Using the identities for sin (A + B) and cos (A+B) express sin (2A) and cos (2A) in terms of sin A and cos A. Also show that cos 3A = 4 cosA - 3 cos A = Major Topic TRIGONOMETRY Blooms Designation AP Score 7 b) The sum to infinity of a GP is twice the sum of the first two terms. Find possible values of the common ratio Major Topic Blooms Score SERIES AND SEQUENCE Designation 7 AN c) Integrate the following i. (cos(3x + 7)dx III. [3x(4x² + 3)dx

Answer:

Area of the shaded region = 450.52 square inch

Step-by-step explanation:

Area of the shaded region = Area of the circle - Area of the right triangle inscribed in the semicircle

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

                        = (21)² + (20)²

Hypotenuse = \(\sqrt{441+400}\)

                     = \(\sqrt{841}\)

                     = 29

Since, hypotenuse of the right triangle is the diameter of the circle.

Therefore, radius of the circle = \(\frac{29}{2}\)

                                                  = 14.5 in.

Area of the circle = πr²

                             = π(14.5)²

                             = 660.519

                             ≈ 660.52 in²

Area of the right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                         = \(\frac{1}{2}(21)(20)\)

                                         = 210 in²

Area of the shaded region = 660.52 - 210

                                            = 450.52 square inch

Answer: 2, 4 then c=4 also and B for the next one :)

Step-by-step explanation: Giving away 100 points be the first to comment on my " question " stay tuned!

Answer:

answer is 20................................

The solution to this equation is x = 1, as 2log3x = 1 implies that log3x = 1/2, and then log3(x2 - 2) = 1/2.

The equation log3x log3(x2 2) = 1 2log3x can be simplified to log3x2 - log32 = 1 2log3x. This equation can be further simplified by combining like terms on both sides, resulting in log3x2 - 2log3x = log32. We can now take the logarithm of both sides, resulting in x2 - 2x = 2. This equation can be rearranged to x2 - 2x - 2 = 0, and then solved using the quadratic formula. The solutions of this equation are x = 1 and x = 2. However, since log3x must be positive, the only valid solution to the equation is x = 1. This implies that 2log3x = 1, and then log3(x2 - 2) = 1/2. Therefore, the solution to the equation log3x log3(x2 2) = 1 2log3x is x = 1.

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Answer:4^3a^2b^2 or 4^3ab^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter of a triangle with sides l=m/3, n=l+m-15, and m is 65 feet. You want to know the lengths of the sides.

The perimeter is the sum of the side lengths.

  P = l +m +n

  P = (1/3)m +m +(l +m -15) = (1/3)m +m +(1/3)m +m -15

  65 = 8/3m -15 . . . . . simplify, use P=65

  80 = 8/3m . . . . . . . . add 15

  30 = m . . . . . . . . . . . multiply by 3/8

Then the other sides are ...

  l = 1/3m = 1/3(30) = 10

  n = l +m -15 = 10 +30 -15 = 25

The lengths of the sides are l = 10 ft, n = 25 ft, m = 30 ft.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =80 \end{cases}\implies A=\cfrac{(80)\pi (6)^2}{360} \\\\\\ A=8\pi \implies A\approx 25.13~mi^2\)

Answer:

Step-by-step explanation:

We have proved that expression (x² + 1 )² is equal to (x² - 1)² + 2x².

What is factorization ?

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

It is given that the expression is (x² + 1 )².

Let's simplify the above expression.

So ,

(x² + 1 )²

As per the definition of exponent ; we can write it as :

= (x² + 1 ) (x² + 1 )

Applying distributive property now :

= x²(x² + 1 ) + 1 (x² + 1 )

Now , applying simplification process : we get :

= \(x^{4}\) + x ² + x² + 1

Adding the like terms (i.e., x²) :

=  \(x^{4}\) + 2x ² + 1

Applying factorization method : we can write middle term 2x² equal to 4x² - 2x² and it will be :

= \(x^{4}\) + 4x - 2x ² + 1

Reordering the terms :

=  \(x^{4}\) - 2x ² + 1 + 4x²

We know that , factorization of (a - b)² is : a² + b² - 2ab. Use this to simplify above equation :

= (x² - 1)² + 4x²

Now , we can re write 4x² as square of 2x.

i.e.,

= (x² - 1)² + 2x²

It is proved that (x² + 1 )² = (x² - 1)² + 2x².

