let a and b be n × n matrices such that ab = in . prove that the rank of a is n

This expression has only 3 terms, which confirms that our initial expression with 6 terms does indeed simplify to an algebraic expression with 3 terms.

Sure, here is an expression with 6 terms which when simplified is an algebraic expression with 3 terms:

2x + 3y + 4x + 2y + 5x + y

To simplify this expression, we can combine like terms.

First, let's group all the x terms:

2x + 4x + 5x = 11x

Next, let's group all the y terms:

3y + 2y + y = 6y

So our simplified expression is:

11x + 6y

As we can see, this expression has only 3 terms, which confirms that our initial expression with 6 terms does indeed simplify to an algebraic expression with 3 terms.

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Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Answer:

- infinite 3 for the first one. x<3

x>2 ....2 infinite

Answer:

\({x}^{2} - 10x + 25\)

Step-by-step explanation:

For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.

(x - 5) (x - 5)

First, multiply the two Xs together.

X * X =

\( {x}^{2} \)

Now, the outer numbers and values.

X * -5 =

\( - 5x\)

Then, it's the inner numbers and values.

-5 * x =

\( - 5x\)

Finally, multiply the last numbers.

-5 * -5 =

\( 25\)

Now that we have multiplied all of the values, we can put the answers from FOIL together.

\( {x}^{2} - 5x - 5x + 25\)

Now, add any like terms.

\( - 5x - 5x = - 10x\)

The answer is

\( {x}^{2} - 10x + 25\)

The expected correlation between the supply of a commodity (x) and the price of a commodity (y) depends on the nature of the commodity and market dynamics. However, in general, we would expect a **negative correlation** between the supply of a commodity and its price. Correct option is C.

The law of supply states that as the supply of a commodity increases, assuming demand remains constant, the price tends to decrease. This is because an increase in supply leads to a higher quantity of the commodity available in the market, potentially causing an excess supply or surplus. In such situations, suppliers may lower prices to attract buyers and reduce their inventory.

Conversely, when the supply of a commodity decreases, assuming demand remains constant, the price tends to increase. A decrease in supply results in a lower quantity available in the market, potentially leading to a scarcity or shortage. In such scenarios, suppliers may increase prices to maximize their profits due to the limited availability of the commodity.

It's important to note that real-world markets can be influenced by various factors, including changes in demand, production costs, technological advancements, government policies, and market competition, which can complicate the relationship between supply and price. Nonetheless, the general expectation is that a decrease in supply tends to lead to an increase in price, and an increase in supply tends to lead to a decrease in price, indicating a negative correlation.

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Answer: To find the percentage of the down payment to the purchase price, just multiply the down payment by 100 and divide the result by the   purchase

i.e 15,000 x 100/ 150,000= 10%

Also for the second part, multiply the down payment by 100 and divide by the purchase price

i.e 67,500 x 100 / 150,000= 45%

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

for profit percentage

p% =(sp-cp/cp)×100%

=(25-20/20)×100%

=25%

The profit percentage is 25%

Answer:

26

Step-by-step explanation:

first, solve the problem in the parentheses (4x6) which is 24.

next, add 12+24 and you get 36.

now, subtract 10 from 36, and you get 26.

The null hypothesis (H0) states that the average age is equal to or greater than 30.8 years, while the alternative hypothesis (Ha) states that the average age is less than 30.8 years.

In hypothesis testing, we set up the null hypothesis (H0) and the alternative hypothesis (Ha) to investigate a claim or conjecture. In this case, the conjecture is that the average age of a senior surgical resident in the United States is less than 30.8 years old.

The null hypothesis (H0) assumes that the average age is equal to or greater than 30.8 years, and any difference observed in the sample is due to random chance or sampling variability. Therefore, the null hypothesis can be stated as:

H0: The average age of senior surgical residents in the United States is greater than or equal to 30.8 years.

The alternative hypothesis (Ha) represents the claim or the opposite of the null hypothesis. In this case, the alternative hypothesis states that the average age is less than 30.8 years, indicating that there is a significant difference or evidence against the null hypothesis. Therefore, the alternative hypothesis can be stated as:

Ha: The average age of senior surgical residents in the United States is less than 30.8 years.

