The solution to -3x + 5x - 7 = -11 is _____.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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9514 1404 393

Answer:

  $67.03

Step-by-step explanation:

The interest formula is ...

  I = Prt

Using the given values, we have ...

  I = $390·0.0625·2.75 = $67.03125 ≈ $67.03

The simple interest is $67.03.

_____

Additional comment

Here, the time period is given in years. The number of days per year is only relevant if the time period is given as a number of days or other sub-unit of a year.

Reduced matrix to its reduced echelon form Original Matrix:

\($$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$\)

Pivot Positions (Original): (1,1), (2,2), (3,4)

Pivot Columns (Original): 1, 2, 4

Reduced Echelon Form:

\($$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$\)

Pivot Positions (Reduced): (1,1), (2,2), (3,4)

Pivot Columns (Reduced): 1, 2, 4

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column

4. Divide row 2 by 3 to get the coefficient 2/3 in the third column

5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column

6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column

Exercise 4:

Original Matrix:

\($$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$\)

Pivot Positions (Original): (1,1), (2,2), (3,3)

Pivot Columns (Original): 1, 2, 3

Reduced Echelon Form:

\($$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$\)

Pivot Positions (Reduced): (1,1), (2,2), (3,3)

Pivot Columns (Reduced): 1, 2, 3

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract row 1 from row 3 to get the leading 1 in the third column

4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column

5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column

6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively

7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column

8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column

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Answer: the answer is $63.14.

Step-by-step explanation:

I took the test and got it correct.

Answer:

$63.14

Explanation:

I got it right on the test

Answer:

9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

Step-by-step explanation:

An integer that has 12, 20, and 28 as factors must be divisible by the least common multiple (LCM) of these numbers. The LCM of 12, 20, and 28 is 420. So we need to find the number of integers between 2023 and 5757 that are divisible by 420.

The first integer greater than or equal to 2023 that is divisible by 420 is 5 * 420 = 2100. The last integer less than or equal to 5757 that is divisible by 420 is 13 * 420 = 5460. So the integers between 2023 and 5757 that are divisible by 420 are 2100, 2520, ..., 5460. This is an arithmetic sequence with a common difference of 420.

The number of terms in this sequence can be found using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Substituting the values for this sequence, we get:

5460 = 2100 + (n - 1)420 3360 = (n - 1)420 n - 1 = 8 n = 9

So there are 9 integers between 2023 and 5757 that have 12, 20, and 28 as factors.

(a). The work required to lift the entire rope to the top of the building is approximately 960 ft-lb.

(b). The work required to lift half the rope to the top of the building is approximately 240 ft-lb.

(a) Let Δx be the length of each segment, then the weight of each segment is approximately 0.6 Δx lb/ft, and the height of each segment is approximately 80 Δx / 30 ft. The work required to lift each segment is then approximately (0.6 Δx lb/ft) * (80 Δx / 30 ft) ft = 1.6 Δx^2 lb-ft.

W ≈ ∑ (1.6 Δx^2), where the sum is taken over all segments.

As Δx → 0, the Riemann sum approaches the integral:

W = ∫ [0,30] (0.6x/30) (80 - x) dx

where x represents the length of rope lifted above the ground level.

Evaluating this integral, we get:

W = 960 ft-lb

(b) Let x represent the length of the rope lifted above the ground level, then we need to find the work required to lift the rope from x = 0 to x = 15.

W = ∫ [0,15] (0.6x/30) (80 - x) dx

Evaluating this integral, we get:

W = 240 ft-lb

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Answer:

The actual height of telescope is 42.85 inches

Step-by-step explanation:

Given that:

Height of model of telescope = 15 inches

Diameter of model of telescope = 3.5 inches

Actual diameter of telescope = 10 inches

Actual height of telescope = x

Ratio of model's diameter to height :: Ratio of actual diameter to height

3.5 : 15 :: 10 : x

Product of extreme = Product of mean

3.5*x = 10*15

3.5x=150

Dividing both sides by 3.5

\(\frac{3.5x}{3.5}=\frac{150}{3.5}\\x=42.85\)

Hence,

The actual height of telescope is 42.85 inches

In the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

We are given that Zachery has to write a total of 95,234 words.

