2, 6, 18, 54. 162,...
The first five terms of a geometric sequence are given above.

Write a recursive function rule for the sequence.

a
f\left(n\right)=3f\left(n\right)+2

b
f\left(n\right)=2n

c
f\left(n\right)=3f\left(n-1\right),\ n1=2

d
f\left(n\right)=3n+2

The energy required to change 71.8 g of liquid water at 25.7 °C to ice at 16.1 °C is approximately -2,513.06 kJ.

To calculate the energy in the form of heat required for this phase change, we need to consider three main steps: heating the liquid water from its initial temperature to its boiling point, vaporizing the water at its boiling point, and cooling the resulting steam to the final temperature of ice.

First, we calculate the energy required to heat the liquid water from 25.7 °C to its boiling point (100 °C). Using the specific heat capacity of liquid water (4.184 J/g·K), we find that the energy required is (71.8 g) × (4.184 J/g·K) × (100 °C - 25.7 °C).

Next, we calculate the energy required for vaporization. The heat of vaporization of water is given as 2256 J/g. Therefore, the energy required is (71.8 g) × (2256 J/g).

Finally, we calculate the energy released when the steam cools down to the final temperature of ice at 16.1 °C. Using the specific heat capacity of ice (2.06 J/g·K), we find that the energy released is (71.8 g) × (2.06 J/g·K) × (100 °C - 16.1 °C).

By summing up these three energy values, we find the total energy required for the phase change from liquid water to ice.

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Answer:

1.) The two numbers are 36 and 6.

2.) 42cm + 20cm = 62cm

3.) 3km/hr = rate of current

4.) Each cost 0.79 cents

5.) Mixed is 16 lbs

Blended is 28 lbs

Step-by-step explanation:

Answer:

1.  16 ft

\(\sf 2.\quad \dfrac{29}{99}\)

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given:

Substitute the given area into the formula and solve for s:

\(\sf \implies 256=s^2\)

\(\sf \implies \sqrt{256}=\sqrt{s^2}\)

\(\sf \implies s=\pm 16\)

As distance is positive, the length of one side of Keisha's kitchen is 16 ft.

Converting a recurring decimal to a fraction

Let x equal the recurring decimal:

\(\implies \sf x=0.292929...\)

Create another number with recurring 29s by multiplying the above by 100:

\(\implies \sf 100x=29.292929...\)

To solve these two equations and write x as a fraction, subtract the first equation from the second to remove all the recurring digits after the decimal point:

\(\begin{array}{r r c l}& \sf 100x &= &\sf 29.292929...\\- & \sf x&=& \sf \phantom{..}0.292929...\\\cline{1-4} & \sf 99x&=& \sf29\\\cline{1-4}\end{array}\)

Therefore:

\(\implies \sf 99x=29\)

\(\implies \sf x=\dfrac{29}{99}\)

Therefore:

\(\sf \implies 0.\overline{29}=\dfrac{29}{99}\)

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The expression is already in decimal form.

0

3×10^9

Answer: The input force (effort) on the rope is 20 N.

Step-by-step explanation:

In a frictionless pulley system, the tension in the rope is constant throughout. Therefore, the force applied to the rope on one side of the pulley system is equal to the force exerted on the other side of the system.

In this problem, we know that the weight of the block is 20 N. This means that there is a force of 20 N acting downwards on one side of the pulley system.

Since the pulley system is frictionless, the tension in the rope is also 20 N. Therefore, the force applied to the rope on the other side of the pulley system (i.e., the input force or effort) must also be 20 N in order to balance the weight of the block.

So the input force (effort) on the rope is also 20 N.

Answer:

1000

Step-by-step explanation:

Answer:

1 meter = 1000 Millimeter

Step-by-step explanation:

The radius of the cylindrical container with a volume and height of 125.7cm³ and 10cm is 2cm.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

To determine the radius of the cylindrical container, plug the given values into the formula above and solve for r.

V = π × r² × h

r² = V / ( π × h )

r² = 125.7cm³ / ( 3.14 × 10cm )

r² = 125.7cm³ / ( 31.4cm )

r = √( 125.7/31.4 cm² )

r = 2cm

Therefore, the radius of the container is 2 centimeters.

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The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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The three roots of 125i are:

To find these roots, we can use de Moivre's identity. The de Moivre's identity states that for any complex number z and any integer n, we have:

\(z^n\) = (r * e^{iθ})^n = r^n * e^{inθ}

where r is the absolute value of z and θ is the angle of z.

In our case, we have z = 125i and n = 3. So, we have:

\(z^3\) = \((125i)^3 = (5 * i)^3 = 125i^3\)

Using de Moivre's identity, we can write this as:

\(125i^3\) = 5^3 * e^{3iθ} = 125 * e^{i(3π/2)} = -125i

Therefore, the three roots of 125i are the three cube roots of -125i. We can find these roots using the following formula:

z = r * e^{iθ/3}

where r is the cube root of 125 and θ is the angle of -125i.

