Which statement is true about the function f(x) = -x?
It has the same domain as the function f(x) = --x.
It has the same range as the function f(x) = -V-X.
It has the same domain as the function f(x) = -VX.
It has the same range as the function f(x) = -VX

Reasonable estimate of the total cost is $10.

We know that Reasonable estimate does not exceed the original numbers.

We can round down the number to the nearest number to estimate the answer.

Given that Jenny buys four items that cost $1.43, $3.72, $2.21 and $ 5.60 which estimates to $0 , $0, &0, $10.00 respectively.

Therefore total cost of estimated numbers will be

$0 + $0 + $0 + $10.00 = $10

Hence reasonable estimate of the total cost is $10.

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(a) No

\(f(x) = 12 - 5x\)

\(f(0) = 12 - 5(0)\)

\(f(x) = 12 - 0\)

\(f(x) = 12\)

Hence,

f(0) is unequal to 0.

(b)

\(f(x) = 12 - 5x\)

\(f( - 1) = 12 - 5( - 1)\)

\(f( - 1) = 12 + 5\)

\(f( - 1) = 17\)

(c)

\(f(x) = 12 - 5x\)

\(f(x) = 6\)

\(6 = 12 - 5x\)

\(6 - 12 = - 5x\)

\( - 6 = - 5x\)

\(6 = 5x\)

\( \frac{6}{5} = x\)

The conclusion about the functions is they have the same y-intercept.

The complete question is added as an attachment

The function is given as:

f(x) = (x + 4)^2

From the attached graph, the graph has a y-intercept at:

y = 16

This can be represented as:

(0, 16)

Next, we set x = 0 in f(x) = (x + 4)^2

f(0) = (0 + 4)^2

Evaluate

f(0) = 16

This means that the y-intercept of f(x) = (x + 4)^2 is (0, 16)

So, the functions have the same y-intercept

Hence, the conclusion about the functions is they have the same y-intercept.

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An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each are chosen, and three replicates of a 2323 factorial design are run.

The chosen terms, effect, and factorial can be defined as follows:

Terms: A - Cutting Speed B - Tool Geometry C - Cutting Angle Effect :In experimental design, the term "effect" refers to the difference in the outcome caused by a change in the treatment, given that other possible sources of variation are accounted for and controlled. Therefore, a factor's effect refers to the variation in the response variable (life of the machine tool) that is linked to changes in the factor level.

Factorial: The factorial experiment is a statistical experiment in which many variables are studied at once to determine the influence of each of these variables on the response variable. In a factorial experiment, the effect of each factor and the effect of each combination of factors are investigated.

The results of the experiment are shown in the following table:

Here is the table representing the data. Replicate A B C I II III - - - 22 31 25 + - - 32 43 29 - + - 35 34 50 + + - 55 47 46 - - + 44 45 38 + - + 40 37 36 - + + 60 50 54 + + + 39 41 47The factor effect of A, B, and C is shown in the table below. The computation of each factor effect is made by calculating the average response across all replicates of each level and subtracting the grand average from the level average.Here is the table representing the factor effect of A, B, and C:Factor A Factor B Factor C -7.25 -3.5 0.75 +7.25 +3.5 -0.75 -1.25 -4.5 +9.25 +3.75 +0.5 -0.25 +3.75 -0.5 +7.25 -3.75 -1.25 -7.25 +0.5 +4.25 Grand Average 39.875From the results obtained above, the most significant factor effect was tool geometry (B), which ranged from -4.5 to 3.75. The effect of factor C was also significant because the difference between the levels is only 0.5, which is relatively small.

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The effects that appear to be large are the effect of cutting speed (A).

The engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each are chosen, and three replicates of a 2323 factorial design are run. The given table shows the results of the experiment for 8 different treatment combinations:

Replicate A B C

I II III- - -

22 31 25+ - -

32 43 29- + -

35 34 50+ + -

55 47 46- - +

44 45 38+ - +

40 37 36- + +

60 50 54+ + +

39 41 47

We have the following calculations:

$$N=8, \quad k=3, \quad r=3$$

Sum of treatment combinations = $$\sum y_{ij}=22+31+25+32+43+29+35+34+50+55+47+46+44+45+38+40+37+36+60+50+54+39+41+47=869$$

