Value of x on 10x+12=2

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 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: 84 feet and 10 ¼ inches

Step-by-step explanation:

A quadrilateral with one pair of parallel side is a D) Trapezium

Given :

A quadrilateral with one pair of parallel side is.

we know that ,

Trapezium :

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.

The trapezium is a two - dimensional shape that appears as a table when drawn on a sheet of paper.

In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices.

so a trapezium also has four sides, four angles and four vertices.

Area of trapezium = 1/2 * ( a+ b ) h

where a and  b are bases

and h is height of altitude.

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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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A statement that describes the result of running the code segment is: the number 10 is displayed

The correct answer is an option (B)

In this question, we have been given the program code.

We need to select a correct statement that describes the result of running the code segment.

Consider the given code.

Start by setting n and sum to 0.

Add the value of n to sum. The first time, the value of n is 0, so sum remains 0.

Increment n by 1, so now the value of n is 1.

The Boolean condition (n = 5) is still false, so the loop will run again. Add 1 to sum (which is now 1), and then increment n (so n is now 2).

Repeat this three more times (while the value of n = 2, 3, and 4)

Increment n, so the value of n is now 5. Now the Boolean condition is true, so the loop stops.

Display sum is 10

Therefore, the result of running the code segment : the number 10 is displayed

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The complete question is:

Consider the following program code.

Which of the following best describes the result of running the program code?

A. The number 0 is displayed.

B. The number 10 is displayed.

C. The number 15 is displayed.

D. Nothing is displayed; the program results in an infinite loop

Answer:

Left shift, 6 units

Step-by-step explanation:

In the equation:

f(x)=3 |x+6| +9

the " +6 " in close to the x represents the horizontal shift. X always tells us about horizontal or right/left moves. So an adjustment to the x is a horizontal adjustment.

But Caution! It is the opposite of what you might think. A PLUS6 is a LEFT shift. (While a MINUS6 would be a right shift, not the case here).

The parent function is:

f(x) = |x|

So our equation:

f(x)=3 |x+6| +9

has two changes made to it. LEFT6 because of the

" +6 " by the x. And the +9 tacked onto the end of the equation is a vertical shift UP9.

Answer: $37.80

Step-by-step explanation: To calculate the percentage of the discount, we should recall the formula:

Percent = whole number * part percent / 10

So, now we should plug in the numbers

42 * 10 / 100

so 42 * 10 = 420

So, 420 / 100 = 4.2

Now, we subtract 4.20 from 42 and get $37.80. We don't need to worry about tax, because It isn't listed and it said "the price BEFORE tax." I hope this helped.

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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In the given diagram, the length of arc AB is 10.05.

From the question, we are to determine the length of arc AB.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended by the arc = 48°

Radius, r = 12

Therefore,

The length of the arc = 48/360 × 2×3.14×12

Length of the arc = 2/15 × 1884/25

Length of the arc = 10.05

Hence, the length of AB is 10.05

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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:

When the net is folded into the rectangular prism

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. Another name for it is a cuboid.

Applying science of vision to see technical details in the prism, seeing letter B on the top means that D will be on the bottom.

the side we face will be C while the bac will be A

on the other side, the left end not showing is E and this make up all the part of the prism

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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:

The value of lim F(t) for F(t) if F is a solution to the logistic differential equation dF/dt is 10 in option (c).

Finding through differential equation

[tex]\small \text{Consider the differential equation}\\ \frac{\mathrm{d} F}{\mathrm{d} t}=0.2\left ( 5F-\frac{F^2}{2} \right ),\quad F(0)=47\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{0.2}{2}\left ( 10F-F^2 \right )\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{F}{10}\left ( 10-F \right )\\[/tex]

[tex]\text{Separable the variables of F and t on both sides}\\ \int \frac{1}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{10}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{(10-F)+F}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{10F}dF-\int \frac{1}{10\left(F-10\right)}dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{F}dF-\int \frac{1}{\left(F-10\right)}dF= \int \: dt\\[/tex]

[tex]\small \ln \left|F\right|- \ln \left|F-10\right|=t+\ln C\\ \ln \left|\frac{F}{F-10}\right| =\ln \left |Ce^{t} \right |\\ \frac{F}{F-10}=Ce^{t}\\ F(0)=47\Rightarrow \frac{47}{47-10}=C\Rightarrow C=\frac{47}{37}\\ \text{Therefore,}\\ \frac{F}{F-10}=\frac{47}{37}e^{t}\\ F=\frac{47}{37}e^{t}(F-10)\\ F=\frac{47}{37}e^{t} F-\frac{470}{37}e^{t}\\ F\left ( \frac{47}{37}e^{t}-1 \right ) =\frac{470}{37}e^{t}\\ =\frac{\frac{470}{37}e^{t}}{\left ( \frac{47}{37}e^{t}-1 \right )}\\[/tex]

[tex]\small F(t) =\frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ \lim_{t\rightarrow \infty }F(t)=\lim_{t\rightarrow \infty } \frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ = \frac{\frac{470}{37}}{\left ( \frac{47}{37}-0 \right )}\\ = \frac{\frac{470}{37}}{\frac{47}{37}}\\ =\frac{470}{47}\\ =10\\[/tex]

If F is a solution to the logistic differential equation then dF/dt is 10 in option (c).

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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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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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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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A predicate nominative is a noun or a pronoun which follows the verb and describes the subject.

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The linear feet of fencing in the rectangular garden s 692 feet

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

Length  = 204 feet

Width = 142 feet

To calculate the amount of linear feet of fencing that is required, we make use of the following perimeter equation

Linear feet of fencing = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Linear feet of fencing = 2 * (204 + 142)

Evaluate

Linear feet of fencing = 692

Hence, the linear feet of fencing is 692 feet

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Answer:

One plus one is equal to two

Step-by-step explanation:

1. Identify the numbers being added: In this case, the numbers being added are "one" and "one."

2. Write the equation using the proper mathematical notation: The equation would be written as "1 + 1."

3. Perform the addition: To solve the equation, you would add the numbers together. In this case, 1 + 1 = 2.

4. Write the final answer: The final answer to the equation "one plus one" is "two."

I hope this helps! Let me know if you have any other questions.

Answer:

90 x 7= 630 minutes

Step-by-step explanation:

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 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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Answer:

See below for the graph

It is proportional.  The graph is a straight line going through the origin.

Step-by-step explanation:

The equation of the line is

y = 11x