.Question 4: For the following, make sure that you keep your information organized and concise (within two pages). It should be easy to follow, and should showcase your understanding of polynomial functions, so show your steps/reasoning. For each of the pieces in your (piecewise) design: State the equation for the polynomial function used. Determine the degree of the polynomial function. State the domain and range of the restricted function piece. • Assuming that each function piece was unrestricted, for each, determine whether the function piece has even or odd symmetry, or neither. If neither, determine which transformations, if any, could be applied to make it even or odd over its unrestricted domain?

Answer:

True

Step-by-step explanation:

Answer: false

Step-by-step explanation:

i think its 4x and I'm sure

Answer:

c option 4x because it is multiplied

Answer:

62.5%

Step-by-step explanation:

We know that Mike's whole drink is 16 ounces.

If he drinks 6 ounces, that means we are subtracting 6 from the total (16 ounces)

16 - 6 = 10

Now that we have 10 ounces left, we have to find out what percent that is out of the total (16 ounces)

To do this, we must create a fraction: 10/16

You can simplify this by dividing both sides by 2, getting us 5/8

Now, you can either use long division, or a calculator or know that 1/8 is .125, then multiply that by 5 to get .625

Now, the question is asking us for a percent, not a decimal, so we must convert .625 to a percent by multipling everything by 100. This just means moving every number to the right 2 (keep the decimal still)

Once done, you will get 62.5% left!

Answer:

1 foot?

Step-by-step explanation:

You subtract 13 from 12 to get the base divider.

Confirmation bias

Confirmation bias

is a cognitive bias that refers to the tendency of individuals to interpret information in a way that confirms their pre-existing beliefs or hypotheses. It can lead to flawed conclusions because it disregards or discounts evidence that contradicts one's beliefs while selectively accepting information that supports them. This bias can occur in various contexts, including scientific research, data analysis, and

decision-making processes

. When confirmation bias is present, it can hinder objectivity and lead to biased interpretations or flawed conclusions based on incomplete or skewed information. It is important to be aware of this bias and strive for impartiality and open-mindedness when analyzing data or drawing conclusions.

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Answer:

1. )0.35

2. )1.15

3.)0.5 (5 repeating's)

4.)2.72

Step-by-step explanation:

7 divide  20=0.35

-23 divide 20=1.15

-60 divide 22 = 2.727272 but it is 2.72

Answer: 18/9 if not it's something along that-

Step-by-step explanation:

7^2 = 49 so like 49-31 equals 18 and the denominator 3^2 = 9 , so if it's not 18/9 then it's like 1/2 or something bc 9 + 9 is 18 yk-

(a) The number of solutions is 455

(b) The number of solutions if each variable xi is an integer greater than or equal to one is 165

(a) This problem can be solved using the stars and bars technique. We need to distribute 12 identical objects (stars) among 4 distinct boxes (corresponding to the variables) such that each box can have zero or more stars. The number of solutions is therefore (12+4-1) choose (4-1) = 455.

(b) We can convert this problem into the previous one by subtracting 1 from each xi, so that we are now looking for non-negative integers. We need to distribute 8 identical objects (12-4) among 4 distinct boxes (corresponding to the variables) such that each box can have zero or more objects. The number of solutions is therefore (8+4-1) choose (4-1) = 165.

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Your question is incomplete but probably the full question is:

How many solutions are there to the equation x1+x2+x3+x4=12 if:

(a) Each variable xi is an integer greater than or equal to zero?

(b) Each variable xi is an integer greater than or equal to one?

The probability that it takes at most 1 hour of machining time to produce a randomly selected component is approximately 0.00003 or 0.003%.

To solve this problem, we need to first calculate the total mean and standard deviation for the machining time of a single component.

The total mean machining time can be found by adding the means for each component:

30 + 20 + 15 = 65 minutes

The total standard deviation can be found using the formula:

\(\sqrt{((1^2 + 2^2 + 1.2^2)/3)} = 1.247 minutes\)

Now we need to find the probability that it takes at most 1 hour (60 minutes) to produce a randomly selected component. We can use the standard normal distribution to calculate this probability.

z-score = (60 - 65) / 1.247 = -4.01

Using a standard normal distribution table, we can find that the probability of a z-score being less than or equal to -4.01 is approximately 0.00003.

