plant is BOD=−55.42+1.502 TOC Both BOD and TOC are measured in milligrams per liter of water. (a) What does the slope of this line say about the relationship between BOD and TOC? TOC rises (falls) by 1.502mg/l for every 1mg/l increase (decrease) in BOD BOD rises (falls) by 1.502mg/l for every 1mg/l increase (decrease) in TOC BOD rises (falls) by 55.42mg/l for every 1mg/l increase (decrease) in TOC TOC rises (falls) by 1.502mg/I for every 55.42mg/l increase (decrease) in BOD (b) What is the predicted BOD when TOC=0 ? Values of BOD less than 0 are impossible. Why do you think the prediction gives an impossible value? This arises from extrapolation; the data used to find this regression formula must not have included values of 0. The regression equation is incorrect; a correct regression equation would never provide impossible values. There must be lurking variables; these factors have created a regression equation that allows for impossible values.

(a) The first ten Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The first ten Lucas numbers are: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76.

(b) The pattern observed is that Fₙ₊₁Fₙ₋₁ - F is always equal to Fₙ². So, the general formula for Fₙ₊₁Fₙ₋₁ - F₂ in terms of n is Fₙ².

(c) The pattern observed is that Lₙ₊₁Lₙ₋₁ - L is always equal to 5Fₙ². So, the formula for Lₙ₊₁Lₙ₋₁ - L in terms of n is 5Fₙ².

(d) The equation F₃+6 = F₆F₄ + F₅F₃ allows us to calculate F₃+6 using the earlier terms F₃, F₄, F₅, and F₆ instead of using F₇ and F₈. By using the equation F₃+6 = F₆F₄ + F₅F₃ and substituting known values, we find that F₂₀ = 80.

Let us discuss in a detailed way:

(a) The first ten Fibonacci numbers are:

F₀ = 0

F₁ = 1

F₂ = 1

F₃ = 2

F₄ = 3

F₅ = 5

F₆ = 8

F₇ = 13

F₈ = 21

F₉ = 34

The first ten Lucas numbers are:

L₀ = 2

L₁ = 1

L₂ = 3

L₃ = 4

L₄ = 7

L₅ = 11

L₆ = 18

L₇ = 29

L₈ = 47

L₉ = 76

(b) Let's calculate Fₙ₊₁Fₙ₋₁ - F for a few values of n:

For n = 2:

F₃F₁ - F₂ = 2 * 1 - 1 = 1

For n = 3:

F₄F₂ - F₃ = 3 * 1 - 2 = 1

For n = 4:

F₅F₃ - F₄ = 5 * 2 - 3 = 7

For n = 5:

F₆F₄ - F₅ = 8 * 3 - 5 = 19

From these calculations, we observe that Fₙ₊₁Fₙ₋₁ - F is always equal to the square of the corresponding Fibonacci number: Fₙ₊₁Fₙ₋₁ - F = Fₙ².

Therefore, a general formula for Fₙ₊₁Fₙ₋₁ - F₂ in terms of n is Fₙ².

(c) Let's calculate Lₙ₊₁Lₙ₋₁ - L for a few values of n:

For n = 2:

L₃L₁ - L₂ = 3 * 1 - 3 = 0

For n = 3:

L₄L₂ - L₃ = 7 * 3 - 4 = 17

For n = 4:

L₅L₃ - L₄ = 11 * 4 - 7 = 37

For n = 5:

L₆L₄ - L₅ = 18 * 7 - 11 = 95

From these calculations, we observe that Lₙ₊₁Lₙ₋₁ - L is always equal to the square of the corresponding Fibonacci number multiplied by 5: Lₙ₊₁Lₙ₋₁ - L = 5Fₙ².

Therefore, a formula for Lₙ₊₁Lₙ₋₁ - L in terms of n is 5Fₙ².

(d) We are given the equation F₃+6 = F₆F₄ + F₅F₃. Let's calculate both sides:

F₃ + 6 = 2 + 6 = 8

F₆F₄ + F₅F₃ = 8 * 3 + 5 * 2 = 34

Both sides of the equation yield the same result, 8.

Therefore, we can indeed use F₃, F₄, F₅, and F₆ to calculate F₃+6 without knowing F₇ and F₈.

