x2y3z - y3z2 - x2yz2 + yz3

Answer:

Step-by-step explanation:

2. 1, 0.16

3. 1.5 , 0.24

4. 2, 0.32

Answer:

Decompose each number:

\begin{gathered}6) 90 = 9 \times 10\\\\7) 40 = 4 \times 10\\\\8)890 = 89 \times 10\\\\9) 300 = 3 \times 100\\\\10) 7000 = 7 \times 1000\\\\11)3700 = 37 \times 100\\\\\end{gathered}

6)90=9×10

7)40=4×10

8)890=89×10

9)300=3×100

10)7000=7×1000

11)3700=37×100

Correct the error. Write the correct decomposition:

\begin{gathered}12) 560 = 56 \times 10\\\\13) 4300 = 43 \times 100\\\\14) 6000 = 60 \times 100 \ \ or \ \ 6 \times 1000\end{gathered}

12)560=56×10

13)4300=43×100

14)6000=60×100 or 6×1000

The explanation of how to convert a general form equation to a standard form equation is given below:

Let's first look at how to convert a general form equation to a standard form equation. Given a general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Complete the square for both x and y:

a. Divide the coefficients D and E by 2, and square the results. Let's call these values Cx and Cy:

Cx = (D/2)^2

Cy = (E/2)^2

b. Add and subtract Cx and Cy on both sides of the equation:

x^2 + Dx + Cx + y^2 + Ey + Cy = -F + Cx + Cy

Rearrange the equation to form the standard form equation:

a. Group the x and y terms and rewrite as perfect squares:

(x + D/2)^2 + (y + E/2)^2 = -F + Cx + Cy

b. Now, compare this to the standard form equation:

(x - h)^2 + (y - k)^2 = r^2

c. Identify the values of h, k, and r:

h = -D/2

k = -E/2

r^2 = -F + Cx + Cy

Now let's see how to convert a standard form equation to a general form equation. Given a standard form equation:

(x - h)^2 + (y - k)^2 = r^2

Expand the squares:

(x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2

Rearrange the equation to form the general form equation:

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

Compare this to the general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Identify the values of D, E, and F:

D = -2h

E = -2k

F = h^2 + k^2 - r^2

Now you can convert equations between the general form and the standard form. If you're missing some variables in the general form equation, just treat them as zero and proceed with the same steps.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

$2,300 after 2 years

Step-by-step explanation:

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

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Answer:

The probability that they will both break down would be 8%

Step-by-step explanation:

I believe it is 8% (sorry if its wrong) because tractor 1 is 3% and tractor 2 is 5% add them together and that is where you get 8%

The numerator is 15 and the denominator is 1.

Let's solve the given problem:

We are given that the numerator of a rational number is 15 times the denominator and the numerator is also 14 more than the denominator. Let's represent the numerator as "n" and the denominator as "d."

From the given information, we can write two equations:

Equation 1: n = 15d

Equation 2: n = d + 14

To find the numerator and denominator, we need to solve these equations simultaneously.

Substituting Equation 1 into Equation 2, we get:

15d = d + 14

Simplifying the equation:

15d - d = 14

14d = 14

Dividing both sides of the equation by 14:

d = 1

Substituting the value of d back into Equation 1, we can find the numerator:

n = 15(1)

n = 15.

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True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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Answer:

\(x^{2} -8x+12\) (that means u got it right)

Step-by-step explanation:

basically use the distributive property to multiply everything by each other.

x*x=\(x^{2}\)

x*(-2) + x*(-6)= -8x

-6*-2=12

Put it all together and u get the original.

Sorry if this is confusing.

Answer:

Both the mean and median decrease.

Step-by-step explanation:

Median (without 1,000,000):

25, 25, 25, 35, 35, 45, 45, 55, 55

= 35

Median (with 1,000,000):

25, 25, 25, 35, 35, 45, 45, 55, 55, 1,000,000

= average of 35 and 45

= 40

As you can see, without the outlier, the value of the median decreases.

Mean (without 1,000,000):

= (25 + 25 + 25 + 35 + 35 + 45 + 45 + 55 + 55) / 9

= 38.3

Mean (with 1,000,000):

= (25 + 25 + 25 + 35 + 35 + 45 + 45 + 55 + 55 + 1,000,000) / 10

= 100,0034.5

As you can see, without the outlier, the value of the mean dramatically decreases.

Answer:

x = 5 and y = 8.7

See attached image for working

Step-by-step explanation:

Since it's a right angle triangle you can use sin and cos.

Answer:

1.7ft

Step-by-step explanation:

Given data

Volume of tank=  300π 〖ft〗^3

Height of tank= 10ft

The expression for the volume of a cylinder is given as

Volume= πr^2h

Substitute

300π = π *r^2*10

300= r^2*100

3= r^2

r= √3

r= 1.7 ft

Hence the radius of the cylinder is 1.7ft

The equation 2log25 - log125 - log5 = 0 is **true**. This can be justified by referring to the properties of logarithms.

In this equation, we have three logarithmic terms being subtracted from each other. To simplify the expression, we can use the following properties of logarithms:

1. Product Rule: log(ab) = log(a) + log(b)

2. Quotient Rule: log(a/b) = log(a) - log(b)

3. Power Rule: log(a^b) = b * log(a)

Let's apply these properties to the given equation step by step:

2log25 - log125 - log5

Using the Power Rule, we can rewrite log25 as log(5^2):

= log(5^2) - log125 - log5

Applying the Quotient Rule, we can divide log125 by log5:

= log(5^2) - log(125/5)

Simplifying further, we can evaluate 5^2 as 25 and 125/5 as 25:

= log(25) - log(25)

Now, applying the Product Rule to the log(25) terms, we can combine them:

= log(25/25)

Since 25/25 equals 1, we have:

= log(1)

Finally, the logarithm of 1 is always 0:

= 0

Therefore, we have shown that 2log25 - log125 - log5 simplifies to 0, which means the equation is true.