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The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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If we multiply both numerator and denominator of the first ratio by 3, we will get the second ratio, thus, these are equivalent.

For any ratio:

a/b

If we multiply both numerator and denominator by the same real number, we will get an equivalent ratio.

In this case, we can start with the smaller of the two ratios:

1/6.

Now we can multiply both numerator and denominator by 3, then we will get:

(3*1)/(3*6) = 3/18

So yes, the ratios 1/6 and 3/18 are equivalent.

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By answering the given question, we may state that k is an integer, equation where. This number becomes squared to give us: \(n^2\) = \((100k + 9)^2\) = 10000\(k^2\) + 1800k + 81

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

Assume for the moment that there is a 10-digit number M, which is one more than the square of another integer and has unique digits throughout. This integer can be written as:

\(M = a 110*9*a 210*8*a 310*7*a 410*6*a 510*5*a 610*4*a 710*3*a 810*2*a 9*10*a 10\)

where M's digits a 1, a 2,..., a 10 are.

\(n = 10k + 1\)

k is an integer, where. This number becomes squared to give us:

\(n^2 = (10k + 1)\)

\(n^2 = 100k^2 + 20k + 1\)

\(n = 100k + 9\)

k is an integer, where. This number becomes squared to give us:

\(n^2\) = \((100k + 9)^2\) = 10000\(k^2\) + 1800k + 81

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The values of a, h and k on the function are given as follows:

The meaning of the transformations is given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = 1/x.

Hence the meaning of the transformations is given as follows:

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The salary of someone working in the industry with a z-score of -1.12 is approximately $43,825.

To find the salary of someone with a specific z-score, we can use the formula:

X = μ + (z * σ),

where X is the salary, μ is the mean annual salary, z is the z-score, and σ is the standard deviation.

Given that the mean annual salary (μ) is $47,581 and the standard deviation (σ) is $3,354, we can substitute these values into the formula:

X = 47,581 + (-1.12 * 3,354).

Performing the calculations, we get:

X ≈ 47,581 - 3,753.48.

Rounding to the nearest dollar, the salary is approximately $43,825. This means that an employee working in the industry whose salary has a z-score of -1.12 earns approximately $43,825 per year. The negative z-score indicates that the salary is below the mean, as expected since the z-score is negative.

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The entire area of flag made with yellow and orange fabric is found as 397 square inches.

The given data is-

The following computation must be done to estimate the flag's overall area:

228 + 228/2 + (228/3 - 24) = X

228 + 114 + (76 - 24) = X

228 + 117 + 52 = X

228 + 169 = X

397 = X

Thus, the entire area of the flag made with yellow and orange fabric is found as 397 square inches.

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The correct question is-

Frakies's group designed a flag. they used 228 sq inches of green fabric. twice as much green fabric as orange fabric. 3 times as much green fabric as yellow fabric and they had 24 sq inches of yellow fabric left. how can raineys group determine the total area of the flag?

Table 3 shows a relationship between x and y, where y is always equal to 8 less than the product of x and 3.

We are given that y is always equal to 8 less than the product of x and 3, which can be written as y = 3x - 8. We can create a table of values for x and y using this equation.

Table 1:

+x y

1 -5

2 -2

3 1

4 4

5 7

Table 2:

x y

1 -7

2 -4

3 -1

4 2

5 5

Table 3:

x y

1 -5

2 1

3 7

4 13

5 19

Checking each table, we can see that only Table 3 satisfies the condition that y is always equal to 8 less than the product of x and 3. Therefore, Table 3 shows the relationship between x and y as given in the question.

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Which table shows a relationship between x and y, where y is always equal to 8 less than the product of x and 3?

The value of g(5) can be determined by integrating the given derivative function and using the initial condition g(2) = -7.  The value of g(5) is approximately 57.955.

