1. Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists. (a) A relation R on N that is reflexive and symmetric but not transitive. (b) A relation S on N that is reflexive and transitive but not symmetric. (c) A relation T on N that is transitive and symmetric but not reflexive.

ANSWER

c

It is c because i did the work and  i know.

The average speed of the trains are Bullet train = 91.4 km/hr and Ordinary train = 24.9 km/hr

From the question, we have the following parameters that can be used in our computation:

Bullet train

Distance = 320 km

Time = 3 and half hours = 3.5

Ordinary train

Distance = 212 km

Time = 8 and half hours = 8.5

By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object

Mathematically, this can be represented as

Speed = Distance : Time

Express as fraction

Speed = Distance/Time

So, we have

Bullet train = 320/3.5 = 91.4

Ordinary train = 212/8.5 = 24.9

Hence, the speed of the ordinary train is 24.9 km per hour

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Answer:

Step-by-step explanation:

A rectangle measures 75 cm by 15 cm.Find the length of the perimeter?

P = (75 + 15) x 2

P = 90 x 2

P = 180 cm

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

What is the direct variation?

A direct variation, also called direct proportion is a relationship between two variables [tex]x[/tex] and [tex]y[/tex] that can be written as [tex]y = kx[/tex], [tex]k\neq 0[/tex].

Here given that,

The direct variation and [tex]y=75[/tex] when [tex]x=25[/tex],

As we know that,

[tex]y[/tex]α[tex]x[/tex]

[tex]y=kx[/tex]

[tex]75=k(25)\\\\k=\frac{75}{25}\\\\k=3[/tex]

So, when [tex]y=48[/tex]

[tex]y=kx\\\\48=3x\\\\x=\frac{48}{3}\\\\x=16[/tex]

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

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Part a: Roy sweeps out 2.15/0.7 radians.

Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial

Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail

The radius of the ski trail= 0.7 km

Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.

Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.

Now, using the formula for arc length.

Arc length=(Radius)(angle at center)

2.15=(0.7)θ

θ=2.15/0.7

Roy sweep out 2.15/0.7 radians.

Part b:

When Roy stops skiing how many km is Roy to the right of the ski trial

In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle

Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,

As in part, a central angle is 2.15/0.7=3.071.

Therefore,

cos(3.071)=OP/0.7

OP=cos(3.071)(0.7)  

cos(3.071)(0.7) km.  

Part c:

When Roy stops skiing how many km is Roy above the centre of the ski trial

From figure part of part b, we have to calculate side BP.

In right angle triangle sin(θ)=Opposite side/hypotenuse

Therefore,

sin(3.071)=BP/0.7

BP=sin(3.071)/(0.7)

sin(3.071)(0.7) km.

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The circumference of the given circle with the diameter 27.6 yards is 86.7 yards.

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated a pole.

Given that, the diameter of circle is 27.6 yards

Radius of a circle is the distance from the center of the circle to any point on it's circumference and radius of a circle is half of Diameter.

That is, radius =Diameter/2

So, radius of circle =27.6/2 =13.8 yards

We know that, the circumference of the circle is 2πr

Now, circumference = 2×3.14×13.8

= 86.664

≈ 86.7 yards

Therefore, 86.7 yards is the circumference of the circle.

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The shape of the sampling distribution of the mean for samples of size 45 will be normal.

This is because the sampling distribution of the mean approaches normality as the sample size increases. The center of the sampling distribution will be 67 inches, which is the mean height of the population. The spread of the sampling distribution will be determined by the standard deviation of the population and the sample size. Specifically, the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution will be 3.8 inches / sqrt(45) = 0.55 inches.

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On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25

In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.

Given, geometric sequence

24, 6, 1.5

First term of this sequence = 6

a1 = 6

Recursive formula geometric sequence

[tex]a_{n} = a_{(n-1)}r[/tex]

[tex]Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\[/tex]

r = a2/a1

r = 6/24

r = 0.25

[tex]Recursive formula of the given sequence will be,[/tex]

[tex]a_{n} = a_{(n-1)}(0.25)[/tex]

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Answer:

  (d)  P ≥ -40

Step-by-step explanation:

You want the solution to P/8 ≥ -5.

Multiply both sides of the inequality by 8.

  8(P/8) ≥ 8(-5)

  P ≥ -40

The value of the stock yield will be;

⇒ 3.1%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Now,

Since, McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Hence, The value of the stock yield is;

⇒ 2.80/90.24  ×  100

⇒ 0.0310 × 100

⇒ 3.1%

Thus, The value of the stock yield will be;

⇒ 3.1%

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The value of the annuity due is $39,744.59.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = [tex]P\frac{(1 + r)^n -1(1+ r)}{r}[/tex].

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, r = 10% semiannually so it is (10/2) = 5% or 0.05 and n = 8×2 = 16.

∴ A = [tex]1600\frac{(1 + 0.05)^{16} -1(1+ 0.05)}{0.05}[/tex].

A = [tex]1600\frac{(1.05)^{16} -1(1.05)}{0.05}[/tex]

A = [tex]\frac{1600(2.18 -1.05)}{0.05}[/tex].

A = (1600×1.13)/0.05.

A = $39,744.59

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Answer:

9

Step-by-step explanation:

2|-9| - |-2|

=2+9-2 the negative number becomes positve when it come out of absolute value

=11-2

=9

Solving the expression 35.1 = 12.9 + 10.2x gives x to be 2 3/17

A group of numbers or variables coupled with the operations +, -,, or form an expression.

Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.

The given algebraic expression is 35.1 = 12.9 + 10.2x

solving for x

35.1 - 12.9 = 10.2x

10.2x = 22.2

x = 22.2/ 10.2

x = 2 3/17 as a mixed number in simplest form

the value of x is 2 3/17

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Answer:

The correct answer is (1, -3).

Step-by-step explanation:

To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:

4x + y = 1

4x + (x - 4) = 1

We simplify the left side of the equation and then solve for x.

5x - 4 = 1

5x = 5

x = 1

We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.

y = x - 4

y = 1 - 4

y = -3

Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).

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The graph of the system of equations -2x - y = -2 and 13x - y = -2 is attached and the solution is

(0, 2)

Graphs are plotted using the input values in the x coordinates and the output in the y coordinate

assuming an input of -4 0 4 we calculate the output for the graphs as

-2x - y = -2

y = -2x + 2

For x = -4, y = -2 * -4 + 2 = 10

For x = 0, y = -2 * 0 + 2 = 2

For x = 4, y = -2 * 4 + 2 = -6

table of values

x     y

-4   10

0     2

4     -6

13x - y = -2 rearranging gives y = 13x + 2

y = 13x + 2

For x = -4, y = 13 * -4 + 2 = -50

For x = 0, y = 13 * 0 + 2 = 2

For x = 4, y = 13 * 4 + 2 = 54

table of values

x     y

-4   -50

0     2

4     54

The point of intersection of the two line is the solution and this is (0, 2)

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Step-by-step explanation:

???

(x + y) + 3

this is 3 more than the sum of x and y.

The function of calculatenum() is int calculatenum(int n){ return n*6; }.

Function for math operation in many of programming language is same. It is some of math operation symbol,

+ = function for math addition operation

- = function for math subtraction operation

* = function for math multiplication operation

/ = function for math division operation

Keep in mind, that all math operations can only be performed for int data.

Since the question already give code for input integer parameter, we only write function for multiplication operation. So the function is,

int CalculateNum(int n) {

   return n * 6;

}

Thus, the code int calculatenum(int n){ return n*6 } is a function for calculatenum().

Your question is incomplete, but most probably your full question was

define a function calculatenum() that takes one integer parameter and returns 5 times the parameter. ex: if the input is 3, then the output is: 15 (code image attached)

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Answer:

Write in Standard Form

1. The standard form of a linear equation is

Ax + By = Cx-y=-1

2. x = 16

Ig?

I'm not sure.

The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given as,

A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)

The slope of line AB is given as

m₁ = (7 - 1) / (-2 - 8)

m₁ = 6 / (-10)

m₁ = - 0.6

The slope of line XY is given as

m₂ = (1 - 2) / (-1 + 6)

m₂ = - 1 / (5)

m₂ = - 0.2

The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.

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[tex]2^{x}[/tex] + [tex]\frac{2}{3}[/tex],  [tex]2^{x}[/tex], [tex]2^{x}+2[/tex], [tex]2^{x}-3[/tex] are examples of exponential parent function.So all of the given options are true.

Parent function:  The most basic function in a family of functions is the parent function. A family of functions is a collection of functions that have similar graph shapes because they all have the same greatest degree.

Four graphs that illustrate the U-shaped graph, or parabola, are displayed in the graph above. We can classify them as belonging to the same family of functions since they all have the same highest degree of two and the same form.

Exponential parent function: Algebraic expressions appear in the exponent of exponential functions. The formula for its parent function is y = [tex]b^{x}[/tex], where b can be any non-zero constant.

For above definitions we can conclude that all options given to us are exponential parent function.

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The angle of inclination of the hill is 1.369 degrees .

Given :

a bulldozer exerts 1000 pounds of force to prevent a 5000 lb lboulder from rolling down a hil determine the angle of inclination of the hill .

Angle of inclination :

Inclination of a line is the angle between the line and the positive direction of x − axis. Value of this angle is between 0 and 180 degrees . It is measured in anti - clockwise direction from the positive direction of x − axis .

Angle of inclination cos x = 1000 / 5000

cos x = 100 / 500

= 10 / 50

= 1 / 5

x = cos^-1 ( 1/5 )

x = 1.369 degrees .

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Answer:

2-3=4-5

Step-by-step explanation:

The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

It is known that,

Cos(A + B) = cosAcosB - sinAsinB

Cost(A - B) = cosAcosB + sinAsinB

As per the given,

cos(θ + π/4) - cos(θ - π/4)

(cosθ cos π/4 - sinθ sin π/4) - (cosθ cos π/4 + sinθ sin π/4)

-2 sinθ sin π/4

-2 sinθ (1/√2)

-√2 sinθ

Hence "The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ".

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In linear equation, 11x  * f(x) + 7 * f(X)  is (fg)(x) in standard form .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(x) . g(x) = f(x) . ( 11x + 7 )

Multiplicative Distribution Law   = f(x) * 11x + f(x) * 7

                                 = 11 * f(x) *  x+ 7 * f(x)

                                 = 11x * f(X) + 7 * f(x)

                                = 11x  * f(x) + 7 * f(X)

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We can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

What is a derivative of a function?

The derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

To determine whether the rocket is ascending or descending at a given time, we need to find the derivative of the function h(t) and determine whether it is positive or negative.

The derivative of h(t) is given by h'(t) = -t²+42t+43. This is the rate of change of the height of the rocket at any given time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

At t = 1 second, h'(t) = -1 + 42 + 43 = 44. Since the derivative is positive at t = 1, we know that the rocket is ascending at this time.

Hence, we can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

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Answer:

A

Step-by-step explanation:

2p - 5p < 8 + 4

- 3p < 12

-3/-3 p > 12/-3

p  > -4

-2, - 3

The Method of Cylindrical Shells will be used to assist.

As previously, we construct a region R that is enclosed on the top by the graph of the function y = f (x), on the bottom by the x axis, and on the left and right by the lines x = a and x = b, respectively (a).

As seen in Figure 1, we then rotate this region around the y-axis (b). Be aware that this is distinct from what we have previously done..

Previously, areas that were described in terms of x-functions were centered on the x-axis or a line that ran parallel to it.

Since the shell is a cylinder, its volume equals the cross-sectional area times the cylinder's height. The cross-sections are annuli, which are essentially circles with holes in the middle and are formed like rings.

According to our question-

V= 2π ∫025/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units

USING THE WASHER METHOD

V = ∫05 π (1/4) y4 d y = 625π/ 4 cubic units

Hence, The Method of Cylindrical Shells will be used to assist.

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In image.

In the Image is the anser and explanation.

The required slope-intercept form of the equation of the line is y = x/4 + 3.

To determine the equation of the line in slope-intercept form passing through the points (4, 4) and (0, 3).

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,

m = (y₂ - y₁) /  (x₂ - x₁)

Substitute the points,
m = [3 - 4] / [0 - 4]
m = 1 / 4

Standard equation of the line
y - y₁ = m (x - x₁)

Substitute one point and m in the above equaiton
y - 3 = 1/4 [x - 0]
y = x/4 + 3

Thus, the required slope-intercept form of the equation of the line is y = x/4 + 3.

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