Is this a linear function
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-2
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5
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11

Answer:8.44

Step-by-step explanation:

Area of the circle is 56.

Divide 56 by 3.14(Pi)

56/3.14=17.8343949

Square root it

Square root of 17.8343949=4.223078841

4.22 is the radius so to find the diameter you just multiple by 2.

4.223078841x2=8.446157683

Step-by-step explanation:

Given,

6x - 5y = 10.5 .............. (1)

5x - 3y = -2 .................. (2)

Multiplying eq (1) by 3 and (2) by 5 then subtracting,

18x - 15y = 31.5

(-) 25x - 15y = -10

-----------------------------

-7x = 41.5

x = - 41.5 / 7 = -83 / 14

Inserting the value of x in eq (2)

5 * (-83 / 14) - 3y = -2

y = -129 / 14

x = -83 /14 and y = -129 /14

Answer:

Perimeter=38cm

Step-by-step explanation:

We have sides 9, 10, 5, and 4 cm

But there are 2 sides missing.

We see that 1 missing side is part of a square, in which all sides are equal, so the top missing side is 4cm.

We calculate the other missing side by taking the bottom side and subtracting 4cm from that.

This way we get the second missing side=6cm

Now we can add all of them

9+10+5+4+4+6=38cm

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

\(u (x) = - 0.04x ^ {2} + 44x-4000\)

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

\(\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}\)

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

\(u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000\)

         \(= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000\)

x₂ = 620

\(u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000\)

         \(= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904\)

Compute the average rate of change as follows:

\(\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}\)

                                      \(=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5\)

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Answer:

A

Step-by-step explanation:

Edge 2021

The sum of the 48 terms will be $2,496. Then the correct option is A.

Let a₁ be the first term, n the number of the terms, and l be the last term of the sequence.

Then the sum of all the terms will be given as,

S = [n (a₁ + l )] / 2

Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as

\(\rm a_n = a_1 + (n - 1)d\)

Beginning with Rodney’s first month of high school, his father deposits $5 into Rodney’s savings account.

Each month after the first month, his father deposits $2 more than the previous month.

Then the first term is $5 and the common difference is $2.

The total amount deposited in Rodney’s account after four years can be represented using the expression.

Then the total number of the terms will be

n = 4 x 12

n = 48 months

Then the 48th term of the sequence will be

a₄₈ = 5 + (48 – 1) · 2

a₄₈ = 5 + 47 · 2

a₄₈ = 5 + 94

a₄₈ = 99

Then the sum of the 48 terms will be

S = 48 (5 + 99) / 2

S = 24 × 104

S = $2,496

Then the correct option is A.

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Answer:

The answer is d

Step-by-step explanation:

Answer:

it  D

Step-by-step explanation:

hope it helps

Answer:

The answer is c

Step-by-step explanation:  

Theater 2 is less than the mean absolute deviation of the data for theater.  

I hope this helps

Answer: C

Step-by-step explanation: if im wrong let me know ill fix

A 2x3x2 factorial design has three independent variables. What is a factorial design? A factorial design is an experimental design that studies the impact of two or more independent variables on a dependent variable.

The notation of a factorial design specifies how many independent variables are used and how many levels each independent variable has. In a 2x3x2 factorial design, there are three independent variables, with the first variable having two levels, the second variable having three levels, and the third variable having two levels.

The number of treatments or conditions required to create all feasible combinations of the independent variables is equal to the total number of cells in the design matrix, which can be computed as the product of the levels for each factor.

In this case, the number of cells would be 2x3x2=12.Therefore, a 2x3x2 factorial design has three independent variables and 12 treatment groups..

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Answer:

false

Step-by-step explanation:

cube root implies that the number equal to it, in this case 30, can be multiplied thrice and equal the cube root.

for example, √25 = 5, meaning that 5 x 5 = 25.

if this equation were true, 30 x 30 x 30 would equal 90. because it does not, this equation is false.

The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:

C. m∠5 + m∠6 =180°.

D. m∠2 + m∠3 = m∠6.

E. m∠2 + m∠3 + m∠5 = 180°.

In Geometry, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:

m∠5 + m∠6 =180°.

