Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week

In picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

What is exponential smoothing model?

Using the exponential window function, exponential smoothing is a general method for blending time series data. Exponential functions are used to assign exponentially decreasing weights over time, as opposed to the simple moving average, which weights previous observations equally.

The correct answer is, produces values which compare well with actual values based on a standard measure of error.

Quantitative forecasting utilizes a compilation of past performance data of the organization to arrive at an accurate forecast for any given process.

The smoothing constant selected requires to optimize accuracy the unknown parameters and the initial values need to be considered with the implementation of the sum of squared errors providing the required accuracy.

Hence, in picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

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Complete question:

Complete question is attached below.

A true average strain in a way that converys information about precision and reliability  (23.0616, 26.9384)

In this question we have been given:

sample size n = 15

the mean failure strain x(bar) = 25.0

the standard deviation s = 3.5

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = n - 1

df = 15 - 1

df = 14

and the column with α =(1-c)/2

                                   =0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.5/√15​

E ≈1.9384

The confidence interval's outer limits are thus:

x{bar} - E = 25.0 - 1.9384

               = 23.0616

x{bar} + E = 25.0 + 1.9384

                = 26.9384

Therefore, the confidence interval is: (23.0616, 26.9384)

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In 480 ways these 8 people can be seated in a row so that no two software engineers are together

In this question, we need to find the number of ways 8 people can be seated in a row so that no two software engineers are together.

3 software engineers can sit in 3! ways

2 nurses can sit in 2! ways

2 technicians can sit in 2! ways

and a doctor need only one seat

Given that no 2 software engieers are to be seated together.

we first place the 5 people in a row and  software engineers  has to sit between them so no 2 software engieers are to be seated together.

In 6 place they can sit in 6c3 ways and 3 can be combine themself in 3! ways.

Using the formula of combination,

6c3 = 20

so total will be 2 * 2* 1*20*6=480 ways.

Therefore, the number of possible ways = 480

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True Matrix organizations have a flexible structure that brings together specialists from different Areas.

Teams in a matrix organization report to several leaders inside the business. The matrix structure promotes open communication between teams and can assist businesses in producing more creative goods and services. By using this framework, teams are spared the hassle of constantly realigning themselves for new projects.

How can teams be empowered to work fast on challenging projects without being slowed down by reviews and approvals from stakeholders? The solution might lie in organizational structure. Most workplaces have established hierarchies of command so that everyone is aware of who has the final say.

There are two or more management reporting structures in matrix organizations. Team members often have a principal manager for their department, despite the fact that this may at first seem unclear.

Comparable to a traditional organizational structure is reporting to a department manager. For instance, team members in the IT department answer to the head of the department. The vice president of their division is responsible for overseeing the IT department. All reporting lines ultimately lead to the CEO.

In contrast, team members in a matrix organization also report to project managers. It is appropriate to choose a separate manager for each project because tasks associated with them frequently require assistance from employees from different areas, such as IT, marketing, and finance.

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Answer:

The shorter piece is 13 inches long.

Step-by-step explanation:

39=2x+x

39=3x

/3    /3

13=x

Answer:

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

Given parabola:

Convert the equation into vertex form y = a(x - h)² + k, where (h, k) is the vertex.

The vertex is ( - 4, 0).

The x-intercepts are the points with the y = 0, which as we see is same as the vertex:

Answer:

The two sides of the triangle are the same as marked.

118+Y=180

Y=180-118=62

Y=62

X+Y+Y=180

X+2Y=180

X=180-2Y

X=180-2x62

X=56

Step-by-step explanation:

Here, on solving the provide question to us, we got to know that - 210 feet represents  = 825/4

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Here,

15 feet represents = 1/8 of an inch

1 feet represents = 1/8 X 15

210 feet represents = 1/8 X 15 X 210 = 825/4

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The polynomial with given roots is,  

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

What is factor of polynomial?

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

Given:

The polynomial y(x) that has roots at x = -0.7, x = 0.5, x = 3.4 and x = 5.8.

Since if 'a' is a root of the polynomial then (x - a) is the factor of the polynomial.

So, the factors of the polynomial are, (x + 0.7), (x - 0.5), (x - 3.4), (x - 5.8).

