Evaluate the expression.
5+ [4•3(2 + 1)]

The approximations to the equation of order n = 0, n = 1, n = 2, and n = 3 are given as follows:n=0: f(y) ≈ f(k) = ry,n=1: f(y) ≈ f(k) + f'(k)(y-k) = ry,n=2: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! = rk + r(y-k),n=3: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! + f'''(k)(y-k)^3/3! = rk + r(y-k).

In order to find the first four terms of the Taylor series of f(y) around y = k, we will use the formula given below:f(y) = f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! + f'''(k)(y-k)^3/3! + ...The right-hand side of the differential equation is f(y) = ry in C. Hence,f(k) = rk, f'(k) = r, f''(k) = 0, f'''(k) = 0, ...Substituting the above values in the formula, we getf(y) = rk + r(y-k) + 0(y-k)^2/2! + 0(y-k)^3/3! + ...Therefore, the first four terms of the Taylor series of f(y) about y = k are given as follows:f(y) = rk + r(y-k) = ryExercise 4:

We will use the series obtained in exercise 3 to find approximations to the equation of order n = 0, n = 1, n = 2, and n = 3, where n is the highest power of (y-k) in the expansion.

The approximations are given below:n=0: f(y) ≈ f(k) = rk = f(k) = ry,n=1: f(y) ≈ f(k) + f'(k)(y-k) = rk + r(y-k) = ry,n=2: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! = rk + r(y-k) + 0(y-k)^2/2! = rk + r(y-k),n=3: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! + f'''(k)(y-k)^3/3! = rk + r(y-k) + 0(y-k)^2/2! + 0(y-k)^3/3! = rk + r(y-k).

Therefore, the approximations to the equation of order n = 0, n = 1, n = 2, and n = 3 are given as follows:n=0: f(y) ≈ f(k) = ry,n=1: f(y) ≈ f(k) + f'(k)(y-k) = ry,n=2: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! = rk + r(y-k),n=3: f(y) ≈ f(k) + f'(k)(y-k) + f''(k)(y-k)^2/2! + f'''(k)(y-k)^3/3! = rk + r(y-k).

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Answer:

If the force (F units) between two particles is inversely proportional to the square of the distance (x units) between them, we can write the relationship between F and x as F = k/x^2, where k is a constant.

When the distance between the particles is reduced to 0.5x, the relationship between the new force (F') and the distance (0.5x) can be written as F' = k/(0.5x)^2.

If we divide F' by F, we find that the ratio of the new force to the original force is equal to (k/(0.5x)^2) / (k/x^2) = (1/(0.5x)^2) / (1/x^2) = (4/x^2) / (1/x^2) = 4.

Therefore, the ratio of the force to the original force when the distance between the particles is reduced to 0.5x is 4.

Answer:

$6.75

Step-by-step explanation:

25 hours times $9= $225/week

3% increase from $9.00= $0.27

$9.27 times 25 hours= $231.75

$231.75-$225= $6.75 more per week

Answer:

x = -5

Step-by-step explanation:

Im not very sure but here it is. =D

Tell me if it helps you.

Answer:

1-B
2-E

3-D

4-A

5-C

Step-by-step explanation:

-4x + 3y = 3

3y = 4y + 3

y = 4/3 y + 1 => slope is 4/3, y-intercept is (0,1)

Equation 1 matches with Letter B

12x - 4y = 8

4y = 12x - 8

y = 3x - 2 => slope is 3, y-intercept is (0,-2)

Equation 2 matches with Letter E

8x + 2y = 16

2y = -8x + 16

y = -4x + 8 => slope is -4, y-intercept is (0,8)

Equation 3 matches with Letter D

-x + 1/3 y = 1/3

1/3 y = x + 1/3

y = 3x + 1 => slope is 3, y-intercept is (0,1)

Equation 4 matches with Letter A

-4x + 3y = -6

3y = 4x = -6

y = 4/3 x - 2 => slope is 4/3, y-intercept is (0,-2)

Equation 5 matches with Letter C

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Answer:

6 mm²

Step-by-step explanation:

1/2 x 3 x 4 = Area of triangle

=> 2 x 3 = Area of triangle

=> 6 mm² = Area of triangle.

Hoped this helped.

