Find a pattern for the sequence below.
1, 4, 9, 16, 25, ...

If a=4, b=6, and sina=3/5 in triangle abc, then sin b equals: 9/10

To find sin(b) in triangle ABC, we can use the sine function in a right angle and the given information.

Given:

a = 4

b = 6

sin(a) = 3/5

We know that the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, let's label the side opposite angle a as side c and the hypotenuse as side h.

sin(a) = c / h

Substituting the given values:

3/5 = 4 / h

To solve for h, we can cross-multiply:

3h = 5 * 4

3h = 20

h = 20 / 3

Now, we can use the sine function to find sin(b):

sin(b) = side opposite angle b / hypotenuse

sin(b) = 6 / (20 / 3)

sin(b) = 6 * (3 / 20)

sin(b) = 18 / 20

sin(b) = 9 / 10

Therefore, sin(b) equals 9/10.

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Answer:

D/C, Cubic

Step-by-step explanation:

7x^3 is the highest degree term. 3 is highest degree. Anything with a 3rd degree is called a cubic polynomial (think something cubed is raised to the third power). Therefore, the answer is cubic. It says, D, cubic, but it is the third answer.

Answer:

2/5

Step-by-step explanation:

Answer:

i think it's 2/5 not sure tho

Answer:

22

Step-by-step explanation:

A(n) focus indicates when an object sends or receives a message and is identified by a narrow vertical shape that covers the lifeline. A) focus.

A focus, in the context of UML, is a graphical element that represents the point in time when an object is actively sending or receiving a message. It is indicated by a narrow vertical shape that covers the lifeline of the object in a sequence diagram.

The other options, subclass and instance, do not refer to elements used in sequence diagrams. Subclass refers to a type of object that inherits attributes and behaviors from a parent class, while instance refers to a specific occurrence of an object with its own unique set of attribute values. Activity is a type of diagram used to model business processes or workflows.

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Answer:

20

Step-by-step explanation:

a negative times a negative is a positive

Answer:

im failing too!

Step-by-step explanation:

Answer: x = 2.1 or x = 9.9

Step-by-step explanation: rewrite as: \(x^2\)-12x+21 = 0

a = 1, b = -12, c = 21 [sub into quadratic formula: \(x\)=\(\frac{-b\frac{+}{-} \sqrt{b^2-4ac}}{2a}\)]

Approximately 35% of students prefer swimming as their preferred type of exercise. So, correct option is B.

To find the marginal relative frequency for students who prefer swimming as their preferred type of exercise, we need to add up the percentage of boys and girls who prefer swimming.

The percentage of boys who prefer swimming is 16% and the percentage of girls who prefer swimming is 19%.

So, the total percentage of students who prefer swimming is:

16% + 19% = 35%

Therefore, the marginal relative frequency for students who prefer swimming as their preferred type of exercise is 35%.

So, correct option is B.

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Answer:

i. <DCB = \(53.13^{o}\)

ii. Sin of <DCB = 0.8

Step-by-step explanation:

Let <DCB be represented by θ, so that;

Sin θ = \(\frac{opposite}{hypotenuse}\)

Thus from the given diagram, we have;

Sin θ = \(\frac{4}{5}\)

        = 0.8

This implies that,

θ = \(Sin^{-1}\) 0.8

   = 53.1301

θ = \(53.13^{o}\)

Therefore, <DCB = \(53.13^{o}\).

So that,

Sin of <DCB = Sin \(53.13^{o}\)

                    = 0.8

Sin of <DCB = 0.8

A stock split is a corporate action in which a company increases the number of shares it has outstanding by giving each shareholder more shares. This action does not affect the proportionate equity that each shareholder holds in the corporation. Instead, it adjusts the number of shares and the share's par value. In the case of Giacomo Company, a manufacturer of outdoor tables and chairs for European-style cafes, specific information is provided.

On January 1st, Year 1, Giacomo issues 500,000 shares of $2 par value common stock for $10 per share. This marks the first time Giacomo has issued common stock during Year 1, and no other stock issuances occur throughout the year.

Assuming Giacomo executes a 9:4 stock split, each old share would be transformed into 2.25 new shares (9/4). Consequently, the number of shares outstanding would increase by 125 percent. To calculate the new par value of Giacomo's stock, we can utilize the formula:

New par value per share = Old par value per share / (Split ratio)

In this case, the old par value is $2 per share, and the split ratio is 9/4. Substituting these values into the formula, we find:

New par value per share = $2 per share / (9/4)

New par value per share ≈ $0.888888888888889 or $0.89 per share

Therefore, the new par value of Giacomo's stock after a 9:4 stock split would be $0.89.

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The grounded ends of the guy wires are 15 meters apart.

Using the Pythagorean theorem, we can calculate the length of the base (distance between the grounded ends of the guy wires).

Let's denote the length of the base as 'x.'

According to the problem, the height of the tower is 20 meters, and the length of each guy wire is 25 meters. Thus, we have a right triangle where the vertical leg is 20 meters and the hypotenuse is 25 meters.

Applying the Pythagorean theorem:

x² + 20² = 25²

x² + 400 = 625

x² = 225

x = √225

x = 15

Therefore, the grounded ends of the guy wires are 15 meters apart.

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Answer:

The height in feet of the pine tree is 36 feet

Step-by-step explanation:

Please see the attachment below for an illustrative diagram.

In the diagram,

/AB/ represents the height of the pine tree

/BD/ represents the length of the shadow cast by the pine tree

/EC/ represents the length of the ruler ( one foot)

/CD/ represents the length of the shadow cast by the one-foot ruler

Consider triangle ADB and triangle EDC

Triangles ADB and EDC are similar triangles.

Hence, we can write that

\(\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}\)

/AB/ = ??

/EC/ = 1 ft

/BD/ = 24 ft

/CD/ = 8 inches

First we will convert 8 inches to feet

Since, 12 inches = 1 foot

Then, 8 inches = \(x\)

\(x = \frac{8}{12} \\\) ft

\(x = \frac{2}{3}\\\) ft

Hence.

/CD/ = \(\frac{2}{3}\) ft

Now, putting the values into

\(\frac{/AB/}{/EC/} = \frac{/BD/}{/CD/}\)

\(\frac{/AB/}{1} = \frac{/24/}{/\frac{2}{3} /}\)

\(/AB/= \frac{/24/}{/\frac{2}{3} /}\\\)

\(/AB/ = 36\) ft

Hence, the height in feet of the pine tree is 36 feet.

The volume of the remaining portion of the sphere is 2.096 cubic units.

Let's take the volume of the remaining portion of the sphere = V

The volume of the sphere = \(\frac{4}{3}\) * π * \(r^3\)

The volume of the sphere with radius 1  = 4/3 * π

The volume of the cylinder = π * \(r^2\) * h

The volume of the cylinder with height 2 and radius 1 = π * \(r^2\) * h = 2 * π.

The difference between the volume of the sphere and the cylinder is

V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.

By taking π = 3.14

V = \(\frac{2}{3}\) * 3.14

V= 2.096.

So, the volume of the remaining portion of the sphere is 2.096 cubic units.

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The measure of this angle is equal to half the measure of the intercepted arc. ASG angles that intercept the same arc are congruent, and they are always less than or equal to 180 degrees.

When two chords intersect inside a circle, an angle is formed. The ASG angle is a type of angle formed by two chords that intersect within a circle. This angle is also known as an inscribed angle or central angle. Let's go over some important concepts related to this type of angle and explore some of its properties.
An inscribed angle is an angle that forms when two chords intersect within a circle. In particular, the angle is formed by the endpoints of the chords and a point on the circle. The measure of an inscribed angle is equal to half the measure of the intercepted arc. Therefore, we can find the measure of an ASG angle if we know the measure of the arc that it intercepts.
A central angle is another type of angle that forms when two chords intersect within a circle. This angle is formed by the endpoints of the chords and the center of the circle. The measure of a central angle is equal to the measure of the intercepted arc. This means that if we know the measure of a central angle, we can also find the measure of the intercepted arc.
One important property of ASG angles is that they are congruent if they intercept the same arc. This means that if we have two ASG angles that intercept the same arc, then the angles are equal in measure.

Another important property of ASG angles is that they are always less than or equal to 180 degrees. This is because the arc that they intercept cannot be larger than half the circumference of the circle.

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.

Answer:

The answer is -8.7

Step-by-step explanation:

-5(-2.1) + 4(-4.8)

10.5 + 4(-4.8)

10.5 + (-19.2) =  -8.7

The area of the resulting surface of this infinite curve is π units.

In this question,

The infinite curve is y = e^−2x, x ≥ 0.

The curve is rotated about x-axis.

Since x ≥ 0, the limits will be 0 to ∞.

Then the area of the resulting surface is,

\(A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )\)

Now substitute,

u = -2x

⇒ du = -2dx

⇒ dx = \(-\frac{1}{2} du\)

Then,

\(\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du\)

Now substitute u and du, we get

⇒ \(-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx\)

⇒ \(-\frac{-2}{2} \int\limits {e^{-2x} } \, dx\)

⇒ \((1) \int\limits {e^{-2x} } \, dx\)

⇒ \(\int\limits {e^{-2x} } \, dx\)

Thus the area of the resulting surface is

\(A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx\)

⇒ \(A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0\)

⇒ \(A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\\)

⇒ \(A= -\pi [0-1} \,]\\\)

⇒ \(A= \pi\)

Hence we can conclude that the area of the resulting surface is π units.

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Answer:

hhhhi be a good time and consideration and I have a great day when mother

Step-by-step explanation:

good time to be a good idea to be able to be the best to you send me the day and time to explore the possibility of working with you send me the day of the way for free from any device to start this is a good idea to have to be the first time in group of doing a great time in group only for the FF to be the best to be able to get to be the way you can you send the way you are you still there be a good day

Answer:

Yes there are three lines that are right beside each other making them parrel.