Therefore , we have proved that expression (x² + 1 )² is equal to (x² - 1)² + 2x².

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The area of the propeller-shaped region enclosed by the curves x = \(y^3\) and x - y = 0 is 1 square unit.

To find the area of the propeller-shaped region enclosed by the curves, we need to determine the points of intersection between the curves and then integrate the appropriate function over the interval between these points.

The curves given are:

Curve 1: x = y^3

Curve 2: x - y = 0

First, we find the points of intersection by setting the equations of the curves equal to each other:

y^3 = y

y(y^2 - 1) = 0

This equation has three solutions: y = 0, y = -1, and y = 1.

The intersection points are:

A: (0, 0)

B: (-1, 1)

C: (1, 1)

To find the area of the propeller-shaped region, we need to evaluate the integral of the function representing the region over the interval [y1, y2], where y1 and y2 are the y-coordinates of the intersection points.

The region can be divided into two parts: the upper part, enclosed by the curve x = y^3, and the lower part, enclosed by the line x - y = 0.

For the upper part, the function representing the region is given by the difference between the curves:

f1(y) =\(y^3 - (y^3 - y) = y\)

For the lower part, the function representing the region is given by the line equation:

f2(y) = x - y = y - y = 0

Therefore, the area of the propeller-shaped region can be calculated as:

Area = ∫[y1, y2] (f1(y) - f2(y)) dy

= ∫[-1, 0] (y - 0) dy + ∫[0, 1] (y - 0) dy

= ∫[-1, 0] y dy + ∫[0, 1] y dy

=\([y^2/2] [-1, 0] + [y^2/2] [0, 1]\)

= \((0/2 - (-1)^2/2) + (1^2/2 - 0/2)\)

= 1/2 + 1/2

= 1

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Answer:

9/2

Step-by-step explanation:

This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.

To apply the conditional formatting as described:

1. In column B, highlight cells with the number of movies greater than 15 in red.
-Select the data range in column B where the number of movies is listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
- Select "Greater Than" and enter 15 in the input box.
- Choose "Custom Format," go to the "Font" tab, and select red from the "Standard Colors" section.
Click OK to apply the formatting.

2. In column E, change the number format for all zero values to a currency with no decimals:
- Select the data range in column E where the medical expenses are listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
-Select "Equal To" and enter 0 in the input box.
- Choose "Custom Format," go to the "Number" tab, select "Currency" from the "Category" list, and set the "Decimal Places" to 0.
Click OK to apply the formatting.

This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.

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The  two additional questions that would be meaningful to drill down into with this same dataset is that What type of variation occurs within my variables? and What type of covariation occurs between my variables?.

The term data set is defined as a collection of related sets of information that is composed of separate elements but can be manipulated as a unit by a computer.

Here we need to find the two additional questions that would be meaningful to drill down into with this same dataset,

As per the definition we have know that the question that need to be asked over the data set are listed as follows:

They are type of variation occurs within my variables and the type of covariation occurs between my variables.

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Step-by-step explanation:

there are 2 formulas to calculate the length of a chord, depending on what pieces of information we have.

here now we have the length of the chord, which we need to find the radius, which we need to find the angle at the center.

chord length = 2×sqrt(r² - d²)

chord length = 2×r×sin(c/2)

r is the radius, d is the distance of the chord from the center of the circle, c is the angle of the chord at the center of the circle.

20 =2×sqrt(r² - 12²) = 2×sqrt(r² - 144)

10 = sqrt(r² - 144)

100 = r² - 144

244 = r²

r = 15.62049935... cm

20 = 2×r×sin(c/2) = 2×15.62049935...×sin(c/2)

10 = 15.62049935...×sin(c/2)

sin(c/2) = 10/15.62049935... = 0.6401844...

c/2 = 39.80557109...°

c = 79.61114218...° ≈ 79.6°

(a) the angle subtended by the chord at the center of the circle is about 79.6°.

(b)

the arc length of a segment is 2pi×r × c/360

in our case

2×3.142×15.62049935...×79.61114218.../360 =

= 21.70713182... cm

the whole perimeter of the segment is then arc length + chord length =

= 21.70713182... + 20 = 41.70713182... ≈ 41.7 cm

the perimeter of the minor segment cut off by the chord is about 41.7 cm.

