What are the benefits and limitations of quadratic models in real-world applications such as bridge design?

Answer:

  see attached for a graph; see below for the check

Step-by-step explanation:

You want to solve this system of equations by graphing, then check the result.

The graph of the equations is attached. The fist has a slope of 1/4 and a y-intercept of -1; the second has a slope of 1/2 and a y-intercept of -2.

The solution is seen to be (x, y) = (4, 0).

In the first equation:

  -4 +4(0) = -4 . . . . . true

In the second equation:

  0 = 1/2(4) -2 . . . . . true

The explicit rule for the g(x) is g(x) = 54000 + 6000x

The definition of the function is given as

Initial = 60000

And the table of values

The definitions from the table imply that we simply add 6000 to the previous term to get the current term

This means that

Common difference, d = 6000

The sequence is then represented as

f(x) = a + (x - 1)d

So, we have

f(x) = 60000 + (x - 1) * 6000

Evaluate

f(x) = 54000 + 6000x

Hence, the equation is f(x) = 54000 + 6000x

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Answer:

Step-by-step explanation:

1. the variable 'y' is absent in the equation given in the condition. It means, the given line is vertical. Then

2. if line is vertical, it is parallel to Y-axis, then no y-interception.

3. if to re-write the given equation into x=1, then x-interception is x=1.

4. graph is in the attachment.

a) given any two real numbers a and b, there is a real number c such that c is between a and b.

b) for any two real numbers a and b, there exists c such that a < c < b.

What are real numbers?

Simply put, in the number system, real numbers are a combination of rational and irrational numbers. In general, all arithmetic operations can be applied to these numbers, and they can also be represented in a number line.

Imaginary numbers, which cannot be expressed on a number line and are frequently employed to symbolise complex numbers, are also unreal numbers that are not expressed in the real world. The letter "R" stands for real numbers, which can be positive or negative. This group encompasses all natural numbers, fractions, and decimals.

For the given question, in the first part, it is said that there is always a real number between every two real numbers.

Using this statement we have to fill in the following blanks.

If we have two given numbers a and b, then there exists a real number c, such that c is between a and b.

Therefore the complete statement is:

a) given any two real numbers a and b, there is a real number c such that c is between a and b.

b) for any two real numbers a and b, there exists c such that a < c < b.

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Answer:

Step-by-step explanation:

This is just the normal parent sin graph, y = sinx

The missing number is 20.

An amount of something often expressed as a number out of hundred. It is denoted by the symbol '%'.

25% of 20 = [tex]\frac{25}{100}*20[/tex]

                 =5

Then the another number is 20+5=25

The percentage to the number 25 becomes 20 is,

               [tex]\frac{x}{100} *25=20[/tex]

            ⇒x=[tex]\frac{20}{25} *100[/tex]

            ⇒x=80%

Hence, the missing number is 20 and the missing percentage is 80%.

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Answer:

B, C, D

Step-by-step explanation

bascially flip the figure upside down. whatever was parallel before stays parallel

The construction of the graph is shown here.

Also cumulative frequency in the table form mentioned here. This can be solved using the concept of frequency distribution.

Tables or charts of frequency distributions are used to represent them. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

Relative frequency distributions and cumulative frequency distributions are the two primary forms of frequency distributions utilised in data analysis. Both depend on frequency, which is the amount of times something happens inside a specific data set in descriptive statistics.

Class                       Frequency                        Cumulative frequency              

0.180-0.199                  2                                      2

0.200-0.219                10                                     12

0.220-0.239               39                                    51

0.240-0.259               56                                    107

0.260-0.279               60                                     167

0.280-0.299               49                                     216

0.300-0.319               27                                      243

0.320-0.339               12                                      255

0.340-0.359                1                                        256

The construction of the graph is shown below:

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The complete question is as follows:

The solution is, the value we get 3:4.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

1/2 (x+8) -:xy +z

when x=4 y=12 and z=-40

so, we get,

1/2*12 : 48+ (-40)

=6:8

=3:4

Hence, The solution is, the value we get 3:4.

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It is possible that the standard deviation is greater than the mean for a list of positive numbers.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Take into consideration, the list of numbers -

1,2,3,4,5,20

The mean formula is - Number of observations / Total observations.

Substitute the values in the equation -

Mean = 1 + 2 + 3 + 4 + 5 + 20 / 6

Mean = 35 / 6

Mean (x') = 5.833

The number of observations is n = 6

The variance is the sum of squared deviations from the mean divided by

n−1.

The standard deviation is the square root of the variance -

s = {√(1 - 35/6)² + .... + (20 - 35/6)²} / (6-1)

s = 7.0828

Therefore, the standard deviation is higher than the mean.

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The value of t for a t-distribution with 15 degrees of freedom is -2.131.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Degree of freedom df = 15

and area to the left of t = 0.025

Hence, area right of t = 1-0.025 = 0.975

From the table of t-distribution for the area left of t = 0.025 and 15 degrees of freedom, the corresponding value of t is -2.131.

Hence, t = -2.131

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According to the previous sentence, simple interest is equivalent to $157.92.

With only the starting principal and a fixed interest rate, simple yearly interest of government debt interest is calculated. Compounding, which results in borrowers paying tax on both the principal and interest across a number of payment intervals, is not included. To calculate simple interest, multiply the original by the timeframe, rates of return, and duration.

Due to it,

P = $582.09

R = 8.3%

T = 89 days

Now, Simple Interest = P*R*T/100

Simple Interest = 582.09 * 8.3 * 89/100

Simple Interest = 4299.89

Simple Interest would be $4299.89 as a result.

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The cost of sales for Sheridan Industries, given the gross profit and the sales, is $ 6, 498, 000

The cost of sales refers to the amount that the company invested to be able to make the sales they did. This includes the cost of purchases of goods which were then sold ( or their cost of manufacturing ).

The cost of sales to Sheridan Industries can be found by the formula :

= Sales - Gross profit

The cost of sales is therefore :

= 7, 752, 000 - 1, 254, 000

= $ 6, 498, 000

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The full question is:

Sheridan Industries had sales in 2021 of $7,752,000 and gross profit of $1,254,000. Management is considering two alternative budget plans to increase its gross profit in 2022. To do this this, management first needs to determine its cost of sales. Find the cost of sales for 2021.

The formula in this problem is classified as recursive.

The terms are given as follows:

The features that we are given for the formula are given as follows:

Considering that we need the previous term to obtain the nth term, this is an recursive formula.

Then the terms are given as follows:

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The length of the fence that Winston installs is 200 yards

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Winston installs a fence post every eight yards after the first post he installs 25 more, therefore:

The length of the fence = 8 yards * 25 post = 200 yards

The length of the fence is 200 yards

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Answer:

x = 2

Step-by-step explanation:

To obtain a 40% antifreeze solution, we need to add more antifreeze to the 30% solution. Let's call the amount of pure antifreeze that needs to be added x. Then, the amount of antifreeze in the solution will be 2 + x quarts.

The concentration of antifreeze in the solution will be:

(0.30 * 2) + (0.100 * x) = 0.40 * (2 + x)

Solving for x:

0.60 + 0.100x = 0.40 * (2 + x)

Expanding the right-hand side:

0.60 + 0.100x = 0.80 + 0.40x

Solving for x:

0.100x = 0.20

x = 2

So, 2 quarts of pure antifreeze must be added to obtain a 40% antifreeze solution.

Answer: Given f(x) = -4x + 9 and g(x) = x^2 - x - 10, the composition of functions fog(x) is defined as fog(x) = f(g(x)).

To find the value of fog(5), we need to evaluate g(5) first:

g(5) = 5^2 - 5 - 10 = 20

Now that we have g(5) = 20, we can substitute it into f(x) to find fog(5):

fog(5) = f(g(5)) = f(20) = -4 * 20 + 9 = -79

So, the value of fog(5) is -79.

Step-by-step explanation:

The value of 1 unit = 11/8

The value of 5 units = 11/8 × 5 = 55/8

The value of 5 units as a mixed fraction= 6 7/8

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If 8 units = 11

therefore 1 unit will be ;

8 units/8 = 11/8

1 units = 11/8

Therefore 5 units = 11/8 × 5 = 55/8

5 units in improper fraction is 55/8

= 6 7/8

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There are several strategies that can be used to help students understand that a whole number can be divided into parts:

Remember, it may take time for some students to fully grasp the concept of dividing a whole number into parts. Keep practicing and using different strategies until the concept clicks for them.

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Answer:

  (x, y) = (-4, 3)

Step-by-step explanation:

You want the solution to the matrix equation ...

  [tex]\left[\begin{array}{cc}2&5\\1&3\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}7\\5\end{array}\right][/tex]

Perhaps the easiest solution is to let a calculator reduce the augmented matrix to row-echelon form. This is done in the attachment. It shows the solution is (x, y) = (-4, 3).

Alternatively, you can left-multiply the equation by the inverse of the coefficient matrix. The inverse of the 2×2 coefficient matrix is easily found.

The inverse is the transpose of the cofactor matrix, divided by the determinant. For a 2×2 matrix, the transpose of the cofactor matrix negates the off-diagonal terms and swaps the diagonal terms. The determinant is the difference of the products of the diagonal and off-diagonal terms:

  [tex]\left[\begin{array}{cc}2&5\\1&3\end{array}\right]^{-1}=\dfrac{1}{2\cdot3-1\cdot5}\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right] =\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right][/tex]

Multiplying this by the constant vector, we have ...

  x = 3(7) -5(5) = -4

  y = -1(7) +2(5) = 3

__

Additional comment

Using row-reduction avoids the problem of the inverse matrix being undefined — when the determinant is zero. That happens when the equations are dependent or inconsistent. The result of row-reduction will tell you which of those is the case: the bottom row is 0 for dependent equations, and 0 0 1 for inconsistent equations.

The speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

The Latin word for carrier is vector. Points A and B are transported by vectors. The magnitude of the vector is the length of the line connecting points A and B, and the vector's direction is the direction in which point A moves in relation to point B. Other names for vectors are Euclidean vectors and spatial vectors. In many different domains, including mathematics, physics, engineering, and others, vectors are used.

Since there is no external force applied, So using momentum conservation:

Pi = Pf

Since the wreckage is locked onto each other after collision, So their final velocity will be same

m1*v1 + m2*v2 + m3*v3 = (m1 + m2 + m3)*V

m1 = mass of ball1 = 60 g

m2 = mass of ball2 = 20 g

m3 = mass of ball3 = 30 g

v1 = initial velocity of m1 = 4.0 m/sec towards 45 deg South of east = (4*cos(45deg) i - 4*sin(45 deg) j) m/sec

v2 = initial velocity of m2 = 2.0 m/sec towards North = (2.0 j) m/sec

v3 = initial velocity of m3 = 2.9 m/sec towards west = (-2.9 i) m/sec

V = final velocity of blob = x i + y j

So,

60*(4*cos(45deg) i - 4*sin(45 deg) j) + 20*(2.0 j) + 30*(-2.9 i) = (60+20+30)*(x i + y j)

(60*2.83 - 30*2.9) i + (-60*2.83 + 20*2.0) j = 110x i + 110 j

82.8 i - 129.8 j = 110x i + 110y j

By comparing both sides:

x = 82.8/110 = 0.753 i

y = -129.8/110 = -1.18 j

then, final speed will be:

V = 0.753 i - 1.18 j

Part - A

Speed of resulting blob of clay,

|V| = √((0.753)² + (1.18)²)

|V| = 1.4 m/s

Part-B

Direction after collision will be:

Direction = arctan (Vy/Vx) = arctan (-1.18/0.753) = -57.46 deg

Direction = 57.46 deg below +ve x-axis

Hence, the speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

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Answer: x=18 and y=-6

Step-by-step explanation:

y=-6; x+3y=0    

The length of the line segment after the dilation with a scale factor of 2 is given by the equation A' = L ( 2 ) , where L is the length of the segment

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the length of the line segment be represented as L

Now , the dilation factor is represented as d = 2

And , the dilation centered at the origin

So , the length of the line segment after the dilation is A'

On simplifying the equation , we get

The length of the line segment after the dilation A' = L x ( dilation factor )

The length of the line segment after the dilation A' = L ( 2 )

Hence , the dilation A' = 2L

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Answer:

No

Step-by-step explanation:

to be right angled triangle,

h^2=p^2+b^2

,15^2=12^2+8^2

,225=144+64

,225=208

Since 225 is not equal to 208

It is not a right angled triangle

Answer:

x² + x

Step-by-step explanation:

x(x+1) →

[a(b + c) = ab + ac]

x (x) + x (1) →

[x • x = x²] + [x • 1 = x] →

x² + x

Answer:

36π in.³

113 in.³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)π(3 in.)³

V = 36π in.³

V ≈ 113 in.³

Answer:

2 hours and a half

Step-by-step explanation:

The straight line distance is 13 blocks.

We know that we can be able to obtain the straight line distance by looking at the information that has been provided by the question. We are told in the question that; you go north 3 blocks turn East and go blocks, and go 7 blocks turn South turn West and go 3 blocks.

We know that the distance is not a vector quantity as such, we do not look at the direction of the movement. We would only be concerned about the magnitude of the distance.

Thus we have the straight line distance as; 3 + 7 + 3 = 13 blocks

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