A new shopping mall records 150 total shoppers on their first day of business. Each day after that, the number of shoppers is 15 percent more than the number of shoppers the day before.

Answer:

46 and 47.

Step-by-step explanation:

Let the 1st number be x,

Now,

or, x + x = 92

or, 2x = 92

or, x = 46

Again,

Let the 2nd number be x + 1

And,

x + 1 = 46 + 1 = 47.

Branch and Bound method is an algorithmic technique used in the optimization problem, particularly in the mixed-integer programming problem. The primary purpose of this method is to cut the branches that do not provide any optimal solution to the problem.

The process involves two essential steps which are branching and bounding. Branching refers to dividing the initial problem into smaller subproblems that are easily solvable and then obtaining the upper and lower bound on the solutions of the subproblem. On the other hand, bounding is all about the process of checking the bounds so that the algorithm may run smoothly.

Given:

Max z = 3x₁ + x₂ s.t5x₁ + x₂ ≤ 122x₁ + x₂ ≤ 8X₁ ≥ 0, X₂ ≥ 0, x₁, x₂

integer We begin by drawing the feasible region in a graph. This involves identifying the points that satisfy all the given constraints. Below is the graph of the feasible region:Graph of feasible region From the graph, it's evident that the feasible region is a polygon with vertices (0, 0), (0, 12), (4, 4), and (8, 0).We then proceed with the Branch and Bound algorithm to solve the problem.Step 1: Formulate the initial problem and solve for its solution.Let the initial solution be x₁ = 0 and x₂ = 0. From the constraints, we obtain the equations:5x₁ + x₂ = 0; 2x₁ + x₂ = 0.Substituting the values of x₁ and x₂, we get the solution z = 0. Thus, z = 0 is the optimal solution to the problem.Step 2: Divide the problem into smaller subproblems.In this case, we divide the problem into two subproblems. In the first subproblem, we assume that x₁ = 0, while in the second subproblem, we set x₁ = 1.Step 3: Solve the subproblems and obtain their upper and lower bounds.Subproblem 1: If x₁ = 0, the problem becomes:max z = x₂s.t.x₂ ≤ 12; x₂ ≤ 8; x₂ ≥ 0The solution to this problem is z = 0. The upper bound for this subproblem is 0 (the optimal solution from the initial problem), while the lower bound is 0.Subproblem 2: If x₁ = 1, the problem becomes:max z = 3 + x₂s.t.5 + x₂ ≤ 12;2 + x₂ ≤ 8;x₂ ≥ 0The solution to this problem is z = 4. The upper bound for this subproblem is 4, while the lower bound is 3.Step 4: Select the subproblem with the highest lower bound.In this case, the subproblem with the highest lower bound is subproblem 2 with a lower bound of 3.Step 5: Repeat steps 2-4 until the optimal solution is obtained.In the next iteration, we divide subproblem 2 into two subproblems, one where x₂ = 0 and the other where x₂ = 1. We solve both subproblems to obtain their upper and lower bounds as follows:Subproblem 2.1: If x₁ = 1 and x₂ = 0, the problem becomes:max z = 3s.t.5 ≤ 12;2 ≤ 8;The solution to this problem is z = 3. The upper bound for this subproblem is 4, while the lower bound is 3.Subproblem 2.2: If x₁ = 1 and x₂ = 1, the problem becomes:max z = 4s.t.6 ≤ 12;3 ≤ 8;The solution to this problem is z = 4. The upper bound for this subproblem is 4, while the lower bound is 4.The subproblem with the highest lower bound is subproblem 2.1. We repeat the process until we obtain the optimal solution. After several iterations, we obtain the optimal solution z = 4 when x₁ = 2 and x₂ = 2. Thus, the optimal solution to the problem is x₁ = 2 and x₂ = 2 with a maximum value of z = 4.

