mean, median, mode or standard deviation best represents the data​

Answer:

C. The mean absolute deviation is 2.

Step-by-step explanation:

In order to find the mean absolute deviation, follow the following steps:

Let's work it out.

STEP: 1

|9 - 14| = 5

|13 - 14| = 1

|14 - 14| = 0

|15 - 14| = 1

|15 - 14| = 1

|18 - 14| = 4

STEP: 2

5 + 1 + 0 + 1 + 1 + 4 = 12

STEP: 3

Mean Absolute deviation [tex] =\frac{12}{6}= 2[/tex]

Answer:

y(t) =  3u₂(t) [ [tex]e^{-2t+4} - e^{-5t + 10)}[/tex] ] - 4u₅(t) [ [tex]e^{-2t+10)} - e^{-5t + 25)}[/tex] ]

Step-by-step explanation:

To find - y″+ 5y′ + 6y = 3δ(t − 2) − 4δ(t −5); y(0) = y′(0) = 0

Formula used -

L{δ(t − c)} = [tex]e^{-cs}[/tex]

L{f''(t) = s²F(s) - sf(0) - f'(0)

L{f'(t) = sF(s) - f(0)

Solution -

By Applying Laplace transform, we get

L{y″+ 5y′ + 6y} = L{3δ(t − 2) − 4δ(t −5)}

⇒L{y''} + 5L{y'} + 6L{y} = 3L{δ(t − 2)}  − 4L{δ(t −5)}

⇒s²Y(s) - sy(0) - y'(0) + 5[sY(s) - y(0)] + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒s²Y(s) - 0 - 0 + 5[sY(s) - 0] + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒s²Y(s) + 5sY(s) + 6Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒[s² + 5s + 6] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒[s² + 3s + 2s + 6] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒[s(s + 3) + 2(s + 3)] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒[(s + 2)(s + 3)] Y(s) = 3[tex]e^{-2s}[/tex] - 4[tex]e^{-5s}[/tex]

⇒Y(s) = [tex]\frac{3e^{-2s} }{(s + 2)(s + 3)} - \frac{4e^{-5s} }{(s + 2)(s + 3)}[/tex]

Now,

Let

[tex]\frac{1}{(s+2)(s+3)} = \frac{A}{s+2} + \frac{B}{s+3} \\\frac{1}{(s+2)(s+3)} = \frac{A(s + 3) + B(s+2)}{(s+2)(s+3)}\\1 = As + 3A + Bs + 2B\\1 = (A+B)s + (3A + 2B)[/tex]

By Comparing, we get

A + B = 0 and 3A + 2B = 1

⇒A = -B

and

3(-B) + 2B = 1

⇒-B = 1

⇒B = -1

So,

A = 1

∴ we get

[tex]\frac{1}{(s+2)(s+3)} = \frac{1}{s+2} + \frac{-1}{s+3}[/tex]

So,

Y(s) = [tex]3e^{-2s}[ \frac{1}{(s + 2)} - \frac{1}{(s + 3)}] - 4e^{-5s}[ \frac{1}{(s + 2)} - \frac{1}{(s + 3)}][/tex]

⇒Y(s) = [tex]3e^{-2s} \frac{1}{(s + 2)} - 3e^{-2s} \frac{1}{(s + 3)} - 4e^{-5s}\frac{1}{(s + 2)} + 4e^{-5s}\frac{1}{(s + 3)}[/tex]

By applying inverse Laplace , we get

y(t) = 3u₂(t) [ [tex]e^{-2(t-2)} - e^{-5(t - 2)}[/tex] ] - 4u₅(t) [ [tex]e^{-2(t-5)} - e^{-5(t - 5)}[/tex] ]

⇒y(t) =  3u₂(t) [ [tex]e^{-2t+4} - e^{-5t + 10)}[/tex] ] - 4u₅(t) [ [tex]e^{-2t+10)} - e^{-5t + 25)}[/tex] ]

It is the required solution.