Grand mean:

$$\bar{y}_{...} = \frac{1}{N} \sum_{i=1}^r \sum_{j=1}^k y_{ij} = \frac{1}{8\cdot 3} \cdot 869 = 36.21$$

Sum of squares for each treatment:

$\text{SS}_A=3\cdot [(32.75-36.21)^2+(48.5-36.21)^2]=79.0450$$\text{SS}_B=3\cdot [(38.25-36.21)^2+(41.5-36.21)^2]=10.5234$$\text{SS}_C=3\cdot [(42.75-36.21)^2+(40.5-36.21)^2]=23.9822$$

Total sum of squares:

$\text{SST}=\sum_{i=1}^r\sum_{j=1}^k(y_{ij}-\bar{y}_{...})^2=1557.75$

The sums of squares of treatments (SST) were calculated using the following formula:

$$\text{SST} = \sum_{i=1}^{r} \frac{(\sum_{j=1}^{k} y_{ij})^2}{k} - \frac{(\sum_{i=1}^{r} \sum_{j=1}^{k} y_{ij})^2}{Nk}$$

The sums of squares of errors (SSE) were calculated using the following formula:$$\text{SSE} = \text{SST} - \text{SS}_A - \text{SS}_B - \text{SS}_C$$

The degrees of freedom are $df_T = Nk-1 = 23$, $df_E = N(k-1) = 16$, and $df_A = df_B = df_C = k-1 = 2$.

$$MS_A=\frac{\text{SS}_A}{df_A}=\frac{79.0450}{2}=39.5225$$

$$MS_B=\frac{\text{SS}_B}{df_B}=\frac{10.5234}{2}=5.2617$$$$MS_C=\frac{\text{SS}_C}{df_C}=\frac{23.9822}{2}=11.9911$$

$$F_A=\frac{MS_A}{MS_E}=\frac{39.5225}{\frac{107.9063}{16}}=5.77$$$$F_B=\frac{MS_B}{MS_E}=\frac{5.2617}{\frac{107.9063}{16}}=0.94$$

$$F_C=\frac{MS_C}{MS_E}=\frac{11.9911}{\frac{107.9063}{16}}=1.63$$

The $p$-value for $F_A$ with 2 and 16 degrees of freedom can be found using an $F$-distribution table or calculator. We can use an online calculator to find that the $p$-value for $F_A$ is approximately 0.015.

The $p$-value for $F_B$ with 2 and 16 degrees of freedom can be found using an $F$-distribution table or calculator. We can use an online calculator to find that the $p$-value for $F_B$ is approximately 0.401.

The $p$-value for $F_C$ with 2 and 16 degrees of freedom can be found using an $F$-distribution table or calculator. We can use an online calculator to find that the $p$-value for $F_C$ is approximately 0.223.

The effects are significant for $A$, while they are not significant for $B$ and $C$. Therefore, the effects that appear to be large are the effect of cutting speed (A).

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The absolute maximum value of f(x)=2x³ +3x² +1 on the closed interval [-3, 1] is 6, which occurs at x=1.

To find the absolute maximum value of the function f(x) on the closed interval [-3, 1], we need to evaluate the function at the endpoints of the interval and at any critical points in the interior of the interval.

First, we evaluate the function at the endpoints of the interval

f(-3) = 2(-3)³ + 3(-3)² + 1 = -17

f(1) = 2(1)³ + 3(1)² + 1 = 6

Next, we find the critical points of the function f(x) by taking its derivative and setting it equal to zero

f'(x) = 6x² + 6x

6x(x+1) = 0

x = 0 or x = -1

Now we evaluate the function at these critical points

f(0) = 1

f(-1) = 2(-1)³ + 3(-1)² + 1 = 2

Therefore, the absolute maximum value of f(x) on the closed interval [-3, 1] is 6, which occurs at x=1.

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The given question is incomplete, the complete question is:

Let f be the function given by f(x)=2x³ +3x² +1. What is the absolute maximum value of f on the closed interval [-3,1] ?

