20 POINTS
Data Analysis and Probability - Computing mean absolute deviation from a list of numerical values
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15

The mass of the regular hippo at birth to that of the pygmy hippo is 49/11

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The pygmy hippo had a mass of 5 1/2 kg at birth = 5.5 kg.

The regular hippo had a mass of 24 1/2 kg at birth = 24.5 kg

Hence:

Ratio of regular hippo to pygmy hippo = 24.5 / 5.5 = 49/11

The mass of the regular hippo at birth to that of the pygmy hippo is 49/11

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Answer:

49/11 or 4 5/11

Step-by-step explanation:

just did it on khan Academy.

The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

According to the statement

we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.

So, The given expression are:

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]

And we have to prove the answer.

So, For this

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]

[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]

Then the equation become

[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]

Now solve it then

[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]

Now take 2 common from answer then equation become

[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]

Hence proved.

So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.

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Answer:

[tex]\Large\boxed{x=-3}[/tex][tex]\Large\boxed{y=6}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~y=3x+15[/tex]

[tex]2)~3x+3y=9[/tex]

Divide 3 on both sides of the 2) equation

[tex]3x+3y=9[/tex]

[tex]3x\div3+3y\div3=9\div3[/tex]

[tex]x+y=3[/tex]

Current system

[tex]1)~y=3x+15[/tex]

[tex]2)~x+y=3[/tex]

Substitute 1) equation into the 2) equation

[tex]x+(3x+15)=3[/tex]

Combine like terms

[tex]x+3x+15=3[/tex]

[tex]4x+15=3[/tex]

Subtract 15 on both sides

[tex]4x+15-15=3-15[/tex]

[tex]4x=-12[/tex]

Divide 4 on both sides

[tex]4x\div4=-12\div4[/tex]

[tex]\Large\boxed{x=-3}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]y=3x+15[/tex]

[tex]y=3(-3)+15[/tex]

[tex]y=-9+15[/tex]

[tex]\Large\boxed{y=6}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

∠KJI≅ZJX is the additional information.

What are the AAS congruency criteria?

⇒ AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

We have been given that

⇒ kJ=ZJ

⇒∠KJI=∠ZJX (vertically opposite angle)

And we require one more angle which can't be on the non-included side

so we have only one angle that can satisfy this  

⇒∠JIK=∠JXZ

⇒ Now we can say that △KJI ≅ △ZJX is congruent with AAS congruency criteria

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Answer:

Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.

Step-by-step explanation:

3/5 = 0.6

The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6

This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.

Hope this helps!

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Equivalent functions are different functions that have equal values when evaluated and compared

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

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I've done it on the attached pages.

I hope this helps you...

45 kilograms of meat is required to feed 2 pet dragons each day.

Amara needs 45 kilograms of meat to feed 2 pet dragons each day.

Unitary method is a mathematical way of deriving a single unit then obtaining the required units by multiplying it with the single unit.

According to the given question Amara needs 90 kilograms of meat to feed her 4 pet dragons each day.

Also given that each pet dragon eats the same amount of meat.

∴ 1 pet dragon eat 90/4 kilograms of meat which is

= 22.5 kilograms of meat.

So, Amara need (22.5×2) = 45 kilograms of meat to feet 2 pet dragons.

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Answer:

Area=length× berngth

A=5×2x

A=10x square

Answer: D

Step-by-step explanation:

The first term is 3 and the common difference is 2.

Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.

Answer:

The answer is (3,11) or x = 3, y = 11

Step-by-step explanation:

:)

Answer:

(3, 11 )

Step-by-step explanation:

y = x + 8 → (1)

y = 3x + 2 → (2)

substitute y = 3x + 2 into (1)

3x + 2 = x + 8 ( subtract x from both sides )

2x + 2 = 8 ( subtract 2 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

y = 3 + 8 = 11

solution is (3, 11 )

Considering the given inequality, the solution is given by graph D.

The inequality is given by:

-36 ≤ 2x + 4(x-3)

Applying the operations:

-36 ≤ 2x + 4x - 12

-24 ≤ 6x

6x >= -24

x >= -24/6

x >= -4.

Hence option D is correct.

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D. 16

Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.

You get:

8(x-4) = 6x

Expand bracket to get:

8x - 32

Now solve for x :

8x - 32 = 6x

- 8x

- 32. = - 2x

÷ - 2

16 = x

Or

8x - 32 = 6x

+ 32

8x. = 6x + 32

- 6x

2x. = 32

÷2

x =16

Check:

16 - 4 = 12, then ÷ 6 is 2

16/8 = 2

Hope this helps!

For the first representation, the equation is : y = 3x-5.

For the second representation, the equation is : y = -12x+2.

For the third representation, the equation is : y = 5/4x-5.

For the fourth representation, the equation is: y = -6x+3.

Analyze the representations given in the question, in order to find its corresponding equation.

According to the question,

For the first representation, y=1 when x=2, y=-2 when x=1 and y=4 when x=3. On substituting these values of x and y in the given equations, we get that y = 3x-5.

Similarly, for the second representation, we get, y = -12x+2.

