There are 2 different maps of North Carolina. The scale on the first map is 1 cm to 2 km. The distance from Durham to Cary is 15 cm. The scale of the second map is 1 cm to 5 km. What is the distance from Durham to Cary on the second map

Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.

[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]

Integrate by parts with

[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]

By substitution,

[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]

so that for [tex]k=n[/tex], we end up with

[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]

We then have the inverse transform relation

[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]

and so

[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]

The largest number of rods that the pole can be cut into is 86.

Given:

Length of Metal Pole = 500 cm

The pole is cut into rods.

Length of each rod = 5.8 cm

To determine the number of rods we can divide the total length of the pole by the length of each rod.

Number of rods that the pole can be cut into = (Length of Metal Pole) ÷ (Length of each rod )

⇒ Number of rods = 500 ÷ 5.8 = 86.2 ≈ 86

Therefore, the largest number of rods that the pole can be cut into is 86.

To know more about word problems visit:

https://brainly.com/question/28376263

#SPJ9

Answers to your questions with explanations are below. You can ask a question, feel free. I wish you success!

This answer should be Vertical Angles.

Vertical angles are angles that are opposite of each other when two lines cross and equal each other. [tex](a^o=b^o)[/tex]

A pair of vertical angles is formed when two lines intersect each other at a single point. They are said to be linear if the angles are adjacent after the intersection of the two lines. The sum of the angles of a linear pair is always equal to [tex]180^o[/tex]. Such angles are also known as complementary or supplementary angles.

The answer is [tex]2^{nd}+4^{th}+5^{th}[/tex]

The answer is the first option. Adjacent angles. The rule is simple. If [tex]a+b=90^o[/tex] if they're adjacate angles.

The answer is the third option. Supplementary angles. The rule is simple. If [tex]a+b=180^o[/tex] if they're supplementary angles.

AE and BE are congruent lines or we can say lines with same length.

What are congruent lines?

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent.

As given in the question,

AC = BD, and

EC = ED

We can see in the figure that:

AC - EC = AE ___(1)

BD - ED = BE ___(2)

Substituting the value of AC and EC in equation (1):

AE = BD - ED ___(3)

From equations (2) and (3), we can conclude that,

AE = BC

Therefore, AE and BE are congruent lines.

To know more about congruent line, go to link

https://brainly.com/question/24934161

#SPJ13

The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.

An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.

Since the sum of supplementary angles is 180 degrees, hence;

<1 + <3 = 180 degrees

Also <1 + <2 = 180 degrees (sum of angles on a straight line)

<1 = 180 - <3

<1 = 180 - <2

Equate

180 - <3 = 180 - <2

-<3 = -<2

<2 = <3 (corresponding angle)

Since <2 is equivalent to <3, hence the line a is parallel to b

Learn more on line and angle theorem here: https://brainly.com/question/24839702

#SPJ1

Answer:

11

Step-by-step explanation:

A whole number is an integer greater than 0.

-76 , -34 , -57 are all negative so they are not whole numbers.

0 is too small so it also is not a whole number.

By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.

Answer:

0 and 11

Step-by-step explanation:

Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.

Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.

Answer:

5

Step-by-step explanation:

Since 7 into 42 is six we know the answer can't be 7 because it's too high. We can also rule out 6 because 6 times 7.94 is more than 41. The first answer choice is wrong because if you take away the .94, 7 times 4 is 28 which is pretty far from 41. If you multiply 5 and 7, it comes out to 35. That's significantly closer than four.

Hope this helps! :)

Answer:

Step-by-step explanation:

8(2+3)

Answer:

First question mark is 4, second question mark is 64

Step-by-step explanation:

For the first question mark, 7 is half of 14, and half of 8 is 4, so they would be the same ratio, and then for the second, 12 to 24 is just one half, meaning you would need to find double 32, which is just 64

The decimal is equal to (294117647)/(1000000000).

Answer:

Subtract 66.5 from Devon's total to find how much he has left

Answer:

(i) 7 + 4√2  cm^2.

(ii) 50 - 8√2  cm^2.