Answer:

1. 28.26 2. 94.985 3. 113.04 4. 50.24 5. 153.86

Step-by-step explanation:

For the circles that have a long line that is the size of the circle is the diameter so the number for the diameter for example is 6 so divide it by 2 which is 3. Multiply 3 by 3 which is 9 and multiply by 3.14 and its 28.26

For the circles that have a line that goes halfway of the circle its more quick so 5.5 x 5.5 equals 30.25 and multiply by 3.14 and you get 94.985

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

im assuming were solving for k so we wanna get it by itself

9k - 18 = -6

start by adding 18 to both sides

9k = 12

then divide both sides by 9

k = 12/9

hope this helps <3

Answer:

the answer is

k= 4/3

Step-by-step explanation:

9k-18=-6

9k=-6+18

9k=12

k= 12/9

simplify it which gives k=4/3 or in decimal form 1.333

Answer:

Mercantilism allowed for government regulation of trade, which interfered with natural market forces.

Given:

Jazmine made [tex]3\dfrac{1}{3}[/tex] cups of jam.

One jar can hold [tex]\dfrac{2}{5}[/tex] cup.

To find:

Number of jars of jam can Jasmine make.

Solution:

We have,

Capacity of each jar = [tex]\dfrac{2}{5}[/tex] cup

Total jam made by Jazmine = [tex]3\dfrac{1}{3}[/tex] cups

                                              = [tex]\dfrac{3(3)+1}{3}[/tex] cups

                                              = [tex]\dfrac{10}{3}[/tex] cups

Now,

[tex]\text{Number of Jars of jam}=\dfrac{\text{Total jam made by Jazmine}}{\text{Capacity of each jar}}[/tex]

[tex]\text{Number of Jars of jam}=\dfrac{\dfrac{10}{3}}{\dfrac{2}{5}}[/tex]

[tex]\text{Number of Jars of jam}=\dfrac{10}{3}\times \dfrac{5}{2}[/tex]

[tex]\text{Number of Jars of jam}=\dfrac{25}{3}[/tex]

[tex]\text{Number of Jars of jam}=8\dfrac{1}{3}[/tex]

Approx the value to the next integer.

[tex]\text{Number of Jars of jam}\approx 9[/tex]

Therefore, Jasmine make 9 cups of jam in which 8 are completely filled and one is filled one third.

Step-by-step explanation:

The given angle is a 90° . Therefore the sum of both angles is 90° .

> 40 + x = 90

> x = 90 - 40

> x = 50

Solution 2 ;-

> 20 + x = 90

> x = 70

Answer:

636

Step-by-step explanation:

SA=2LW+2LH+2WH

SA= 2(12)(10)+2(12)(9)+2(10)(9)= 636

Answer:

The answer is 636

Step-by-step explanation:

Brainliest maybe?

:)

Answer:

True very true

Step-by-step explanation:

Answer:

B?

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

no idea what the guy on top is saying

Answer:

51.2

Step-by-step explanation:

Answer:

B) Independent

Step-by-step explanation:

Independent events:

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A) \times P(B)[/tex]

In this question:

[tex]P(A \cap B) = \frac{63}{200}[/tex]

[tex]P(A) \times P(B) = \frac{9}{20}*\frac{7}{10} = \frac{9*7}{20*10} = \frac{63}{200}[/tex]

Since [tex]P(A \cap B) = P(A) \times P(B)[/tex], these events are independent.

Answer:

[tex]Cost= \$3520[/tex]

Step-by-step explanation:

Given

[tex]l = \frac{1}{4}in[/tex]

[tex]Unit\ Cost = \$11[/tex] per ft^2

Required

Cost  of dining room

Start by calculating its area.