To calculate F₂₀, the 21st Fibonacci number, using the most efficient algorithm, we can split it up as F₃+6+11. This means we can use the previously calculated terms F₃, F₄, F₅, F₆, F₁₁, and F₁₆ to calculate F₂₀. By using the given equation F₃+6 = F₆F₄ + F₅F₃ and substituting F₁₁ = F₆ + F₅ and F₁₆ = F₁₁ + F₅, we can calculate F₂₀:

F₃+6 = F₆F₄ + F₅F₃

F₁₁ = F₆ + F₅

F₁₆ = F₁₁ + F₅

F₃+6 = F₁₆F₄ + F₁₁F₃

F₃+6 = (F₁₁ + F₅)F₄ + F₁₁F₃

F₃+6 = (F₆ + F₅)F₄ + F₆F₃ + F₅F₃

F₃+6 = F₆F₄ + F₅F₄ + F₆F₃ + F₅F₃

F₃+6 = F₆(F₄ + F₃) + F₅(F₄ + F₃)

F₃+6 = F₆F₅ + F₅F₆

Substituting the previously calculated values:

F₃+6 = 8 * 5 + 5 * 8 = 80

Therefore, F₂₀ = F₃+6 = 80.

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Answer:

\(4\sqrt{5}\)

Step-by-step explanation:

In order to solve this problem, we can use the pythagorean theorem, which is

a^2 + b^2 = c^2, where and b are the legs of a right triangle and c is the hypotenuse. Since we are given the leg lengths, we can substitute them in. So, where a is we can put in a 4 and where b is we can put in an 8:

a^2 + b^2 = c^2

(4)^2 + (8)^2 = c^2

Now, we can simplify and solve for c:

16 + 64 = c^2

80 = c^2

c = \(\sqrt{80}\)

Our answer is not in simplified radical form because the number under is divisible by a perfect square, 16. We can divide the inside, 80,  by 16, and add a 4 on the outside, as it is the square root of 16:

c = \(4\sqrt{5}\)

The length of the hypotenuse in the given right triangle, with legs measuring 4 and 8, is approximately 8.94.

To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse's length is equal to the sum of the squares of the lengths of the other two sides.

In this case, let's label the lengths of the legs as 'a' and 'b', with 'a' being 4 and 'b' being 8. The hypotenuse, which we need to find, can be represented as 'c'.

Applying the Pythagorean theorem, we have:

\(a^2 + b^2 = c^2\)

Substituting the given values:

\(4^2 + 8^2 = c^2\)

16 + 64 = \(c^2\)

80 = \(c^2\)

To find the length of the hypotenuse 'c', we need to take the square root of both sides:

√80 = √ \(c^2\)

√80 = c

The square root of 80 is approximately 8.94.

Therefore, the length of the hypotenuse in the given right triangle, with legs measuring 4 and 8, is approximately 8.94.

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The income that's made based on the equation when 1 comb is sold is $0.5.

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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Answer:

The value of digit 3 in 63,297 is in the thousands place while the digit 3 in the number 60,325 is in the hundreds place

Hope this helps!

Answer:

answer in the diagram I hope it helps

Answer:

Tan 37 = opp/adj  =   1250/x    

where x = horiz distance

7535 = 1250/x      

x = 1658.8 ft

The horizontal distance from the helicopter to the landing pad is 1658.81 feet

Answer:

625: 1296

Step-by-step explanation:

625: 1296 cannot be further simplified because they share no common factor.  The decimal form around 0.5822531

This is a photo of answer

Answer:

  see attached

Step-by-step explanation:

The constants in the function shift the absolute value graph right 4 units and up 2 units. The attachment shows the translated function.

The limit is greater than zero, we can conclude that our function also diverges as x approaches infinity. Therefore, the integral does not converge.

To find the integral, we need to integrate the function S(x)ln(x)+11ch(x) with respect to x. However, before we do that, we need to determine if the integral converges or not.

One way to do this is to use the limit comparison test. We can compare our function to a known function that we know either converges or diverges. Let's choose the function ln(x), which we know diverges as x approaches infinity.

Taking the limit as x approaches infinity of the ratio of our function to ln(x), we get:

lim x->∞ [(S(x)ln(x)+11ch(x))/ln(x)]
= lim x->∞ [S(x)+11ch(x)/ln(x)]

Using L'Hopital's rule, we can evaluate this limit by taking the derivative of the numerator and denominator with respect to x:

= lim x->∞ [(S'(x)+11sh(x))/1/x]
= lim x->∞ [x(S'(x)+11sh(x))]
= ∞

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Reasonable inputs for the function are values of t ≥ 0, while reasonable outputs for the function are values of F(t) ≥ 180.

The function for this problem is defined as follows:

F(t) = 180 + 12t.

The input and output variables are given as follows:

The time cannot be negative, hence reasonable values for the input are given as follows:

t ≥ 0.

The frequency is modeled by an increasing linear function with initial value of 180, hence reasonable values for the output are given as follows:

F(t) ≥ 180.

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70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

Given that,

We have to find what percentage of the original roland-morris score of 20 was improved to the final score of 6.

We know that,

The original roland-morris score of 20 was improved to the final score of 6.

The initial score = 20

Final Score = 6

The improvement is 20 - 6 = 14

So,

The percent improvement is (14/20)* 100 = 70%

Therefore, 70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

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Answer:

Step-by-step explanation:

Aaahhhhh!!! Ja haw has b ha HA n zzz's

Answer:

B 0.5

Step-by-step explanation:

Answer:

x=36° (180/5x because 2x+3x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

12z - 3 > 27z - 15

-15z - 3 > -15

-15z > -12

z < 12/15= 4/5

Answer:

C.

Step-by-step explanation:

On edge 2020

Marie should write the expression as -3(8) + -3(-8) = 0. The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The expression shows that the product of -3 and -8 is positive and will be written by the equations as,

E = -3(8) + -3(-8) = 0

E = -24 + 24

E = 0

Hence the right expression is -3(8) + -3(-8) = 0.

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Answer:

31/3

Step-by-step explanation:

Multiply the denominator by the whole number 3×10=30

Then add the numerator 30+1=31

Hope this helps :)

The resulting improper fraction is 31 / 3.

To convert the mixed number 10 1 / 3 to an improper fraction, we first multiply the whole number (10) by the denominator of the fractional part (3), which gives us 30.

Then, we add the numerator of the fractional part (1) to get 31. We write the sum (31) as the numerator and keep the denominator (3) the same.

The resulting improper fraction is 31 / 3.

This means that 10 1/3 is equivalent to 31 / 3. The improper fraction emphasizes the total number of thirds, which is 31, without any whole number component.

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a. To prove that for all n ≥ 0: an = 5.3 + 7(an-1) + an-2 + an-3, we will use mathematical induction.

Base Case: For n = 0, we have a0 = 5.3 + 7(a-1) + a-2 + a-3. Substituting the given initial values, we get a0 = 5.3 + 7(29) + 12 + 0 = 213.3.

Inductive Hypothesis: Assume that for some k ≥ 0, the statement holds true, i.e., ak = 5.3 + 7(ak-1) + ak-2 + ak-3.

Inductive Step: We need to prove that the statement holds for k+1, i.e., ak+1 = 5.3 + 7(ak) + ak-1 + ak-2.

Using the recurrence relation, we have ak+1 = b = 5.3 + 7(ak) + ak-1 + ak-2.

Now, by the inductive hypothesis, ak = 5.3 + 7(ak-1) + ak-2 + ak-3. Substituting this into the equation above, we get:

ak+1 = 5.3 + 7(5.3 + 7(ak-1) + ak-2 + ak-3) + ak-1 + ak-2

    = 5.3 + 37.1 + 49(ak-1) + 7ak-2 + 7ak-3 + ak-1 + ak-2

    = 52.4 + 48(ak-1) + 8ak-2 + 7ak-3.

This shows that ak+1 can be expressed in the desired form, completing the inductive step. Therefore, by mathematical induction, we have proven that for all n ≥ 0: an = 5.3 + 7(an-1) + an-2 + an-3.

b. The given recurrence relation, an = an-1 + an-2 + an-3, does not match the desired statement, an ≤ 3^n. Hence, it is not possible to prove an ≤ 3^n using the given recurrence relation.

c. The given recurrence relation, an = an-1 - 6an-2 + an-3, does not match the desired statement, an ≤ (amount of money that is greater than or equal to 13 cents). Hence, it is not possible to prove an ≤ (amount of money that is greater than or equal to 13 cents) using the given recurrence relation.

d. To prove that if you only have 3 cent and 5 cent coins available, you can generate any amount of money that is greater than or equal to 8 cents, we will use the concept of the Chicken McNugget theorem.