Answer:

315

Step-by-step explanation:

You're welcome
Answer above is rounded btw

Full number is:315.24444

Answer:

An inequality is a relation which makes a non equal comparison between two of more numbers or other mathematic equations. > I'd greater than < is less than = equal to. ≥ is greater than or equal ≤ less than or equal to. = equal to ≠ not equal

Step-by-step explanation:

Inequality- is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Answer:

-392x9 py4

Step-by-step explanation:

1. Multiply the numbers.

(-8x4 p . 7) ( 7 y4 x5)

(-56 x4 p) (7 y4 x5)

2. Multiply the numbers.

-56 x4 p. 7 y4 x5

-392 x4 py4 x5

3. Combine exponents.

-392 x4 py4 x5

-392 x9 py4

Answer: -392x9 py4

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

As per the given curvature, the value of PC is 1785.68 and PT is 1787.55

Curvature:

In statistics, curvature means amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

Given,

PI is at station (20 00), the radius of curvature is 800 feet, and the angle of curvature is 30 degrees.

Here we need to determine the value of PC and PT.

According to the given value, the tangent distance is calculated as,

=> T = 800 x tan (30/2)

=> T = 800 x 0.2679

=> T = 214.32

Now, the value of PC is calculated as,

PC = PI - T

=> PC = 2000 - 214.32

=> PC = 1785.68

And the value of PT is calculated as,

PT =  PC + L

=> PT = 1785.68 + (100 x (30/1600))

=> PT = 1785.68 + 1.875

=> PT = 1787.55

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Pairwise comparison voting, also known as Condorcet voting, satisfies both majority rule and pairwise victory (the Condorcet criterion).

1. Pairwise comparison: In pairwise comparison voting, each candidate is compared to every other candidate in a head-to-head contest. Voters rank the candidates in order of preference, and the outcomes of these individual contests are used to determine the overall winner.

2. Majority rule: Majority rule is satisfied in pairwise comparison voting because, in each head-to-head contest, the candidate who receives more than 50% of the votes is considered the winner. This ensures that the candidate with the majority of votes in each comparison is acknowledged as the preferred choice.

3. Pairwise victory (Condorcet criterion): The Condorcet criterion states that if there is a candidate who can beat every other candidate in a one-on-one contest, that candidate should be the overall winner. Pairwise comparison voting satisfies the Condorcet criterion because it directly compares each candidate against all others, ensuring that any candidate who consistently wins these head-to-head contests is recognized as the overall winner.

In conclusion, pairwise comparison voting (Condorcet voting) satisfies both majority rule and pairwise victory (the Condorcet criterion) by comparing candidates in head-to-head contests, ensuring that the candidate with the majority of votes in each contest is acknowledged as the preferred choice, and recognizing any candidate who consistently wins these head-to-head contests as the overall winner.

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Answer:

14j + 2

Step-by-step explanation:

Answer:

answer : 90

Step-by-step explanation:

Answer:

90 m

Step-by-step explanation:

30% of 300 m =

= 30% * 300 m

= 0.3 * 300 m

= 90 m

Answer:

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ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎

ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎

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Step-by-step explanation:

Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

Let's assume that Enrique needs to read for 'm' minutes to complete his assignment of reading at least 40 pages.

Since Enrique reads 2 pages every minute, the number of pages he will read in 'm' minutes will be 2m. Therefore, to satisfy the condition of reading at least 40 pages, we can write the following inequality:

2m + 16 ≥ 40

Simplifying the above inequality, we get:

2m ≥ 24

Dividing both sides by 2, we get:

m ≥ 12

Hence, Enrique must read for at least 12 more minutes to complete his assignment of reading at least 40 pages.

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Answer:

All rational numbers are whole numbers so yes, 4/7 is an irrational number

Irrational numbers are those real numbers which are not rational numbers. 4/7 is a rational number.

Rational numbers are numbers which can be written in the form of a/b where a and b are integers.

Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.

Irrational numbers are those real numbers which are not rational numbers.

For example √2, π, √13, etc.

It is important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.

Since Rational numbers are numbers which can be written in the form of a/b where a and b are integers. And 4/7 is written in p/q form and both 4 and 7 are natural numbers.

Hence, it can be concluded that 4/7 is a rational number.

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Answer:

the answer is D hope it hleps

The first step in the four-step model of problem solving is to define the problem. the four-step model of problem solving is a simple and effective way to identify and solve problems.

The steps are: Define the problem. This step involves understanding what kind of problem is being presented, and identifying people, organizational, and technology factors that may be contributing to the problem.

Generate solutions. Once the problem has been defined, the next step is to generate possible solutions. This can be done by brainstorming, or by considering different approaches to solving the problem.