To find the value of g(5), we need to integrate the derivative function g'(x). The antiderivative of √\(x^3\) + x with respect to x will give us the original function g(x). Let's perform the integration:

∫√\(x^3 + x dx\) = ∫\((x^(3/2) + x) dx = (2/5)x^(5/2) + (1/2)x^2 + C\)

Now, using the initial condition g(2) = -7, we can determine the constant of integration C:

\((2/5)(2)^(5/2) + (1/2)(2)^2 + C = -7\)

Simplifying the equation, we can solve for C:

(8/5) + 2 + C = -7

C = -7 - (8/5) - 2

C = -7 - (16/5) - (10/5)

C = -7 - (26/5)

C = -35/5 - 26/5

C = -61/5

Now that we have the value of C, we can substitute it back into the original function and evaluate g(5):

g(5) = \((2/5)(5)^(5/2) + (1/2)(5)^2 - (61/5)\)

Calculating this expression will give us the value of g(5).

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Answer:

B and C

Step-by-step explanation:

radius of a ball is half its diameter, ball C has a diameter less than the inner rim, easily fitting through (13<14)

Ball B has a radius of 6, and since we know that radius is half the diameter, 6 x 2 is 12 and 12 is ball B's diameter. 12 is less than 14 which means ball B can fit through. Hurray!

Ball D has a radius of 8 inches, we need its diameter so 8 x 2 = 16, but 16 is greater than 14, which means ball D cannot fit through. Phooey..

Ball A has a circumference of 45 inches, to get the diameter of the ball when given circumference is simple, just divide the circumference by pi. This works because in order to get the circumference of a ball from diameter we multiply by pi. Now, 45 divided by π (or 3.14) gives us 14.33, 14.33 is ball A's diameter. 14.33 is a little over 14, that means ball A will not fit through the basketball hoop!

I hope this helped!

A statement which best describe the transformation from Figure 1 to Figure 2 is: C. reflection over the y-axis.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of figure 1, the coordinates of figure 2 include the following:

(x, y)                               →              (-x, y)

Coordinate A = (-6, 5)   →  Coordinate A' = (-(-6), 5) = (6, 5).

Coordinate B = (-4, 5)   →  Coordinate B' = (-(-4), 5) = (4, 5).

Coordinate C = (-3, 5)   →  Coordinate C' = (-(-3), 5) = (3, 5).

Coordinate D = (-5, 4)   →  Coordinate D' = (-(-5), 4) = (5, 4).

Coordinate E = (-5, 3)   →  Coordinate E' = (-(-5), 3) = (5, 3).

Coordinate F = (-7, 3)   →  Coordinate F' = (-(-7), 3) = (7, 3).

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Answer:

B makes the most sense.

Step-by-step explanation:

The others make little to no sense.

Answer:

B is the correct answer. it makes sense

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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Lamar's office will take 12 weeks to recycle a total of 24 kilograms of paper

Information about the problem:

To solve this problem, we have to state the equation using the information of the problem:

Calculating the recycle rate of Lamar's office, we get:

Rate = Kg recycled / time

Rate = 6 kg/3 weeks

Rate = 2 kg/week

Calculating how many weeks Lamar's office will take to recycle 24 kilograms:

Weeks = Total recycle/ rate

Weeks = 24 kg / 2kg/week

Weeks = 12 weeks

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

\(\boxed {\boxed {\sf D. \ x=20}}\)

Step-by-step explanation:

If line m and line r are parallel, the two angles must be congruent, because they are alternate interior angles. Notice how the 2 lines and the transversal form a backwards "Z" and the angles are in the inner corners.

So, if the angles are congruent, we can set them equal to each other.

\(7x-115=3x-35\)  

Now, solve for x by isolating the variable. First, move all the constants to one side and the terms with variables to another.

115 is being subtracted and the inverse of subtraction is addition. Add 115 to both sides.

\(7x-115+115=3x-35+115\\7x= 3x+(-35+115) \\7x=3x+80\)

3x is being added and the inverse of addition is subtraction. Subtract 3x from both sides.

\(7x-3x=3x-3x+80 \\4x=80\)

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.

\(4x/4=80/4\\x=20\)

If the lines are parallel, then x=20 so the angles are congruent.

Answer:

-8.4 is the answer.(cross multiply )

Answer:

p= -8.4

Step-by-step explanation:

cross multiply

p=-7* 1.2

p=-8.4000001

Answer:

Step-by-step explanation:

b

The justification for Step 1 is the subtraction property of equality. Option B

The justification for Step 1 within the arrangement prepare, which changes the condition 15x − 8 = 14x + 13 into 15x = 14x + 21, is the subtraction property of uniformity.

