Charlie watches as a pattern develops. In month 1, he starts with 3 guppy fish in his fish tank. The next month, he finds 6 guppy fish in his tank. The following month, he finds 11 guppy fish in his fish tank. Write an expression to model the pattern of guppy fish in Charlie’s fish tank. Use your expression to determine the number of guppy fish Charlie will observe in month 6.
In month 6, Charlie should observe
_______

The arc length of the curve is 1.3125

The length of an arc is the separation of two locations along a segment of a curve.

A defined integral between the two points is used to calculate the area under a curve between two points. Integrate y = f(x) between a and b's limits to find the area under the curve y = f(x) between x = a & x = b. Integration within the defined bounds can be used to calculate this area.

the arc length formula

[tex]$$L=\int_C d s=\int_a^b \sqrt{1+\left(\frac{d x}{d y}\right)^2} d y$$[/tex]

now

[tex]$$\begin{aligned}16 x y^2-y^6 &=8 \\y^2\left(16 x-y^4\right) &=8 \\16 x-y^4 &=8 y^{-2} \\16 x &=8 y^{-2}+y^4 \\x &=\frac{1}{2} y^{-2}+\frac{1}{16} y^4\end{aligned}$$[/tex]

[tex]\frac{d x}{d y}=-y^{-3}+\frac{1}{4} y^3[/tex]

now differential line element is

[tex]$$\begin{aligned}d s &=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y \\&=\sqrt{1+\left(-y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\sqrt{1+y^{-6}-\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{y^{-6}+\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{\left(y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\left(y^{-3}+\frac{1}{4} y^3\right) d y\end{aligned}$$[/tex]

now arc length of the curve in the given interval

[tex]$$\begin{aligned}L &=\int_C d s \\&=\int_1^2\left(y^{-3}+\frac{1}{4} y^3\right) d y \\&=\left[-\frac{1}{2} y^{-2}+\frac{1}{16} y^4\right]_1^2 \\&=-\frac{1}{2}\left(\frac{1}{2^2}-\frac{1}{1^2}\right)+\frac{1}{16}\left(2^4-1^4\right) \\&=\frac{\mathbf{2 1}}{\mathbf{1 6}} \approx \mathbf{1 . 3 1 2 5}\end{aligned}$$[/tex]

this is the arc length of the curve

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The quadratic function h(x) = x^2 - 12x + 36 is a quadratic function in standard form

The quadratic function is given as:

h(x) = x^2 - 12x + 36

Quadratic functions in standard form are represented as

h(x) = ax^2 + bx + c

Where the value of a is not 0

This means that we can conclude that h(x) = x^2 - 12x + 36 is a quadratic function in standard form

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The distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.

We are given the two points:

( − 2 , 5 ) and ( − 8 , − 3 )

We need to find the distance between the two points.

The formula for distance is given as:

Distance = √ (x₂ - x₁)² + (y₂ - y₁)²

Substituting the values, we get that:

Distance = √ ( - 8  + 2 )² + (- 3 - 5)²

Distance = √ ( - 6 )² + ( - 8 )²

Distance = √ 36 + 64

Distance = √ 100 .

Distance = 10 units.

Therefore, we get that, the distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.

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Answer:

9.22 units (3 s.f.)

Step-by-step explanation:

The distance between a pair of points can be found using the distance formula shown below, where [tex](x_1, y_1)[/tex] is the 1st coordinate and [tex](x_2,y_2)[/tex] is the 2nd coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Substituting the coordinates into the formula:

Distance between (21, 5) and (28, -1)

= [tex]\sqrt{(-1-5)^{2} + (28-21)^{2} } }}[/tex]

= [tex]\sqrt{(-6)^2+7^2}[/tex]

= [tex]\sqrt{85}[/tex]

= 9.22 units (3 s.f.)

Additional:

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25 students are taking algebra and drafting but not both.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values.

given that

10 students are taking both algebra and drafting.

24 students taking algebra.

11 students who are taking drafting only.

now, find how many students are taking algebra or drafting but not both?

from the question

10 students are taking both algebra and drafting.

24 students taking algebra.

so, subtract 10 in 24

24 - 10 = 14

so, 14 students are taking algebra only.

now, add the both students who are taking algebra and drafting.

11 + 14 = 25.

Hene, 25 students are taking algebra or drafting but not both.

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Answer:

How many chapters does Dan read in 56 hours?

Step-by-step explanation:

The pounds of green beans in the vegetable medley is 2.78 pounds

Pounds of green beans in the vegetable medley = Fraction of green beans in vegetable medley × Total pounds of vegetable medley

= 5/9 × 5

= (5 × 5) / 9

= 25 / 9

= 2.777777777777777 pounds

Approximately,.

Pounds of green beans in the vegetable medley = 2.78 pounds

Therefore, the pounds of green beans in the vegetable medley is 2.78 pounds

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Answer:

Answer:

420 miles

Step-by-step explanation:

Distance traveled per hour = 55 miles

Distance traveled in 6 hours = 55 * 6 = 330 miles

Distance of the trip = 330 + 90  = 420 miles

Step-by-step explanation:

Answer:

Domain { -3,-1,6,9}

Step-by-step explanation:

The domain is the input values

Domain { -3,-1,6,9}

Answer:

[tex]y+2.9=-12(x-1)^2[/tex]

Step-by-step explanation:

Vertex form of a quadratic function:

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

Given vertex:  (1, -2.9)

Therefore:

Substitute the values of h and k into the formula:

[tex]\implies y=a(x-1)^2-2.9[/tex]

As the function has no x-intercepts, and the vertex is in Quadrant IV, the parabola will open downwards.  Therefore, "a" will be negative.  Without any further information, any number can be substituted for "a".  Therefore, according to the given answer, let a = -12:

[tex]\implies y=-12(x-1)^2-2.9[/tex]

Note:  If "a" was positive, the parabola would open upwards, which means there would be two x-intercepts (two points at which the curve intercepts the x-axis).

