PLEASE HELP!! Puzzle One
Determine the volume of the following cylinders with the given dimensions. To break the code, substitute your answers in for the correct letters. Make sure to follow the order of operations! Round your answers to the hundredth place. Use 3.14 for an approximation for pi.

It has been proved from the given equation that (2 + -7 + 2 = -3)

A rational equation is defined as an equation that containins at least one fraction whose numerator and denominator are polynomials. These fractions may be on one or both sides of the equation.

Now, we are given the rational expression as:

√(2 + -7 + 2 = -3)

In order words, we want to prove that:

(2 + -7 + 2 = -3)

The left hand side, when we multiply + and - sign, we have negative sign and as such we will have:

2 - 7 + 2

= 4 - 7

= -3

This is same as the right hand side of the original equation

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The formula for the volume of a cylinder is [tex]r^{2}[/tex]h, where r is the radius and h is the height. To solve for h, h = r + 3, and to find the total surface area, lateral surface area = 2rh, top and bottom areas = 2[tex]r^{2}[/tex], and total surface area = 826.59 [tex]cm^{2}[/tex].

Let's calculate for the radius and height using the cylinder's volume formula:

Volume = π[tex]r^2h[/tex], where r is the radius and h is the height.

We have Volume = 1540 [tex]cm^3[/tex], so we can write:

1540 = π[tex]r^2h[/tex]

Also, we know that the difference between the height and radius is 3 cm:

h - r = 3

We can solve for h in terms of r by rearranging the above equation:

h = r + 3

Now we can substitute this into the formula for volume:

1540 = π[tex]r^2(r + 3)[/tex]

Simplifying and solving for r:

1540 = π[tex]r^3[/tex] + 3π[tex]r^2[/tex]

π[tex]r^3[/tex] + 3π[tex]r^2[/tex] - 1540 = 0

r ≈ 7.38 cm

Using the equation h = r + 3, we can find the height:

h = 7.38 + 3 = 10.38 cm

Now we can use the formulas for the lateral surface area and the top and bottom areas to find the total surface area of the cylinder:

Lateral surface area = 2πrh

Top and bottom areas = 2π[tex]r^2[/tex]

Substituting in the values we found, we get:

Lateral surface area = 2π(7.38)(10.38) ≈ 483.87 [tex]cm^2[/tex]

Top and bottom areas = 2π[tex](7.38)^2[/tex] ≈ 342.72 [tex]cm^2[/tex]

Total surface area = Lateral surface area + Top and bottom areas

Total surface area ≈ 826.59 [tex]cm^2[/tex]

Therefore, the total surface area of the cylinder is approximately 826.59 [tex]cm^2[/tex].

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0.7994 portion of persons with myopia will differ from the population portion by less than 3%.

Here we have to implement the central limit theorem,

therefore,

the formula is Z = x- a /s where, a = mean , d= standard deviation

let us consider that 42% has myopia

then p = 0.42

size of random sample given is 442

therefore, n = 442

then, a = p = 0.42

standard deviation is

s = [tex]\sqrt{p(1-p)/n}[/tex]

=[tex]\sqrt{0.42* 0.58/442}[/tex]

=0.0235

portion between 0.42 +0.03 = 0.45 and 0.42 - 0.03 = 0.39

there for there are two values of X = 0.45 , X = 0.39

Z = X - a/s

Z = 0.45 - 0.42 / 0.0235

Z = 1.28 have a p-value of 0.8997

Z = X - a /s

Z = 0.39 - 0.42 / 0.0235

Z = -1.28 have a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 portion of persons with myopia will differ from the population portion by less than 3%.

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We predict that approximately 17,204 adults in Grand City have television as their main source of news.

To predict the number of adults in Grand City whose main source of news is television, we need to use the proportion of adults in the sample who selected television as their main source of news and apply it to the entire population of 46,000 adults.

The proportion of adults in the sample who selected television as their main source of news is:

135/361 = 0.374

To get the predicted number of adults in Grand City whose main source of news is television, we multiply this proportion by the total population:

0.374 x 46,000 = 17,204

Rounding this to the nearest whole number, we get:

17,204 adults

Therefore, we predict that approximately 17,204 adults in Grand City have television as their main source of news.

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Answer: 286 toppings

Step-by-step explanation:

the price of the laptop without VAT (excluding VAT) is R5 814.

Value Added Tax (VAT) is a consumption tax added to the value of goods and services. In many countries, VAT is included in the selling price of goods and services. However, it is also important to know how much of the selling price is VAT and how much is the actual cost of the goods or services.

In this problem, Sam bought a laptop for R6 840, which includes VAT of 15%. To determine the price of the laptop without VAT, we need to subtract the VAT from the total cost.

The VAT amount can be found by multiplying the total cost by the VAT rate. In this case, the VAT rate is 15%, so the VAT amount is:

VAT = 15/100 * R6 840

VAT = R1 026

To find the price of the laptop without VAT, we need to subtract the VAT amount from the total cost:

Price without VAT = Total cost - VAT

Price without VAT = R6 840 - R1 026

Price without VAT = R5 814

Therefore, the price of the laptop without VAT (excluding VAT) is R5 814.

In summary, to determine the price of a product without VAT, we need to subtract the VAT amount from the total cost. The VAT amount can be found by multiplying the total cost by the VAT rate. Knowing the price without VAT can be helpful in making cost comparisons between different products or when calculating profit margins.

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Answer:

Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)

Step-by-step explanation:

The average daily balance is $1,372.57 and the finance charge is $23.69.

What is the formula for the average daily balance?

The formula for the average daily balance is (1/number of days in billing period) x (sum of daily balances)

To calculate the finance charge, we need to first calculate the average daily balance for the billing period.

So, in this case, the billing period is 31 days (8 days for the previous unpaid balance plus 23 days for the current charges).

The sum of the daily balances is (8 x 1,876.00 + 10 x 778.12 + 3 x 2,112.50 + 10 x 1,544.31) = $42,559.42

Therefore, the average daily balance is (1/31) x 42,559.42 = $1,372.57

Next, we need to calculate the monthly periodic rate, which is the APR divided by 12 ,

19.2% / 12 = 1.6%

Then, we can calculate the finance charge using the following formula,

average daily balance x monthly periodic rate x number of days in billing cycle

$1,372.57 x 0.016 x 31 = $676.10

Rounding this amount to the nearest cent gives us a finance charge of $676.09, which is closest to option B: $23.69.

Therefore, the answer is B) $23.69.

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Answer: a1 = 3 and an = an-1 + 3(-1)n

Step-by-step explanation:

* start off with the first term being a1 = 3

* add on 3 to get to 6 as the second term

* add on -3, to get back to 3 once more

*  add on the general term 3*(-1)^n (bc the pattern continues like, forever)

* term is found by a(n) = a(n-1) + 3*(-1)^n

I think This is correct as I found a similar brainly post

The probability to pick one candy at random that is yellow or green through which relation satisfied is [tex]\frac{65}{139}[/tex]

What about probability ?

Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).

Probability theory is used in a wide range of fields, including statistics, economics, physics, engineering, and computer science, to model and analyze phenomena that involve uncertainty or randomness. It is also used in many practical applications, such as risk assessment, decision making, and game theory.

According to the given information:

The probability it is yellow:

[tex]\frac{20}{20+42+45+32} = \frac{20}{139}[/tex]

The probability it is green:

[tex]\frac{45}{45+20+42+32} = \frac{45}{139}[/tex]

P(green, yellow):

⇒ [tex]\frac{20}{139} + \frac{45}{139}\\\\\frac{65}{139}[/tex]

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Answer:

65/139

Step-by-step explanation:

Acellus

The end behavior of the function is: as x → -∞, f(x) → -∞, and as x → ∞, f(x) → ∞.

The end behavior of the function f(x) = 3 * cube root of x can be determined by examining the function as x approaches negative and positive infinity.
1. As x → -∞, the cube root of a large negative number will also be negative, and 3 times a negative number is still negative.

Therefore, as x → -∞, f(x) → -∞.
2. As x → ∞, the cube root of a large positive number will be positive, and 3 times a positive number is still positive. Therefore, as x → ∞, f(x) → ∞.

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Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.

To find out how many games the soccer team won, we need to multiply the total number of games they played by the percentage of games they won.

25% of 32 games can be calculated as:

0.25 x 32 = 8

Therefore, the soccer team won 8 games out of 32.

Two equations that represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are [tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] and [tex]y = (\frac{3}{4})x - 5[/tex]. So, option A and D are correct.

We know that a line parallel to 3x - 4y = 7 will have the same slope as the given line. So, we can rearrange the equation 3x - 4y = 7 into slope-intercept form y = mx + b to find the slope:

3x - 4y = 7

-4y = -3x + 7

[tex]y = (\frac{3}{4}) x - \frac{7}{4}[/tex]

Therefore, the slope of the line is 3/4.

Now, we can use the point-slope form of the equation of a line to write the equations of the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2):

[tex]y - (-2) = \frac{3}{4} *(x - (-4))[/tex] or [tex]y - (-2) = \frac{3}{4} x - 3[/tex]

Simplifying these equations, we get:

[tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] or [tex]y = (\frac{3}{4})x - 5[/tex].

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The equation [tex]y = x^2 + 4x - 12[/tex] represents a parabolic curve in a 2D coordinate system.

What is graph?

A graph is a concept in mathematics and computer science that involves a set of nodes or vertices, linked together by edges to depict the interconnections between objects. Graphs are a powerful method for examining complex relationships within diverse systems, including communication networks, transportation systems, and social networks.

To graph this equation, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you might choose x values from -6 to 2.

For each x value, calculate the corresponding y value by plugging it into the equation. For example, if x = -6, then y = [tex](-6)^2[/tex] + 4(-6) - 12 = 0.

Plot each (x, y) pair on the graph.

Connect the plotted points with a smooth curve to represent the parabolic shape of the equation.

Using these steps, you can graph the equation [tex]y = x^2 + 4x - 12[/tex] to visualize its shape and better understand its behavior.

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Answer: cylinder a is 12.45cm^3

cylinder b is 49cm^3

Step-by-step explanation: been through this my guy it was a struggle frl but bro igy frls

Answer:

Step-by-step explanation:

1/4 divided by 3/2 as a fraction

1/4 : 3/2 =  (flip 3/2 and change the sign from division to multiplication)

1/4 × 2/3    (semplify)

1/2 × 1/3 =  (solve)

1/6

Answer:

= 1/6

Step-by-step explanation:

(1/4) ÷ (3/2) = (1*2) ÷ (4*3) = 2/12

= 1/6

The value of the given linear equation to satisfied the given expression of the equation is = [tex]\frac{-9}{10}[/tex]

What about linear equation?

A linear equation is a mathematical equation that represents a straight line in a Cartesian coordinate system. It is an algebraic equation in which the highest power of the variable is 1.

The general form of a linear equation in one variable is:

ax + b = 0 where "a" and "b" are constants and "x" is the variable. The solution to this equation is: x = -b/a

The general form of a linear equation in two variables is:

ax + by + c = 0

Define equation:

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent a wide range of relationships between variables.

According to the given information:

Here, the value of x and y are given

Put the value of x and y in the given expression we have that,

⇒ 4y - x

⇒ 4 x [tex]\frac{-3}{20}[/tex] - [tex](\frac{3}{10} )[/tex]

⇒ [tex]\frac{-12}{20}[/tex] - [tex](\frac{3}{10} )[/tex]

⇒ [tex]\frac{-18}{20}[/tex]

⇒ [tex]\frac{-9}{10}[/tex]

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Answer: 17

Step-by-step explanation:

First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps

To solve this problem, you will need to use the Pythagorean theorem. According to this theorem, a^2 + b^2 = c^2, where a and b are the two sides of a right-angled triangle and c is the hypotenuse or the longest side. In this case, the two sides are the distance traveled by Pepper and Lemon respectively, and the hypotenuse is the distance between them.

Distance between Lemon and Pepper. Let's say that after 15 minutes, Lemon has traveled a distance of d1, and Pepper has traveled a distance of d2. Since they are moving in perpendicular directions, we can say that the distance between them is the hypotenuse of the right-angled triangle formed by their paths.

Using the Pythagorean theorem, we can write this as:d^2 = d1^2 + d2^2Distance traveled by LemonIn 15 minutes, Lemon travels a distance of 40 x 15/60 = 10 miles.Distance traveled by PepperIn 15 minutes, Pepper travels a distance of 25 x 15/60 = 6.25 miles.Distance between Lemon and Pepper. Using the Pythagorean theorem, we can find the distance between Lemon and Pepper:d^2 = 10^2 + 6.25^2d^2 = 100 + 39.0625d^2 = 139.0625d = sqrt(139.0625)d = 11.7858 miles.  

Differentiating this expression with respect to time (t), we get:d/dt (d^2) = d/dt (d1^2 + d2^2)2d * (dd/dt) = 2d1 * (dd1/dt) + 2d2 * (dd2/dt)(dd/dt) = (d1 * dd1/dt + d2 * dd2/dt)/dd/dt = (10 * 40/60) + (6.25 * 25/60)dd/dt = 6.25 + 2.6042dd/dt = 8.8542 miles per hourThe distance between Lemon and Pepper is increasing at a rate of 8.8542 miles per hour. Therefore, the answer is that the distance between them is increasing.

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The given statement "  to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)" is true. Assuming that 5 is g(1), we can use the growth factor of 3 to find the value of g(50) using the formula g(n) = 5*3^(n-1).

Assuming that 5 is the first term of the sequence g(n), we can use the formula g(n) = 53^(n-1) to find any term of the sequence. This formula gives us the value of the nth term in the sequence, where n is any positive integer.

For example, if we want to find the 50th term of the sequence, we simply substitute n = 50 into the formula and calculate g(50) = 53^(50-1) = 5*3^49. Therefore, we can use this formula to find any term of the sequence, given the first term and the growth factor. so, the given statement is true.

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--The given question is incomplete, the complete question is given

" true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)."--

The formula for continuous compounding is given by:

A = Pe^(rt)

where:

A = final amount

P = principal amount (initial investment)

e = 2.71828 (constant)

r = annual interest rate (as a decimal)

t = time in years

We can solve for P as follows:

P = A/e^(rt)

We know that we want to save $12,000, the interest rate is 3.95%, and the time is 5 years. Substituting these values into the formula, we get:

P = 12000/e^(0.0395*5)

P = 12000/e^0.1975

P = 12000/1.2183

P = 9854.16

Therefore, Max should put $9,854.16 into the account that pays 3.95% interest compounded continuously for 5 years.

The required sample size is 108, to estimate the population mean with a 98% confidence level.

The following formula can be used to determine the required sample size.

n = ((z*σ) / E)^2

where:

n = sample size

z = z-score corresponding to desired confidence level (98% = 2.33 for two-sided test)

σ = population standard deviation (specified in the problem)

E = tolerance (2 for the problem)

After plugging in the values ​​it looks like this:

n = ((2.33*) / 2)^2

n=107.13

Rounding up to the nearest integer, the required sample size is 108.

Therefore, a sample size of at least 108 is required to estimate the population mean with a 98% confidence level and a margin of error of 2, taking the population standard deviation as approximate.

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The ratio representing the sine of angle ∠M in triangle MNO, where ∠O = 90°, MO = 8, ON = 15, and NM = 17, is 17/8.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this problem, we are given a right triangle MNO, with a right angle at O. The side opposite angle M is MN, and the hypotenuse is MO.

To find the sine of angle M, we use the formula sin(M) = opposite/hypotenuse, where the opposite side is MN and the hypotenuse is MO.

Using the Pythagorean theorem, we can find the length of side MN:

[tex]MN^2 = MO^2 + ON^2[/tex]

[tex]MN^2 = 8^2 + 15^2[/tex]

[tex]MN^2[/tex] = 289

MN = 17

Therefore, the sine of angle M is:

sin(M) = MN/MO

sin(M) = 17/8

The ratio that represents the sine of angle M is 17/8.

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Answer:

48a^3 + 14a^2 - 52a + 15.

Step-by-step explanation:

To multiply these two polynomials, we need to use the distributive property and multiply each term of the first polynomial by each term of the second polynomial, like this:

(6a^2 + 4a - 5) x (8a - 3)

= 6a^2 x 8a + 6a^2 x (-3) + 4a x 8a + 4a x (-3) - 5 x 8a - 5 x (-3)

= 48a^3 - 18a^2 + 32a^2 - 12a - 40a + 15

= 48a^3 + 14a^2 - 52a + 15

So the simplified answer is 48a^3 + 14a^2 - 52a + 15.

This is because, in this scenario, the total cost per hour (-$432/hour) is the lowest compared to the costs of having two or three workers (-$864/hour and -$1,066/hour, respectively).

To determine the optimal maintenance crew size for servicing the machines at Three-Guys Vending Inc., we need to consider the average rate of breakdowns, downtime costs, and worker costs for each crew size.

The breakdowns are distributed in a Poisson manner, and the service rates are distributed exponentially.
1. Average breakdown rate: 3 machines/hour
2. Downtime cost: $230/hour per machine
3. Worker cost: $28/hour per worker.
Crew Size Scenarios:
A. One worker: services 5 machines/hour
B. Two workers: service 7 machines/hour together
C. Three workers: service 8 machines/hour together
First, we'll calculate the downtime and worker costs for each scenario:
A. One worker:
Downtime cost = (3 breakdowns/hour - 5 services/hour) x $230 = -$460/hour
Worker cost = 1 x $28 = $28/hour
Total cost = -$460 + $28 = -$432/hour
B. Two workers:
Downtime cost = (3 breakdowns/hour - 7 services/hour) x $230 = -$920/hour
Worker cost = 2 x $28 = $56/hour
Total cost = -$920 + $56 = -$864/hour.
C. Three workers:
Downtime cost = (3 breakdowns/hour - 8 services/hour) x $230 = -$1,150/hour
Worker cost = 3 x $28 = $84/hour
Total cost = -$1,150 + $84 = -$1,066/hour
From the calculations above, the optimal maintenance crew size for servicing the machines is one worker.

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Thus, the distance between Caden’s house and school is found as: 12 km.

Pythagoras theorem triangles are right triangles that adhere to the Pythagoras theorem. Pythagorean triples are the name given to the three sides that make up this triangle.

The axiom that the hypotenuse's square in a right triangle equals the sum of its squares on the other sides (c² = a² + b²)

Given data:

From the attached diagram for question:

Distance between Caden’s house and Eva’s house CA = 13 kilometers.

Distance between school and Eva’s house CB = 5 kilometers.

using Pythagorean theorem:

CA²  = CB² + BA²

BA² = CA²  - CB²

BA² = 13²  - 5²

BA² = 169  - 25

BA = 12

Thus, the distance between Caden’s house and school is found as: 12 km.

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Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.

When comparing quantities and figuring out how they relate to one another, ratio and proportion are two related mathematical ideas.

A ratio is a comparison between two values that is typically stated as a fraction. The ratio of red to blue marbles, for instance, would be 3/5 if there were 3 red and 5 blue marbles in a bag.

Contrarily, the proportion equation declares that two ratios are equivalent. For instance, if there are 3/5 red to 5/5 blue marbles in one bag and 6/10 red to blue marbles in the other, we have two bags of marbles.

From the given bar graph the ratio of adult to teen items is 18 : 6 or 3:1.

Thus for 24 items,

24:x = 3:1

Cross-multiplying, we get:

24 * 1 = 3 * x

x = 24/3

x = 8

Therefore, Jenna should plan to have 8 teen items in the store to maintain the same ratio of adult to teen items.

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The complete question is:

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \pink\bigstar \underline{{ \boxed{ \sf{ \color{lightgreen}Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²}}}}}[/tex]

[tex] \: [/tex]

Solution:-

[tex] \sf{D = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }[/tex]

[tex] \: [/tex]

where ,

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \sf \: D = \sqrt{( 9 - 0 )² + ( -6 - 7)²} [/tex]

[tex] \: [/tex]

[tex] \sf \: D = \sqrt{ ( 9 )² + ( - 13 )²}[/tex]

[tex] \: [/tex]

[tex] \sf \:D = \sqrt{ 81 + 169} [/tex]

[tex] \: [/tex]

[tex] \underline{ \underline{ \sf{ \color{hotpink} \: D = \sqrt{{250}\: }}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)