Answer:

In other words, a net increase in jobs from energy efficiency, for the most part, is the result of two major changes: 1) an initial expenditure or effort that drives energy bill savings; and 2) the subsequent adjustment in spending patterns brought about by that initial expenditure or effort.

Step-by-step explanation:

Answer: n = 20

Step-by-step explanation:

Given that the problem goes thus:

When a number, n is added to 1/5 n of itself, the outcome obtained is 24.

Mathematically,

n + 1/5 of n = 24

n + (1/5n) = 24

1n + 1/5n = 24

(5n + 1n) / 5 = 24

6n / 5 = 24

6n = 24 × 5

6n = 120

n = 120 / 6

n = 20

Answer:

B on edg, n=20

Step-by-step explanation:

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

The answer would be y = 5x + 3

Step-by-step explanation:

Statistically significant linear relationship between the independent variables (study hours and GPA) and the dependent variable (ACT score), and the multiple regression equation can be used to predict the ACT score based on the hours studied and the student's GPA.

In this scenario, the dependent variable is the ACT score, while the independent variables are the number of hours spent studying (x1) and the student's GPA (x2).

To find the p-value for the regression equation, we can use a statistical software or calculator to perform a multiple linear regression analysis. The p-value represents the probability that the observed relationship between the independent and dependent variables is due to chance.

Assuming that we have performed the analysis and obtained the results, we can say that the p-value is less than 0.01 (since the level of significance is set at 0.01). This suggests that there is a statistically significant linear relationship between the independent variables (study hours and GPA) and the dependent variable (ACT score).

To identify the multiple regression equation that best fits the data, we can look at the coefficients for each independent variable. These coefficients represent the change in the dependent variable (ACT score) for every one unit increase in the independent variable, holding all other variables constant.

Based on the given data, we can write the multiple regression equation as:

ACT score = b0 + b1(hours studied) + b2(GPA)

where b0 is the intercept, b1 is the coefficient for hours studied, and b2 is the coefficient for GPA.

Using the regression analysis results, we can plug in the values of the coefficients to obtain the specific equation that fits the data.

Overall, we can conclude that there is a statistically significant linear relationship between the independent variables (study hours and GPA) and the dependent variable (ACT score), and the multiple regression equation can be used to predict the ACT score based on the hours studied and the student's GPA.

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Answer:

8 Hours

Step-by-step explanation:

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

\(\frac{220}{5}x=352\)

Multiply both sides by 5

\(220x=1760\)

Divide both sides by 220

\(x=8\)

Therefore it would take 8 hours.

8 Hours long would it take to travel 352 miles,

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

Multiply both sides by 5

Divide both sides by 220

Hence, it would take 8 hours.

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The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set.

When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.The horizontal axis represents one variable while the vertical axis represents the other. Each point on the graph represents one set of data that corresponds to both variables, with the x-value and y-value corresponding to the respective data points being plotted.Scatterplot versus: A scatter plot has two axes that correspond to two variables. In a scatter plot, we can determine how one variable changes as the other variable changes. The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set. When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.

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Answer:

4 3/10

Step-by-step explanation:

I hope this helps you out!

Answer:

the answer is 104/21  or 4 20/21

Step-by-step explanation:

Answer:

330 seconds.

Step-by-step explanation:

32 are made in 60 seconds

1   ..  ...     ..          60/32  ..

So 176 are made in (60/32) * 176 = 330 seconds.

Answer:

C x = 119

Step-by-step explanation:

> greater than

< less than

119 > 111

a) The probability that in the next eight tries, the number of free throws he will make exactly 8 is equals to the 0.27249.

b) The probability that in the next eight tries, the number of free throws he will make exactly 5 is equals to the 0.08386.

We have a professional basketball player makes 80% of the free throws he tries.

let X be the number of free throws he will make in the next 8 tries. He makes 80% of the free thwors he tries. So, for binomial distribution, X~Bin(8,0.80)

so the probability mass function of X is P[X =x] = ⁸Cₓ 0.85ˣ (1-0.85)⁽⁸⁻ˣ⁾, x = 0,1, 2,..8

P[ X = x] = 0 otherwise.

a) So, the probability that he makes exactly 8 throws isP,(X=8)

= ⁸C₈(0.85)⁸ (1- 0.85)⁰

=0.27249

b) the probability that he makes exactly 5 throws is, P[X=5]

=⁸C₅0.855(1-0.85)⁽⁸⁻³⁾=56×0.855×0.153

=0.08386

Hence required probability is 0.083.