⇒ y(x) = (x + 0.7)(x - 0.5)(x - 3.4)(x - 5.8)

          = (x^2 - 0.5x + 0.7x - 0.35)(x^2 - 5.8x - 3.4x + 19.72)

          = (x^2 + 0.2x - 0.35)(x^2 - 9.2x + 19.72)

   y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902

The graph of the polynomial on the domain -1 ≤ x ≤ 6 is attached below.

Hence, the polynomial with given roots is,  

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

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Answer:

p=11

Step-by-step explanation:

59+8p+3p=180

59+11p=180

-59.        -59

11p=121

/11.  /11

p=11

hopes this helps

The 90% confidence interval for the given data is 4.8 ± 2.73.

A confidence interval is a type of interval computation used in statistics that determines the true value of an unknown parameter based on the observed data. The interval estimates the deterministic parameter with a level of confidence that is quantified by the confidence level.

Given, sample mean (x) = 4.8

           z at 90% confidence level = 1.645

           sample standard deviation (s) = 5.25

           sample size (n) = 10

We know that, Confidence interval = x ± (z × s) ÷ √n

                                                           = 4.8 ± (1.645×5.25)/√10

                                                           = 4.8 ± 8.63625/3.1622

                                                           = 4.8 ± 2.73

            ∴ Lower bound = 4.8 - 2.73 = 2.07

       and, Upper bound = 4.8 + 2.73 = 7.53

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The value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]

What is Combination of Function ?

The domain of an arithmetic combination of functions f and g consists of all real numbers that are common to the domains of f and g.

Given expression,

f(x) = 4x + 1

g(x) = √x

Now, find (f · g)(x)

(f · g)(x) = f( g(x) )

Next, insert the value of g(x) in f(x) value by replacing x value in f(x)

(f · g)(x) = 4 ( √x ) + 1

            = 4√x + 1

Next, find (g · f)(x)

(g · f)(x) = g( f(x) )

Now, insert the value of f(x) in g(x) value by replacing x value in g(x)

(g · f)(x) = √4x + 1

            = [tex]\sqrt{4x+1}[/tex]

Hence, the value of (f · g)(x) is 4√x + 1 and (g · f)(x) is [tex]\sqrt{4x+1}[/tex]

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Answer:

179,768

Step-by-step explanation:

Greenpoint had 224,710 residents at the time of its founding. Currently it is 20% smaller. What is the current population?

100% - 20% = current population is now 80%

80% = 0.8

0.8 * 224,710 = 179,768

The sinusoidal function is y = -4.5cos(8(x + π/2)) + 1/2

From the question, we have the following parameters that can be used in our computation:

Maximum = (-π/2, 5)

Minimum = (π/4, -4)

A cosine function is represented as

y = A cos(B(x+C)) + D

Where

The cosine function has a max and min of 1 and -1.

So, we have

Difference = |-4 - 5|

Difference = 9

This means that

Amplitude, A = 9/2

A = 4.5

Also, we have

Vertically shift = (5 - 4)/2

Vertically shift = 1/2 up

So, the function becomes

y = 4.5cos(θ) + 1/2

Next, we calculate the value of θ

The period is calculated as

Period = π/4 + π/2

Period = -π/4

This means that

2π/B = -π/4

So, we have

B = -8

This gives

y = 4.5cos(-8(x + c)) + 1/2

cos(0) = 1,

So we want -8(-π/2) - 8C = 0

Solving for c, we have

8C = 8(π/2)

Divide

C = π/2

Substitute C = π/2 in y = 4.5cos(-8(x + c)) + 1/2

y = 4.5cos(-8(x + π/2)) + 1/2

y = -4.5cos(8(x + π/2)) + 1/2

Hence, the function is y = -4.5cos(8(x + π/2)) + 1/2

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Complete question

The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)

Determine a cosine equation for this function.

The fraction that will be equivalent to 5/8 with a denominator of 16 is 10/16

From the question, we have the following parameters that can be used in our computation:

Fraction = 5/8

This fraction is to be converted to a fraction  with a denominator of 16

This is so because the scale only measures in 16ths

So, we have the following representation

Fraction = 5/8

When 8 is multiplied by 2, the result is 16

So, we multiply 5 and 8 by 16

This gives

Fraction = 10/16

Hence. the solution is 10/16

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The length of pregnancy does play a role in the education level of the baby. A significant relationship can be established using the chi square test.