The cube root of 125 is 5.

The angle of -125i is π/2.

So, the three roots of 125i are:

\(z_1\) = 5 * e^{iπ/6} = 5(12+i√32)

\(z_2\) = 5 * e^{i5π/6} = -5

\(z_3\) = 5 * e^{i9π/6} = 5(12-i√32)

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Answer:

91°

Step-by-step explanation:

We are given the equation:

y=6.88x - 199

The number of visitors at a pool = y = 426 visitors

The air temperature in degrees

Fahrenheit, x. = ??

Hence,

426= 6.88x - 199

6.88x = 426 + 199

6.88x = 625

x = 625 / 6.88

= 90.843023256°

The expected air temperature on that day, approximately to the nearest degree = 91°

Answer: Is 91 degrees Fahrenheit

The answer for The equation

y

=

6.88

x

−

199

models the number of visitors at a pool, y, and the air temperature in degrees Fahrenheit, x.

There are 426 visitors at the pool during one hot day.

What is the expected air temperature on that day? Round your answer to the nearest degree.

Step-by-step explanation:

Answer:

Step-by-step explanation:

So what’s the question

Answer:

yea?

Step-by-step explanation:

Two-person, non-zero sum games can have a single unique Nash equilibrium in pure strategy, such as the Prisoner's Dilemma, or multiple Nash equilibria in pure strategy, like the Battle of the Sexes.

Example of a two-person, non-zero sum game with a single unique Nash equilibrium in pure strategy:

Prisoner's Dilemma:

Player 1 options: Cooperate (C) or Defect (D)

Player 2 options: Cooperate (C) or Defect (D)

        | Player 2 Cooperate | Player 2 Defect |

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

Player 1 |      (-1, -1)      |    (-3, 0)     |

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

Player 2 |       (0, -3)      |    (-2, -2)    |

In this game, both players have a dominant strategy to defect (D) regardless of the other player's action. The Nash equilibrium is (D, D) since neither player can unilaterally deviate to improve their payoff.

Example of a two-person, non-zero sum game with multiple Nash equilibria in pure strategy:

Battle of the Sexes:

Player 1 options: Opera (O) or Football (F)

Player 2 options: Opera (O) or Football (F)

        | Player 2 Opera | Player 2 Football |

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

Player 1 |    (2, 1)     |      (0, 0)      |

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

Player 2 |    (0, 0)     |      (1, 2)      |

In this game, there are two pure strategy Nash equilibria: (O, O) and (F, F). Each player prefers a different outcome, but both players agree on their preferred action at each Nash equilibrium.

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Answer:

381.51 in^3

Step-by-step explanation:

Volume of a sphere = 4/3 x pi x r^3

r = 9/2 = 4.5

4/3 x 3.14 x 4.5^3 = 381.51 in^3

The rate of each plane is,

First plane = 110 mph

Second plane = 15 mph

Let x = rate of the slower plane (First plane!)

x + 45 = rate of the faster plane (Second plane!)

The planes fly for 3 hours, where Distance = RT

Distance between the planes = SUM of the distances.

RT + RT= 795 miles

3x + 3(x + 45) = 795

3x + 3x + 135 = 795

6x + 135 = 795

6x = 795 - 135

6x = 660

x = 110 mph First plane

And, x + 45 = 110 + 45 = 15 mph Second plane.

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer:

If I rounded to the hundreths place, the answer would be 0.92%.

Step-by-step explanation:

The measure of the angles are 28 and 152  degrees respectively

Lines and angles

An angle is the point where two lines meet. From the given lines, we will take the sum of the angles and equate to 180 degrees.

x + 2 + 4x - 132 = 0

Collect the like terms

5x - 130 = 0

Add 130 to both sides

5x - 130 + 130 = 0 + 130

5x = 130

x = 130/5

x = 26

Find the measured angles

A = x + 2 = 28 degrees

B = 4x - 122 = 152 degrees

Hence the measure of the angles are 28 and 152  degrees respectively

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a) The probability of finding oil is 0.70, or 70%.

b) The new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is  1.00 or 100% .

(a) The probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, since both of these outcomes are considered positive for the oil company:

P(find oil) = P(high-quality oil) + P(medium-quality oil) = 0.50 + 0.20 = 0.70

Therefore, the probability of finding oil is 0.70, or 70%.

(b) To interpret the soil test, we can use Bayes' theorem:

P(Ai | S) = P(S | Ai) * P(Ai) / P(S)

where P(Ai | S) is the updated probability of finding oil given the soil test, P(S | Ai) is the probability of observing the soil test result given that there is oil of the corresponding quality, P(Ai) is the prior probability of finding oil of the corresponding quality, and P(S) is the probability of observing the soil test result regardless of the presence of oil.