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Answer:

Step-by-step explanation:

Its B I just took the test

The main criticism of differential opportunity theory is that it overlooks the fact that most delinquents become law-abiding adults (option c).

Differential opportunity theory, developed by Richard Cloward and Lloyd Ohlin, focuses on how individuals in disadvantaged communities may turn to criminal activities as a result of limited legitimate opportunities for success.

However, critics argue that the theory fails to account for the fact that many individuals who engage in delinquency during their youth go on to become law-abiding adults.

This criticism highlights the idea that delinquent behavior is not necessarily a lifelong pattern and that individuals can change their behavior and adopt prosocial lifestyles as they mature.

While differential opportunity theory provides insights into the relationship between limited opportunities and delinquency, it does not fully address the complexities of individual development and the potential for desistance from criminal behavior.

Critics suggest that factors such as personal growth, social support, rehabilitation programs, and the influence of life events play a significant role in individuals transitioning from delinquency to law-abiding adulthood.

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a) There are 9! (9 factorial) orders of shows John can watch if he watches one episode of each of the 9 different television shows.

b) There are 126 combinations for John to download 5 random episodes from the 9 shows.

c) There are 1,320 different ways to select a captain, equipment manager, and sound manager from a group of 12 students without any person holding two positions.

a) If John watches one episode of each of the 9 different television shows, the number of orders of shows he can watch is 9!.

b) If John wants to download 5 random episodes of these 9 shows, the number of combinations is given by the binomial coefficient:

C(9, 5) = 9! / (5!(9-5)!) = 126

c) To select a captain, equipment manager, and sound manager from a group of 12 students without any person holding two positions, the number of different ways is given by the product of the choices for each position:

12 * 11 * 10 = 1,320

Therefore, there are 1,320 different ways to select a captain, equipment manager, and sound manager in this scenario.

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The test statistic is approximately -2.03.

To calculate the test statistic, we can use the one-sample t-test formula:

t = (x - μ) / (s / √n)

Where:

x is the sample mean,

μ is the hypothesized population mean,

s is the sample standard deviation,

n is the sample size.

In this case, we have:

x = 44.3 (sample mean)

μ = 44.6 (hypothesized population mean)

s = 1.01 (sample standard deviation)

n = 46 (sample size)

Plugging in the values, we can calculate the test statistic:

t = (44.3 - 44.6) / (1.01 / √46)

= -0.3 / (1.01 / √46)

= -0.3 / (1.01 / 6.782)

≈ -0.3 / 0.148

Rounding to 2 decimal places, the test statistic is approximately -2.03.

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Complete question =

Testing:

H0:μ=44.6

H1:μ<44.6

Your sample consists of 46 subjects, with a mean of 44.3 and standard deviation of 1.01.

Calculate the test statistic, rounded to 2 decimal places.

A propositional function can either be true or false. A proposition function cannot be used for induction. It is not possible to write a proof by induction of a statement of the form "for all n in d, p(n)" where p(n) is a propositional function with domain d.

Thus, it is not possible to prove any statement about propositional functions by induction. A domain is a set of values from which a propositional function takes its input values. It is an essential part of the proposition. Therefore, the answer to the question is that it is not possible to write a proof by induction of a statement of the form "for all n in d, p(n)" where p(n) is a propositional function with domain d.

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The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Answer:

i am sure it is number 3 238,600

the answer is option 2....

Answer:

Option 2

Step-by-step explanation:

when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1

Answer: B. Niche

Explanation:

Definition of niche: a niche is the match of a species to a specific environmental condition. It describes how an organism or population responds to the distribution of resources and competitors and how it in turn alters those same factors.

Answer: Niche

Niche is basically like a type of place of something or someone

After using the formula of a trapezoid, we know that the area is 25 units².

The size of a patch on a surface is determined by its area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The shape can also be placed on a grid, and the number of squares can be counted: The area of the rectangle is 15.

For instance, if each square is 1 meter in size, the area is 15 m² (15 square meters).

So, we  have the vertices as follows:

A(−3, 2), B(2, 2), C(2, −4), and D(−3, −2)

See, the plotted vertices on the graph.

The figure is a trapezoid.

The area of a trapezoid is as follows:

A = 1/2(AD+BC)AB

Now, find the distance:

AD = 4

BC = 6

AB = 5

Substitute as follows:

A = 1/2(4+6)5 = 25 units²

Therefore, after using the formula of a trapezoid, we know that the area is 25 units².

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To determine if the given points are part of the (200) plane, we need to check if their coordinates satisfy the equation of the plane.

The equation of a plane in three-dimensional space is typically written in the form Ax + By + Cz + D = 0, where A, B, C, and D are constants. For the (200) plane, the equation would be 2x + 0y + 0z + 0 = 0, which simplifies to 2x = 0. Let's check the given points: a) (1/2, 0, 0): When we substitute x = 1/2 into the equation 2x = 0, we get 2(1/2) = 0, which is true. Therefore, point a) lies on the (200) plane. b) (-1/3, 0, 0): Substituting x = -1/3 into the equation 2x = 0 gives us 2(-1/3) = 0, which is also true. So, point b) is part of the (200) plane. c) (0, 1, 0):When we substitute x = 0 into the equation 2x = 0, we get 2(0) = 0, which is true. Thus, point c) lies on the (200) plane. All three given points (a), b), and c)) are part of the (200) plane.

In conclusion, all three given points (a), b), and c)) are part of the (200) plane.

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Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²