A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different parameters, first being the population of people who are married and the other about their educational qualification, we will get two distinct table of values without any significant co relation. But now if we want to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convincing relationship between the two parameters or can be a alternate hypothesis with significant co relation.

Following data can be represented on tabular form and calculated:

                                                  Gestation Period (Observed)

                                     22-27       28-32       33-36       37-42       43+    Tot

Less than high   YES    14              34            140           1010         81     1279

school degree     NO    26             65            343          3032      208   3674

                                      40             99            483          4042      289   4953

                                                   Gestation Period (Expected)

                              YES   10.32     25.56        124.72    1043.75    74.62

                              NO     29.67    73.43        358.27    2998.24   214.37

χ2 = ∑ [tex]\frac{(Observed-Expected)^2}{Expected}[/tex]

= [tex]\frac{13.54}{10.32} +\frac{71.23}{25.56} +\frac{233.47}{124.72} +\frac{1139.06}{1043.75} +\frac{40.70}{74.62} +\frac{13.46}{29.67} +\frac{233.17}{358.27} +\frac{1139.73}{2998.24}+\frac{40.57}{214.37}[/tex]

= 1.31+2.78+1.87+1.09+0.54+0.45+0.96+0.65+0.38+0.18 = 10.21

Now, calculating the degree of freedom= (coulmn-1)(row-1)= (5-1)(2-1) = 4

Looking at the reference table at 0.05 significance level, the value is 9.488

As the calculated value is more than the table value/critical value, null hypothesis can be rejected proving the alternate hypothesis that there might be a relationship between gestation period of a mother and the education level of her kid.

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The number of gums available, with the 12 boxes, each containing 12 dozens of gums and one open box containing 32 gums, found using the values of the non verbal units of measure, indicates that the number of gums are 1760 gums.

Non verbal units of measure are used to describe the quantity of an item using verbal terms such as pairs (2 units), dozens (12 units), scores (20 units), gross (12 dozens or 144 units), bushels (8 gallons or 4 pecks), ream (500 units).

The number of dozens of pieces of gum are in a box = 12 dozens

The number of boxes of gum available = 12 boxes

The remaining number of gums = 1 open box with 32 gums

1 dozen of an items = 12 units of the specified item

12 dozens of an item = 1 gross of the item

The number of pieces of gums in a box, therefore is 1 gross of gums.

Therefore, the number of pieces of gum in all = 12 × 12 × 12 + 32 = 1760

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When used inside a function with a parameter, an asterisk groups a variable number of positional arguments into a single tuple of parameter values

Tuples are utilized to store different things in a solitary variable. A tuple is one of 4 implicit information types in Python used to store assortments of information, the other 3 are Rundown, Set, and Word reference, all with various characteristics and use. A tuple is an assortment that is requested and unchangeable. At the point when we say that tuples are requested, it implies that the things have a characterized request, and that request won't change. Python likewise incorporates the * administrator, which permits you to make another rundown with the components rehashed the predetermined number of times. *args permits us to pass a variable number of non-catchphrase contentions to a Python capability. In the capability, we ought to utilize a bullet ( * ) before the boundary name to pass a variable number of contentions.

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The statement " when adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree" is true.

A tree is a type of data structure made up of nodes and contains the following features:

1- Every tree has a root node (also known as a parent node) at the top that contains some value (can be any datatype).

2- There are 0 or more child nodes of the root node.

3- There are zero or more child nodes for each child node, and so forth. As a result, the tree gains a subtree. Each node has a separate subtree that consists of its offspring and their offspring, etc. This implies that any node can function as a tree on its own.

In addition, a binary search tree (BST) has the following two features:

1- Each node has a maximum of up to two children.

2-For each node, the values of its left descendent nodes are less than that of the current node, which in turn is less than the right descendent nodes (if any).

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The statement -7 < y < 12 meant y is greater than -7 and less than 12.

{-7 < y < 12}

This is a compound inequality.

A compound inequality is a type of inequality which combones two or more simple inequality.

-7 < y < 12

This can be broken down into two parts;

This can also be written together as y is greater than -7 and less than 12.