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:

m∠2 + m∠3 = m∠6.

Additionally, the sum of all the angles that are formed by a triangle is equal to 180º and this is given by:

m∠2 + m∠3 + m∠5 = 180°,

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Answer:

$373

Step-by-step explanation:

$100 - $42 = $58

$58 - $35 = $23

$23 + $350 = $373

Mrs. Smith has $373 in her bank account

The value of U and V will be (x – 3) and 8y, respectively. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression is given below.

⇒ (U + V)(U – V)

Where U and V are either constant or single variable expression.

Then the expression will be

⇒ U² – V²

Then the value of U and V will be (x – 3) and 8y, respectively.

Then the correct option is A.

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Answer:

see photo for your analysis

Step-by-step explanation:

The first four terms of the series are -3 + (11/2)x - 5x^2/2 + (7/6)x^3 + ...

We know that the nth derivative of f at x = 2 is given by f(n) (2) = n!/(n-1)!, which simplifies to f(n) (2) = n for n ≥ 2. Also, we know that f(2) = 1. Using this information, we can write the Taylor series for f about x = 2 as:

f(x) = ∑[n=0 to ∞] f(n)(2) * (x-2)^n / n!

  = f(2) + f'(2)(x-2)^1/1! + f''(2)(x-2)^2/2! + f'''(2)(x-2)^3/3! + ...

  = 1 + (x-2)^1 + 2(x-2)^2/2! + 3(x-2)^3/3! + ...

Simplifying the terms and combining coefficients, we get:

f(x) = 1 + (x-2) + (x-2)^2 + (x-2)^3/2 + ...

The first four terms are:

f(x) = 1 + (x-2) + (x-2)^2 + (x-2)^3/2 + ...

= 1 + (x-2) + (x^2 - 4x + 4) + (x^3 - 6x^2 + 12x - 8)/2 + ...

= 1 + (x-2) + x^2 - 4x + 4 + x^3/2 - 3x^2 + 6x - 4 + ...

= -3 + (11/2)x - 5x^2/2 + (7/6)x^3 + ...

The general term of the series is:

f(n)(2) * (x-2)^n / n!

= n * (x-2)^n / n!

= (x-2)^n / (n-1)!

Therefore, the Taylor series for f about x = 2 is:

f(x) = 1 + (x-2) + (x-2)^2 + (x-2)^3/2 + ... + (x-2)^n / (n-1)! + ...

The first four terms of the series are -3 + (11/2)x - 5x^2/2 + (7/6)x^3 + ...

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Answer:

-3a^2+11a

Step-by-step explanation:

Answer:

4a-a×3a+7a

or, 3a×3a+ 7a

or,9a+7a

or,16a

:. a =16

Answer:

The difference would be 1/12.

Step-by-step explanation:

2/3 is 8/12.

Answer:

0.00108754758 If 4/3678 and 919.5 if 3678/4

Step-by-step explanation:

Answer:

Answer: 2/1839

Step-by-step explanation:

4 ÷ 3678 = 0.00108754758 or 2/1839

\( \large \bf \implies{y-axis}\)

[The y-coordinate is the same, the x-coordinate is the opposite of each other, Symmetric about the y-axis]

the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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Answer:

True

Thx for the points :)

The output of the following code snippet will be 1, 2, 3, and 4.

The reason is that the while loop runs infinitely until the break statement is executed. The break statement terminates the loop if the value of x is divisible by 5. However, the value of x is incremented at each iteration of the loop before checking the condition. Here is the step-by-step explanation of how this code works:

Step 1: Assign 1 to x.x = 1

Step 2: Start an infinite loop using the while True statement.

Step 3: Check if the value of x is divisible by 5 using the if x % 5 == 0 statement.

Step 4: If the value of x is divisible by 5, terminate the loop using the break statement.

Step 5: Print the value of x to the console using the print(x) statement.

Step 6: Increment the value of x by 1 using the x += 1 statement.

Step 7: Repeat steps 3-6 until the break statement is executed.

Therefore, the output of the code will be: 1 2 3 4.

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The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.