Answer:

It's 15

Step-by-step explanation:

Answer:

1st term is 12

12th term is 144

Step-by-step explanation:

48-36=a4-a3=a1 so a1 is equal to 12  now to get from a3 to a4, you must add 12, so d=12.

a12=12+11*12=12+132=144

Answer:

\( \displaystyle \boxed{k = 3}\)

Step-by-step explanation:

to determine the Value of k we need to find the equation of f(x) and g(x)

finding the equation of f(x):

f(x) is a linear function which form is given by:

\( \displaystyle f(x) =mx + b\)

where:

from the graph we acquire that

\(b = 4\)

to figure out m we can consider the following formula:

\( \displaystyle m = \frac{ \Delta y}{ \Delta x} \)

from the graph we obtain that both ∆x and ∆y is 1 thus substitute:

\( \displaystyle m = \frac{ 1}{ 1} \)

simplify:

\( \displaystyle m = 1\)

altogether we acquire:

\( \displaystyle f(x) =x + 4\)

finding the equation of g(x):

likewise f(x)

from the graph we obtain that

thus substitute:

\( \displaystyle m = \frac{ 3}{ 1} \)

simplify:

\( \displaystyle m = 3\)

from the graph we acquire

altogether substitute therefore

\( \displaystyle g(x) =3x + 4\)

finding the value of k:

given that,

\( \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4\)

so our equation is

\( \displaystyle kx + 4 = 3x + 4\)

cancel 4 from both sides:

\( \displaystyle kx = 3x \)

divide both sides by x:

\( \displaystyle \boxed{k = 3}\)

and we're done!

Disclaimer:

at the following link we posted the complete question

the complete question:

Answer:

k = 3

Step-by-step explanation:

Graph is in attachment .

Finding equation of first line [ f(x) ] :-

We can see that the line passea through point ( 0,4) . Therefore ,

Also it passes through (-4,0 )

Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.

Equation of f(x) :-

Similarly when we will find the equⁿ of g(x) :-

By question :-

Send us a pciture and we will be able to answer

Answer:

C)

Step-by-step explanation:

The midpoint is the average of the two points.

Thus,

Midpoint = [ ( 7 + 3i) + (-5 - 8i) ] / 2 = ( (7-5) + i(3-8) ) / 2 = (2 - 5i)/2 = 1 - 2.5i

The right response is, "5 hexagons are made up of 15 pattern block trapezoids."

Geometric shapes known as pattern block trapezoids are frequently utilized in arithmetic instruction. On a flat surface, they are one of a number of forms that can be used to make tessellations, or repeating patterns. Different colored plastic or foam pattern block trapezoids are available in a variety of sizes, with each color denoting a distinct size and form. Pattern block trapezoids are frequently used to teach geometry principles like area, perimeter, and angles in addition to their application in making tessellations. They can also aid in the development of kids' spatial reasoning and problem-solving skills.  

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The appropriate symbol is greater then used for the given data will be as  \(9.2 > 9.12\)

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

The given expression will be witten as:

\(9.2 > 9.12\)

Since 9.2 is greater then 9.12 so we will use greater then sign.

Hence the appropriate symbol is greater then used for the given data will be as  \(9.2 > 9.12\)

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At least 5 expected observations in each cell in order to apply the chi-square test of independence, we prefer to have at least 5 expected observations in each cell. The correct answer is c.

The chi-square test of independence is a statistical method used to determine whether two categorical variables are independent or associated with each other.

To apply this test, it is preferred to have at least 5 expected observations in each cell of the contingency table. The expected frequency is calculated based on the assumption of independence between the two variables.

If the expected frequency is less than 5 in any cell, the chi-square test may not be valid and alternative methods, such as Fisher's exact test, should be considered. Having a sufficient sample size can also improve the accuracy and reliability of the test results.

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The observed score on y for Carl is 7.

In regression analysis, the predicted values of the dependent variable (in this case, happiness) are calculated based on the values of the independent variable(s) (in this case, average amount of sleep) using a regression equation. If Carl's predicted happiness score based on the regression equation is 6, but his actual reported happiness score is 7, then his observed score on y is 7.

The difference between his predicted and observed score can be used to evaluate the accuracy of the regression equation in predicting happiness based on sleep, and to identify any outliers or other factors that may be influencing the relationship between the two variables.

Overall, the observed score on y for Carl is 7.

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Option B "Perpendicular Lines"  is correct.

"Perpendicular Lines" are two lines that intersect at a right angle, forming 90-degree angles between them. Thus, Option B holds the truth.

Perpendicular lines are a fundamental concept in geometry and they are defined as two lines that meet at a right angle; forming four 90-degree angles. This means that the slopes of the two lines are negative reciprocals of each other. Perpendicular lines are important in many areas of mathematics and physics because they allow us to calculate angles, distances and other geometric properties.

Perpendicular lines are useful in many practical applications such as: architecture, engineering and construction. By understanding the properties of perpendicular lines, one can better understand the geometry of our world and solve real-world problems.

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Yes, the radiometrically dated basaltic clasts within the conglomerate can be considered a reliable age for the conglomerate.

The reliable age of conglomerate basaltic clasts radiometrically dated to 50 million years ago is the Eocene era.

The sedimentary rock called conglomerate has basaltic clasts embedded in it that have been radiometrically dated to 50 million years ago. Therefore, this is a reliable age for the conglomerate because the basaltic clasts would have been derived from the volcanoes that were active at the time, which would have deposited ash and pyroclastic material in the surrounding area. This means that the conglomerate itself must have been formed sometime later after the volcanic activity, during the Eocene era.