Step-by-step explanation:

(i)

Area = (3 + √8)(5 - 4/√2)

= 3(5 - 4/√2) + √8(5 - 4/√2)

= 15 - 12/√2 + 5√8 - 4√4

= 15 - 8 -( 12√2)/2 + 5*(2√2)

= 7 - 6√2 + 10√2

= 7 + 4√2.

(ii)

Area of the square

= AC^2

= (3 + √8)^2 + (5 - 4/√2)^2            (By Pythagoras)

= 9 + 6√8 + 8 + 25 - 40/√2 + 16/2

= 9 + 8 + 8 + 25 + 12√2 - 20√2

= 50 - 8√2.

Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The equation is given in its point slope form :

[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]

And the general equation in point slope form is :

[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]

by comparing these two, we can get

And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

On subtracting 20 from twice a number we get 50, then the number is 35 in this context.

This is referred to as a type of mathematical operation in which one number is taken or deducted from the other and the sign is ( - ). this expression is used in every facet of life for their daily activities.

We were told that 20 was subtracted from twice a number to give 50 which means that twice the number is 70. The exact number will therefore be 70/2 which will then result in 35 and is therefore the most appropriate choice.

Read more about Subtraction here https://brainly.com/question/17301989
#SPJ1

Answer: 7 units

Step-by-step explanation:

The measure of each angle is 34.1° and 55.9°

complementary angles are angles that gives 90° when added to together.

if the first angle is x and the other complementary angle is y,

then x+y=90

x= y-21.8

representing y-21.8 for x in equation x+y=90

y+ y-21.8= 90°

2y= 111.8

y= 55.9°

and x= 34.1°

learn more about complementary angles from

https://brainly.com/question/98924

#SPJ1

Answer:

yes

Step-by-step explanation:

The coordinates of a centroid of a triangle with vertices  [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex]  are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].

Centroid of a triangle

For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.

Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.

Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”

As D is the midpoint of the side LM, we can write,

D = ((x2+x3)/2, (y2+y3)/2)

Now, we know that, G intersects AD in the ratio 2:1 , we get

Hence, using section formula we can write,

The x-coordinates of G will be:-

x = (2(x2+x3)/2 + 1.x1 )/ (2+1) =  (x2+x3+x1)/3  = (x1+x2+x3)/3

The y-coordinates of G will be :-

y =(2(y2+y3)/2 + 1.y1 )/ (2+1) =  (y2+y3+y1)/3 =  (y1+y2+y3)/3

To learn more about centroid, here:-

https://brainly.com/question/10708357

#SPJ1

well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]

Answer:its D

Step-by-step explanation:

The depreciation equation is given by

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

After one year, the car value corresponds to x=1, that is,

Now, let's find the depreciation percentage by means of a rule of three:

so we have

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year

Answer:

11, 110

Step-by-step explanation:

Constant of proportionality: Ratio of distance to time, which is 11.

Distance at 10s: Multiply time by the constant of proportionality, giving 110.

Answer:

Option 4

Step-by-step explanation:

Each x-value corresponds to only one y-value

Based on the results of Mean and Median, we can say that Mean is larger than median in value .

Mean of n observations can be calculated using the formula

Mean = (sum of all observations)/(number of observations) .

After arranging the data in ascending or descending order , the middle value can be called as Median .

In the question ,

the set of numbers is given as 4, 5, 11, 12, 5, 38, 44

rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44   .

the sum of all the number = 4+5+5+11+12+38+44

                                           = 119

number of observations = 7

hence the mean = 119/7 = 17

So, mean = 17

from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that

the middle value of the set of numbers is 11 .

So , median = 11 .

On comparing the mean = 17  and the median = 11 ,

we can say that the mean is greater than median.

Therefore , based on the results of Mean and Median, we can say that

Mean is larger than median in value .

Learn more about Mean here

https://brainly.com/question/1533925

#SPJ1

Answer:

B and C

Step-by-step explanation:

I think that you mean -1 -1.  That would equal -2

-2 is an integer and a rational number.