From question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng

To calculate the interest charges for Sheng's credit cards, we need to use the following formula:

Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365

Using this formula, we can calculate the interest charges for each of Sheng's credit cards:

For Credit Card A:

Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94

For Credit Card B:

Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01

So, the total interest charges for Sheng's credit cards are:

Total Interest Charges = $4.94 + $6.01 = $10.95

Now, let's calculate the total cost of the debt consolidation loan:

Total Cost = Total Monthly Payments x Number of Payments - Loan Amount

Total Monthly Payments = $179.37

Number of Payments = 6 x 12 = 72

Loan Amount = ?

To find the loan amount, we need to solve for it using the interest rate and the total interest charges:

Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)

Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000

So, the total cost of the debt consolidation loan is:

Total Cost = $179.37 x 72 - $25,000 = $2,008.64

Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:

Additional Interest Charges = Total Cost - Total Interest Charges

Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69

Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges

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Answer:

Pt. 1: D

Pt. 2: what are the options for part 2?

Step-by-step explanation:

Harold needs 71 tomato plants.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Harold wants to make a tomato patch.

And, It will have 7 long rows of plants, each with 8 plants in the row, and 3 short rows of plants, each with 5 plants in the row.

Now, For the total number of tomato plants Harold needs, we can multiply the number of plants in each row by the number of rows for each section (long and short) and then add the results as,

Hence, the expression for number of tomato plants Harold needs is:

⇒  (7 long rows x 8 plants per row) + (3 short rows x 5 plants per row) Simplifying the expression, we get:

⇒ 56 + 15 = 71

Therefore, Harold needs 71 tomato plants.

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Answer:

29.7263957575

Step-by-step explanation:

hope this answer help you (:

Aimee is using the defense mechanism of rationalization.

Rationalization is a defense mechanism in which individuals justify or explain their behavior or feelings in a way that makes them more acceptable to themselves or others. It involves providing a seemingly logical or reasonable explanation for their actions or choices, often to avoid facing uncomfortable truths or taking responsibility.

1. In this scenario, Aimee had a clear goal of studying for an exam and knew she needed to get home early enough to accomplish it.

2. However, she chose to continue shopping and ended up getting home too late to study.

3. When her mom asks her why she didn't leave enough time to study, Aimee responds with a rationalization by stating, "I probably would not do well on the exam if I did study."

4. By making this statement, Aimee is providing a rationalization for her behavior. She is justifying her decision to continue shopping by suggesting that studying would not have made a difference in her performance on the exam.

5. Aimee's rationalization allows her to avoid taking responsibility for her actions and the consequences of not studying. It provides her with a sense of comfort and protects her self-esteem by creating a belief that studying would not have been effective anyway.

In summary, Aimee's response of not studying because she believes it would not have made a difference on the exam is an example of rationalization, a defense mechanism used to justify her behavior and avoid facing the reality of her choices.

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Using the master theorem, the Θ-class are: a) T(n) = Θ(n)b) T(n) = Θ(n) and c) T(n) = Θ(√n log n).

a) T(n)=2T(n/2)+n³

To find the Θ class of T(n), we need to apply the Master Theorem. In the Master Theorem, if T(n) = aT(n/b) + f(n) where a >= 1, b > 1, and f(n) is an asymptotically positive function, then:

T(n) = Θ(nᵈ)

where d = logₐ(b).

Here a = 2, b = 2 and f(n) = n³.

So, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

b) T(n)=2T(n/2)+3n−2

Similarly to part (a), we can find the Θ class of T(n) by using the Master Theorem.

In this case, a = 2, b = 2 and f(n) = 3n - 2.

Here, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

c) T(n)=4T(n/2)+nlogn

For this recurrence relation, a = 4, b = 2 and f(n) = nlogn.

In this case, d = log₄(2) = 0.5.

So,

T(n) is

= Θ(nᵈ)

= Θ(n⁰.⁵)

= Θ(√n log n)

Therefore, the Θ class of T(n) is Θ(√n log n).

Hence, the correct options are:a) T(n) = Θ(n)b) T(n) = Θ(n)c) T(n) = Θ(√n log n).

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Answer:

7

Step-by-step explanation:

12-x

Let x = 5

12-5

7

Answer:

Options b) d) e)