For the third representation, we get, y = 5/4x-5.

For the fourth representation, we get, y = -6x+3.

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Based on the stock price and its growth rate, the function that models the situation is 48 (1 + 8%) ^ n. The price of the stock 6 years from now is $76.17.

The value of a stock in future can be calculated using several types of formulas that take into account the various characteristics of the stock.

For this stock, the value of the stock at any given year is:

= Current price of stock x ( 1 + growth rate) ^ number of years from now

Assuming the number of years is n, the function becomes:

= 48 x ( 1 + 8%) ^n

In 6 years, the price will be:

= 48 x ( 1 + 8%) ⁶

= $76.17

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75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function

The smallest of the numbers in the set {1, 2, 3, …} is 1.

So, the number 1 is the smallest positive integer.

7300

If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.

7300-75=7225

(85)^2=7225

75 to be subtracted

√7300 ≥ 85

Perfect Square = 85² =  7225     or (7300-7225 = 75)

75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

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Using the arrangements formula, the number of orders is given as follows:

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are no restrictions, the number of ways is:

[tex]A_{11} = 11! = 39,916,800[/tex]

When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:

[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]

When the first and last are cats, we have that:

Hence:

20 x 9! = 7,257,600.

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Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'

Answer:  108 square feet

===============================================

Work Shown:

L = 4 = length

W = 3 = width

H = 6 = height

SA = surface area of the box

SA = 2*(LW + LH + WH)

SA = 2*(4*3 + 4*6 + 3*6)

SA = 108

generally, tanA=opposite/adjacent

answer:tanC=36/15=12/5

Answer:

[tex]Tan \space\ \theta =\frac{\boxed{12}}{\boxed5}}[/tex]

Step-by-step explanation:

The tangent (Tan) of an angle is the ratio of the opposite side and the adjacent side, so that:

[tex]\boxed{Tan\space\ \theta = \frac{opposite}{adjacent}}[/tex].

In this case, with respect to angle C:

• opposite = AB =  36 units

• adjacent = CB = 15 units.

Substituting the values into the equation:

[tex]Tan \space\ C = \frac{36}{15}[/tex]

           = [tex]\bf \frac{12}{5}[/tex]   (simplified)

Based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6

The line of best fit is the line that best represents the relationship between 2 variables. The equation of a line in slope-intercept form is expressed as:

y = mx + b

where

m is the slope

b is the intercept

Using the coordinate points on the plane (0, 6) and (10, 28)

Determine the slope

Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2

Determine the y-intercept

6 = 2.2(0) + b

b = 6

Determine the equation of aline of best fit.

y = 2.2x + 6

Hence based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6

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Answer:

figure A = 3 units

figure B = 9 x 3 = 27 units

scale factor =

[tex] \frac{3}{27 } = \frac{1}{9} [/tex]

so the scale factor = 9

2x4=8

8x2=16

the answer is 16

Using the Geometric mean theorem and the Pythagorean theorem:

x = 3√3, and y = 6.

The Geometric mean theorem or the right triangle altitude theorem states that the geometric mean of the the two segments equals he length of the altitude of a right triangle.

The geometric mean theorem is expressed by the equation, h = √(ab), where:

Given the following:

h = x

a = 9

b = 3

x = √(9 × 3)

x = 3√3

Find y using the Pythagorean theorem

Based on the Pythagorean theorem, we would have the following:

y = √(x² + 3²)

y = √((3√3)² + 3²)

y = √(27 + 9)

y = √(36)

y = 6

Thus, in the simplest radical form, the value of x = 3√3, and y = 6.

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45 candidates are expected to be rejected.

What is a percentage in math?

Here, we want to calculate the number of candidates to be rejected

The number of candidates to be rejected can be calculated from;

100% - (28% + 12%) = 60%

So 60% of the 75 interviewed are to be rejected

Thus, we have

60/100 * 75

= 45

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The simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.

To find the simplified expression:

Given -

Thus,

Therefore, the simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.

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The complete question is given below:
Joy is training for a triathlon. She runs a distance of 2x miles, cycles a distance of (x2 + 7) miles, and swims a distance of (x - 2) miles. Which simplified expression is equivalent to the total distance, in miles, Joy covers?

(A) x2 + 3x + 5

(B) x2 + 3x + 9

(C) 3x2 + 5

(D) 3x2 + 9

Answer:

The person on top is right.

ITS A

Step-by-step explanation:

The given expression is a (A) linear expression.

Therefore, the given expression is a (A) linear expression.

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The correct question is given below:

Classify the expression: 5x 2.

(A) linear expression

(B) quadratic expression

(C) cubic expression

(D0 quartic expression

It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.

Species exist as organisms that contain similar characteristics and exist capable of interbreeding. A common example is human beings.

It has been observed that over the years, species have been going extinct due to human reasons such as excessive hunting, environmental factors such as natural disasters, global warming, and also due to changes in their genetic makeup or reduced reproduction.

It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.

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Answer: Edge 2022, B. 72

Answer:

16

Step-by-step explanation:

6/3 = 2 postcards per day

2x8 = 16 postcards