15.Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explainwhy the system has a unique solution.What must be true of a linear system for it to have a unique solution? Select all that apply.A.The system has no free variables.B.The system is inconsistent.C.The system has one more equation than free variable.D.The system is consistent.E.The system has at least one free variable.F.The system has exactly one free variable.
Use the given assumption that the coefficient matrix of the linear system of four equations in four variables has a pivot ineach column to determine the dimensions of the coefficient matrix.The coefficient matrix hasrows andcolumns.fourfourLet the coefficient matrix be in reduced echelon form with a pivot in each column, since each matrix is equivalent to oneand only one reduced echelon matrix. Construct a matrix with the dimensions determined in the previous step that is inreduced echelon form and has a pivot in each column.1000010000100001Now find an augmented matrix in reduced echelon form that represents a linear system of four equations in four variablesfor which the corresponding coefficient matrix has a pivot in each column. Choose the correct answer below.100a010b100001001000a0100b
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001c000d001000010010c0001d00c01000d1Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by theaugmented matrix consistent?
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Write the system of equations corresponding to the augmented matrix found above to determine the number of freevariables.x1=ax2=bx3=cx4=dFree variables are variables that can take on any value. How many free variables are in the system?

Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

A polynomial is factored when it is expressed as the product with two or more factors; this is somewhat the opposite of multiplying.

One of a single-variable polynomial's linear expressions is referred to as a factor. Many variables can affect a polynomial,

Given word problem.

2x cubed minus 5x squared minus 5x plus 11

This can be written as:

2x³ - 5x² - 5x + 11

So,

dividend : 2x³ - 5x² - 5x + 11

divisor =  x-3 , x = 3

Put x = 3 in dividend , if it comes zero, it is the factor.

= 2x³ - 5x² - 5x + 11

= 2(3)³ - 5(3)² - 5(3) + 11

= 5 (remainder)

Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

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The equation of a parabola in standard form is:

where a is the standard coefficient. We know that this has to be 1 and that the parabola opens down. This means that our parabola has the form:

To shift the parabola 3 units to the left we need to add a 3 to the variable, this means that we have:

Finally to shift the parabola down to units we need to substract 2 to the whole parabola. therefore we have the parabola:

The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, we set up the composite result function f(g(x)).

f( x ) = x² + 9

f( g(x) ) = f( x² - 9 ) = ( x² - 9  )² + 9

f( g(x) ) = ( x² - 9  )² + 9

Expand the parenthesis

f( g(x) ) = ( x² - 9 )( x² - 9 )  + 9

f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9

f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9

Collect and add like terms

f( g(x) ) = x⁴ - 18x² + 81 + 9

f( g(x) ) = x⁴ - 18x² + 90

Therefore,  ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.

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Answer:

7.53 x 10²

Step-by-step explanation:

10² two time the 10 is 100

Answer:

Uuuuuuuh. What is n? There's no n in your question.

Step-by-step explanation:

Also that scientific notation equation there is false. It would be 7.53x10 to the 10th power.

The dimensions for the width and height of the fish tank will be 4 feet and 2 feet .

Dimension is the measurable extent of a particular kind, such as length, breadth, depth, or height.

According to the given problem,

let , b = is the width of the fish tank

h = is the height of the fish tank given that , hold at least 35 cubic feet of water .

so ,

4×b×h ≥ 35

⇒ h ≥ 35/4b

now , surface area of the fish tank

⇒ 4b + 2× 4h + 2× bh

now substitute the value of h

here

⇒ ≥ 4b +70/b + 35/2

⇒ ≥ 40(70)^1/2 + 35/2 (if and only if b= (70)^1/2 / 2 , the equal sign holds )

therefore ,

= (70)^1/2 / 2 b ≈ 4.18 so b is 4 . when b = 4 ,

h = 35 / 4 × 4 = 2.1875 round off h = 2

so , the minimum surface area of fish tank is

⇒ 4×4+ 2× 4×2 + 2× 4×2⇒ 48

hence , the height and the width of the fish tank is 2 and 4 .

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

There are 4 common factors of 30 and 72, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 72 is 6.

Step-by-step explanation:

84/18=14/3

60/32=15/8

Answer:

y = 6x + 10

Step-by-step explanation:

This is because the slope is 6 and the y intercept is 10, therefore the answer is y = 6x + 10

Length of the golf club where Bruce plays = 7,040 yards

Solution:

1. Let's convert 7,040 yards to miles:

1 yard = 0.000568182 mile

Now, we can use Direct Rule of Three, as follows:

Yards Miles

1 0.000568182

7,040 x

2. Solve for x:

1 * x = 0.000568182 * 7,040

x = 4 miles

Jane travels 8 miles much farther than her trainer. The solution is obtained using arithmetic operations.

What are arithmetic operations?

By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions add, subtract, divide, and multiply additionally allow for the specification of arithmetic operations.