We have:

[tex]Area = 4l * 5l[/tex] ---- the squares

Substitute [tex]l = \frac{1}{4}in[/tex]

[tex]Area = 4 * \frac{1}{4} * 5* \frac{1}{4}[/tex]

[tex]Area = \frac{5}{4}in^2[/tex]

Convert to [tex]ft^2[/tex]

[tex]Area = \frac{5}{4} * (16ft)^2[/tex]

[tex]Area = \frac{5}{4} * 256ft^2[/tex]

[tex]Area = 320ft^2[/tex]

So, the cost is:

[tex]Cost = Unit\ Cost * Area[/tex]

[tex]Cost= \$11/ft^2 * 320ft^2[/tex]

[tex]Cost= \$11 * 320[/tex]

[tex]Cost= \$3520[/tex]

Answer:

∠TRU is supplementary with ∠PQS as SQ║TR.

Supplementary angles add up to 180°.

Consider ΔRTU

∠RUV is exterior angle and therefore is sum of ∠TRU and ∠RTU:

<TRU

Sum of 2 interiors =exterior

<RTU

Answer:

The FICA tax for an employee who earns 60,000 a year is $ 3,390.

Step-by-step explanation:

Given that you pay 5.65% on the first 110,000 of income and 1.45% in excess of $ 110,000, to calculate the FICA tax for an employee who earns 60,000 a year the following calculation must be performed:

60,000 <110,000

60,000 x 0.0565 = X

3,390 = X

Therefore, the FICA tax for an employee who earns 60,000 a year is $ 3,390.

Answer:

Explanation:

x2+14x+40

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:

N1⋅N2=a⋅c=1⋅40=40

and,

N1+N2=b=14

After trying out a few numbers we get N1=10 and N2=4

10⋅4=40, and 10+4=14

x2+14x+40=x2+10x+4x+40

=x(x+10)+4(x+10)

Here (x+10) is common to both terms.

So the factorised form is=(x+4)(x+10)

Answer: 84

Step-by-step explanation:

The horizontal line is the line tangential to a circle. The measure of the missing angle "x" is 84 degrees

From the figure given, the horizontal line is the line tangential to a circle.

Given the following parameter

measure of minor arc = 168 degrees

Required

angle at the vertex "x"

Using the theore " angle the vertex is half of the measure of its intercepted arc. Mathematically;

x =1/2 minor arc

x= 1/2 (168)

x = 84 degrees

Hence the measure of the missing angle "x" is 84 degrees

Learn more on circle geometry here: https://brainly.com/question/24375372

#SPJ2

Answer:

c

Step-by-step explanation:

Answer:

D. 24.5

Step-by-step explanation:

5x + 8° + 3x - 24° = 180° { Being linear pair}

8x - 16° = 180°

8x = 196°

x = 196° / 8

x = 24.5°

Hope it will help :)❤

Answer:

take 40 degree as reference angle

using tan rule

tan 40 =p/b

0.83=900/x

0.83x=900

x=900/0.83

x=1084.33

x=1084.3(after rounding off to the nearest tenth)

Step-by-step explanation:

Answer:

144.5

Step-by-step explanation:

Area of a triangle = one half of the base length times the height

The given base length is 17 cm and the given height is 17 cm

Hence, area = [tex]\frac{17*17}{2}[/tex]

17 * 17 = 289

289 / 2 = 144.5

Area = 144.5cm²

Answer: 144.5

Step-by-step explanation:

The answer is correct because, the formula of a triangle is base times height divided by 2. Since the base and height is 17, we multiply 17 times 17. The answer for 17 times is: 289. Now we have to divide it by two. 289 divided by 2 equals: 144.5.

Hope This Helps!

Answer:

1)12²+9²=225

X=15km

2)12²+x²=13²

x²= 169-144

x²=25

x=5mi

Answer: z=25 x=114

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

One dozen is 12.

12 x 4 = 48

Answer:

7x+5

Step-by-step explanation:

or, 2x3+x4-3x+5

or, 6x+x4-3x+5

or, 10x-3x+5

or, 7x+5

Answer:

Perpendicular bisector

Step-by-step explanation:

Have a great day!!