An integer are the whole numbers 0,1,2,3 and so on and their opposites, -1, -2, -3 ,-4 and so on

Rational number is when you can write a number as an integer over and integer.  You can write -2 as  -2/1

Answer: a,b,c

I did it in the test

Standard deviation of population mean is 0.33.

Why is there a standard deviation?

it is shown that 5% values are over 2.1 pounds and 5% are under 1.9 pounds

so stastically that means

P( X > 2.1,  μ; σ) = 0.05 and P( X 1.9; μ; σ) = 0.05

where  μ is mean of the sample and σis the standard deviation of the sample.

so mean can be calculated easily μ = (2.1 + 1.9)/2 = 2.0

and as we can interpret P(1.9 <x < 2.1; 2.0; σ) = 0.90 by normal distribution the Z value for 90% confidence interval is 1.65

so σ = (2.1 -2) /1.65 = 0.06

standard deviation of the sample mean= 0.06

and by that standard deviation of population mean = 0.06 * (30) 0.5  = 0.33

Learn more about standerd deviation

brainly.com/question/16350351

#SPJ9

The complete question is -

A production process is checked periodically by a quality control inspector. the inspector selects simple random samples of 30 finished products and computes the sample mean product weight. If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? What is the population mean? (to 1 decimal) What is the population standard deviation (to 2 decimals)?

It's (1, 0) - first option

Hope this helps!

9. Option b. The two lines are perpendicular to each other

  Given:

   6x+10y = 20

   5x- 3y = 21

Consider the first line,

10 y = -6x+ 20

y = -3/5 x + 2

This is of the form y = mx+ b

where, slope =m = - 3/5

Consider the second line,

5x- 3y = 21

3y = 5x- 21

y = 5/3 x - 21

This is of the form y = mx+ b

where, slope= m = 5/3

Since the slopes of the two lines are negative reciprocals ,they are perpendicular.

10. Option a. The equation of the line  passing through (2, -9) with a slope -5 is y = - 5x + 1

Given:

slope = m= -5

point = (2,-9)

We know that ,the slope -intercept form is given by ,

y = mx+ b ---(1)

Substituting the given values in (1)

-9 = -5(2)+b

10- 9 = b

b = 1

Substituting m and b in (1)

y = -5x+1

Thus, the slope-intercept form equation of the line is y = -5x + 1

11. The  equation of the line perpendicular to y= -2x+8 and passing through the point (4,-7) is y = 1/2x- 9

Given:

line = y = -2x+8

point = (x, y)= (4, -7)

The given equation is of the form,

y = mx+ b  ---- (1)

m = -2

The line perpendicular to this line will have a negative reciprocal slope,

m = 1/2  

The new line is of the form,

y = 1/2 x+ b   ----(2)

Substituting the given point (4, -7) in (2)

- 7= 2 + b

b = - 9

Substituting b in (2)

y = 1/2x- 9 is the perpendicular line equation

12.  The  equation of the line parallel to 3x- 2y = 14 and passing through the point (-6,-11) is y = 3/2 x -2

Given:

line = 3x- 2y = 14

point = (x, y)= (-6,-11)

The slope - intercept form of the given line is ,

2y = 3x- 14

y = 3/2x - 7  

slope = m = 3/2

The line parallel to this line will have the same slope,

m = 3/2  

The new line is of the form,

y = 3/2 x+ b   ----(1)

Substituting the given point (-6, -11) in (1)

- 11= -9 + b

b = - 2

Substituting b in (1)

y = 3/2 x -2 is the parallel line equation.

To learn more about slope-intercept form, refer:

https://brainly.com/question/1884491

#SPJ13

Based on the given, the variable p from the expression 4.45p represent pounds of tomatoes sold.

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The cost of the tomatoes for a number of packages = 4.45p

If the store sold 2 1/4 pounds of tomatoes

The cost of the tomatoes for a number of packages = 4.45p

= 4.45(2 1/4)

= 4.45(9/4)

= 4.45(2.25)

= $10.0125

In conclusion, the variable p represent pounds of tomatoes sold in the store.

Read more about algebra:

https://brainly.com/question/4344214

#SPJ1