Total words to be written = 95,234 words.

Words already written in the first month = 35,295 words.

Words already written in the second month = 19,240 words.

Words written in total = 35,295 words + 19,240 words.

= 54,535 words

Words left for writing = 95,234 words - 54,535 words

= 39,699 words

months left = 4

Average Words written in remaining month = 39,699 words / 4

= 9924.75 words.

= 10,000 words.

Therefore, in the remaining part of the semester, Zachery wrote an average of 10,000 words per month to complete his final project for the course.

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finish brackets first.

(6) + (9-7)

= 6+2

=8

Answer:

4, -1

Step-by-step explanation:

We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:

x^2 - 3x - 4 = 0

Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.

(x + or - ?) ( x + or - ?) = 0

Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:

(x - 4) (x + 1) = 0

To test that this is equal to the original equation, simply multiply it out using FOIL.

x * x = x^2

x * 1 = x

x * -4 = -4x

-4 * 1 = -4

Putting each component into an equation:

x^2 + x - 4x - 4 = 0

Simplifying:

x^2 - 3x - 4 = 0

Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)

Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.

You can also check your answers by plugging them back into the original equation.

x = 6

Step-by-step explanation:

2 - 12 × x = -70

= -12x +2 = -70

A number divisible by 1 is any number. This is because any number can be divided by 1 with no remainder.

To illustrate this, let's use the number 9 as an example. 9 divided by 1 is equal to 9. This is because any number divided by 1 is equal to itself, so 9 divided by 1 is equal to 9.To calculate this, we can use long division. 9 divided by 1 is written as 9 ÷ 1. After we write this, we can begin the long division process. To start, we divide the 9 by 1. This result is 9, and we can write this on the bottom line of the division symbol. To finish, we write the answer of 9 above the division symbol.This calculation shows that 9 divided by 1 is equal to 9. Since any number divided by 1 is equal to itself, this means that any number is divisible by 1. Therefore, any number is divisible by 1, including the number 9.

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The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

Is this a question? A recipe? Or a challenge?

Step-by-step explanation:

Answer: 7m + 5

Step-by-step explanation:

Distribute the Negative Sign:

=12m+1+−1(5m−4)

=12m+1+−1(5m)+(−1)(−4)

=12m+1+−5m+4

Combine Like Terms:

=12m+1+−5m+4

=(12m+−5m)+(1+4)

=7m+5

Complete question is;

Researchers from the Educational Testing Service (ETS) found that providing immediate feedback to students answering openended questions can dramatically improve students’ future performance on exams (Educational and Psychological Measurement, Feb. 2010). The ETS researchers used questions from the Graduate Record Examination (GRE) in the experiment. After obtaining feedback, students could revise their answers. Consider one of these questions. Initially, 50% of the students answered the question correctly. After providing immediate feedback to students who answered incorrectly, 70% answered correctly. Consider a bank of 100 open-ended questions similar to those on the GRE. a. In a random sample of 20 students, what is the probability that more than half initially answer the question correctly? b. Refer to part a . After providing immediate feedback, what is the probability that more than half of the students answer the question correctly?

Answer:

A) 41.2%

B) 95.2%

Step-by-step explanation:

This is a binomial probability distribution problem, so we will use the formula;

P(k) = (n!/(k!(n - k)!) × p^(k) × (1 - p)^(n-k)

A) Initially, 50% of the students answered the question correctly.