The subtraction property of equality states that in the event that we subtract the same amount from both sides of an condition, the condition remains genuine. In this case, we are subtracting 14x from both sides of the condition to confine the term with x.

To clarify Step 1 utilizing the subtraction property of correspondence:

The condition 15x − 8 = 14x + 13 is given.

We need to disconnect the x term on one side of the condition. To do this, we got to dispose of the 8 on the cleared out side.

By subtracting 14x from both sides of the condition, we evacuate the 14x term from the correct side:

15x − 14x − 8 = 14x − 14x + 13

Simplifying:

x − 8 = 13

Now, the 14x term is dispensed with from the proper side of the condition.

To advance streamline the condition, we are able include 8 to both sides to dispose of the -8 term on the cleared out side:

x − 8 + 8 = 13 + 8

Simplifying:

x = 21

Now, we have effectively isolated the x term on one side of the condition.

Therefore, the justification for Step 1 is the subtraction property of equality  (B).

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Complete question

What is the justification for step 1 in the solution process?

15x − 8 = 14x + 13

Step 1: 15x = 14x + 21

A.

the addition property of equality

B.

the subtraction property of equality

C.

the division property of equality

D.

the multiplication property of equality

The amount of dry cells that are taken from the full container is 473.

To find the total number of dry cells taken from the full container, we need to add up the number of dry cells placed in the stockroom, on the shelf, and sold to customers. We can use the following equation:

  Total dry cells taken = Dry cells in stockroom + Dry cells on shelf + Dry cells sold to customers

Plugging in the given values, we get:

  Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6

Using the order of operations, we can simplify the equation:

Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 370 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 388 + 25 + 30 + 24 + 6
Total dry cells taken = 413 + 30 + 24 + 6
Total dry cells taken = 443 + 24 + 6
Total dry cells taken = 467 + 6
Total dry cells taken = 473

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Therefore, The pair (2/5, 1/5) minimizes the sum of squares x^2 + y^2 for 2x + y = 9.

To find the pair of (x, y) that minimizes the sum of squares x^2 + y^2, we can use the method of Lagrange multipliers. Let f(x, y) = x^2 + y^2 be the function to minimize subject to the constraint g(x, y) = 2x + y - 9 = 0. The Lagrange multiplier method states that the minimum occurs when the gradient of f and a multiple of the gradient of g are parallel. Solving these equations gives x = 2/5 and y = 1/5 as the pair of fractions that minimize x^2 + y^2.
To find the pair (x, y) that minimizes the sum of squares x^2 + y^2, follow these steps
1. From the given equation 2x + y = 9, isolate y: y = 9 - 2x
2. Substitute this expression for y in the sum of squares: x^2 + (9 - 2x)^2
3. Expand the equation: x^2 + 4x^2 - 36x + 81
4. Combine like terms: 5x^2 - 36x + 81
5. To minimize the sum of squares, differentiate the equation with respect to x and set it equal to zero: 10x - 36 = 0
6. Solve for x: x = 18/5
7. Substitute x back into y = 9 - 2x to find y: y = 9 - 2(18/5) = 27/5
The pair (x, y) that minimizes the sum of squares is (18/5, 27/5).

Therefore, The pair (2/5, 1/5) minimizes the sum of squares x^2 + y^2 for 2x + y = 9.

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Therefore, the given equation is true and we have successfully proved that the first side is equal to the second side.

Given, A + (AB) = A + B

First we take LHS, then expand using distributive property:

A + (AB) = A + B

=> A + AB = A + B

=> AB = B

Subtracting B from both the sides we get:

AB - B = 0

=> B (A - 1) = 0

So, either B = 0 or (A - 1) = 0.

If B = 0, then both sides are equal as 0 equals 0.

If (A - 1) = 0, then A = 1.

Substituting A = 1, the given equation is rewritten as:(1 + B) = 1 + B => 1 + B = 1 + B

Thus, both sides are equal.

Hence, we can say that the first side is equal to the second side.

Proof: A + (AB) = A + B(1 + B) = 1 + B [As we have proved it in above steps]

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Answer: what is the question?

Step-by-step explanation: