8. A

a) Unique

is a field in a table which uniquely identifies each row/record in a table.

b) Primary Key

9 Which symbol is used to display all the records in the table?

a) +

b) %

c) Default​

We use a similar strategy as in your previous question. Rewrite:

sin(5x) = sin(6x - x) = sin(6x) cos(x) - cos(6x) sin(x)

sin(7x) = sin(6x + x) = sin(6x) cos(x) + cos(6x) sin(x)

→ sin(5x) - sin(7x) = -2 cos(6x) sin(x)

sin(4x) = sin(6x - 2x) = sin(6x) cos(2x) - cos(6x) sin(2x)

sin(8x) = sin(6x + 2x) = sin(6x) cos(2x) + cos(6x) sin(2x)

→   sin(8x) - sin(4x) = 2 cos(6x) sin(2x)

cos(5x) = cos(6x - x) = cos(6x) cos(x) + sin(6x) sin(x)

cos(7x) = cos(6x + x) = cos(6x) cos(x) - sin(6x) sin(x)

→   cos(7x) - cos(5x) = -2 sin(6x) sin(x)

cos(4x) = cos(6x - 2x) = cos(6x) cos(2x) + sin(6x) sin(2x)

cos(8x) = cos(6x + 2x) = cos(6x) cos(2x) - sin(6x) sin(2x)

→   cos(4x) - cos(8x) = 2 sin(6x) sin(2x)

Then

(sin(5x) - sin(7x) - sin(4x) + sin(8x)) / (cos(4x) - cos(5x) - cos(8x) + cos(7x))

= (2 cos(6x) sin(2x) - 2 cos(6x) sin(x)) / (2 sin(6x) sin(2x) - 2 sin(6x) sin(x))

= (2 cos(6x) (sin(2x) - sin(x))) / (2 sin(6x) (sin(2x) - sin(x)))

= cos(6x) / sin(6x)

= cot(6x)

QED

The question asks us to find the a graph which represents the width of the rectangle increasing by 1 unit while the area remains constant. The best graph to model this, would be answer choice C

The graph in option 3 models the length of the new rectangle.

According to the problem,

Now if width becomes (x+1) units

∴ Length will be represented as 10/(x+1)

Now from the given options we need to find the exact graph of              f(x) = 10/(x +1)

Here if x = 4 , y =2

So the point (4 , 2) is satisfied which is only happening in the graph of option 3

Option 3 represents the correct graph

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Answer:

B) 21/29

Step-by-step explanation:

Answer: b

Step-by-step explanation: trust me i have done that question before

Answer:

your answers should be 4, 4, 12, 1/12. in that specific order. the first one is wrong because if it was 12 thirds there would be 36 equal parts. Hope this helps. :)

Step-by-step explanation:

Answer:

1st dot: 195,3

2nd dot : 390,6

Using the bisection concept, it is found that the measure of angle PQR is of 130º.

A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:

Hence the value of x is given as follows:

3x + 5 = 2x + 25

x = 20º.

Hence the measure of angle PQR is given as follows:

m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.

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Answer:

Step-by-step explanation:

20

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( \(e^{(-λ)\) * \(λ^k\)) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = (\(e^{(-72.8)\)* \(72.8^(70)\)) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

\(Z = (X - mean) / \sqrt{(variance)\)

Fοr X = 70, we have:

Z = (70 - 1.4) / \(\sqrt{(1.4)\) ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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Answer:

m∠ABD = 88º

m∠CBD = 23º

Step-by-step explanation:

(-10x + 58) + (6x + 41) = 111

Combine like terms

-4x + 99 = 111

Subtract 99 from both sides

-4x = 12

Divide both sides by -4

x = -3

------------------------

m∠ABD = -10x + 58

m∠ABD = -10(-3) + 58

m∠ABD =  = 30 + 58

m∠ABD = 88º

m∠CBD = 6x + 41

m∠CBD = 6(-3) + 41

m∠CBD = -18 + 41

m∠CBD = 23º

Answer:

88, 23

Step-by-step explanation:

<ABD + <DBC = <ABC

(-10x + 58) + (6x + 41) = 111

-10x + 58 + 6x + 41 = 111

99 - 4x = 111

-4x = 111-99

-4x = 12

x = 12/-4

x = -3

m∠ABD = -10x + 58

m∠ABD = -10(-3) + 58

m∠ABD =  = 30 + 58

m∠ABD = 88º

<DBC = 6x + 41 = 6*-3 + 41 = -18 + 41 = 23

Hope it helps u

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U+W satisfies these three conditions, it is a subspace of V.

If V = R^3, U = x-axis, and W = y-axis, then U+W represents the set of all vectors formed by the addition of vectors from U and W.

To prove that U+W is a subspace of V, we must show the following:

1. U+W contains the zero vector: Since both U and W contain the zero vector (0,0,0), their sum, which is (0,0,0), is also in U+W.

2. U+W is closed under vector addition: Let x, y ∈ U+W. Then, we can write x = u1 + w1 and y = u2 + w2, where u1, u2 ∈ U and w1, w2 ∈ W. Now, x + y = (u1 + w1) + (u2 + w2) = (u1 + u2) + (w1 + w2). This is in U+W because u1 + u2 ∈ U and w1 + w2 ∈ W.

3. U+W is closed under scalar multiplication: Let x ∈ U+W and c be a scalar. Then, we can write x = u + w, where u ∈ U and w ∈ W. Now, cx = c(u + w) = cu + cw. This is in U+W because cu ∈ U and cw ∈ W.

Since U+W satisfies these three conditions, it is a subspace of V.

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Answer: x=5

Step-by-step explanation:

First you gotta box the variable so you don't get confused. The opposite of adding 2 is subtracting so you subtract 2-2 which gives you 0 and subtract 17-2 which gives 15. THEN, you will have left 3x=15 in order to get rid of the three you have to divide by the 3 on both sides. Lastly, you get your answer! Hope this helps :D

Answer:

11.5

Step-by-step explanation:

We solve using :

Pythagoras Theorem

LM² = MN² + NL²

NL² = LM² - MN²

NL = √LM² - MN²

NL = √14² - 8²

NL =  √(132)

NL = 11.489125293

NL = 11.5

Therefore, the length of NL = 11.5

Answer:

=6×3/4×3

Now, 3cut3

=6×4

=24

The ratio of the amounts is x/24.

The amount invested in company A is unknown. The amount is represented by the variable "x". The amount invested in company B is $24. We need to find out the ratio of the amount invested in company A to that of company B. We need the answer as a fraction.

Let the ratio be represented by the variable "r". A ratio compares two numbers. A ratio expresses how much of one thing there is in comparison to another. A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction denotes the number of components of a specific size.

r = x/24

Hence, the ratio of the amount invested in company A to that of company B is x/24.

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To show that every amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills, we can use a technique called "proof by induction."

First, let's check the base case: can we make 18 dollars using only 3-dollar and 10-dollar bills? Yes, we can use two 3-dollar bills and one 10-dollar bill: 3 + 3 + 10 = 16.

Now, let's assume that we can make any amount greater than n dollars using only 3-dollar and 10-dollar bills. We want to prove that we can make any amount greater than n+1 dollars as well.

To do this, we can consider two cases:

1. The amount we want to make includes at least one 10-dollar bill. In this case, we can subtract 10 dollars from the amount and use our induction hypothesis to make the remaining amount using only 3-dollar and 10-dollar bills. Then we add the 10-dollar bill back in, and we have made the original amount.

2. The amount we want to make does not include any 10-dollar bills. In this case, we can use our induction hypothesis to make the amount n-7 using only 3-dollar and 10-dollar bills (since 10 - 3 = 7). Then we add a 10-dollar bill and a 3-dollar bill to get n+3, and we can add another 3-dollar bill to get n+6. Finally, we add one more 3-dollar bill to get n+9, which is greater than n+1.

Therefore, we have shown that any amount greater than 17 dollars can be made from a combination of 3-dollar and 10-dollar bills using proof by induction.

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The double dot plot shows the quiz scores for two different class periods, represented by the two sets of data points. Each data point represents the score of a single student on the quiz.

The first population, represented by the data points on the left side of the plot, appears to have a center at around 16-18 points and a variation that is more spread out. This suggests that the students in this class period had a wider range of quiz scores, with some students scoring higher and some scoring lower.