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Answer:

dhdhrjfidgegehfr fhfn fhc fn dncc c. f byn

Step-by-step explanation:

h(t) = -16t² + 64t + 32

When h(t) = 80, -16t² + 64t + 32 = 80.

=> 16t² - 64t + 48 = 0

=> t² - 4t + 3 = 0

=> (t - 1)(t - 3) = 0

=> t = 1 or t = 3.

Hence the difference between the times is 2 seconds. (B)

Answer:

sas

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

SAS

This report provides a construction sequence for two components of a project: a civil laboratory and a garage. The construction sequence outlines the step-by-step process for each component, highlighting the key activities and their respective order.

1) Civil Laboratory Construction Sequence:

Step 1: Site Preparation and Excavation

- Clear the site and mark the boundaries for the laboratory building.

- Excavate the foundation area according to the approved design and engineering specifications.

Step 2: Foundation Construction

- Construct the foundation by pouring concrete into the excavated area.

- Install necessary reinforcement and formwork as per the structural design.

Step 3: Structural Framework

- Erect the structural steel framework or build the load-bearing masonry walls.

- Install the floor slabs, beams, and columns based on the architectural and engineering plans.

Step 4: Roofing and Enclosure

- Install the roofing system, such as metal sheets or reinforced concrete slabs, ensuring proper insulation and weatherproofing.

- Construct exterior walls, windows, and doors to enclose the laboratory building.

Step 5: Interior Construction

- Install electrical, plumbing, and HVAC systems as per the laboratory requirements.

- Build interior walls, partitions, and ceilings.

- Apply finishes, such as flooring, painting, and tiling.

- Install laboratory-specific equipment and fixtures.

Step 6: Testing and Commissioning

- Conduct thorough testing and inspection of all installed systems and equipment.

- Address any deficiencies or issues identified during the testing phase.

- Obtain necessary certifications and approvals for the civil laboratory.

2) Garage Construction Sequence:

Step 1: Site Preparation and Excavation

- Excavate the area for the garage foundation and any required utility lines.

Step 2: Foundation Construction

- Pour concrete for the garage foundation, considering the design requirements and load-bearing capacity.

- Install reinforcement and formwork to ensure structural integrity.

Step 3: Structural Construction

- Build the structural framework, including columns, beams, and slabs, using reinforced concrete or steel.

- Install precast concrete elements, if applicable.

Step 4: Wall and Roof Construction

- Construct exterior and interior walls using brick, concrete blocks, or other suitable materials.

- Install roofing materials, ensuring proper insulation and waterproofing.

Step 5: Finishes and Services

- Install electrical and lighting systems, plumbing fixtures, and ventilation for the garage.

- Apply finishes to the walls, floors, and ceilings.

- Paint, tile, or apply any other desired finishes.

Step 6: Garage Equipment and Access

- Install garage-specific equipment, such as car lifts, storage systems, and vehicle access doors.

- Ensure proper functionality and safety of all installed equipment.

Step 7: Testing and Commissioning

- Test all systems, equipment, and safety features within the garage.

- Address any identified issues or deficiencies.

- Obtain necessary certifications and approvals for the garage.

The construction sequence for the civil laboratory and garage involves a series of steps, starting from site preparation and excavation, progressing through foundation construction, structural framework, enclosure, interior finishes, and installation of specific equipment and systems.

Following a well-defined construction, sequence ensures that the project progresses smoothly, adheres to safety and quality standards, and achieves the desired functionality and aesthetics. It is crucial to collaborate closely with architects, engineers, and contractors to ensure the successful completion of both the civil laboratory and the garage, meeting the project's objectives and requirements.

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Answer:

Step-by-step explanation:

Answer is 65 simple

The annual maintenance cost for the equipment is Php 80,000 and the capitalized cost is Php 5,400,000.

Formula:

Capitalized cost = Equipment cost - Salvage value

Annual maintenance cost = Total maintenance cost / Period of depreciation

Annual maintenance cost = (Lump sum for maintenance) / Period of depreciation

Step-by-step solution:

\(Capitalized cost = Php 6,000,000 - Php 600,000\)

= Php 5,400,000

Annual maintenance cost = Php 400,000 / 5 years

= Php 80,000

Therefore, the annual maintenance cost for the equipment is Php 80,000 and the capitalized cost is Php 5,400,000.

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