Thus, p = 0.5

Also,n = 20

Now, the probability that more than half initially answer the question correctly would be:

P(k > 10)

This can be expressed as;

P(k > 10) = P(11) + P(12) + P(13) + P(14) + P(15) + P(16) + P(17) + P(18) + P(19) + P(20)

P(11) = (20!/(11!(20 - 11)!) × 0.5^(11) × (1 - 0.5)^(20-11) = 0.1602

Similarly,

P(12) = (20!/(12!(20 - 12)!) × 0.5^(12) × (1 - 0.5)^(20-12) = 0.1201

P(13) = (20!/(13!(20 - 13)!) × 0.5^(13) × (1 - 0.5)^(20-13) = 0.0739

Using online binomial probability calculator we can get the remaining values which are;

P(14) = 0.037

P(15) = 0.0148

P(16) = 0.0046

P(17) = 0.0011

P(18) = 0.0002

P(19) = 0.00002

P(20) = 0

Thus;

P(k > 10) = 0.1602 + 0.1201 + 0.0739 + 0.037 + 0.0148 + 0.0046 + 0.0011 + 0.0002 + 0.00002 + 0 ≈ 0.41192 = 41.2%

B) After providing immediate feedback, we are told that 70% answered correctly.

Thus; p = 70% = 0.7

Similar to A above and using online binomial probability calculator, we have;

P(11) = 0.0654

P(12) = 0.1144

P(13) = 0.1643

P(14) = 0.1916

P(15) = 0.1789

P(16) = 0.1304

P(17) = 0.0716

P(18) = 0.0278

P(19) = 0.0068

P(20) = 0.0008

Thus;

P(k > 10) = 0.0654 + 0.1144 + 0.1643 + 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.952 = 95.2%

cos(2π/3)can be expressed as,

Since cos(π-x)=-cosx, we can write

We know,

Therefore,

The equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

To rewrite the expression \(x^2 + 5x + 6\) in the form \(x^2 + rx + sx + 6\), we need to find values for r and s such that the coefficients of the x terms match.

Given expression: \(x^2 + 5x + 6\)

To factorize this expression, we need to find two numbers that multiply to give 6 and add up to 5. The numbers that satisfy these conditions are 2 and 3.

Now, let's rewrite the expression using these values:

\(x^2 + 2x + 3x + 6\)

By grouping the terms, we can rewrite it as:

\((x^2 + 2x) + (3x + 6)\)

Factoring out the common terms in each group:

x(x + 2) + 3(x + 2)

Now, notice that (x + 2) appears as a common factor in both terms. We can further simplify the expression:

(x + 2)(x + 3)

Thus, the equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

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Answer:

Step-by-step explanation:

Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. Since it is a binomial probability distribution, the probability if success, p = 78/100 = 0.78

The probability of failure, q = 1 - p = 1 - 0.78 = 0.22

Number of samples = 6

Mean = np = 6 × 0.78 = 4.7

Variance = npq = 6 × 0.78 × 0.22 = 1.0

Standard deviation = √variance = 1.0

Most samples of 6 adults would differ from the mean by no more than 1

Answer:So you would start with 40/n because quotient means division and then it would be (40/n) - 13  (40 divided by n then minus 13) because the answer is thirteen less than the quotient of those numbers. since it wants you to evaluate for n=2 you would do 40/2 which is 20 then subtract 13 which is 7.

So write the expression as (40/n) -13 and when you evaluate just stick the 2 where the n is for (40/2) - 13

                               20 - 13

                                  = 7

Step-by-step explanation: HOPE THAT THIS WILL HELP YOU ❤️

Answer:

Here's an answer I used <3

Explanation:

You would then get to 40/n because quotient means division, then 40/n-13 because the outcome is 13 below the quotient. You can divide 40 by 20 to get 20, then 13 to get 7 because it asks you to test n=2.

Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

<95141404393>

The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Answer:

E

Step-by-step explanation:

as = = t² - 2p

as / a = (t²-2p)/a

s = (t²-2p)/a

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Answer:

In the given graph h(x)

When x=3, h(3)=1

1 is the right answer.

Answer:

Step-by-step explanation:

Dimensions of the framed photograph are:

Area of the framed photograph is:

Answer:

x = 24°

Step-by-step explanation:

Here we can see that 120° with the right angle is equal to 180° :

120° + right angle = 180°

then:

right angle = 180° - 120° = 60°

The right angle with 5x angle is equal to 180° too ;

right angle + 5x = 180°

solve for x :

5x = 180° - 60°

x = 24°

That its.

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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