Find (f/g)(x) using long division for f(x)=x^2+4x+5 g(x)=x+3 The quotient is_______ The remainder is________

(a) The limit lim f(x) as x approaches -2 = -12 + m. B) The limit  lim f(x) as x approaches ∞ = 0 , To find the limit of f(x) as x approaches -2, we substitute -2 into the function f(x) = 6x + m.  c) value of m that satisfies the condition is m = 38.

So, lim f(x) as x approaches -2 = 6(-2) + m = -12 + m.
(b) To find the limit of f(x) as x approaches ∞ (infinity), we need to consider the highest power of x in the function.
Since the highest power of x is x2, we divide every term in the function by x2 to find the limit.

So, lim f(x) as x approaches ∞ = lim (6x/x2) + (m/x^2) + (2 - 7x2)/x^2.
As x approaches ∞, the terms (6x/x2) and (m/x2) both approach 0, and the term (2 - 7x2)/x2 approaches 0 as well.
Therefore, lim f(x) as x approaches ∞ = 0 + 0 + 0 = 0.

(c) To find the values of m such that the limit of f(x) as x approaches 2 exists, we need to find the values of m for which the left-hand limit and the right-hand limit are equal.  Let's first find the left-hand limit, lim f(x) as x approaches 2- (from the left side).  Substituting x = 2 into the function f(x) = 6x + m, we have lim f(x) as x approaches 2- = 6(2) + m = 12 + m.

Now let's find the right-hand limit, lim f(x) as x approaches 2+ (from the right side). Substituting x = 2 into the function f(x) = 2 - 7x2 + 2m, we have lim f(x) as x approaches 2+ = 2 - 7(2)2 + 2m = 2 - 28 +2m = -26 + 2m.

To find the values of m such that the left-hand limit equals the right-hand limit, we equate the expressions:
12 + m = -26 + 2m. Solving this equation for m, we have m = 38. Therefore, the value of m that satisfies the condition is m = 38.

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If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters, is the "if-then" form of A side of a square measures 3 decimeters if the side's measure is 30 centimeters.

A statement with an assumption and a conclusion is known as a conditional statement (also known as an if-then statement). The hypothesis is the initial clause, or "if," part of a conditional statement which is followed by the second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.

Thus, option B is correct which is, if the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.

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Answer:

216

Step-by-step explanation:

you can use a calculator to do 6^3

Answer:

216

Step-by-step explanation:

6 x 6 x 6 = 216

Answer:

The first one is x.

Second one is z

Third one is y.

Step-by-step explanation:

The answers to your questions are:

From the diagram there are three different planes and three different lines. one line intersects two of the planes ( Line X ) while another line intersects just one of the planes ( Line Z ) while line Y has points on all three planes.

Line y has points  A and B on all three planes

A plane is simply a flat surface that can be cut across with a straight line joining any two points of the plane.

Therefore from the diagram we can conclude that

The line that intersects two of the planes is : Line X

The line that intersects one of the planes is : Line Z

The line that that has points on three of the planes shown is Line Y

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After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Answer:

450

Step-by-step explanation:

this question requires us to find the least common multiple of 90 and 50

let's take the first 5 multiples of each and see if we find one in common:

90, 180, 270, 360, 450, 540

50, 100, 150, 200, 250, 300

we can use another method by breaking down each number into a product of its prime numbers:

90 = 5 x 18  =  5 x 2 x 9  =  5 x 2 x 3²

50 = 5 x 10  = 5² x 2

take out any numbers they have in common, which are:

one 2 and one 5

take out any numbers they do not have in common, which are:

2 and 5 and 3²

multiply the ones in common  ⇒ 2 x 5 = 10

multiply the ones not common  ⇒ 2 x 5 x 3² = 45

multiply 10 and 45 to get the least common multiple of 450

we can be 95% confident that the true population proportion falls between 0.575 and 0.645. we can be 99% confident that the true population proportion falls between 0.554 and 0.666. The difference in interpretation between the two confidence intervals lies in their level of confidence.

To construct the confidence intervals, we need to first calculate the sample proportion, which is the number of successes divided by the sample size:

p = 732/1200 = 0.61

a. To construct a 95% confidence interval for p, we can use the formula:

0.61 ± 1.96*√(0.61(1-0.61)/1200) = (0.575, 0.645)

Therefore, we can be 95% confident that the true population proportion falls between 0.575 and 0.645.

b. To construct a 99% confidence interval for p, we use the same formula, but with a z-score of 2.58:

0.61 ± 2.58*√(0.61(1-0.61)/1200) = (0.554, 0.666)

Therefore, we can be 99% confident that the true population proportion falls between 0.554 and 0.666.

c. The difference in interpretation between the two confidence intervals lies in their level of confidence.

Interpretation refers to the act of explaining or translating something in a way that makes it understandable to others. It can be applied to various fields, such as language, art, music, literature, and data analysis. In language interpretation, a person is responsible for conveying the meaning of a message from one language to another. In art interpretation, a person may explain the meaning or symbolism behind a piece of artwork.

In music interpretation, a performer may interpret a piece of music in a unique way, adding their own personal style to it. In data analysis interpretation, analysts may draw conclusions or insights from data and present them in a way that is understandable to others. Interpretation can also involve making sense of ambiguous or complex situations and providing explanations or solutions. Ultimately, interpretation involves understanding something and communicating that understanding to others in a clear and meaningful way.

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Step-by-step explanation:

so like you use sine rule to find line BC and i got 7.3 the you have to split the triangle in half to get a right angle triangle then divide 7.3 by two to get 3.7 and then use .pythagoras theorem to find the height and then use the area of a triangle formula to get your answer as option (C)

Answer:

Solved: To estimate your average monthly salary, divide your yearly salary by the number of months in a year. Write an equation to determine your yearly salary when your average monthly salary is $4560. - Slader.

Answer

The inequality to solve this is

(330/Time) ≤ 55

The solution of this inequality is

Time ≥ 6 hours

Explanation

We are told that the car's maximum speed is 55 miles per hour.

To solve this, we should note that

Speed = (distance/time)

But for this question, we are told that the car has a maximum speed of 55 miles per hour.

So,

(Distance/Time) ≤ 55

If the distance covered is 330 miles

(Distance/Time) ≤ 55

(330/Time) ≤ 55

55 (Time) ≥ 330

Divide both sides by 55

Time ≥ (330/55)

Time ≥ 6 hours

Hope this Helps!!!

Answer:

Figure 1 Line segment. It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.)

Hey there!

It’s basically the points that are lie along C & D with it not necessarily being the distance points of C & D.

Example: EF are perpendicular to CD or AB are perpendicular to CD. (Either of these should work because perpendicular simply is the line that most likely intersects at a 90° angle

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

s = 12

Step-by-step explanation:

Since the triangles are similar then corresponding sides are in proportion, that is

\(\frac{AB}{XY}\) = \(\frac{AC}{XZ}\) , substitute values

\(\frac{6}{9}\) = \(\frac{8}{s}\) ( cross- multiply )

6s = 72 ( divide both sides by 6 )

s = 12

After 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

Let's start by defining some variables:

We can then use this information to set up two equations that represent how much money each person has saved:

J = 20j + 8

M = 18m + 26

We want to know when J and M are equal, so we can set these equations equal to each other:

20j + 8 = 18m + 26

We can simplify this equation by subtracting 8 from both sides:

20j = 18m + 18

Then, we can divide both sides by 2 to simplify the equation further:

10j = 9m + 9

We want to find the smallest values of j and m that make this equation true. We can start by trying j = 1 and then incrementing j until we find a value that makes the right-hand side of the equation (9m + 9) divisible by 10. We can then solve for m and check that the left-hand side of the equation (10j) is equal to the same value.

If we try j = 1, we get:

10(1) = 9m + 9

Simplifying this equation gives us:

m = 1

So, if Jeremy tutors his cousin for 1 week and Mary babysits her sister for 1 week, they will both have the same amount of money saved. We can check this by plugging j = 1 and m = 1 into the original equations for J and M:

J = 20j + 8 = 20(1) + 8 = 28

M = 18m + 26 = 18(1) + 26 = 44

So, after 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

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The given function is,

The graph of the g(x) will be shifted 3 units upward with respect to the parent function f(x),

Thus, the above figure is the graph of g(x).

The time complexity of finding a source in a directed graph or determining such a source does not exist if the graph is represented by its adjacency matrix is V².

If a directed graph is represented by an adjacency matrix, the following approach may be used to either discover a source inside the network or establish that there isn't one:

This approach has an O(V²) time complexity, where V is the number of graph vertices. This is due to the fact that it takes O(V²) time to traverse the whole adjacency matrix in order to determine each vertex's in-degree. The next step requires traversing the inDegree array in O(V) time in order to discover a vertex with in-degree 0. In the worst scenario, it takes O(V²) time to determine if there is a path connecting this vertex to every other vertex.

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There are 50,257 permutations of the 10 digits that either begin with the three digits 987, contain the digits 45 in the fifth and sixth positions, or end with the three digits 123.

To find the number of permutations that meet the given criteria, we can break the problem into three cases:

Case 1: Permutations that begin with the three digits 987.
For these permutations, we have 7 digits remaining that can be arranged in any order. Therefore, there are 7! = 5040 permutations that begin with 987.

Case 2: Permutations that contain the digits 45 in the fifth and sixth positions.
For these permutations, we can first place the digits 45 in the fifth and sixth positions, leaving us with 8 digits remaining. These 8 digits can be arranged in any order, so there are 8! = 40,320 permutations that contain the digits 45 in the fifth and sixth positions.

Case 3: Permutations that end with the three digits 123.
For these permutations, we have 7 digits remaining that can be arranged in any order before the final three digits. Therefore, there are 7! = 5040 permutations that end with 123.

To find the total number of permutations that meet at least one of these criteria, we can use the principle of inclusion-exclusion.

First, we add the number of permutations from each case:

5040 + 40,320 + 5040 = 50,400

Next, we subtract the number of permutations that meet two of the criteria. There are two pairs of criteria that overlap:

- Permutations that begin with 987 and contain 45 in the fifth and sixth positions
- Permutations that contain 45 in the fifth and sixth positions and end with 123

To count the number of permutations that meet both of these criteria, we can first place the digits 987 at the beginning, followed by the digits 45 in the fifth and sixth positions, and then the remaining 5 digits can be arranged in any order before the final 123. Therefore, there are 5! = 120 permutations that meet both criteria.

We can do the same for the other pair of overlapping criteria:

- Permutations that begin with 987 and end with 123
- Permutations that contain 45 in the fifth and sixth positions and end with 123

To count the number of permutations that meet both of these criteria, we can first place the digits 987 at the beginning, followed by the remaining 4 digits which can be arranged in any order before the final 123. Therefore, there are 4! = 24 permutations that meet both criteria.

Now we can subtract the total number of permutations that meet two criteria:

120 + 24 = 144

Finally, we add back in the number of permutations that meet all three criteria:

There is only one permutation that meets all three criteria: 98745*****123

Therefore, the total number of permutations that meet at least one of the given criteria is:

50,400 - 144 + 1 = 50,257

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The correct answer is (c) normal distribution.

When comparing two proportions, the difference between them can be calculated, and its sampling distribution can be approximated by a normal distribution when the sample sizes are sufficiently large.

The mean of the sampling distribution is the difference between the true population proportions, and the standard deviation of the sampling distribution is calculated as:

\(sqrt[(p1*(1-p1)/n1) + (p2*(1-p2)/n2)]\)

where p1 and p2 are the population proportions, and n1 and n2 are the sample sizes.

Therefore, the sampling distribution of the difference between two proportions is approximated by a normal distribution with mean (p1-p2) and standard deviation given by the above formula.

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To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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Answer:

????

Step-by-step explanation:

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

Midpoint = (2,2.5)

Step-by-step explanation:

Midpoint = \((\frac{5 + -1}{2} , \frac{7 + -2}{2} ) = (2,2.5)\)

3Answer:

7%, 1/12, 0.1, 2/9, 0.26, 1/3

Step-by-step explanation:

To solve this question, the first step is converting all numbers into decimals.

7% = 0.07

1/3 = 0.33

0.1

0.26

1/12 = 0.083

2/9 = 0.2222

Now we can sort them, from least to greatest, leaving us with:

7%, 1/12, 0.1, 2/9, 0.26, 1/3

Converting fractions to decimals

1/3

1/3 is one divided by three

1/12

This is one divided by 12.

The eigenvalues of the coefficient matrix a(t) are 5,1,-1.

To find the eigenvalues of the coefficient matrix, we need to first form the coefficient matrix A by taking the partial derivatives of the given system of differential equations with respect to x, y, and z. This gives us:

A = [y, x, -1; 0, 5, 0; 0, 1, -1]

Next, we need to find the characteristic equation of A, which is given by:

det(A - λI) = 0

where I is the identity matrix and λ is the eigenvalue we are trying to find.

We can expand this determinant to get:

(λ - 5)(λ - 1)(λ + 1) = 0

Therefore, the eigenvalues of the coefficient matrix are λ = 5, λ = 1, and λ = -1.

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Answer: x^2 =2 or the Linear Equation is 2^2 x 2/2^4 = 1/2

There are 30 adults in the swimming pool.

The ratio is a quantitative approach that shows the relation between two proportions.

From the given relation, the ratio of of the children to adults = 8 : 3

The total number of the ratio = 8 + 3 = 11

Given that there are 110 people in the population.

The number of adults that are there will be:

\(\mathbf{=\dfrac{3}{11}\times 110}\)

= 30 adults

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Net reimbursement per patient will be \(90\)% of the total reimbursement per patient.

Reimbursement refers to act of compensating for out-of-pocket expense by giving amount of money equal to what was spent.

Let R be the total reimbursement per patient.

Now, the net reimbursement per patient can be calculated as follows:

Net Reimbursement = Total Reimbursement - Variable Costs

Net Reimbursement = R - (0.10 * R)

Net Reimbursement = R * 0.9

Net Reimbursement = 0.9R

So, the net reimbursement per patient will be 90% of the total reimbursement per patient.

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Answer:

-12

Step-by-step explanation:

h(10)

h(t)

means t=10

substitute g into voth equations and then minus the second from the first

(2(10)+5)-(4(10)-3)

25-37=-12