In conclusion, the Branch and Bound method is a powerful algorithmic technique that is used to solve optimization problems, particularly mixed-integer programming problems. The method involves dividing the initial problem into smaller subproblems that are easily solvable and then obtaining the upper and lower bounds on the solutions of the subproblem. By applying the Branch and Bound algorithm to the problem Max z = 3x₁ + x₂ s.t. 5x₁ + x₂ ≤ 12; 2x₁ + x₂ ≤ 8; x₁ ≥ 0, x₂ ≥ 0, x₁, x₂ integer, we obtain the optimal solution x₁ = 2 and x₂ = 2 with a maximum value of z = 4.

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Answer:

Step-by-step explanation:

Answer:

We can use the formula A = P(1 + r/n)^(nt) to find out how long it takes for William's money to triple, where A is the final amount, P is the principal, r is the interest rate, t is the time in years and n is the number of times the interest is compounded per year.

A = P(1 + r/n)^(nt) = 550(1 + 0.02/12)^(12*t) = 3P

Solving for t we get

t = (ln(3)/ln(1+0.02/12))/12 = 49.41

For Violet's account, using the formula A=Pe^(rt) where A is the final amount, P is the principal, r is the interest rate, t is the time in years, we get:

t = ln(3) / (2 * e^-2) = 49.41

Therefore, it will take approximately 49.41 years for William's money to triple, and 49.41 years for Violet's money to triple.

So the difference in time is 0.

Explanation:

2008 - 2002 = 6 years have passed

In that time frame, we lost 26 cubic miles of ground water.

This means we lost about 26/6 = 4.333 cubic miles of ground water per year.

Answer:

Let's go part by part:

14 raised to 2 = 196

-9+7x2=-9+14 = 5

196/5= 39,2 (final result)

Answer:

-3.2

Step-by-step explanation:

14 SQUARED is 196

196 - 34 = 5.7647

- 9 + 7.2 = - 1.8

5.7647 / -1.8 = -3.2

-3.2 would be your answer.

Using concepts of sample and population, it is found that the sample variance is representative of 362 and 5530 customers ages, option D.

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

In sampling, the information is taken from a sample, and is used to estimate it for the whole population.

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Answer: 362

Step-by-step explanation:

Step-by-step explanation:

if there are no typos, then the second and the fourth answers are correct.

1 - 1.7 = -0.7 or -2×0.35

-2x = -2(x)

Answer:

b. c. d.

not -0.7-2-x

Step-by-step explanation:

Answer:

y=2x+1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

SohCahToa

Sin opposite/hypotenuse

Cos adjacent/hypotenuse

Tan opposite/adjacent

so if sin is 1/3 the opposite is 1 and the hypotenuse is 3

to find cos do a^2+b^2=c^2

1^2 + x^2 = 3^2

1+x^2=9

subtract 1 from both sides

x^2=8

do the square root x=2 sq root 2

that leaves u with

opposite is 1

hypotenuse is 3

adjacent is 2 sq rt 2

cos= 2 sqrt 2 / 3

tan= 1 / 2 sq rt 2 which is also eqal to sq rt 2 / 4

B

Answer:

-11y^5+2x

Step-by-step explanation:

subtract 3y^5 from -8y^5

The Product of the given equation is 5x³y - 20x²y² + 5xy³

in mathematics, how to find the product. A number can be multiplied by another number to determine each of its products. For instance, 9 x 3 equals 27, so 27 is a product of 9 and 3.

Algebraic expressions can be multiplied using the following procedures. To calculate the algebraic sum of the like and unlike terms, multiply the term coefficients, add the variable powers with the same base, and then add the variable powers.

By using the common factor :

5xy from the expression (x² - 4xy + y²); (x² - 4xy + y²)(5xy) = 5xy(x² - 4xy + y²)

Next, we can distribute the 5xy to each term inside the parentheses: 5xy(x² - 4xy + y²) = 5xy(x²) — 5xy(4xy)+5xy(y²)

Simplifying each term, we get:

5xy(x2)-5xy(4xy) +5xy(y²) = 5x³y - 20x2y2+5xy³

Therefore, the product of (x² - 4xy + y²)(5xy) is: 5x³y - 20x²y² + 5xy³

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Answer:

Step-by-step explanation:

The surface area of the figure is sum of areas of two triangles and three ractangles:

\(A=2\cdot\frac12\cdot10\cdot8,3+3\cdot10\cdot14=83+420=503\,cm^2\)

Answer:

-10/7   or - 1 3/7

Step-by-step explanation:

Make improper fractions

5/2 / -7/4

multiply by the recriprical

5/2 * -4/7 = -20/14    Reduce  

-10/7   or - 1 3/7

Answer:

2/21.