The second population, represented by the data points on the right side of the plot, appears to have a center at around 8-10 points and a variation that is more tightly clustered. This suggests that the students in this class period had a narrower range of quiz scores, with fewer students scoring higher and fewer scoring lower.

 Based on these observations, an inference that can be drawn about the two populations is that the class period with higher quiz scores had more students who performed well on the quiz, while the class period with lower quiz scores had fewer students who performed well on the quiz. This suggests that the level of student proficiency in the subject may vary across class periods, and that it may be important to consider this variability when designing instructional strategies.

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As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.\(f(x)=x^2-2x-10\)  general form to vertex form is y=[\((x-1)^{2}\)-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

\(f(x)=x^2-2x-10\)

      = [\((x-1)^{2}\)-9]

Use the form, \(ax^{2} + bx+c\)

a=1

b=2

c=-10

Consider a vertex form of parabola,

\(a(x+d)^{2} + e\)

find the value of d, using the formula d=\(\frac{b}{2a}\)

d=\(\frac{2}{2*(-1)}\)

simplify the right side,

d= -1

find the value of e, using e= \(c-\frac{b^{2} }{4a}\)

e= \(-10\frac{2^{2} }{4*(-1)}\)

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [\((x-1)^{2}\)-9]

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The solution of each of the following systems of linear equations using augmented matrices are below:

(a) x = -2 and y = -1

(b) x = -1/2 and y = 1

(c) x = -7 and y = 2

(d) Either \(S = \frac{16}{3}\) and there are infinite solutions or\(S \neq \frac{16}{3}\) and there are no solutions

a. x - 3y = 1, 2x - 7y = 3 Putting the above linear equation in augmented matrices form we get:

\(\left[\begin{array}{ccc}1&-3&|1\\2&-7&|3\\\end{array}\right]\)

Performing row operations to solve the above matrix we get:

\(\left[\begin{array}{ccc}1&-3&|1\\0&-1&|1\\\end{array}\right]\) therefore y = -1

and \(\left[\begin{array}{ccc}1&0&|-2\\0&1&|-1\\\end{array}\right]\) therefore x = -2.

b. x + 2y = 1, 3x + 4y = 1 Putting the above linear equation in augmented matrices form we get:\(\left[\begin{array}{ccc}1&2&|1\\3&4&|1\\\end{array}\right]\)

Performing row operations to solve the above matrix we get: \(\left[\begin{array}{ccc}1&2&|1\\0&-2&|-2\\\end{array}\right]\) so y = 1

and \(\left[\begin{array}{ccc}1&0&|\frac{-1}{2} \\0&1&|1\\\end{array}\right]\) so x = \frac{-1}{2}

c. 2x + 3y = -1, 3x + 4y = 2 Putting the above equation in matrix form we get: \(\left[\begin{array}{ccc}2&3&|-1\\3&4&|2\\\end{array}\right]\)

Performing row operations to solve the above matrix we get: \left[\begin{array}{ccc}2&3&|-1\\0&1&|2\\\end{array}\right] therefore y = 2

and \(\left[\begin{array}{ccc}1&0&|-7\\0&1&|2\\\end{array}\right]\) therefore x = -7

d. 3x + 4y = 1, 4x + Sy = -3 Putting the above equation in matrix form we get: \(\left[\begin{array}{ccc}3&4&|1\\4&S&|-3\\\end{array}\right]\)

As the above matrix is not in the echelon form, therefore we perform row operations to convert the matrix into echelon form: \\([\begin{array}{ccc}3&4&|1\\4&S&|-3\\\end{array}\right}]\)

Performing row operation R_{2}→ R_{2}-\frac{4}{3}R_{1}

We get: \(\left[\begin{array}{ccc}3&4&|1\\0&S-\fract{16}{3}&|\frac{-7}{3}\\\end{array}\right]\)

Therefore, either \(S = \frac{16}{3}\) and there are infinite solutions or S ≠ 16/3 and there are no solutions.

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A) Absolute maximum = 7 at x = -1, Absolute minimum = -1 at x = 1

(B) Absolute maximum = 242 at x = 4, Absolute minimum = 2 at x = 0

(C) Absolute maximum = 10 at x = 2, Absolute minimum = 7 at x = -1

(A) First, we find the critical points by taking the derivative of f(x) and setting it equal to zero:

\(f'(x) = 4x^3 - 4 = 0\)

\(x^3 = 1\)

x = 1, -1, 0

Next, we evaluate f(x) at these critical points and the endpoints of the interval:

f(-1) = 7

f(0) = 2

f(1) = -1

f(x) is continuous and differentiable over the interval, so the absolute maximum is 7 and the absolute minimum is -1.

(B)  We repeat the same process:

\(f'(x) = 4x^3 - 4 = 0\)

\(x^3 = 1\)

x = 1, -1, 0

f(0) = 2

f(4) = 242

Since the critical points are outside the interval, we only need to compare the values at the endpoints.

Therefore, the absolute maximum is 242 at x = 4 and the absolute minimum is 2 at x = 0.

(C)  \(f'(x) = 4x^3 - 4 = 0\)

\(x^3 = 1\)

x = 1, -1, 0

f(-1) = 7

f(2) = 10

Again, the critical points are outside the interval, so we only need to compare the values at the endpoints.

Therefore, the absolute maximum is 10 at x = 2 and the absolute minimum is 7 at x = -1.

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Answer:

$28.35

Step-by-step explanation:

Divide $20.25 by 15 feet to get around $1.35 per foot.

Then, multiply $1.41 by 21 feet to get your answer...! :>

Thank you to adityakapoor for corrections...!

Answer: 21 feet rope costs $28.35

Step-by-step explanation:

First, we have to see how much 1 foot rope costs. To do this, we have to do 20.25 / 15

20.25 / 15 = 1.35

Now that we know how much 1 foot costs, now we have to see how much 21 feet costs by doing

1.35 x 21

1.35 x 21 = 28.35

So, 21 feet rope costs $28.35

Answer:   \(\text{x}^3\text{y}\)

This is the same as writing x^3y

===================================

Explanation:

When finding the GCF, we look for the smallest exponent for each variable.

The x terms of the given expressions are x^3 and x^5. The smallest exponent here is 3, so x^3 is part of the GCF.

The y terms are y^2 and y. Think of y as y^1, which shows 1 is the smallest exponent. We'll have y as part of the GCF.

-----------

We found that...

The overall GCF is x^3y which can be written as \(\text{x}^3\text{y}\)

Side note: We ignore the coefficients since they are 1 for each monomial.

Therefore, the estimated difference between the cube roots of 343 and 345.1 is approximately 0.0189.

To estimate the difference between the cube roots of 343 and 345.1 using linear approximation, we can use the fact that the derivative of the function f(x) = ∛x is given by f'(x) = 1/(3∛x^2).

Let's start by calculating the cube root of 343:

∛343 = 7

Next, we'll calculate the derivative of the cube root function at x = 343:

f'(343) = 1/(3∛343^2)

= 1/(3∛117,649)

≈ 1/110.91

≈ 0.0090

Using the linear approximation formula:

Δy ≈ f'(a) * Δx

We can substitute the values into the formula:

Δy ≈ 0.0090 * (345.1 - 343)

Calculating the difference:

Δy ≈ 0.0090 * 2.1

≈ 0.0189

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Answer: here's the answers to the problems

6) 17

8) 2.5

Answer:

6.  17

8.  2.5

Step-by-step Explanation:

4 x 3 + 6+9/3          12/3 + 2+7/5-3 - 6

12 + 15/3                  4 + 9/2 - 6

12 + 5                       4 + 4.5 - 6

= 17                          8.5 - 6

                                = 2.5

In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.

A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.

State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.

State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.

State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.

State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.

State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.

To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.

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Answer:

5.46÷7=0.78

0.78=1 pound

0.78×3=$2.34

It is $2.34

Answer:

$12.664

Step-by-step explanation:

Therefore, the standard deviation of the data set is approximately 4.14.

The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared deviations divided by the sample size minus 1.

So, first we need to calculate the variance:

variance = sum of squared deviations / (sample size - 1)

variance = 103 / (7 - 1)

variance = 17.17

Now we can find the standard deviation:

standard deviation = √(variance)

standard deviation = √(17.17)

standard deviation = 4.14 (rounded to two decimal places)

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Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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