assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .

The number of handshakes altogether exists 45.

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.

Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.

Given:

Number of people in the conference = 10

Each person shakes hands with others.

The total number of handshakes [tex]$={ }^n \mathrm{C}_2$[/tex]

Total number of handshakes [tex]$={ }^{10} C_2=(10 \times 9) / 2=45$[/tex] handshakes.

The complete question is:

At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is

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The correct answer is C), because it is possible to create an economic model describing the relationship between fertilizer usage and yield.

The economic model would take into account the nonlinear relationship, which is shown in the graph. Specifically, the slope of the curve between one and two tons of fertilizer is approximately 2 (change in yield divided by change in fertilizer usage). This means that for every ton of fertilizer used, the yield increases by two (change in yield / change in fertilizer usage = 2). Although using more than three tons of fertilizer has minimal effect on yield, the economic model would still take this into account and provide a more accurate representation of the relationship between the two variables.

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The class width of the histogram is 5

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width called the class width.

The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most common type of histogram.

The class width is plotted in the x - direction. this is the difference between the two consecutive values in the boundary.

class width = 100.5 - 95.5 = 5

class width = 85.5 - 80.5 = 5

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If a bag has orange marbles, the number of red marbles it will contain would be also the same as the number of orange marbles.

The Dante's Marble Company sells bags of marbles that contains different types of marbles such as both the red and the orange marbles I'm a particular order.

In a bag of marbles, every red marbles = every orange marbles.

Therefore the number of red marbles found in a bag will be the same amount of orange marbles found in the same bag.

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The speed when the object and dropped from a height of 350 feet and takes exactly 5 seconds is 70 feet per seconds.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity

In this situation, when dropped from a height of 350 feet, it takes exactly 5 seconds for the stone to hit the ground.

The speed will be:

= Distance / Time

= 350 / 5

= 70 feet per seconds

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Complete question

A moving object travels 350 feet in 5 seconds assuming that the object travels at a constant speed , When dropped from a height of 350 feet , It takes exactly 5 seconds for the stone to hit the ground. Calculate the speed.

Answer:

pie/8, 3pie/8

Or

B

Answer:

2 1/2 + b = 4 2/3

The equation of the straight line would be -

y = 4x + 5.

Given is that a line y = mx + 5 that passes through the point (1, 6) and is parallel to y = 4x + 6.

       y = mx + c

Equation of the line is -

y = mx + 5

It is parallel to -

y = 4x + 6

Then -

m = 4  {slopes of || lines are equal)

So, we get the equation as -

y = 4x + 5

Therefore, the equation of the straight line would be -

y = 4x + 5.

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To get the initial mass, set t = 0.

A(0) = 621 (1/2)0/30 g = 621 (1) g = 621 g

To get the mass after 100 years, just plug t = 100 into A(t) and evaluate.

A(100) = 621 (1/2)100/30 g = ? g

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The in-house production  amount costs per foot of cables A, B, and C are $6, $8, and $10, respectively.

1. The question states that a company produces three types of cables, A, B, and C.

2. The in-house production amount costs for each type of cable is given in the question. The cost per foot of cable A is $6, the cost per foot of cable B is $8, and the cost per foot of cable C is $10.

The company produces three types of cables, A, B, and C, and each type of cable has a different in-house production cost. Cable A has a cost per foot of $6, cable B has a cost per foot of $8, and cable C has a cost per foot of $10. This means that if the company produces 100 feet of cable A, the in-house production cost would be $600, whereas if they produce 100 feet of cable B, the in-house production cost would be $800, and if they produce 100 feet of cable C, the in-house production cost would be $1000.

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Answer: 9/80

Step-by-step explanation:

1/8 = 10/80

1/10 = 8/80

9/80 is fraction between 1/8 and 1/10

Have A Good Day :)

Answer:

this is a little typical

The probability of rolling two ones in a row is equal to P = 1/36

We want to find the probability of rolling two ones in a row.

Remember that a dice has 6 sides, so the probability of randomly rolling a 1 is just:

p = 1/6

And if we want to do that two times then we need to have that probability twice:

q = 1/6

And the joint probability (probability of rolling two ones) is equal to the product between the individual ones:

P = p*q = (1/6)*(1/6)

P = 1/36

That is the probability.

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Answer:

5.92

Step-by-step explanation:

Set up a proportion

cups/mg = cups/mg

[tex]\frac{1.5}{148}[/tex] = [tex]\frac{6}{x}[/tex]

1.5 x 4 = 6,

so 1.48 x 4 = 5.92

The linear equation in two variables is -5X + 10 = Y

A linear equation in mathematics is an equation that may be written as follows: Y = aX + b where a and b are the coefficients, which are frequently real numbers, and X and Y are the variables (or unknowns). As long as they don't contain any of the variables, the coefficients can be thought of as equation parameters and can be arbitrary expressions. The coefficients must not all be 0 in order to produce a meaningful linear equation.

A linear polynomial over a field, from which the coefficients are taken, can also be equalised to zero to produce a linear equation.

Such an equation's solutions are the values that, when used as placeholders for the unknowns, result in the equality being true.

