A team of researchers measured the length of 5 different rainbow trout pulled from different locations in a lake. length, in.: {18, 22, 15, 28, 17} what is the estimated mean absolute deviation of the lengths of rainbow trout in the lake? 1.3 in. 4 in. 20 in. 61 in.

Answer:

[tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] +[tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns [tex]\int\limits {\sqrt{x^{2}+4 } } \, dx[/tex] into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into [tex]\frac{x}{2}[/tex] (see substitutions) while secθ will resolve into [tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]

sec(θ)=[tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]  is from its ratio identity of hyp/adj where the hyp. is [tex]\sqrt{x^{2} +4}[/tex]  and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= [tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] + [tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Answer:

247.29 ft

Step-by-step explanation:

Need to find the opposite side, so use sine

4725sin 3 = 247.29

Answer:

Step-by-step explanation:

x + 4 = 2x + 1 -x -x 4 = 1x + 1 -1 -1 3 = 1x -- -- 1 1 3 = x

Check: 3 + 4 = 2(3) + 1 7 = 6 + 1 7 = 7

Answer:

x > 2

Graph in picture

Step-by-step explanation:

Given:

7x + 10 < 11x + 2

To Find:

Solve and graph on a number line. Show your work in the box below.

Solve:

Subtract 10 from both sides

7x + 10 -10 < 11x + 2-10

Simplify

-4x < - 8

Multiply both sides by -1 which reverse the inequality

Simplify

4x > 8

Now, Divide both sides by 4

4x ÷ 4 > 8 ÷ 4

Simplify

x > 2

Solution: x > 2

Now graphing:

> means greater than

that means x is greater than 2

Thus, the line is going to the right.

Graph below:

Answer: x > 2

Step-by-step explanation:

7x+ 10 < 11x + 2

7x+10-10 < 11x + 2 -10

subtract the numbers

7x < 11x -8

7x < 11x -8

7x - 11x < 11x -8 - 11x

-4x < -8

-4x < -8

-4x/-4 > -8/-4

x > 2

Answer:

[tex] - 60[/tex]

Answer:

simultaneous equations are used to solve for 2 variable

Answer: 97 degrees

Step-by-step explanation:

Answer:

$8.95

Step-by-step explanation:

If Ari spent $35.80 for 4 posters and each of the poster price was the same therefore if we want the price for one poster we have to divide $35.80 by four to see the cost for one poster which will be $8.95. If you want to know if the price of each poster was the same you can just multiply $8.95 by 4 and you'll actually see that you got back the same money that Ari used to spend for the four posters .

Answer:

  add the areas of the parts

Step-by-step explanation:

The area of an unusual shape is often easily found by decomposing it into shapes that you have formulas for. Divide the shape into parts, and add the areas of those parts.

__

Alternatively, some shapes are conveniently described by "missing" parts, For example, your "plus shaped" figure may be described as an overall rectangle with rectangles removed from the corners. Then the area of the shape is found by subtracting the missing area from that of the overall rectangle.

__

As a rule, you want the parts to be non-overlapping. That way, you can add the areas of the parts without counting any area twice (or more times). If you have overlapping parts, you need to subtract the area(s) that may be counted multiple times.

__

Sometimes you can take advantage of symmetry, so that you only need to compute part of the total area, then multiply by a factor that takes the symmetry into account.

__

In the attached figure, the dimensions of rectangle A are 6 m wide by 7 m high. The dimensions of rectangle B must be found by adding the width dimensions shown across the top of the figure: 5 m +6 m +6 m = 16 m. It is marked as 4 m high. Then the total area is ...

  area of A + area of B

  = (6 m)(7 m) +(16 m)(4 m)

  = 42 m² +64 m² = 106 m²

This can also be found as the area of the 16 m by 11 m enclosing rectangle, less the two 5 m by 7 m corner cut-outs.

  (16 m)(11 m) -2(5 m)(7 m) = 176 m² -2(35 m²) = 106 m²

Dynamic pricing is typically used to increase ticket sales on low attendance days, offer fans discounts on concessions.

Dynamic pricing is used to set the price of tickets based on the situation of the demand and reduce the number of unsold tickets.

It is used to adjust the prices that tickets are sold during sports which can be based on such variables as demand, weather, team performance and even pitching match-ups.

Therefore, Dynamic pricing is typically used to increase ticket sales on low attendance days, offer fans discounts on concessions.

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Answer:

85 ft^2

Step-by-step explanation:

Base = 5 x 5 = 25 ft^2

FOUR triangles   4  *   1/2 * b * h  = 4 * 1/2 * 5 * 6 = 60 ft^2

added together = 85 ft^2

Answer:

[tex]1\frac{1}{2}[/tex] or 1.5

Step-by-step explanation:

Now we know it's a dilation.  So we can use any two points.  I chose V and V'.

V: (3,6)

V': (2,4)

So how we get from 6 to 4?

[tex]4(x)=6\\x=\frac{6}{4} \\x=1.5[/tex]

You can tell it's 1.5 aswell because 4 times 1 is 4 and 4 times 0.5 is 2.  Add them to get 6.  

Therefore, the dilation factor is 1.5.

Answer:

its this symbol

Step-by-step explanation:

Using it's concept, it is found that there is a 0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 40% of the consoles bought are of the Suny Playcom series, and of those, 1% are defective, hence the probability is given by:

p = 0.4 x 0.01 = 0.004

0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

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Answer:

The answer I got was

Step-by-step explanation:

[7, 4, 3]

You use the matrix calculator and then select a*b

Answer:

a. no

b. no

c. no

d. yes

Step-by-step explanation:

Case I

x = -1

y = -4

7( -1) + 4 ( -4) = -23

-7 - 4 = -23

- 11 [tex]\neq[/tex] -23

Case II

x = 2

y= 6

7 (2) + 4 ( 6) = -23

14 + 24 = -23

38 [tex]\neq[/tex] -23

Case III

x = 6

y = -7

7 ( 6) + 4 (3) =- 23

42+ 12 = -23

54 [tex]\neq[/tex] -23

Case IV

x = -5

y = 3

7 (-5) + 4 ( 3) =- 23

-35 + 12 = -23

-23 = -23

The probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

A regular octagon has 8 sides, and a triangle has 3 sides

Assume that there is a point on the triangle.