Finally, add 2.9 to both sides of the equation so that the equation is in the format of the given answer:

[tex]\implies y+2.9=-12(x-1)^2-2.9+2.9[/tex]

[tex]\implies y+2.9=-12(x-1)^2[/tex]

According to the question, the points are [tex](-3,-10)[/tex] and [tex](-1,-7)[/tex] for the function [tex]f(x).[/tex]

The calculated slope for these values are as follows:

[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(-7-(-10))}{(-1-(-3))} = \frac{3}{2} = 1.5[/tex]

The slope for the function [tex]f(x)[/tex] is: [tex]m=1.5[/tex]

Now, the function [tex]g(x)=\frac{1}{2} x+3[/tex]

Using the standard formula that is [tex]y = mx+c[/tex] to calculate the slope for the function [tex]g(x).[/tex]

Slope(m) for [tex]g(x) = \frac{1}{2} = 0.5[/tex]

As per the question, lance gains [tex]1[/tex] level each time he plays the video game.

Therefore, [tex]slope = \frac{1}{1} =1[/tex]

Hence, the slope for the function [tex]h(x)[/tex] is [tex]1[/tex].

Therefore, the function [tex]f(x)[/tex] has the largest slope and it is [tex]1.5.[/tex]

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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Using proportions, we have that:

A. 0.05x + 0.4(10 - x) = 0.2(10).

B. You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In item A, we have that the total amount that she has is 20% acid of 10 liters, hence:

0.2(10).

She wants to split it into a 5% solution and a 40% solution, a total of 10 liters, hence the amounts to each solution are x and 10 - x, as follows:

0.05x + 0.4(10 - x).

Hence the equation is:

0.05x + 0.4(10 - x) = 0.2(10).

The solution for x is found as follows:

0.05x + 4 - 0.4x = 2.

0.35x = 2

x = 2/0.35

x = 5.7.

Hence, for item b:

You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.

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B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.

The triangle congruence criteria are as follows:

For the given figure it is said that B=E and it is solely not possible to prove that △ABC≅△DEF with any congruency condition.

Therefore, B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.

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The correct question is given below:
Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similarly, then choose NOT.

B = E

Options:

(A) AA

(B) SAS

(C) SSS

(D) NOT

Answer:

60

Explanation below

elowHope this helps :)

Step-by-step explanation:

1. Substitute the variables with the given numbers.

(4 + 2) (2 + 8)

2. Add the numbers to get the sum.

(6) (10)

3. Since they are in parenthesis multiply the two numbers.

(6) (10) = 60

Answer:

Hello,

y=4x-2

Step-by-step explanation:

1: slope.

[tex]\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\[/tex]

2:

[tex]\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\[/tex]

Slant asymptote is     y=4x-2

Using proportions, the coordinates of F are given as follows: F(-3,5).

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Point F divides the segment such that DF:EF is 5:3, hence the point F is 5/8 of the way, that is:

F - D = 5/8(E - D).

The x-coordinate of F is given by:

x + 13 = 5/8(3 + 13)

x + 13 = 10

x = -3.

The y-coordinate of F is given by:

y + 10 = 5/8(14 + 10)

y + 10 = 15

y = 5.

The coordinates of F are given as follows: F(-3,5).

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The width of the rectangle is 8 feet.

What is the Area of Rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.

Perimeter = 44

Length = width + 6

perimeter formula of rectangle = 2(L +W)

44 = 2(W+6 +W)

22 = 2W +6

11 = W + 3

W = 8

therefore , the width of the rectangle is 8 feet

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Answer:

A

Step-by-step explanation:

Answer:

your answer will be A the first one

Step-by-step explanation:

If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3

Given,

The number of siblings each person has = 1,2,3,4 and 10

Arrange them in ascending order =1,2,3,4 and 10

We know the median is the middle term of the ordered pair

The number of terms n= 5

Middle term is = [tex]\frac{n+1}{2}[/tex]

=[tex]\frac{5+1}{2}[/tex]

=3

The 3rd term is 3.

The median = 3

Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3

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Answer:

c.143

Step-by-step explanation:

No estoy seguro de que esté Mal o mal

Answer:

Step-by-step explanation:

The left option

(4,3), (1,3), (0,5), (1,8)

Answer:

ans) 4G and 6/x+y

Step-by-step explanation:

10) it says the product of both so when both multiply each other , we get the product

Cost of 4 pound box of blackberries = $16.64

Cost of 1 pound box of blackberry = [tex]\bf\frac{\cancel{16.64}}{\cancel{4}}4.16[/tex]

Hence, the cost of 1 pound of blackberry is $4.16.

Answer:

300 minutes

Step-by-step explanation:

1 hour = 60 Minutes

60x5=300

Answer:

so if add everything and subtract them for d you get 7

The total commission of Jorge was $2459.173.

So,

Now,

3.5% of $16,583

5.4% of $34,792

Total commission: $580.405 + $1,878.768 = $2459.173

Therefore, total commission of Jorge was $2459.173.

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