SOMEONE HELPPP! Plss

Answer:

x = -4

Step-by-step explanation:

Plug in -15 into the equation:

f(x) = 2x - 7

-15 = 2x - 7

Solve for x:

-15 = 2x - 7

-8 = 2x

-4 = x

The value of m in the proportion is given as follows m = 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The proportion is defined as follows:

3/4 = (1/4)m.

As the values have a proportional relationship, the value of m can be obtained applying cross multiplication, as follows:

3/4 = (1/4)m

cross multiplication;

3/4 x 4 = m

m = 3

Hence m =3 is the value that satisfies the proportion in this problem.

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Answer:

The squares and cubes values can be defined follows:

Step-by-step explanation:

\(Number \ \ \ \ \ \ \ \ \ \ \ \ Squares \ \ \ \ \ \ \ \ \ \ \ \ Cubes\\\\\)

\(1\ \ \ \ \ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \ \ \ \ 1 \\\\2\ \ \ \ \ \ \ \ \ \ \ \ 4\ \ \ \ \ \ \ \ \ \ \ \ 8\\\\ 3\ \ \ \ \ \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ \ \ \ \ 27\\\\ 4 \ \ \ \ \ \ \ \ \ \ \ \ 16\ \ \ \ \ \ \ \ \ \ \ \ 64\\\\ 5\ \ \ \ \ \ \ \ \ \ \ \ 25\ \ \ \ \ \ \ \ \ \ \ \ 125\\\\ 6\ \ \ \ \ \ \ \ \ \ \ \ 36\ \ \ \ \ \ \ \ \ \ \ \ 216\\\\ 7\ \ \ \ \ \ \ \ \ \ \ \ 49\ \ \ \ \ \ \ \ \ \ \ \ 343 \\\\8\ \ \ \ \ \ \ \ \ \ \ \ 64\ \ \ \ \ \ \ \ \ \ \ \ 512\\\\\)

\(9\ \ \ \ \ \ \ \ \ \ \ \ 81 \ \ \ \ \ \ \ \ \ \ \ \ 729\\\\ 10\ \ \ \ \ \ \ \ \ \ \ \ 100 \ \ \ \ \ \ \ \ \ \ \ \ 1000\\\\11\ \ \ \ \ \ \ \ \ \ \ \ 121\ \ \ \ \ \ \ \ \ \ \ \ 1331 \\\\12\ \ \ \ \ \ \ \ \ \ \ \ 144\ \ \ \ \ \ \ \ \ \ \ \ 1728\\\\13 \ \ \ \ \ \ \ \ \ \ \ \ 169\ \ \ \ \ \ \ \ \ \ \ \ 2197 \\\\14\ \ \ \ \ \ \ \ \ \ \ \ 196 \ \ \ \ \ \ \ \ \ \ \ \ 2744\\\\ 15\ \ \ \ \ \ \ \ \ \ \ \ 225 \ \ \ \ \ \ \ \ \ \ \ \ 3375\\\\ 16 \ \ \ \ \ \ \ \ \ \ \ \ 256 \ \ \ \ \ \ \ \ \ \ \ \ 4096 \\\\\)

\(17\ \ \ \ \ \ \ \ \ \ \ \ 289\ \ \ \ \ \ \ \ \ \ \ \ 4913\\\\ 18\ \ \ \ \ \ \ \ \ \ \ \ 324\ \ \ \ \ \ \ \ \ \ \ \ 5832\\\\ 19\ \ \ \ \ \ \ \ \ \ \ \ 361\ \ \ \ \ \ \ \ \ \ \ \ 6859\\\\ 20\ \ \ \ \ \ \ \ \ \ \ \ 400 \ \ \ \ \ \ \ \ \ \ \ \ 8000 \\\\21\ \ \ \ \ \ \ \ \ \ \ \ 441\ \ \ \ \ \ \ \ \ \ \ \ 9261\\\\ 22\ \ \ \ \ \ \ \ \ \ \ \ 484 \ \ \ \ \ \ \ \ \ \ \ \ 10648\\\\ 23 \ \ \ \ \ \ \ \ \ \ \ \ 529\ \ \ \ \ \ \ \ \ \ \ \ 12167\\\\\)

\(24 \ \ \ \ \ \ \ \ \ \ \ \ 576 \ \ \ \ \ \ \ \ \ \ \ \ 13824 \\\\25\ \ \ \ \ \ \ \ \ \ \ \ 625 \ \ \ \ \ \ \ \ \ \ \ \ 15625\)

The resulting relations are:

R1({P, R, Q, U, Z})

R2({P, S, T}, {R → R2})

R3({U, V, W}, {R → R3})

R4({S, X, Y}, {P → R4}) or ({R → R4})

To find the key for R, we need to determine which attribute(s) uniquely identify each tuple in R. We can do this by computing the closure of each attribute set using the given functional dependencies F.

Starting with P, we have {P}+ = {P, R, U, V, W, Z}, since we can derive all other attributes using the given functional dependencies. Similarly, {R}+ = {R, U, V, W, Z}. Therefore, both {P} and {R} are candidate keys for R.

To decompose R into 2NF, we need to identify any partial dependencies in the functional dependencies F. A partial dependency exists when a non-prime attribute depends on only a part of a candidate key. In this case, we can see that {P}→{S, T} is a partial dependency since S and T depend only on P but not on the entire candidate key {P,R}.

To remove the partial dependency, we can create a new relation with schema {P, S, T} and a foreign key referencing R. This preserves the functional dependency {P}→{S,T} while eliminating the partial dependency.

The resulting relations are:

R1({P, R, Q, U, V, W, Z})

R2({P, S, T}, {R → R2})

To decompose R into 3NF, we need to identify any transitive dependencies in the functional dependencies F. A transitive dependency exists when a non-prime attribute depends on another non-prime attribute through a prime attribute.

In this case, we can see that {U}→{V,W} is a transitive dependency since V and W depend on U through the prime attribute R. To eliminate this transitive dependency, we can create a new relation with schema {U, V, W} and a foreign key referencing R.

The resulting relations are:

R1({P, R, Q, U, Z})

R2({P, S, T}, {R → R2})

R3({U, V, W}, {R → R3})

To decompose R into BCNF, we need to identify any non-trivial functional dependencies where the determinant is not a superkey. In this case, we can see that {S}→{X,Y} is such a dependency since S is not a superkey.

To remove this dependency, we can create a new relation with schema {S, X, Y} and a foreign key referencing P (or R). This preserves the functional dependency while ensuring that every determinant is a superkey.

The resulting relations are:

R1({P, R, Q, U, Z})

R2({P, S, T}, {R → R2})

R3({U, V, W}, {R → R3})

R4({S, X, Y}, {P → R4}) or ({R → R4})

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Therefore, the diameter of the circle with an area of pi is 2. We can round this to the nearest tenth to get 2.0, since there are no decimal places beyond the first digit after the decimal point. Thus, the diameter of the circle is 2.0.

To find the diameter of a circle with an area of pi, we need to use the formula for the area of a circle which is A = πr^2, where A is the area of the circle, π is pi, and r is the radius of the circle.

Since we are given the area of the circle as pi, we can substitute that into the formula as follows:A = πr^2pi = πr^2Dividing both sides of the equation by pi gives us

:r^2 = 1r = sqrt(1)

Since the radius is equal to the square root of 1, which is 1, we can now use the formula for the diameter of a circle to find the diameter. The formula for the diameter of a circle is

:d = 2rd = 2(1) = 2

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Step-by-step explanation:

I hope this answer is helpful ):

If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.

There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Since possibility and probability are equivalent, you may define probability as the likelihood that a specific event will occur.

given

A fair coin is repeatedly flipped until it comes up heads.

The coin is impartial.

On the third try, we need to calculate the likelihood of the first landing being on heads.

We are aware that each flip of a fair coin is independent of the others, and that each effort results in P(H) = P(T) = 0.5.

Required probability is the likelihood that the third attempt's first landing will be on heads.

= Chance of (I two trials result in tail and third result in head)

=P(I head) P(II head) P(III tail) (since each trial is independent)

= ( 1 /2 ) (1/2)(1/2) = (1/8 )

If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.

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Answer:

I believe that it is the last answer. have a great day!

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

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To determine the number of 0.5 litre bottles and 0.7 litre bottles sold by Matti, we can solve the problem using the determinant method, also known as Cramer's rule.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y. We can set up a system of equations based on the given information:

0.5x + 0.7y = 16.5   (equation 1) - representing the total volume of moonshine sold

8x + 10y = 246   (equation 2) - representing the total earnings from selling the moonshine

To apply Cramer's rule, we need to calculate the determinants of the coefficient matrix and the matrices obtained by replacing each column of the coefficient matrix with the constants from equation 1 and equation 2.

The determinant of the coefficient matrix is (0.5)(10) - (0.7)(8) = -1.4.

Replacing the first column with the constants from equation 1, the determinant is (16.5)(10) - (0.7)(246) = 129.

Replacing the second column with the constants from equation 2, the determinant is (0.5)(246) - (16.5)(8) = -84.

Now, using Cramer's rule, we can solve for x and y:

x = determinant of the matrix with the first column replaced by the constants divided by the determinant of the coefficient matrix

  = 129 / -1.4

  = -92.14

y = determinant of the matrix with the second column replaced by the constants divided by the determinant of the coefficient matrix

  = -84 / -1.4

  = 60

Since we cannot have a negative number of bottles, we round x to the nearest whole number, which is 92. Therefore, Matti sold 92 bottles of 0.5 litres and 60 bottles of 0.7 litres.

Using Cramer's rule allows us to solve the problem by considering the coefficients and constants involved. By calculating determinants, we can find the values of x and y that satisfy the given equations. It is an efficient method for solving systems of linear equations, especially when there are only two variables involved.

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Transformations that may have been used to construct A'B'C include a 90° upward rotation and a 3 unit up and 3 unit right shift.

Transformation in mathematics refers to the process of changing the position, size, or shape of a geometric object. The following are the most common types of transformations: Translation: It involves moving an object from one location to another without changing its size or orientation. Reflection: It involves flipping an object over a line of reflection, so that the object and its image are mirror images of each other. Rotation: It involves rotating an object around a fixed point, called the center of rotation. Dilation: It involves changing the size of an object, either making it larger or smaller, while preserving the shape of the object. Shear: It involves skewing an object in a given direction, causing its shape to be distorted. Similarity Transformation: It is a combination of transformations that preserve the shape of an object, but changes its size and orientation.

Here,

Triangle A’B’C’ is the image of triangle ABC. Transformations could have been used to create A’B’C,

Rotation of 90° upwards.

Shift of 3 units up and 3 units to the right.

Transformations could have been used to create A’B’C is Rotation of 90° upwards and Shift of 3 units up and 3 units to the right.

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The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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The first and second cars are 7724 feet apart from each other.

The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:

     tan = opposite/ adjacent

⇒  tan(31°) = 3500/x

⇒ 0.60086 = 3500/x

⇒ 0.67 x = 3500            [ rounding up 0.60086 = 0.67]

⇒ x = 5223.88

That means the first car is 5223.88 feet from the point on the highway below the plane.

We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:

    tan(53°) = 3500/x

⇒ 1.327 = 3500/x

⇒ 1.4x = 3500            [ rounding 1.327 = 1.4]

⇒ x = 3500/1.4
⇒ x = 2500

That means the second car is 2500 feet from the point on the highway below the plane.

Add the two distances together to get the total distance from car to car:

5223.88 + 2500.00 = 7723.88

So, rounded to the nearest foot, the cars are 7724 feet apart.

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Step-by-step explanation:

form the quadratic equation

solve for x by the use of completing square method.

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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Answer:

$1.25 per pound

The test is two-tailed because we are testing for a change in either direction. we reject the null hypothesis and support the College's claim that the algebra ability of their students has changed

(a)The hypothesis for this test can be stated as follows:

H0: The average number of equations that students can solve per day is still 10. (μ = 10)

H1: The average number of equations that students can solve per day has changed. (μ ≠ 10)

The alternative hypothesis (H1) suggests that there has been a change in the algebra ability of the students. The test is two-tailed because we are testing for a change in either direction.

(b) A t-test should be used in this case because the population standard deviation is unknown, and the sample size is relatively small (n = 113). The t-test is appropriate when the population standard deviation is unknown and when the sample size is small.

(c) To compute the test statistic, we can use the formula for the t-test:

t = (x(bar) - μ) / (s / √n)

where x(bar) is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Given: x(bar) = 13 μ = 10 s = 1.5 n = 113

Substituting the values into the formula, we have:

t = (13 - 10) / (1.5 / √113)

t = 2.186

(d) The critical value for a two-tailed test at a significance level of 99% can be obtained from the t-distribution table or using software. The critical value will depend on the degrees of freedom, which is n - 1 = 113 - 1 = 112.

Assuming the critical value to be tα/2,112,

(e)we can determine whether the calculated test statistic falls in the region of rejection or not. If it falls in the region of rejection, we reject the null hypothesis and support the College's claim that the algebra ability of their students has changed. If it does not fall in the region of rejection, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim of a change in algebra ability.

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Answer:

.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

.59

The resulting expressions for \((f\,\circ\,g)(x)\) and \((g\,\circ\,f)(x)\) are \(5- 2\cdot x^{2}\) and \(-4\cdot x^{2} + 12\cdot x -5\), respectively.

A composition is a operation two functions in which the independent variable of the first function is substituted by the entire second function. In other words, we have the following expressions:

\((f\,\circ\,g) (x) = f(g(x))\) (1)

\((g\,\circ \,f)(x) = g(f(x))\) (2)

If we know that \(f(x) = 2\cdot x - 3\) and \(g(x) = 4 - x^{2}\), then we have the following compositions:

\((f\,\circ\, g) (x) = 2(4-x^{2})-3\)

\((f\,\circ\,g)(x) = 5-2\cdot x^{2}\)

\((g \circ f) (x) = 4 - (2\cdot x-3)^{2}\)

\((g\,\circ f) (x) = -4\cdot x^{2} +12\cdot x -5\)

The resulting expressions for \((f\,\circ\,g)(x)\) and \((g\,\circ\,f)(x)\) are \(5- 2\cdot x^{2}\) and \(-4\cdot x^{2} + 12\cdot x -5\), respectively.

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Answer:

b

Step-by-step explanation:

Answer:

\(2 log(x )- (3 log(y) + log(z) ) \\ \equiv log( {x}^{2} ) - log( {y}^{3} ) - log(z) \\ \equiv log( \frac{x {}^{2} }{ {y}^{3} + z} ) \)

The system of equations has a solution at point W is:

C. y = -2x − 3

y = x + 4

If the coordinates of a point makes the equations of a system to be true, then it is a solution to the system of equations, and it is also the point of intersection of their lines.

Find the equation of each of the line that intersects at point W.

The declining line has a slope (m) = rise/run = -2/1 = -2

The y-intercept of the declining line is, b = -3.

Write the equation of the declining line by substituting m = -2 and b = -3 into y = mx + b:

y = -2x - 3

The increasing line has a slope (m) = rise/run = 2/2 = 1

The y-intercept of the declining line is, b = 4.

Write the equation of the declining line by substituting m = 1 and b = 4 into y = mx + b:

y = x + 4

Therefore, the system of equations is:

C. y = -2x − 3

y = x + 4.

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Answer: Situations that exhibit a repeating pattern over time or space, such as the movement of a flag on a windmill or a ball suspended from a string, can be modeled with a periodic function.

Step-by-step explanation:

A periodic function is a function that repeats itself after a certain interval. The situations that can be modeled with a periodic function are those that exhibit a repeated pattern over time or space.

A. Flag on windmill: The movement of a flag on a windmill can be modeled with a periodic function because it oscillates back and forth in a repeating pattern. The movement of the flag can be described by a sine or cosine function.

B. Height of baseball after being hit: The height of a baseball after being hit cannot be modeled with a periodic function because it does not exhibit a repeating pattern.

The height of the baseball will decrease as time passes, and it will eventually hit the ground. This behavior is not periodic.

C. Ball suspended from string: The motion of a ball suspended from a string can be modeled with a periodic function because it oscillates up and down in a repeating pattern. The motion of the ball can be described by a sine or cosine function.

Therefore, situations that exhibit a repeating pattern over time or space, such as the movement of a flag on a windmill or a ball suspended from a string, can be modeled with a periodic function.

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This polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.

What is polynomial?

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

A polynomial with a GCF of 4x² means that 4x² is a factor common to all terms in the polynomial. One example of such a polynomial is:

4x² (x + 2)(x - 1)(x + 3) = 4x⁵ + 24x²- 36x³ - 72x²

In this polynomial, 4x² is the GCF and (x + 2)(x - 1)(x + 3) are the remaining factors.

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In this question, we are provided with a sequence Xn and a related sequence Yn. We need to find the limit of Xn, determine the limit of a given subsequence yn, prove a statement regarding limits of sequences, and discuss the possibility of different limits for sequences a and q. Finally, we calculate the value of a specific limit.

(a) We are asked to find the limit of the sequence Xn. By simplifying the expression and applying limit properties, we can evaluate the limit of Xn as n approaches infinity.

(b) We need to determine where sequence a converges to if sequence yn converges to I. By understanding the relationship between the sequences and the given convergence, we can express the limit of a in terms of I.

(c) A subsequence an is defined by choosing every second element of yn. We are asked to write down the first four elements of an and identify the convergence point of this subsequence. By considering the pattern of the chosen elements, we can express the limit of an in terms of 1, based on the convergence of yn.

(d) We are required to prove the statement that a sequence can have at most one limit. By utilizing the definition of convergence and assuming two different limits, we can arrive at a contradiction, demonstrating that a sequence cannot have more than one limit.

(e) We are asked to argue whether sequences a and q can converge to different limits. By analyzing the given information and using the conclusion from part (d), we can determine whether it is possible for a and q to have distinct limits. Based on this conclusion, we then calculate the value of the specified limit.

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Answer:

I think the answer is d..