Then we select (3 - 1) points from the (8 - 1) sides.

8 - 1 = 7

3 - 1 = 2

So, the total number of selection is:

Selection = 7C2

Evaluate the combination expression

Selection = 21

Adjacent triangles have 5 lines (one line in common).

So, we have:'

n = 5 - 1

n = 4

The number of ways this points can be selected is:

Selection = 4C2

Evaluate

Selection = 6

The probability that the triangle and the octagon do noth have the same side is:

P= 6/21

The probability that at least one of the sides of the triangle is also a side of the octagon is calculated using the following complement rule

P = 1 - 6/21

Evaluate the difference

P = (21 -6)/21

P = 15/21

Reduce fraction

P = 5/7

Hence, the probability that at least one of the sides of the triangle is also a side of the octagon is 5/7

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Answer:

a. All of the whole - 10/10

b. A tenthof the whole - 1/10

Step-by-step explanation:

Step-by-step explanation:

a. since the entire whole represents a 100% , the number of whole that makes up for 100% is the 10 of the ten parts divided by 10 which is equal to 10.

b. since a whole equals 100% , if divided by 10 the entire 100% becomes 10% each for 10 parts. hence a single part equivalent to 1/10 is 10%

The height of the triangle is 8root3 meters.

We have given that,

A tree breaks due to a storm and the broken part bends,

So that the top of the tree touches the ground making an angle of 60 degrees with the ground.

The distance between the feet of the tree to the point where the top touches the ground is 16m.

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and the remaining part (AD) will make an angle of 30 degrees.

Now, in △ABD

cos(30)=BD/AD=BD=root3AD/2

AD=2(8)/root3

also in the same triangle

[tex]tan(30)=AB/BD\implies 8/\sqrt{3}[/tex]

Height of the tree=AB+AD

[tex]=\frac{16}{\sqrt{3} }+\frac{8}{\sqrt{3} } }[/tex]

[tex]=\frac{24}{\sqrt{3} } \\=8\sqrt{3}m[/tex]

Therefore the height of the triangle is 8root3.

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Answer:

[tex]\frac{4}{3}[/tex] miles

Step-by-step explanation:

Check the attachment.

Answer:

X intercepts: (0,12)

Y intercepts: (-32,88)

Answer:

-24/16, -√2, 21/51, 0.42

Step-by-step explanation:

Look at the signs of the numbers. Negative numbers will be on the left, while positive numbers will be on the right. That means -√2 and -24/16 will be on the left, while 0.42 and 21/51 will be on the right.

Part 1:

We can change the negative numbers to decimals to compare them.

-√2 ≈ -1.41

-24/16 = -1.5

-1.5 is smaller, which means the first number in the sequence will be -24/16 and then -√2.

Part 2:

We can also change the positive numbers to decimals to compare them.

0.42 = 0.42

21/51 ≈ 0.41

21/51 is a bit smaller, so the third number in the sequence will be 21/51 and then 0.42.

I hope this helps and please mark me as brainliest!

First, find the mode, median, and mean of the given set of numbers.

Mode

The mode is the number that shows up frequently within the given set. In this case, it will be 10, as it shows up 4 times, 3 times more than any other number.

Mode: 10

~

Median

The median is the number that is in the middle of the given set. In this case, there are 9 numbers, and so the 5th given number is your median:

10 , 10 , 10 , 10 , 11 , 12 , 13 , 15 , 17

Median: 11

~

Mean

The mean is combining all numbers within the given set and dividing by the amount of numbers in that said set:

(10 + 10 + 10 + 10 + 11 + 12 + 13 + 15 + 17)/9 = 108/9 = 12

Mean: 12

Answer:

After adding the numbers the result obtained is called the sum.

Answer:

490 miles

Step-by-step explanation:

7/1.4 = 5

98*5 = 490

Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

Answer: B

Step-by-step explanation:

Answer:

D. [tex]\frac{12x+20}{5y^3}[/tex]

Step-by-step explanation:

When multiplying 2 fractions, you multiply the numerators and denominators, so we have:

[tex](\frac{3x+5}{y^6})(\frac{4y^3}{5}) = \frac{(3x+5)\cdot 4y^3}{y^6\cdot 5} = \frac{(3x+5)\cdot 4}{y^3 \cdot 5} = \frac{12x + 20}{5y^3}[/tex]

Answer:

4th option

Step-by-step explanation:

[tex]\frac{3x+5}{y^6}[/tex] × [tex]\frac{4y^3}{5}[/tex] ( cancel y³ and [tex]y^{6}[/tex] on numerator/denominator by y³ )

= [tex]\frac{3x+5}{y^3}[/tex] × [tex]\frac{4}{5}[/tex]

= [tex]\frac{4(3x + 5)}{5y^3}[/tex]

= [tex]\frac{12x+20}{5y^3}[/tex]

Answer:

Step-by-step explanation:

[tex]\begin{cases}9x-9y=-9&\left(1 \right) \\ 3x+9y=-15&\left( 2\right) \end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9x-9y=-9&\left( 1\right) \\ 12x=-24&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}x-y=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=x+1=-2+1=-1&\left( 1\right) \\ x=-2&\left( 1\right) +(2)\end{cases}[/tex]