

so,

b + x + c + x = x + 2x = 3x

and

2c - 8 = 3x

2c = 3x + 8

c = (3x + 8)/2

Answer:

5.924 I may be wrong though sorry

Step-by-step explanation:

I hope I could help you! (:

Ok so I messed up big time I’m so sorry I don’t understand  

It will take the turkey about 3 hours to roast.

a) It is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population variance σ₁² is different than the population variance σ₂² at α=0.05 significance level

b) We are 95% confident that the true ratio of population variances σ₁²/σ₂² is contained by the interval(0.1041, 0.5578).

In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.

a) The provided sample variances are s₁²=0.36and s₂²=1.44 and the sample sizes are given by n₁=30 and n₂=20.

1) Null and Alternative hypothesis:

The following null and alternative hypothesis are need to be tested.

H₀:σ₁²=σ₂²

Hₐ:σ₁²=σ₂²

2) Rejection Region:

Based on the information provided, the significance level is α=0.05, and the rejection region for this Two-tailed test is R={F:F<0.448 or F>2.402}

3) Teat Statistics:

The F-statistic is computed as follows:

F=s₁²/ s₂²

F=0.36/1.44

F=0.25

4) Decision about the null hypothesis:

Since from the sample information we get that F=0.25<\(F_{L}\)=0.448, it is then concluded that the null hypothesis is rejected.

5) Conclusion:

It is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population variance σ₁² is different than the population variance σ₂² at α=0.05 significance level

b) We need to construct the 95% confidence interval for the ratio of two population variances.

The critical values for α=0.05 and df₁=n₁-1

df₁=30-1

=29

df₂=n₂-1

=20-1

=19

The corresponding 95% interval is computed as follows:

CI=(((0.6)²/(1.2)²)×0.4163, ((0.6)²/(1.2)²)×2.2313)

CI=(0.1041, 0.5578)

Therefore, based on the data provided, the 95% confidence interval for the ratio of the population variance is 0.1041<σ₁²/σ₂²<0.5578.

Therefore, we are 95% confident that the true ratio of population variances σ₁²/σ₂² is contained by the interval(0.1041, 0.5578).

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Answer:negative

Step-by-step explanation:

Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.

The test statistic value for this situation is approximately -2.474.

A hypothesis test comparing the sample mean to the assumed population mean is necessary in order to determine the value of the test statistic. The population mean triglycerides level would be the null hypothesis (H0), and the alternative hypothesis (Ha) would be that the population mean is not 130 units.

The t-statistic, which is calculated as follows, is the test statistic utilized in this circumstance:

t = (test mean - expected populace mean)/(test standard deviation/sqrt(sample size))

Given the data gave, we have:

Expected populace mean (μ): 130 Mean of the sample (x): 122

Test standard deviation (s): 20 (n) sample sizes: 30

Connecting the qualities into the recipe, we can work out the test measurement:

t = (122 - 130) / (20 / sqrt(30)) t = -8 / (20 / sqrt(30)) After calculating this expression, we come to the following conclusion:

t ≈ - 2.474

Hence, the test measurement an incentive for this present circumstance is roughly - 2.474.

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According to given information, answer is \(x = 2/3\).

The equation is \(16 * 4^{(x - 2)} = 64^{-2x}\).

Let's begin by simplifying both sides of the equation \(16 * 4^{(x - 2)} = 64^{-2x}\).

We can write \(64^{-2x}\) in terms of \(4^{(x - 2}\).

Observe that 64 is equal to \(4^3\).

So, we have \(64^{(-2x)} = (4^3)^{-2x} = 4^{-6x}\)

Hence, the given equation becomes \(16 * 4^{(x - 2)} = 4^{(-6x)}\)

Let's convert both sides of the equation into a common base and solve the resulting equation using the laws of exponents.

\(16 * 4^{(x - 2)} = 4^{(-6x)}\)

\(16 * 2^{(2(x - 2))} = 2^{(-6x)}\)

\(2^{(4 + 2x - 4)} = 2^{(-6x)}\)

\(2^{(2x)} = 2^{(-6x)}\)

\(2^{(2x + 6x)} = 12x\)

Hence, \(x = 2/3\).

Answer: \(x = 2/3\).

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Answer:

2    4     6      8       10

1     2    3      4       5

Step-by-step explanation:So if it's filling up 2 gallons per minute then you would multiply  2x2=4 3x2=6 4x2=8 and 5x2=10. So you would multiply every minute by 2.

The given linear time-invariant (LTI) system is described by a third-order linear constant coefficient differential equation. To determine the frequency response of the system, we can take the Laplace transform of the differential equation and solve in the Laplace domain

(a) To find the frequency response, we start by taking the Laplace transform of the given differential equation. Let \(Y(s)\) and \(X(s)\) represent the Laplace transforms of \(y(t)\) and \(x(t)\) respectively. By applying the Laplace transform, we obtain:

\[2s^3Y(s) + 4s^2Y(s) + 10sY(s) = 5X(s) + 2sX(s)\]

Simplifying the equation, we get:

\[Y(s) = \frac{5X(s) + 2sX(s)}{2s^3 + 4s^2 + 10s}\]

This equation represents the transfer function of the system in the Laplace domain. To obtain the frequency response, we substitute \(s = j\omega\) into the transfer function, where \(\omega\) represents the angular frequency.

(b) To approximate the Bode plot, we analyze the frequency response at low and high frequencies. At low frequencies (\(\omega \to 0\)), the terms involving \(s\) dominate, and the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{2j\omega X(j\omega)}{2j\omega}\]

Simplifying, we find that the low-frequency gain is 1, indicating that the system passes low-frequency signals without significant attenuation.

At high frequencies (\(\omega \to \infty\)), the terms involving \(s\) become negligible compared to the constant term. Thus, the transfer function can be approximated as:

\[Y(j\omega) \approx \frac{5X(j\omega)}{10j\omega}\]

In this approximation, the gain decreases by -20 dB/decade, indicating that the system attenuates high-frequency signals.

The cutoff frequencies of the system can be determined from the Bode plot where the gain decreases by -3 dB. These frequencies represent the boundary between the passband and stopband of the system.

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Answer:

y= -1/3x + 1

Step-by-step explanation:

The slope is going down 1  and 3 to the right so its -1/3 and the y intercept is 1 so b=1

Hope it helps !

Answer:

the answer is 72 to the expression.

Answer:

3900

Step-by-step explanation:

40950/1.05

Answer:

3900 I think

the 1 st one is corect

Answer:

See below!

Step-by-step explanation:

1) 720cm - m

2) 983 mm - m

3) 130.5kL - L

4) 0.03 g - mg

5) 997 g - kg

6) 9.1 l - ml

7)3.75 c - ml

8) 41.8 in - cm

9) 156.25 lb - kg

10) 9.5 gal - l

11) 680.4 g - lb

12) 4.725 m - ft

Hope this helps, have a lovely day! :)