Using the given probabilities, we can calculate:

P(S) = P(high-quality oil) * P(S | high-quality oil) + P(medium-quality oil) * P(S | medium-quality oil) + P(no oil) * P(S | no oil)

= 0.50 * 0.20 + 0.20 * 0.80 + 0.30 * 0.20

= 0.26

Now we can calculate the updated probabilities for each quality of oil:

P(high-quality oil | S) = P(S | high-quality oil) * P(high-quality oil) / P(S)

= 0.20 * 0.50 / 0.26

= 0.3846 or 0.38 (rounded to two decimal places)

P(medium-quality oil | S) = P(S | medium-quality oil) * P(medium-quality oil) / P(S)

= 0.80 * 0.20 / 0.26

= 0.6154 or 0.62 (rounded to two decimal places)

P(no oil | S) = P(S | no oil) * P(no oil) / P(S)

= 0.20 * 0.30 / 0.26

= 0.2308 or 0.23 (rounded to two decimal places)

The oil company should interpret the soil test as providing evidence for the presence of medium-quality oil, since the updated probability for this outcome is higher than the updated probability for high-quality oil. The revised probabilities for finding oil are:

P(find high-quality oil | S) = P(high-quality oil | S) = 0.38

P(find medium-quality oil | S) = P(medium-quality oil | S) = 0.62

P(find no oil | S) = P(no oil | S) = 0.23

Therefore, the new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is:

P(find oil | S) = P(find high-quality oil | S) + P(find medium-quality oil | S)

= 0.38 + 0.62

= 1.00 or 100% (rounded to two decimal places)

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Answer:

numerator - the number above the fraction line; tells how many parts of the whole exist

mixed number - a number with an integer part and a fraction part

denominator - the number under the fraction line; tells how many equal parts the whole was broken into

common fraction - a fraction with a whole number for the numerator and a whole number other than zero for the denominator

like denominators - two fractions with the same denominator

improper fraction - a fraction in which the numerator is larger than the denominator

Let:

x = duration of each call

y = cost of the call

Since the cost of the call and the length of the call are related. we can model the situation as a linear equation of the form:

a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86, so:

Let:

Using elimination method:

Replace the value of m into (1):

Therefore, the cost as a function of time is:

We would need to increase the sample size to at least 27 or use a smaller confidence level to achieve a margin of error of $150 or less.

To calculate the 90% confidence interval of the average cost per person for car crashes in Tampa, we can use the formula:

where x is the sample mean, Zα/2 is the critical value of the standard normal distribution corresponding to a 90% confidence level (which is 1.645), σ is the population standard deviation, and n is the sample size.

Plugging in the given values, we get:

CI =\($1900 ± 1.645 * $500/√50\)

= $1900 ± $146.21

= ($1753.79, $2046.21)

Therefore, the 90% confidence interval for the average cost per person for car crashes in Tampa is between $1753.79 and $2046.21.

If the study required a margin of error of $150 or less, we need to adjust the sample size or confidence level. Since the margin of error is inversely proportional to the square root of the sample size, we can use the formula:

n = \((Zα/2 * σ/E)²\)

where E is the desired margin of error ($150) and all other variables are the same as before.

Plugging in the values, we get:

n = \((1.645 * $500/$150)²\)

= 26.18

Therefore, we would need to increase the sample size to at least 27 or use a smaller confidence level to achieve a margin of error of $150 or less.

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The possible value of ∠Y to the nearest tenth of a degrees in triangle WXY is 85.1 degrees.

Let's find angle Y using sine rule,

Hence,

x / sin X = y / sin Y

where

8.5 / sin 100° = 8.6 / sin Y

cross multiply

8.5 sin Y = 8.6 sin 100°

sin Y = 8.6 sin 100° / 8.5

sin Y = 8.4693466759 / 8.5

Y = sin ⁻¹ 0.99639372657

Y = 85.1325941735

∠Y = 85.1°

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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Answer:

0

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

1 + 1/0 = x

-1  

1/0 = x

x0

1 = x

Backwards PEMDAS where each thing you do backwards cancles itself out.

Answer:

37.68 centimeters

Step-by-step explanation:

The circumference of a circle can be found by using the formula πd, where d = diameter. We're given the diameter as 12 centimeters, and we're going to use 3.14 for pi.

Therefore, the answer is 37.68 cm.

Have a lovely rest of your day/night, and good luck w/ your assignments! (‾◡◝)

Answer:

1/4

Step-by-step explanation:

25 people took a vitamin and still got the flu and the total number is 100 so the fraction is 25/100 which can be reduce to 1/4

The P(took a vitamin | got the flu) will be 1/4.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Here, the table below shows one doctor's patients who got the flu and whether or not they took a vitamin each day.

We need to find the P(took a vitamin | got the flu).

Now, 25 people took a vitamin and still got the flu.

The total number is 100.

So, the fraction is 25/100 which can be reduce to 1/4.

P(took a vitamin | got the flu) = 25/100

P(took a vitamin | got the flu) = 1/4

Therefore, the P(took a vitamin | got the flu) will be 1/4.

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