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The given equation is:

34m = 11

To solve the equation, divide both sides by 34

The equation becomes:

Answer:

All the points change, there are no invariant points

Step-by-step explanation:

The given parameters are

To translate the square OABC by the vector  \(\dbinom{1}{3}\), we have;

The coordinates of the point O is (0, 0)

The coordinates of the point A is (3, 0)

The coordinates of the point B is (3, 3)

The coordinates of the point C is (0. 3)

The translation is by moving 1 step right and three steps up to give;

O' is (0+1, 0+3) which is (1, 3)

A' is (3+1, 0+3) which is (4, 3)

B' is (3+1, 3+3) which gives (4, 6)

C' is (0+1, 3+3) which gives (1, 6)

As all the points change, there are no invariant points and the number of invariant points is zero.

y=1/3x-3 equation passes through the point (-3, -4) and is perpendicular to the line 9x+3y=6.

The given equation of line is 9x+3y=6.

Let us rearrange the equation in the form of slope intercept form.

3y=6-9x

Divide both sides by 3:

y=2-3x

y=-3x+2

We know that the slopes of perpendicular lines product is -1.

So the slope of perpendicular line is 1/3.

Now let us find the equation when it passes through (-3, -4).

Let us find the y intercept.

-4=1/3(-3)+b

-4+1=b

-3=b

Hence, equation of perpendicular line is y=1/3x-3.

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Answer:

16p-1

Step-by-step explanation:

-3+17p+2-p

-1+16p

Answer:

16p - 1

Step-by-step explanation:

= -3 + 17p + 2 - p

= 17p - p - 3 + 2

= 16p - 1

Answer:

25/100

Decimal fractions always have a denominator based on a power of 10. ... Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, etc.

Step-by-step explanation:

i g00gled it

The value of x in function cos(3pi/2+2x/3)=1/2 is  x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\)

We are given;

6sinx=5, 6cosx=7, sin2x=0, sin(x+pi/3)+1=0, cos(2x/3-pi/4)=\(\sqrt{2} /2\), cos2x-1=0, 2sin3x=-1, cos(3pi/2+2x/3)=1/2

Now,

1. 6sinx=5

sinx=5/6

x=0.98511078

2. sin2x=0

x=n*pi/2

3. sin(x+pi/3)+1=0

x-intercept= (pi/6+2n*pi)

y-intercept= (0, \(\sqrt{3}\)/2 -1)

4. cos(2x/3-pi/4)=\(\sqrt{2}/2\)

x= (pi/4+n*pi, pi+n*pi)

6. cos2x-1=0

x=n*pi

7. 2sin3x=-1

x= 7pi/18 + 2pi*n/3, 11pi/18+2pi*n/3

8. cos(3pi/2+2x/3)=1/2

x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n

For any value of integer n

Therefore, the answer of trigonometric function will be x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

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Answer:

The correct options are;

A. \(-\dfrac{8}{3} \ miles\)

D.  \(2\dfrac{2}{3} \ mile\) below sea level

Step-by-step explanation:

The given parameters are;

The distance Sasha travels down before a stop = -2/3 mile

The level at which Sasha starts to hike into the canyon = Sea level

Therefore, we have;

Her elevation at the fourth rest station = 4 × -2/3 mile = -8/3 miles

Therefore, we have;

-8/3 mile = \(2\dfrac{2}{3} \ mile\) below sea level

Therefore, the correct options are;

-8/3 mile and  \(2\dfrac{2}{3} \ mile\) below sea level.

Answer:

x+2y = 5

2x+y=4

->

x+3y = 5

6x-y = 11

->

2x+y=10

x-3y=-2

Step-by-step explanation:

solutions of x and y for each system of equation can be solved by graphing

graph the two equations, and the intercepts of the two equations would be the x and y-values, aka the answers

if there are no intercepts, the equations have no solution

Answer:

n the text mining process, the text is first preprocessed by deriving a smaller set of features from the larger set of words contained in a collection of documents.

Step-by-step explanation:

In the text mining process, one of the crucial ways is preprocessing the text data. This involves transforming the raw text into a more manageable and meaningful representation. One common technique in text preprocessing is to derive a smaller set of features from the larger set of words present in a collection of documents.

These features, often referred to as "tokens" or "terms," represent the distinct units of meaning in the text. The process typically includes steps such as tokenization, where the text is divided into individual words or n-grams, and then removing stop words, which are commonly occurring words that do not carry significant meaning.

Additionally, techniques like stemming or lemmatization may be applied to reduce words to their base or root forms. By deriving a smaller set of features, the preprocessing helps to simplify the text data, eliminate noise, and facilitate subsequent analysis tasks such as document clustering, topic modeling, sentiment analysis, or text classification.

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The possible degree sequences for a simple graph are: b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) c. (5, 4, 4, 4, 3, 2)

To determine which of the given degree sequences are possible for a simple graph, we can apply the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

Let's analyze each degree sequence:

a. (5, 3, 3, 3, 3, 2)

To check if this degree sequence is possible, we sum up all the degrees: 5 + 3 + 3 + 3 + 3 + 2 = 19. According to the Handshaking Lemma, the sum of the degrees should be twice the number of edges. Therefore, the number of edges should be 19/2 = 9.5, which is not an integer. Since the number of edges must be a whole number, this degree sequence is not possible for a simple graph.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

Summing up the degrees: 6 + 5 + 5 + 5 + 4 + 4 + 3 + 2 + 2 + 2 = 38. According to the Handshaking Lemma, the number of edges should be 38/2 = 19. The number of edges being an integer, this degree sequence is possible for a simple graph.

c. (5, 4, 4, 4, 3, 2)

Summing up the degrees: 5 + 4 + 4 + 4 + 3 + 2 = 22. The number of edges should be 22/2 = 11. Since the number of edges is an integer, this degree sequence is possible for a simple graph.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1)

Summing up the degrees: 9 + 7 + 3 + 3 + 3 + 2 + 2 + 1 + 1 = 31. The number of edges should be 31/2 = 15.5, which is not an integer. Therefore, this degree sequence is not possible for a simple graph.

Based on the analysis above:

a. (5, 3, 3, 3, 3, 2) is not possible.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) is possible.

c. (5, 4, 4, 4, 3, 2) is possible.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1) is not possible.

Therefore, the possible degree sequences for a simple graph are:

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

c. (5, 4, 4, 4, 3, 2)

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Answer:

sqrt(97)

Step-by-step explanation:

Since the x for both of the points are the same, we can reduce the problem to "find the distance between (-4, 7) and (5, 3)".

To do that, we can use the Pythagorean theorem, where (change in x)^2+(change in y)^2 = (distance)^2:

(5-(-4))^2+(3-7)^2=d^2

(9)^2+(-4)^2=d^2

81+16=d^2

97=d^2

d=sqrt(97).

Answer:

13

Step-by-step explanation:

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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The given inequality is:

x > 5

This means that the values of x are numbers more than 5.

The probability of both Nic and Tim winning the raffle at the same time is 1/100.

Probability is a mathematical measurement of a likelihood of an event to happen. Given that both Nic and Tim each purchase one raffle ticket out of 10 tickets and that there will be two winners selected, the odds of either Nic or Tim winning the raffle out of 10 ticket is 1/10.

Since the odds of either Nic or Tim winning the raffle ticket is 1 out of 10 or 1/10, we can then calculate the mathematical probability of two events occurring at the same time with a multiplication rule formula as follows:

1/10×1/10=1/100

Hence, the odds of both Nic and Tim winning at the same time is 1 out of 100 or 1/100.

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Answer:

4000

Step-by-step explanation:

The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the relationship between these different interest rates.

Subtracting the real rate of interest from the money rate of interest gives us the inflation component, which is then added to the real rate of interest to arrive at the nominal rate of interest.

The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the nominal rate of interest. This is because the nominal rate of interest reflects both the money rate of interest and the inflation rate.

The real rate of interest, on the other hand, reflects the true return on investment after accounting for inflation.

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