Evaluate solutions. Once a number of solutions have been generated, the next step is to evaluate them. This involves considering the pros and cons of each solution, and selecting the solution that is most likely to be successful.

Implement the solution. The final step is to implement the solution. This involves putting the solution into action, and monitoring its effectiveness.

The first step in the four-step model is to define the problem. This is an important step, as it ensures that the right problem is being solved. The wrong problem can lead to wasted time and resources.

To define the problem, it is important to understand what kind of problem is being presented. Is it a technical problem, a people problem, or an organizational problem?

It is also important to identify the factors that may be contributing to the problem. These factors may include people, processes, or technology.

Once the problem has been defined, the next steps in the four-step model can be followed.

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To find the parametric equations for the path of a particle moving along a circle with 0 ≤ t ≤ π, we'll start by considering the equation of a circle with radius r centered at (h, k):
(x-h)² + (y-k)² = r²
Now, to create parametric equations, we'll express x and y in terms of a parameter, t. In this case, t represents the angle (in radians) that the particle has traveled along the circle.
We can use the trigonometric functions sine and cosine to do this. For a circle with radius r centered at (h, k), the parametric equations will be:
\(x(t) = h + r*cos(t)\)
\(y(t) = k + r*sin(t)\)
Since we're given a range for t (0 ≤ t ≤ π), this means that the particle moves along a semicircle, starting at the initial point (h+r, k) when t=0 and ending at the point (h-r, k) when t=π.
To summarize, the parametric equations for a particle moving along a circle with radius r and center (h, k) for 0 ≤ t ≤ π are:
\(x(t) = h + r*cos(t)\)
\(y(t) = k + r*sin(t)\)

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L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

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(1)The proof involves expanding the polynomial f(X) and utilizing the properties of congruences to establish the congruence relationship. (2)   the congruence relations and properties of modular arithmetic and prime numbers. (3) For k ≥ 3, if a^2 ≡ 1 mod 2^k, then a ≡ ±1 mod 2 or a ≡ 2^(k-1)+1 mod 2^k

1. In the first proposition, it is stated that if two integers, a and b, are congruent modulo n (a ≡ b mod n), then the polynomial function f(a) is congruent to f(b) modulo n (f(a) ≡ f(b) mod n). The proof involves expanding the polynomial f(X) and utilizing the properties of congruences to establish the congruence relationship.

2. The second proposition introduces the context of an odd prime number, p, and integer values for a and k. It states that (a^2 ≡ 1 mod p) is equivalent to either (a ≡ 1 mod pk) or (a ≡ -1 mod p). The proof involves analyzing the congruence relations and using the properties of modular arithmetic and prime numbers.

3. The third proposition consists of three parts. It establishes conditions for a and k. (i) If a^2 ≡ 1 mod 2, then a ≡ 1 mod 2. (ii) If a^2 ≡ 1 mod 2^2, then a ≡ ±1 mod 2^2. (iii) For k ≥ 3, if a^2 ≡ 1 mod 2^k, then a ≡ ±1 mod 2 or a ≡ 2^(k-1)+1 mod 2^k. The proofs for each part involve using the properties of congruences, modular arithmetic, and powers of 2 to establish the equivalences.

Overall, these propositions demonstrate relationships between congruences, polynomial functions, and modular arithmetic, providing insights into the properties of integers and their congruence classes.

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Answer:

y= 2x - 3

Step-by-step explanation:

To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.

Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.

• slope = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1}}\)

         = \(\frac{3 - (-1)}{3 - 1}\)

         = \(\frac{4}{2}\)

         = 2  

The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.

• intercept = -3

The slope-intercept equation of a line takes the form:

y = mx + c

where 'm' is the slope and 'c' is the y-intercept.

Substituting the values we found into the equation gives us:

y = 2x + (-3)

∴ y = 2x - 3

The inequality of the statement is -3/4 > w * -2/3

Inequality expressions are mathematical statements where the opposite sides are not equal

From the question, we have:

negative three fourths exceeds the product of a number and negative two thirds.