Step-by-step explanation:

\(\frac{2}{7}\) ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.

Hope this helps!

Write 3 as 3/1

Now you have 2/7 / 3/1.

When you divide by a fraction change the divide to multiply and flip the second fraction over

Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get

2/21

The mean is the most appropriate measure of central tendency as it takes into account all values in the dataset and provides a useful representation of the average value. However, the median and mode can also be useful to consider, particularly if the dataset has extreme values or is not normally distributed.

The appropriate measure of central tendency depends on the level of measurement of the variable.

For nominal level variables, the mode is the most appropriate measure of central tendency. The mode represents the most frequently occurring value in the data and is a useful summary statistic for categorical data.

For ordinal level variables, the median is the most appropriate measure of central tendency. The median is the value that separates the data into two equal parts, with half of the observations above the median and half below. The median is appropriate for ordinal data because it does not assume that the intervals between values are equal.

For ratio and interval level variables, the mean is the most appropriate measure of central tendency. The mean is calculated by adding up all the values and dividing by the number of observations. It is appropriate for ratio and interval data because these data types have equal intervals between values, and the mean takes into account the magnitude of the values.

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Answer:

A.

y = 3(x + 3)^2 + 3

Step-by-step explanation:

The vertex form of the equation is y=a(x-h)2 + k  

You know that the vertex (h,k)  is (-3,3) and a point on the parabola is (4,150). So what you’re needed ing to find is a bc all of the other letters can be replaced into the equation.  

First I would put the equation into vertex form using the vertex given in the problem. : y= (x - (-3))2 + (3). Then I would use the ordered pair (4,150) and replace the x and y with those values

150 = a(4 + 3)2 + 3  

Now simplify

150 = a (7)2 + 3  

150 = 49a + 3      Important: please be sure to square.

147 = 49a

3= a  

Next replace a into the formula now leaving x and y alone.

y = 3 (x+3)2 + 3   [Vertex form]

I hope this helps. Have a great day!

Answer:

A.  \(y = 3(x + 3)^2 +3\)

Step-by-step explanation:

The vertex form is:

\(y = a(x - h)^2 + k\)

Where \(a\) is the variable that determinate if the parabola is facing up or facing down and \(h\) is the \(x\) coordinate of the vertex and \(k\) is the \(y\) coordinate of the vertex.

So with the given values we have:

\(150 = a(4 + 3)^2 + 3\)

Then isolate \(a\) for find the missing value.

\(147 = a49\\\frac{147}{49} = a\\3 = a\)

Then the final answer is \(y = 3(x + 3)^2 +3\)

Answer:

yes

Step-by-step explanation:

It passes the horizontal line test

Answer:

Step-by-step explanation:

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence (\(a_{i}\)) (range) and their respective indexes (\(i\)) (domain):

\(i\)         \(a_{i}\)

1         6

2        11

3        16

4        21

5        26

b) The algebraic expression for the general term of the sequence is \(a(i) = 6 + 5\cdot (i - 1)\).

c) The 25th term in the sequence is 126.

Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence (\(a_{i}\)) (range) and their respective indexes (\(i\)) (domain):

\(i\)         \(a_{i}\)

1         6

2        11

3        16

4        21

5        26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

\(a(i) = a_{1} + r\cdot (i - 1)\) (1)

Where:

\(a_{1}\) - First element of the sequence.

\(r\) - Arithmetic difference.

\(i\) - Index.