Let us assume that given equation as  linear equation in two variables

Y = aX + b

Also, from the given table, the value which satisfy the equations are

X =3, Y = -5 and X = 4, Y = -10

using these values we have

-5 = 3a +b and -10 = 4a +b

subtracting both the equations we get,

-5 = a

Now putting this value in an equation we get

b = 10

so the general equation is -5X + 10 = Y

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your solution

4+13x=57

x=53÷4 = 13.25

Answer:

The coupon that gives $14 rebate off $75 gives a lower price

Step-by-step explanation:

Let's figure out what percentage of $75 the $14 rebate coupon is

If this percentage is greater than 15% then the $14 rebate coupon gives a better discount; if not the 15% discount offers a better buy

To find what % $14 is of the $75 cost of printer, divide 14 by 75 and multiply by 100 to convert to %:

[tex]\dfrac{14}{75} \times 100 = 18.67\%\\\\[/tex]

Since 18.67% is greater than 15%, getting $14 off $75 will give a lower price

Consequently, x∈R denotes that x belongs to the set of Real numbers. This means that x is a real number.

Hence, As a result, the symbol x∈R indicates that x is a member of the Real number set. Thus, x must be a real number.

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Tom's monthly mortgage repayment will be an amount of $1,144.41.

To calculate Tom's monthly mortgage repayment, we can use the formula:

[tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n -1 ][/tex]

Where:

M = monthly repayment

P = the principal amount (loan amount) = $300,000 - $30,000 = $270,000

i = monthly interest rate = 2%/12 = 0.02/12 = 0.0017

n = number of months = 25 years x 12 months/year = 300 months

Plugging in the values:

M = $270,000 [ 0.0017(1 + 0.0017)³⁰⁰ ] / [ (1 + 0.0017)³⁰⁰ – 1 ]

M = $1,144.41

Thus, his monthly mortgage repayment will be $1,144.41.

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Answer:

44 boxes

Step-by-step explanation:

You have to find 20% of 20.
20% = 1/5

1/5 of 20 is 4

So next year she will buy 24 boxes

If you add them together, she will have 44 boxes in all

Slope is y is -1x + 1.

To enter data and find the equation's solution, we can utilize the equation's point-slope form.

use the point ( 2, 3) and the slope of 1.

m \s= \s− \s1

x \s1 \s= \s− \s2

y \s1 \s= \s3

In the point-slope formula,

y \s− \sy \s1 \s= \sm \s( \sx \s− \sx \s1 \s)

the values into the plug

y \s− \s3 \s= \s− \s1 \s( \sx \s− \s( \s− \s2 \s) \s)

symbol reduction

Distribute the 1 according to y 3 = 1 (x + 2).

Use additive inverse to find the y in the equation y = 3 = 1 x 2

y \s− \s3 \s+ \s3 \s= \s− \s1 \sx \s− \s2 \s+ \s3

simplify

y \s= \s− \s1 \sx \s+ \s1.

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Answer: Since the company is running short of cash they have failed or late to pay the shareholders' share of the profit which is the dividend.

Answer:

250u2

Step-by-step explanation:

The volume of a cube is found by multiplying LxWxH. 5x5x5-125, 125x2-250

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The given sequence appears to be an arithmetic sequence, as the common difference between consecutive terms is 4.

The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference and n is the nth term.

Given that the first term of the sequence is 2, the common difference is 4.

To find the 41st term of the sequence, we can use the formula:

a_41 = 2 + (41-1) * 4 = 2 + 40 * 4 = 2 + 160 = 162

Therefore, the 41st term of the sequence is 162.

Answer:

   C

Step-by-step explanation:

2.52/4 =0.63/1

A) r(t) =[tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]  ; B) r(t) = X×e^(∧×t)c ; C) [tex]r_1[/tex](t) = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex], [tex]r_2[/tex](t) =  [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex].

A) The solution to the linear equation in eigenvalue/eigenvector form:

r(t) = [tex]c_{1}[/tex]×e^(∧×t)[tex]v_{1}[/tex]+ [tex]c_{2}[/tex] × e^(∧²×t)[tex]v_2[/tex]

B) The solution to the linear equation in fundamental matrix form:

 r(t) = X×e^(∧×t)c

C) As two equations: The solution to the linear system can also be written as two equations as follows:

 [tex]r_1[/tex](t) = [tex]c_1[/tex] ×e^(∧²×t)[tex]v_1[/tex] = [tex]c_{1}[/tex](-1×[tex]e^{3t}[/tex])×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) -4×[tex]e^{3t}[/tex]

 [tex]r_2[/tex](t) = [tex]c_2[/tex]×e^(∧² ×t)[tex]v_2[/tex] = [tex]c_2[/tex](-1×[tex]e^{3t}[/tex]×cos(t) -1×[tex]e^{3t}[/tex]×sin(t) + 4i×[tex]e^{3t}[/tex]

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Answer:

Angle A = 83.59° (2 d.p.)

Angle C = 56.41° (2 d.p.)

Side a = 193.25 (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the Sine Rule formula:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

Solve for angle C:

[tex]\implies \dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]

[tex]\implies \sin C=\dfrac{162\sin 40^{\circ}}{125}[/tex]

[tex]\implies C=\sin^{-1}\left(\dfrac{162\sin 40^{\circ}}{125}\right)[/tex]

[tex]\implies C=56.4136175...^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies A+B+C = 180^{\circ}[/tex]

[tex]\implies A = 180^{\circ}-B-C[/tex]

[tex]\implies A = 180^{\circ}-40^{\circ}-56.4136175...^{\circ}[/tex]

[tex]\implies A = 83.5863824...^{\circ}[/tex]

Finally, to find a, substitute the found angles and sides into the Sine Rule and solve for a:

[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

[tex]\implies \dfrac{\sin 83.5863824...^{\circ}}{a}=\dfrac{\sin 40^{\circ}}{125}[/tex]

[tex]\implies a=\dfrac{125\sin 83.5863824...^{\circ}}{\sin 40^{\circ}}[/tex]

[tex]\implies a=193.248396...[/tex]

Answer: Add −9b and 2b. −7b + 2n −4