Step-by-step explanation:

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer:

no

Step-by-step explanation:

since n=2 then that means that the inequality would have to be an equal sign cuz on the other side also 2.

Answer:

3

Step-by-step explanation:

Answer:x=3

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

2x+3-3=9-3

2x=6

Step 2: Divide both sides by 2.

2x/2=6/2

X=3

Hope that helps :D

Answer:

Step-by-step Yes it is, assuming we decide to use the Pythagorean Theorem to find the hypotenuse (10) it'll be possible considering the formula is c²=√a²+b²

(c being the longest side of the triangle)

a= 6 and b= 8

c² =√6² + 8²

c² = √100 square root of 100 equals 10

c= 10p explanation:

Answer:

Step-by-step explanation:

Verify the answer:

The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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The overall shape of the distribution of soldiers' foot lengths was likely symmetric or approximately bell-shaped.

The distribution of soldiers' foot lengths can be described as symmetric or bell-shaped. The majority of foot lengths cluster around the center, with fewer foot lengths deviating significantly. The center of the distribution, representing the average foot length, can be determined using the mean.

Analyzing the shape through a histogram or box plot helps identify symmetry. A symmetric shape with a peak in the middle and evenly tapering tails indicates a bell-shaped distribution.

Understanding the distribution's shape and center allows us to infer the overall characteristics of the soldiers' foot lengths.

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The quadrilateral was shifted to the left 6 times and upward 8 times

So the factor is (x-6, y+8)

The coordinate of the unit in the blank is (-6, 8)

For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).

As given in the question,

Given:

Line segment AB with coordinates A( 4,5) and B(12, 9)

Line segment AB divided by point P in the ratio AP : PB = 3: 1

Let (x ,y) be the coordinates of point P .

Coordinates of A(4,5) = ( x₁, y₁)

B(12,9) = (x₂ , y₂)

Ratio m : n = 3 : 1

Coordinates of point P is given by:

x = (mx₂ + nx₁)/ ( m+ n)

  = [3(12) + 1(4)] / (3+1)

  = ( 36 +4)/ 4

  = 40 /4

  = 10

x = (my₂ + n y₁)/ ( m+ n)

  = [3(9) + 1(5)] / (3+1)

  = ( 27 +5)/ 4

  = 32/4

  = 8

P(x ,y) = P(10, 8)

Therefore, For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).

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In Tableau, a filter allows a visualization developer or user to dynamically remove rows from the visualization.  Thus, Option A is the answer.

What is Tableau?

Tableau is an interactive and intuitive data visualization tool that enables people to see and understand data. It provides a variety of data exploration, modelling, and visualization options. Tableau is one of the best data visualization software available in the market. It provides an easy way to integrate data from various sources. With Tableau, you can easily create interactive and visually appealing charts, graphs, and other types of visualizations that are easy to understand and interpret.

What is a filter?

In Tableau, a filter is a tool that allows you to selectively display data from a larger dataset based on certain conditions. Filters help you to narrow down your data to the most relevant information so you can make better decisions based on your analysis. Filters can be applied to different dimensions and measures to help you get a better view of your data. Tableau allows you to filter your data using various types of filters such as categorical, continuous, and relative filters. You can also create custom filters using calculated fields and parameters.

A filter allows a visualization developer or user to dynamically remove rows from the visualization. Therefore, the correct option is (a) Filter.

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Answer:

Using the Lagrange method, the optimal choice is therefore (x1, x2) = (20/9, 4/3).

The optimal choice when pı = 3, P2 = 5 and I = 20 and utility is u(x1, x2) = min{2x1, x2} can be found using the Lagrange method .Lagrange method: This method involves formulating a function (the Lagrange function) which should be optimized with constraints, i.e. the optimal result should be produced while adhering to the constraints provided. The Lagrange function is given by: L(x1, x2, λ) = u(x1, x2) - λ(I - p1x1 - p2x2)

Where L is the Lagrange function, λ is the Lagrange multiplier, I is the budget, p1 is the price of good 1, p2 is the price of good 2.The optimal choice can be determined by the partial derivatives of L with respect to x1, x2, and λ, and setting them to zero to get the critical points. Then, the second partial derivative test is used to determine if the critical points are maxima, minima, or saddle points. The critical points of the Lagrange function L are:

∂L/∂x1 = 2λ - 2p1 = 0 ∂L/∂x2 = λ - p2 = 0 ∂L/∂λ = I - p1x1 - p2x2 = 0

Substitute the first equation into the second equation to get:λ = p2,2λ = 2p1 ⇒ p2 = 2p1,

Substitute the first two equations into the third equation to get: x1 = I/3p1,x2 = I/5p2

Substitute p2 = 2p1 into the above to get:x1 = I/3p1,x2 = I/10p1.Substitute the values of p1, p2 and I into the above to get:x1 = 20/9,x2 = 4/3.The optimal choice is therefore (x1, x2) = (20/9, 4/3).

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