3. Using pythagoras theorem, we get the equation as D² = 12² + 16².

⇒D² = 144 + 256

⇒D² = 400

⇒D = √400

⇒D = 20

4. Jane has traveled 28 miles in total whereas her trainer has traveled 20 miles.

So, the difference is 28-20= 8 miles

Hence, Jane travels 8 miles much farther than her trainer.

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Answer:

12+9q−9p

Step-by-step explanation:

−7p+15−2q+11q−2p−3

Combine −2q and 11q to get 9q.

−7p+15+9q−2p−3

Combine −7p and −2p to get −9p.

−9p+15+9q−3

Subtract 3 from 15 to get 12.

−9p+12+9q

Answer: −9p+9q+12

Step-by-step explanation:

the contstants of the p and q variable will add up to 9 and the number will add to 12

Answer:

it is C

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

5x=20

5x/5=20/5

x=4

x>4

Inequality Notation:

\(x \geqslant 4\)

____o___o___

\(5x - 20 \geqslant 0 \\ 5x - 20 + 20 \geqslant 0 + 20 \\ 5x \geqslant 20 \\ \\ \frac{5x}{5} \geqslant \frac{20}{5} \\ \\ x \geqslant 4\)

I hope I helped you^_^

Answer:

They ate a total of 7.5 apples.

Step-by-step explanation:

The total number of apples that these 4 students ate is:

2 + 2.5 + 1.25 + 1.75 = 7.5

Therefore, they ate a total of 7.5 apples.

Answer: 7.5

Step-by-step explanation: 2 + 2.5 = 4.5

4.5 + 1.25 = 5.75

5.75 + 1.75 = 7.5

Minimax Regret Approach takes place when the decision chosen is the one corresponding to the minimum of the maximum regrets.

In the Minimax Regret Approach, decisions are evaluated based on their maximum possible regret. It aims to minimize the potential regret associated with a decision by selecting the option that corresponds to the minimum of the maximum regrets.

In decision-making scenarios, individuals often face uncertainty about the outcomes and have to choose from various alternatives. The Minimax Regret Approach provides a systematic method for evaluating these alternatives by considering the regrets associated with each decision.

To apply this approach, the decision-maker identifies the potential outcomes for each decision and determines the corresponding payoffs or losses. The regrets are then calculated by subtracting each payoff from the maximum payoff across all decisions for a particular outcome. The decision with the smallest maximum regret is chosen as it minimizes the potential loss or regret.

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The probability of part a is -0.429.

(a) To find the probability that a randomly selected athlete uses a stairclimber for less than 17 minutes, we need to standardize the value using the formula:

z = (x - μ) / σ

where x is the value we're interested in, μ is the mean, and σ is the standard deviation. So, in this case:

\(z = (17 - 20) / 7 = -0.429\)

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than\(-0.429\) is \(0.1664\). Therefore, the probability that a randomly selected athlete uses a stairclimber for less than \(17\)minutes is \(0.1664\).

(b) To find the probability that a randomly selected athlete uses a stairclimber between 20 and 29 minutes, we need to standardize the values 20 and 29 using the same formula as before:

\(z_{1} = (20 - 20) / 7 = 0\)

\(z_{2} = (29 - 20) / 7 = 1.286\)

Using a standard normal distribution table or calculator, we can find the probabilities of a z-score less than \(0\) and less than \(1.286\), and then subtract the former from the latter to get the probability between the two values:

\(P(20 < x < 29) = P(z < 1.286) - P(z < 0) = 0.9003 - 0.5000 = 0.4003\)

Therefore, the probability that a randomly selected athlete uses a stairclimber between \(20\) and \(29\) minutes is \(0.4003\).

(c) To find the probability that a randomly selected athlete uses a stairclimber for more than \(30\) minutes, we can use the same formula and standardize the value:

\(z = (30 - 20) / 7 = 1.429\)

Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than \(1.429\):

\(P(x > 30) = P(z > 1.429) = 1 - P(z < 1.429) = 1 - 0.9236 = 0.0764\)

Therefore, the probability that a randomly selected athlete uses a stairclimber for more than \(30\) minutes is \(0.0764\).

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The related-samples sign test, which is also known as the Wilcoxon signed-rank test, is a nonparametric test that evaluates whether two related samples come from the same distribution. , X is equal to the number of negative ranks, which is 3

A researcher computes a related-samples sign test in which the number of positive ranks is 9, and the number of negative ranks is 3. The test statistic (X) is equal to 3.There are three steps involved in calculating the related-samples sign test:Compute the difference between each pair of related observations;Assign ranks to each pair of differences;Sum the positive ranks and negative ranks separately to obtain the test statistic (X).

Therefore, the total number of pairs of observations is 12. Also, as the value of X is equal to the number of negative ranks, we can conclude that there were only 3 negative ranks among the 12 pairs of observations.The test statistic (X) of the related-samples sign test is computed by counting the number of negative differences among the pairs of related observations.

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Answer:

2.9 meters.

Step-by-step explanation:

First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier).  Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.