Express as numbers

So, we have

negative 3/4 exceeds the product of a number and negative 2/3

Use the actual mathematical operators

-3/4 exceeds a number * -2/3

Let the number be w

So, we have

-3/4 exceeds w * -2/3

Exceeds mean greater than

So, we have

-3/4 > w * -2/3

Hence, the inequality is -3/4 > w * -2/3

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Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

Using the z-distribution, as we are working with a proportion, it is found that:

A. The 98% confidence interval  is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

B. Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

For each sample, they are given by:

\(p_F = \frac{53}{150} = 0.3533, s_F = \sqrt{\frac{0.3533(0.6467)}{150}} = 0.039\)

\(p_M = \frac{89}{275} = 0.3236, s_M = \sqrt{\frac{0.3236(0.6764)}{275}} = 0.0282\)

Hence, for the distribution of differences:

\(p = p_F - p_M = 0.3533 - 0.3236 = 0.0297\)

\(s = \sqrt{s_F^2 + s_M^2} = \sqrt{0.039^2 + 0.0282^2} = 0.048\)

It is given by:

\(p \pm zs\)

98% confidence interval, hence, using a z-distribution calculator, the critical value is of z = 2.327.

Then:

\(p - zs = 0.0297 - 2.327(0.048) = -0.082\)

\(p + zs = 0.0297 + 2.327(0.048) = 0.141\)

The 98% confidence interval  is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.

Item b:

Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.

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Answer: 0.533

Step-by-step explanation:

You could use a calculator.

8÷15=0.533333333...

Answer:

0.533

Step-by-step explanation:

The full answer is 0.5333333333

But since you only need it rounded to the third decimal place, it can be rounded to 0.533

(3 is less than 5, so 3 does not need to be rounded to 4)

Answer:

30/100

Step-by-step explanation:

25%= 25/100

50%= 50/100

3/100 is in the middle of the two fractions. So one of the possible answer can be 30/100 or 30%

Answer:

\(\sf \dfrac{2}{5}\)

Step-by-step explanation:

"per cent" means "per hundred".  Therefore, to change a percent to a fraction, remove the % sign and place the number as the numerator of a fraction with 100 as the denominator.

\(\sf 25\%=\dfrac{25}{100}\)

\(\sf 50\%=\dfrac{50}{100}\)

Any percent between 25% and 50% can be written as a fraction in the same way.  

Choose a number between 25 and 50, place it as the numerator of a fraction with 100 as the denominator:

\(\sf \dfrac{40}{100}\)

Now reduce the fraction to its simplest term by dividing the numerator and denominator by the greatest common factor (GCF):

\(\sf \dfrac{40 \div 20}{100\div 20}=\dfrac{2}{5}\)

Therefore, the fraction ²/₅ is between 25% and 50% as it is equivalent to 40%.

Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations: 2A + 3i = -5i=> 2A - 3i = 5i=> A = -3/2Therefore, A is equal to -3/2.

A polynomial is a mathematical statement with coefficients and uncertainty that uses only additions, subtractions, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to an expression in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression having variables and coefficients. Only addition, subtraction, multiplication, and non-negative integer exponents are permitted in expressions. The word for these expressions is polynomials.

To find A, we need to perform polynomial long division of P(x) by \(x^2 + 1\)and get the remainder equal to -5x.

          x

   --------------

\(x^2 + 1 | x^3 + 3x^2 - 2Ax + 3\)

         \(x^3 + 0x^2 + x\)

          --------------

               \(3x^2 - 2Ax\)

           \(3x^2 + 0x - 3i\)

                ------------

                    \(2Ax + 3i\)

                \(2Ax + 0x - 2iA\)

                       -----------

                        \(3i + 2iA\)

The remainder of the division is (2A + 3i) when the divisor is \(x^2 + 1\). We know that this remainder is equal to -5x, so we can set up the equation:

2A + 3i = -5x

Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations:

2A + 3i = -5i

2A - 3i = 5i

A = -3/2

Therefore, A is equal to -3/2.

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Answer:

228 individual cookies.

Step-by-step explanation:

To convert 19 dozen cookies to individual cookies, we first have to identify that:

\(dozen=12\)

If a dozen is equal to 12, to solve, we simply must multiply the amount of dozens, which is 19, by a dozen, which is 12:

\(19*12=\)

\(228\)

Therefore, there are 228 individual cookies.

-

We can check our  work by dividing the individual number of cookies, 228, by dividing buy the amount of dozens, 19, and a dozen, 12:

\(228\) ÷ \(19=12\)

\(228\) ÷ \(12=19\)

As you can see, our quotients are the two figures we started with, and when multiplied together, give us 228 individual cookies; therefore, our solution is correct!