This means y is between the values that are greater than -7 but less than 12

So,

y could be -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Therefore, y can be said to be within the range of values between -6 and 11

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r = 1 in scatter plot 1, the response. Scatter plot 2, with a r of 0.364 Scatter plot 3, r=-0.995 Scatter plot 4, r = 0.995 Scatter plot 5, with a r of 0.735.

Charts that depict the relationship between two variables are known as scatter charts, sometimes known as scatter plots. They are a very effective type of chart because they enable readers to see relationships or trends right away that are difficult to see in practically any other form.

You can figure out R using the formula R = s t if you've worked in sections. Between 1 and 1 will be the response you receive. Any response that is affirmative demonstrates a positive correlation, with anything over 0.7 often being regarded as a significant link.

r = 1 in scatter plot 1, the response. Scatter plot 2, with a r of 0.364 Scatter plot 3, r=-0.995 Spreadsheet plot 4, r = 0.995 Scatter plot 5, with a r of 0.735.

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As per the given confidence interval, the population mean remodeling costs for the two types of projects is -1.6

Confidence interval

The  range of values that's likely to include a population value with a certain degree of confidence is known as confidence interval.

Given,

A certain association provided data on the cost of the most popular home remodeling projects.

Here we need to find the the population mean remodeling costs for the two types of projects.

Here we will find the point estimate of the difference between the population mean remodeling costs for the two types of projects using an equation,

=> X1​ − X2​

In order to calculate the sample mean we will use equation,

=> X = ∑x/n

Now, we have to substitute values we get,

=> X1 ​= 21.2

=> X2 ​= 22.8

Here X1 refers the sample mean remodeling costs for the kitchen and X2​refers the sample mean remodeling cost for the master bedroom.

Therefore, the point estimate of the difference between the population mean remodeling costs for the two types of projects are,

=> X1 ​− X2​ ​= −1.6

Therefore, we estimate that the remodeling master bedroom has the mean costs of 1.6 greater than mean remodeling costs for the kitchen.

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Answer:6/3 or 1/2

Step-by-step explanation:

The central angle of the given arc LKJ is;  211°

We want to find the length of the arc LKJ. The central angle for this arc length is; 115° + 96° = 211°

The formula for length of arc is;

L = θ/360 * 2πr

where;

θ is central angle

r is radius

We are not given the radius and as such, we can only find the central angle which is 211°

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The statistical method used to predict the values of one numerical variable based on the values of another is regression analysis.

Regression analysis:

Regression analysis is a statistical method that shows the relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

Regression analysis is used to estimate the relationship between a dependent variable and one or more independent variables.

The common form of regression analysis is linear regression. Regression analysis allows us to infer that there is a relationship between two or more variables.

Therefore regression method is used to predict values of one numerical on another.

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In 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.

We have John who started his employment with a salary of $120,000 per annum which was increased by $10,000 every year up to the top of the scale of $1,500,000 per annum.

We can write the equation governing the increase as -

y = 120000 + 10000x

For -

y = 1500000, we can write -

1500000 = 120000 + 10000x

10000(12 + x) = 1500000

x + 12 = 150

x = 138 years

The total amount he would earn during this period will be -

A = 10000 x 138 = $1380000

Therefore, in 138 years time, john will reach to the top scale and the total amount he would earn during this period will be $1380000.

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The Solution for the given system of equations is (-2) and [tex](\frac{5}{3})[/tex].

The given are linear equations as follow:
y = [tex]\frac{2}{3}x[/tex] + 3              .. ... ...(1)
and x  = -2.          .. .... ...(2)

We already know the first part of the solution (x) which is -2.  We can find the other part (y) by putting the value of equation (2) in equation (1).

By putting the values of x in equation (1), we get

y = [tex](\frac{2}{3})(-2)[/tex] + 3
y = [tex]\frac{-4}{3}[/tex] + 3

Taking the L. C. M of denominators which will be '3', we get:

y = [tex]\frac{-4 + 9}{3}[/tex]

y = [tex]\frac{5}{3}[/tex]

So the second part (y) of the solution of the given equation is [tex]\frac{5}{3}[/tex].

Hence, the overall solution to the given system of equation is [tex](-2, \frac{5}{3})[/tex].

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Answer:

-6/7p + 1/7

Step-by-step explanation: