find the 12th term of the geometric sequence
4,12,36,108

Using Pythagorean theorem, the volume of the cylinder is 201.1 cubic units

To determine the volume of the cylinder, we have to find the height of the cylinder.

using Pythagoras theorem, we can find the height of the cylinder.

13² = 5² + x²

x² = 13² - 5²

x² = 144

x = √144

x = 12 units

The volume of a cylinder is given as

V = 1/3 πr²h

v = 1/3 * 3.14 * 4² * 12

v = 64π cubic units

v = 201.1 cubic units

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The conjugate of the complex number z = 12 + i is [tex]\hat{z}=12-i[/tex]

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Complex number are in the form a + bi, where a is the real part and b is the imaginary part. Both a and b are real numbers

The conjugate of a complex number z = a + bi is [tex]\hat{z}=a-ib[/tex]

Given that z = 12 + i

The conjugate of z is [tex]\hat{z}=12-i[/tex]

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6x + 5 + ( -2 )/( x + 7 ), The expression can be written as the quotient of 6x + 5 divided by x + 7, plus the remainder of -2, all divided by the divisor of x + 7.

To calculate (6x+5)/(x+7), first we must add x to both the numerator and the denominator to get (6x+x+5)/(x+7+x), which simplifies to (7x+5)/(2x+7). Then, divide the numerator by the denominator to get (7x+5)/(2x+7) = 3.5x + 2.5. To find the remainder, subtract 3.5x and 2.5 from both the numerator and denominator, which gives us (7x+5)-(3.5x+2.5) = 3.5x + 2.5 - (3.5x + 2.5) = 3.5x - 2.5. Lastly, divide the remainder by the divisor (2x+7) to get (3.5x-2.5)/(2x+7). Therefore, the answer is 3.5x + 2.5 + (3.5x - 2.5)/(2x+7).

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Answer:    -48y+6x+40

Step-by-step explanation: when you multiply two minuses that is +.

It is important to carefully select the survey population and explain why the survey is necessary. It is also important to limit the number of questions and ask them in a clear and concise manner.

Select the survey population carefully: This means selecting a group of people who are representative of the target population and have the relevant knowledge or experience to answer the survey questions. For example, if the survey is about customer satisfaction with a product, the survey population should be customers who have used the product.

Limit the number of questions: It's important to keep the survey short and focused to reduce the risk of respondent fatigue and increase the response rate. A shorter survey also makes it easier to analyze the data.

Explain why the survey is necessary: This helps to increase the response rate by providing a clear explanation of why the survey is being conducted, what the data will be used for, and how it will benefit the target population.

Select the survey population randomly: Random selection helps to ensure that the survey results are representative of the target population and minimize the risk of bias in the sample.

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what tips can you share with the group? check all that apply.

The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.

What is multiplication ?

Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.

To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.

The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:

10 years x 12 months/year x 1,000 units/month = 120,000 units

The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:

$50,000 ÷ 120,000 units = $0.4167 per unit

Rounding this to the nearest penny gives us the final answer of:

$0.42 per unit (option a)

Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.

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An equation that represents the relationship is y = 0.01x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios. Also, it passes through the origin (0, 0) and it can be modeled by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 1/90

Constant of proportionality, k = 0.01.

Therefore, the required equation is given by:

y = kx

y = 0.01x

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the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.

What is probability?

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities are usually expressed as fractions, decimals, or percentages.

The total weight of 35 men in the elevator can be modeled by the sum of 35 independent and identically distributed normal random variables with mean 174 lbs and standard deviation 29 lbs. Let X be the weight of one man, then the total weight of 35 men is W = 35X.

The mean of W is:

μW = E(W) = E(35X) = 35 E(X) = 35 * 174 = 6090 lbs

The variance of W is:

Var(W) = Var(35X) = 35^2 Var(X) = 35^2 * 29^2 = 899150

The standard deviation of W is:

σW = sqrt(Var(W)) = sqrt(899150) = 947.85

To find the average weight beyond which the elevator would be considered overloaded, we need to find the weight that corresponds to the 95th percentile of the distribution of W, since the elevator is overloaded if the total weight is in excess of 6475 lbs.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 95th percentile: z = 1.645 (rounded to 3 decimal places).

We can then find the weight w that corresponds to this z-score:

w = μW + z * σW

w = 6090 + 1.645 * 947.85

w ≈ 7616.56

Therefore, the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.

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Answer:

A. 2(4a^3 - 49a)

In this case, you would simply multiply the numbers and leave the a value and exponents alone.

B. 2a(4a^2 - 49)

First, you would distribute(multiply) 2 with the numbers inside the parentheses just like you did for answer A. Then, you would distribute a with the other a values inside the parentheses, you would add this values instead of multiplying it.

F. 2a(2a - 7)(2a + 7)

You would distribute 2a inside the FIRST set of parentheses just like you did before. Then multiply that set of parentheses with the other set of parentheses.

Step-by-step explanation:

Therefοre , the sοlutiοn οf the given prοblem οf percentage cοmes οut tο be  a)k ≈ 0.0279,b)y = 0.593a  and  c)t ≈ 78.5 .

In statistics, a percentage is a figure οr an integer that is expressed as a fractiοn οf 100. Additiοnally, the wοrds "pct.," "pct," but alsο "pc" are rarely used. The "%" symbοl, hοwever, is cοmmοnly used tο denοte it. There are nο dimensiοns; the percentage tοtal is flat.

Percentages are really just numbers because the numeratοr is 100. Tο indicate that a number is a percentage, either the percent character (%) οr the text "percent" must appear befοre it.

Here,

a) We can apply the exponential decline equation:

=> [tex]y = ae^{(-kt)} (-kt)[/tex]

[tex]0.9a = ae^{(-5k)} (-5k)[/tex]

Using a to divide both sides:

[tex]0.9 = e^{(-5k)} (-5k)[/tex]

Using both sides' natural logarithms:

ln(0.9) = -5k

calculating k:

[tex]k = -ln(0.9)/5[/tex]

k ≈ 0.0279

Consequently, the decline formula's value of k is roughly 0.0279.

b)

[tex]y = ae^{(-kt)} (-kt)[/tex]

[tex]y = an e^{(-0.0279*10)[/tex]

[tex]y = 0.593a[/tex]

As a result, after 10 years, only about 59.3% of the initial DDT is still present.

c)

[tex]0.25a = ae^{(-0.0279t) (-0.0279t)[/tex]

Using a to divide both sides:

[tex]0.25 = e^{(-0.0279t) (-0.0279t)[/tex]

Using both sides' natural logarithms:

ln(0.25) = -0.0279t

calculating t:

t = -ln(0.25)/0.0279

t ≈ 78.5

Therefore, roughly 78.5 years after the ban in 1972, or in the year 2050, the concentration of DDT will drop below 25%.

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There is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes.

The Central Limit Theorem, which asserts that group means of a large sample size from every population, irrespective of its distribution, will be roughly distributed normally with an average equal to the inhabitants imply and a variance equal to the standard deviation of the population multiplied by the square root of the random sample, must be used to solve this problem.

As a result, there is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes. When n is the sample size, x is the sample mean, is the population mean, and seems to be the population standard deviation.

In this instance, n = 12 eggs, x = 68 grammes, = 65 grammes, = 5 grammes. When these values are added to the formula, you obtain:[tex]z = (68 - 65) / (5 / √12) = 1.385[/tex]

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3a, 0 ) and (x₂, y₂ ) = (0, 3b )

m = [tex]\frac{3b-0}{0-3a}[/tex] = [tex]\frac{3b}{-3a}[/tex] = - [tex]\frac{b}{a}[/tex]

the line crosses the y- axis at (0, 3b ) ⇒ c = 3b

y = - [tex]\frac{b}{a}[/tex] x + 3b ← equation of line

to show that (a, 2b ) lies on the line , substitute x = a into the equation and if y = 2b then the point lies on the line

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

then the line passes through the point (a, 2b )

We locate the [tex](5x+4)(x+7)[/tex] in order to solve this trinomial problem.

The quadratic trinomial formula inside one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero. If b2 - 4ac > 0, we're able to factor a quadratic trinomial for any value of a, b, and c. It denotes that, where h and k are real values,

A single-term expression is referred to as a monomial, a two-term expression as a factorial, and a three-term expression as a trinomial. a phrase that contains more than three terms is identified only by the quantity of its terms.

Given,  [tex]5 x^{2} + 4 x + 35 x + 28[/tex]

Regroup terms into two proportional parts [tex](5 x^{2} + 4 x) + (35 x + 28)[/tex]

Factor Greatest Common Factors out [tex]x (5 x + 4) + 7 (5 x + 4)[/tex]

Factor Greatest Common Factors out [tex](5 x + 4) (x + 7)[/tex]

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Answer:

a. i dk how to do this qn

b. cot (cos^-1(a))

let cos^-1(a) = θ

implies, cosθ = a

from the figure, cotθ = [tex]\frac{x}{\sqrt{1 -x^{2} } }[/tex]

pls mrk me brainliest

f(t) = t3 − 8t2 + 25t + 10. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

This equation represents a law of motion, where t is measured in seconds and s in feet. This equation can be broken down into 3 parts; t3, -8t2 and 25t + 10. The t3 part of the equation represents a cubic function, which is usually associated with acceleration. The -8t2 part is a quadratic function, which is typically associated with velocity. Finally, the 25t + 10 is a linear function, which is usually associated with displacement. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

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Answer:

b = 6

Step-by-step explanation:

step one: Simplify 10^2 to 100

Step two: Simplify 8^2 to 64

Step three: Subtract 64 from both sides

Step four: Simplify 100 - 64 to 36

Step Five: Take the square root of both sides

Step Six: Since 6*6=36, the square root of 36 is 6

Step Seven: Switch sides b = positive 6

I hoped this helped

To get distance we use formula derived in Question 15, which gives an approximation of the circumference of the wheel based on its diameter which is 471.24nft

[tex]C = \pi d[/tex]

where d: diameter and C: circumference.

With the diameter of 150 feet provided, we can calculate the wheel's circumference as follows:

[tex]C = π(150) = 471.24 ft[/tex]

For our issue, let's define some variables:

n: the number of times the Ferris wheel has rotated

d: the Ferris wheel's circumference

C: the Ferris wheel's circumference

S: the total distance a passenger travels

Given that a passenger travels one circumference every spin, the overall distance after n rotations is roughly equal to:

S ≈ nC

In place of our values, we obtain:

[tex]S = n(471.24) = 471.24n ft[/tex]

So, assuming the Ferris wheel has a 150-foot diameter, we may use the equation S 471.24n to roughly calculate the total distance a passenger would have travelled in ferris wheel spins. However keep in mind that this is just a rough estimate, and it might not be completely correct depending on things like the size of the carriage and the height of the passenger above the ground.

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The value of x for which PQ and RS are parallel, is 83°.

The two parallel lines PQ and RS are stretched from Q to M and S to N, respectively, in the accompanying figure.

In addition, a line from T to O is drawn parallel to PQ and RS.

Now, in the illustration,

∠MPT = 180° -  135°

∠MPT = 45°

The parallel lines MQ and OT are divided by the transversal line PT.

∠MPT = ∠PTO = 45°

∠TRN = 180° - 142°

∠TRN = 38°

A transversal line TR splits the parallel lines NS and OT.

Then, ∠TRN  = ∠OTR = 38°

∠PTO + ∠OTR = x

x = 45° + 38°

x = 83°

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Hi,

The correct answer should be "CE" and "CB" I just had the same question so my answer should be correct.

I hope that this helped you. :)

To determine the zeros of f(x) and state the multiplicity of each zero, the following steps should be followed:

Step 1: Determine the roots of the polynomial

To solve for the roots of f(x), use the quadratic formula. f(x) = x⁴ + 12x² - 64

a = 1, b = 12, c = -64

Using the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

x = (-12 ± √(12² - 4(1)(-64))) / 2(1)

x = (-12 ± √400) / 2

x = (-12 ± 20) / 2

x₁ = -16

x₂ = 4

x₃ = x₄ = 0

Step 2: State the multiplicity of each zero

After determining the roots of f(x), determine the multiplicity of each root by using the concept of multiplicity. A root has a multiplicity of p if and only if f(x) has a factor of (x - r)ᵖ.

From the quadratic equation above, we have:

x₁ = -16 (multiplicity 1)

x₂ = 4 (multiplicity 1)

x₃ = x₄ = 0 (multiplicity 2)

Therefore, the zeros of f(x) and their multiplicities are: x = -16 (multiplicity 1), x = 4 (multiplicity 1), and x = 0 (multiplicity 2).

The final answer is as follows:

x = -16 with multiplicity 1

x = 0 with multiplicity 2

x = 4 with multiplicity 1.

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The relationship between distance traveled, in miles, d, and driving time, in hours, t. The Equation is 60 miles × 10 hours = 1023 miles

Distance:

Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought,  the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects or some degree of separation.

Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.

According to the Question:

total distance (one way): 1,023 miles

average driving speed: 60 miles per hour

driving time on first day: 10 hours.

Now,

Average driving speed = 60 miles per hour

Driving time on first day = 10 hours.

Total distance on first day = 60 miles × 10 hours

                                           = 600 miles/ Hour.

and,

The relationship obtained from the Given equation is:

60 miles + 10 hours = 1023 miles

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Answer:  pic please so i know some more info thanks

Step-by-step explanation: pic please so i know some more info thanks

The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies.

The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies. If the galaxies are in a spiral elipse, then the tangential velocity of the galaxies may be different, and this could affect the probability of a collision. However, without knowing more information about the galaxies, it is impossible to accurately calculate the probability of a collision.

If the galaxies are in a spiral elipse, then it is important to consider the tangential velocity of the galaxies, as this could affect the probability of a collision. Additionally, the relative angular momentum of the galaxies, their proximity to one another, and their respective trajectories also play a role. Without knowing more information about the galaxies, such as their exact positions, velocities, and masses, it is impossible to accurately calculate the probability of a collision.

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The mark price of the shoes is Php 1250.

Mark price (MP) refers to the original or listed price of a product or service before any discounts, promotions or markdowns are applied. It is the price that a retailer sets for a product with the intention of making a profit.

Since Sarah bought the shoes at a sale of 20%, she paid only 80% of the mark price. This can be expressed as:

80% of MP = Php 1000

0.8MP = Php 1000

To find MP, we need to divide both sides by 0.8:

MP = Php 1000 / 0.8

MP = Php 1250

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Answer:

x = y = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

the triangle is a 90- 45- 45 isosceles triangle with congruent legs, that is

x = y

using Pythagoras' identity in the right triangle

x² + y² = (2[tex]\sqrt{6}[/tex] )² , that is

x² + x² = 24

2x² = 24 ( divide both sides by 2 )

x² = 12 ( take square root of both sides )

x = [tex]\sqrt{12}[/tex] = [tex]\sqrt{4(3)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]

then

x = y = 2[tex]\sqrt{3}[/tex]

The price per unit is equal to R2.29 per unit.

Generally speaking, a unit price is sometimes referred to as price per unit or unit rate and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In this scenario, we would determine the unit price for number of unit of electricity by using the following mathematical expression;

Unit price = Cost of electricity/Number of units

Substituting the given parameters into the unit price formula, we have the following;

Unit price = R350/152.84

Unit price = R2.29 per unit.

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Therefore , the solution of the given problem of circle comes out to be 110°

is the angle 1.

Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."

Here,

Given :

To find: the angle of 1

So,

From  the diagram , we can see it is showing 110 degree

So ,

Angle 1 comes out to be 110°

So, rest of circle angle is = 360° - 110° = 250°

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B. Probability that the biscuit is made by machine and is not broken is:

1-(25% × 2%)

= 50%

c. The probability of breakage: 2% + 3% + 5% = 10%

d. Probability that biscuit is not made by machine = 1-5% = 95%

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. About an event's outcome, we might be certain or uncertain.

When this occurs, we state that there is a possibility that the event will occur. In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence.

Now from the question,

The probability that the biscuit is made by machine and not broken:

1 - 25% × 2%

= 50%

Now not broken probability = 1- 25% × 2%

Now next, the probability of breakage: 2% + 3% + 5% = 10%

Finally, the probability that biscuit is not made by machine = 1-5% = 95%

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