The Chicken McNugget theorem states that for any two relatively prime positive integers a and b, the largest integer that cannot be expressed as a linear combination of a and b (i.e., ax + by where x and y are non-negative integers) is ab - a - b.

In this case, a = 3 cents and b = 5 cents, which are relatively prime since their greatest common divisor is 1. Applying the Chicken McNugget theorem, the largest integer that cannot be expressed as a linear combination of 3 and 5 is 3 * 5 - 3 - 5 = 7.

Thus, any amount of money greater than or equal to 8 cents can be formed using only

3 cent and 5 cent coins. This can be achieved by adding the appropriate number of 5 cent coins and/or 3 cent coins to reach the desired amount, as long as it is at least 8 cents.

For example, to make 8 cents, you can use one 5 cent coin and one 3 cent coin. For 9 cents, you can use three 3 cent coins. By applying this approach, any amount greater than or equal to 8 cents can be formed using only 3 cent and 5 cent coins.

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Answer:

D

Step-by-step explanation:

The shape, when reflected over the X axis, moves into Quadrant IV... its tail is facing downwards

When we rotate it clockwise, we rotate the shape as well as move it to the next Quadrant in a clockwise manner, in this case Quadrant III

Answer:

Our problem is \(x^2-2x+6=0\), but as we can see, we are unable to factor. We have to use the quadratic equation to solve.

\(x^2-2x+6=0\)

\(\frac{-b+-\sqrt{b^2-4ac}}{2a}\)

Positive Quadratic Formula:

\(\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}\)

Negative Quadratic Formula:

\(\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}\)

Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.

*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.

Answer:

D. No real Solution

Step-by-step explanation:

Hello!

Let's use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In our equation:

This comes from the standard form of a quadratic: \(ax^2 + bx + c\)

Now, solve:

Since the radicand (-5) is negative, there are no real solutions. The correct answer is Option D.

Answer:

8550

Step-by-step explanation:

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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There were 2448 votes against the issue.

The ratio of the votes for a particular issue in a poll was 5:3. There were 6528 votes in total. Find out the number of votes in favor of the issue.

Follow the below steps to find out the number of votes in favor of the issue:

Step 1: Add the values of the ratio: 5 + 3 = 8

Step 2: Divide the total votes by the value of the ratio: 6528 / 8 = 816

Step 3: Multiply the numerator of the ratio by the quotient obtained in step 2 to find the number of votes in favor of the issue: 5 × 816 = 4080Therefore, out of 6528 votes in the poll, 4080 were in favor of the issue.

You can also calculate the number of votes against the issue by multiplying the numerator of the ratio by the quotient obtained in step 2: 3 × 816 = 2448.

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Answer:

36

Step-by-step explanation:

14+6+16

Answer:

36

Step-by-step explanation: hope im right. i agree with person above me. give them brainliest :)

Answer:

you have to add all of them up it will get you some of your awner

To create a square with 50px sides, we need to draw four lines that are each 50px long and perpendicular to one another.

A square is a quadrilateral (a four-sided shape) with four equal sides and four equal angles of 90 degrees each. To create a square with 50px sides, we need to follow a few steps.

Step 1: Draw a line that is 50px long using a ruler or any other measuring tool.

Step 2: At the end of the line, draw a second line that is also 50px long and perpendicular to the first line. This will form the first side of the square.

Step 3: From the end of the second line, draw a third line that is also 50px long and perpendicular to the second line. This will form the second side of the square.

Step 4: Finally, draw a fourth line that is 50px long and perpendicular to the third line, connecting back to the starting point of the first line. This will form the remaining two sides of the square.

By following these steps, you have successfully created a square with 50px sides.

In summary, a square is a four-sided shape with four equal sides and angles of 90 degrees each. The resulting shape will be a square with 50px sides.

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