If we know that \(a_{1} = 6\) and \(r = 5\), then the algebraic expression for the general term of the sequence is:

\(a(i) = 6 + 5\cdot (i - 1)\)

c) If we know that \(a(i) = 6 + 5\cdot (i - 1)\) and \(i = 25\), then the 25th term in the sequence is:

\(a(25) = 6 + 5\cdot (25 - 1)\)

\(a(25) = 126\)

The 25th term in the sequence is 126.

Answer:

False

Step-by-step explanation:

The sequential search algorithm is very simple to implement. It scans all the elements in the array starting at the first element, examining each element in turn and stopping when it finds a match

However, it is very inefficient since you are comparing  all the elements prior to the given element

This could be very time consuming for large data arrays

False The sequential search algorithm is simple and most efficient to use with a large data array.

False. While the sequential search algorithm is simple to implement and understand, it is not the most efficient method for searching large data arrays. The sequential search algorithm checks each element in the array one by one until it finds the desired value, resulting in an average case-time complexity of O(n). In comparison, other search algorithms, such as the binary search algorithm, offer better efficiency, particularly when dealing with large datasets. The binary search algorithm, for instance, has a time complexity of O(log n), making it significantly faster for large data arrays.

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The solution to the system of equations is (-6, -9).

Given y=2x+3,

we are to find the solution to the system of equations.

In order to find the solution to the system of equations,

we require another equation in the system.

The system of equations is:

y = 2x + 3 ...

(1)Let's assume another equation:y - 3x = 9 ...

(2)The given system of equations is:

y = 2x + 3 ... (1)y - 3x = 9 ...

(2)Substituting equation (1) into equation (2), we get:

(2x + 3) - 3x = 9 => -x + 3 = 9 => -x = 9 - 3 => -x = 6 => x = -6

Therefore, substituting this value of x in equation (1), we get:

y = 2x + 3 => y = 2(-6) + 3 => y = -12 + 3 => y = -9

Therefore, the solution to the given system of equations is (-6, -9).

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Step-by-step explanation:

Yessss

Answer:

yes

Step-by-step explanation:

Answer:

5.6568 units

Step-by-step explanation:

Given the following points :

(8, - 3) and (4, - 7).

Find the distance between them.

(8, - 3) : x1 = 8, y1 = - 3

(4, - 7): x2 = 4, y2 = - 7

Distance (d) = √[(x2 - x1)² + (y2 - y1)²]

d = √[(4 - 8)² + (-7 - (-3))²]

d = √[(-4)² + (-7 +3)²]

d = √[16 + (-4)²]

d = √16 + 16

d = √32

d = 5.6568

d = 5.66 units

The sum of their probabilities should equal 1, as the total probability of all possible outcomes must be 1.

The equation that describes the relationship between p and q is p + q = 1. In probability theory, p and q represent the frequencies or probabilities of two mutually exclusive events A1 and A2. Since A1 and A2 are mutually exclusive, only one of them can occur at a time. Therefore, the sum of their probabilities should equal 1, as the total probability of all possible outcomes must be 1.

By convention, p is used to represent the probability of event A1, and q is used to represent the probability of event A2. So, the equation p + q = 1 captures the relationship between the frequencies or probabilities of the two events, ensuring that the total probability is accounted for.

For example, if p = 0.7, it means that event A1 has a probability of 0.7 or a frequency of 70%, and q = 0.3 represents event A2 having a probability of 0.3 or a frequency of 30%. The equation p + q = 1 holds true in this case, as 0.7 + 0.3 = 1.

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

Answer:

The length of each side is 2m.

Step-by-step explanation:

A square has an area of s^2

Take the square root of 4 to find the length of each side.

The square root of 4 is 2.

Answer:

Base = 26 in

Step-by-step explanation:

Recall the formula for the area of a triangle as:

Area = (Base x Height) / 2

In our case, this formula converts into:

546 in^2 = Base x 42 in /2

multiply both sides by 2 to get rid of fractions:

1092 in^2 = Base x 42 in

divide both sides by "42 in" to isolate the Base completely

1092 in^2 / 42 in = Base

Therefore Base = 26 in

Answer:

B and C

Step-by-step explanation:

Tahnks for the brainlt