Answer:

i think its 21.83 i may be wrong but im pretty sure its 21.83

Step-by-step explanation:

When he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.

The length of the side of the base is 90 ft. Its speed is 24 ft/s.

Let x = distance he has run at time t and

D = distance from second base at time t, then speed dx/dt = 24 and we calculate dD/dt where x = 45.

From Pythagorean Theorem,

\(D^{2} =(90-x)^{2} +90^{2}\) ,

differentiating with respect to t

2D*dD/dt = 2 (90 − x) (−1) dx/dt + 0

D*dD/dt = − (90 − x)dx/dt

Now, when x = 45,

D =\(\sqrt{(90-45)^{2}+90^{2} }\)

\(=\sqrt{45^{2}+90^{2} }\)

by substituting D we get,

\(\sqrt{45^{2}+90^{2} }\)dD/dt = − (90 − 45) · 24

dD/dt = −45 · 24/\(\sqrt{45^{2}+90^{2} }\)

= −10.73 ft/s

Hence, when he is halfway to the first base, the distance between the second base and the distance is decreasing at the rate of about 10.73 ft/s.

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Answer:

$2

Step-by-step explanation:

30-16=14 so she spent $14 so far

each song cost the same much to download so 14/7=2

she downloaded 7 songs costing $2 each and spent $14

Answer:

One song equals $2

Step-by-step explanation:

$30-$16= $14

$14÷7 songs= $2 per song

Answer:

Step-by-step explanation:

∠MKQ = 145°

∠PKQ = 20°

∠MKP = ∠MKQ - ∠PKQ = 145° - 20°

∠MKP = 125°

If angle measurement is more than 90°, then it is obtuse angle

So, 125° is obtuse angle

While each number between 1 and 10 has an equal probability of being picked as a random number, the frequency of each number being selected can vary slightly due to the nature of randomness.

First, it's important to understand what a random number is. A random number is a value that is chosen from a set of possible values with equal probability. For example, if you were to pick a random number between 1 and 10, each number would have an equal chance of being selected.

Now, let's consider the probability of each number being picked. Since there are ten possible numbers between 1 and 10, the probability of each number being selected is 1/10, or 0.1. This means that if you were to pick a random number between 1 and 10 many times, each number would be picked approximately the same number of times.

However, when we talk about the most picked random number, we are looking at the frequency of each number being selected. The frequency of a number being picked is simply the number of times that number appears in a set of random numbers. For example, if we were to pick ten random numbers between 1 and 10, we might end up with the following sequence: 3, 5, 2, 7, 9, 8, 1, 6, 4, 10. In this sequence, the most picked random number would be 1, since it appears once.

Therefore, there is no one most picked random number between 1 and 10, but rather a distribution of numbers that appear with approximately equal frequency.

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A number that can be distributed across two terms inside parentheses is 3/5.

The terms that can be combined are 18 and -1.

In Mathematics, the distributive property of multiplication states that when the sum of two or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Next, we would multiply both sides of the equation by 3/5 in order to open the bracket as follows;

3x/5 - 6 = 18 - 4x - 1

By combining like terms and simplifying the equation, we have:

3x/5 + 4x = (18 - 1) + 6

3x/5 + 4x = 17 + 6

23x/5 = 23

x = 5

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Complete Question:

Solve this equation: 3/5(x - 10) = 18 - 4x - 1

Answer:

\(\sqrt{7} 2 =x^{8}\)

Step-by-step explanation:

Answer:

the last one since the people in the music and entertainment store are there to only buy records

Answer:

I believe your answer should be \(\sqrt{\frac{10}{3} }\) I hope this helps you! :)

Answer: $13.5

Step-by-step explanation:

1. 15 x 10 =150

2. 150/100=1.5

3. 15.00 - 1.50= 13.5

Answer:

The domain of y = f(x) is [0,8]

Step-by-step explanation:

Since the straight line with negative slope begins on the y-axis at (0. 9) and exits the plane at (8, 1), we get is domain from the minimum and maximum values of x for which the function is valid.

So, the minimum value of x at which the function is valid is x = 0 and the function is y = f(0) = 9.The maximum value of x at which the function is valid is x = 8 and the function is y = f(8) = 1.

So, the domain of the function y = f(x) is [0,8]

Answer:

y = f(x) is [0,8]

Step-by-step explanation:

True.

A 95% confidence interval for the population mean means that if we draw multiple samples from the same population and construct confidence intervals for the mean using each sample, then 95% of those intervals will contain the true population mean. This is because the confidence interval is computed based on the sample mean and the sample's standard deviation, which are random variables that are expected to vary from sample to sample. Therefore, we cannot be 100% certain that the true population mean is within any particular confidence interval, but we can be confident (95% confident, in this case) that most of the intervals we construct will contain the true mean. A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean. This means that you can be 95% confident that the true population mean lies within the calculated interval.

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Answer:

Choice A

Step-by-step explanation:

\( \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}\)

Applying Distributive property;

Choice A is accurate.