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Answer:

The slope is -1.3

Step-by-step explanation:

Plug it in stat, but Ill try to explain it. y2-y1/x2-x1

(-3,4)(3,-4)

-4-4/3-(-3) = -1.3

True. If y is a differentiable function of u and u is a differentiable function of x, then the chain rule states that y is a differentiable function of x.

The chain rule states that if y is a function of u and u is a function of x, then the derivative of y with respect to x is equal to the derivative of y with respect to u multiplied by the derivative of u with respect to x. This means that if y is a differentiable function of u and u is a differentiable function of x, then y is also a differentiable function of x.

In mathematics, a function is said to be differentiable at a point if it is possible to define the derivative of the function at that point. The derivative of a function is a measure of how the function changes as its input (or independent variable) changes. It is defined as the limit of the difference quotient, which is a measure of the rate of change of the function over a small interval around the point of interest.

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The flow rate of water in each steel pipe at 25°C is as follows:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

To calculate the flow rate of water in each steel pipe, we need to consider the properties of the pipes and the lengths of the sections through which the water flows. The schedule 40 pipes mentioned in the question are commonly used for various applications, including plumbing.

Given the lengths of each pipe section, we can calculate the total equivalent length (sum of all lengths) to determine the pressure drop across each pipe. Since the question mentions ignoring minor losses, we assume that the flow is fully developed and there are no significant changes in diameter or fittings that would cause additional pressure drop.

Using the flow rate formula Q = ΔP * A / √(ρ * (2 * g)), where Q is the flow rate, ΔP is the pressure drop, A is the cross-sectional area of the pipe, ρ is the density of water, and g is the acceleration due to gravity, we can calculate the flow rates.

Considering the given data, we can directly assign the flow rates to each pipe:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

The flow rate of water in each steel pipe at 25°C is determined based on the given information. Pipe 1 has a flow rate of 1.2 ft³/s, Pipe 2 and Pipe 3 have flow rates of 0.3 ft³/s each, and Pipe 4 has a flow rate of 0.6 ft³/s. These values represent the volumetric flow rate of water through each pipe under the specified conditions.

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Responder:

2n

Explicación paso a paso:

Dado 2, 4, 6, 8

Enésimo término de una progresión aritmética:

Tn = a + (n - 1) d

d = diferencia común

n = enésimo término

a = primer término

Tn = 2 + (n - 1) * 2

Tn = 2 + 2n - 2

Tn = 2n

Answer: A

Step-by-step explanation: Okay! So the first thing we notice when looking at the diagram is that the units are in centimeters. We want these in feet. They tell us that 1cm = 4ft. Now we know that the actual scale would have the length be 12 ft, and the width would be 8 ft.

Now, we look at the size they want it increased by: 20%. In order to do this, we must multiply the length and width by 0.2. Then we take THOSE values, and add them to the original.

Let's work it out.

Step 1. Multiplying values by 0.2 (20%)

    Length:  (12ft)(0.2)= 2.4

    Width:    (8ft)(0.2)= 1.6

Step 2. Now that we've found 20% of our original length and width, we must add those values to the original length and width.

    Length: 12ft + 2.4ft = 14.4 ft

    Width:   8ft + 1.6ft= 9.6ft

Those are your final answers! Hope that helps :)

The number you thought of is -1.

To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.

The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.

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Here is 29 digits:

3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7

I hope this helped you!

Answer:

556

Step-by-step explanation:

Surface area=2*(lb+bh+lh)=2*(110+80+88)=556

Answer:

84

Step-by-step explanation:

70% of 120= 84

Answer:

They have completed 50% of the race

Step-by-step explanation:

13 is half of 26. So when putting it in fraction form 13/26 can be equal to 50/100/

Now we can see that our fraction is 50/100, which means that 13/26 as a percentage is 50%.

Answer: C.

Step-by-step explanation: To find the volume of something, you multiply the length, width, and height together. Since they have already multiplied the length and width together to form the base, multiply 7 by 12 (base times height) to get 84 cubic inches.

The information that provided by the graph are median and the range. The information that cannot be gotten from the graph is the mode.

The interquartile range is 25.

The outlier would distort the value of the median and mean.

The information that can be derived from the box plot are the minimum value, maximum value, range, median, first quartile and third quartile.

The interquartile range is the difference between the first quartile and third quartile.

Interquartile range = 60 - 35  = 25

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Answer:

PART A: You cannot find the mode from the box plot. However, you can find the mean, median, and the range along with outliers.

PART B: 60-35=25 This is the interquartile range.

PART C: The outliers will cause the mean into increase.

Step-by-step explanation:

Step-by-step explanation:

p varies directly with d.

that means there is a constant k, so that

p = kd

to find k we use the one set of numbers we know about

125 = k×2

k = 125/2 = 62.5

now, when the water is 4.5 meters deep :

p = 62.5 × 4.5 = 281.25 pascal