40 points and brainleyest help

a. The domain of a(r) is [tex]A(r)= 2\pi r^{2} + 16\pi r[/tex].

b. The radius r as a function of a is [tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex] .

The three-dimensional solid shape of a cylinder is made up of two circular bases joined by a curving surface that is created by folding a rectangle. A cylinder's top and bottom faces are parallel to one another. There are 3 faces, 2 edges, and 0 vertices in all.

In this question, we must apply our understanding of cylinders to determine the function that most accurately captures its value:

[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]

The area domain of A can be represented as:

[tex]A(r)= 2\pi r^{2} + 16\pi r[/tex]

Let's divide the equation by 2π and write A(r) as just A to get:

[tex]r^{2} + 8r = \frac{A}{2\pi }[/tex]

So, after we sum on both sides we get,

[tex]r^{2} +8X +16 =\frac{A}{2\pi } + 16[/tex]

[tex](r+4)^{2} = \frac{A}{2\pi } +16[/tex]

By taking the square root of the previous equation and then figuring out r, we get:

[tex]r = -4 +\sqrt{\frac{A}{2\pi } +16[/tex]

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The most likely cause of the change in population mean in year 6 is an increase in the amount of land available, which allowed for an increase in the number of rabbits.

The most likely cause of the change in population size in year 6 shown in the graph is an increase in the amount of land available. The graph shows the population size of rabbits over different years, beginning at year 4 and ending at year 7. At the beginning of year 4, the population size of rabbits is 95, and the population size increases and decreases slightly through year 6. After year 6, the population size increases greatly, ending at 275. This suggests that there was an increase in the amount of land available, which allowed for an increase in the population size of rabbits. This increase in the available land could have been due to any number of factors, such as increased human settlement, a decrease in the number of predators, or improved access to food sources. All of these factors could have led to an increase in the number of rabbits, and the resulting change in population size in year 6.

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Step-by-step explanation:

complement angle means together they are 90°.

supplementary means together they are 180°.

x = the angle

90 - x = (180 - x)/3

270 - 3x = 180 - x

90 - 3x = -x

90 = 2x

x = 45°

On solving the provided question, we can say that the probability that at least two students pick the same integer is = 10/10 = 1

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

number of favorable  outcome = 1,2 ; 2,3; 3,4; 4,5; 5,6; 6,7; 7,8;8,9;9,10; 1,10

number of total outcome = 10

probability = 10/10 = 1

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Answer:

x=-36

Step-by-step explanation:

To do this we do the inverse of the equaison which is 9×-4 and the answer to that is -36

There are 40 hoses with loose fittings should the manufacturer expect out of 2,900 hoses.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A hose manufacturer tests the fittings on every 20th hose on an assembly line.

And, Out of 145 hoses tested, 2 had issues with loose fittings.

Let number of hoses with loose fittings should the manufacturer expect out of 2,900 hoses = x

So, By definition of proportion, we get;

⇒ 2 / 145 = x / 2900

⇒ 2×2900 / 145 = x

⇒ x = 40

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The correct answer to the given question is an option (C) -the size of the confidence interval increases.

In statistics, the confidence interval for the population means signifies the range in which it could lie at a given confidence level. The confidence interval is usually approximated by using the standard deviation, mean, and sample size of a representative sample drawn from population data.

The margin of error is given by:

= (Z-score * Standard error)

= [tex]\frac{Z -score * Standard deviation}{\sqrt{Sample Size} }[/tex]

Now, the width of a confidence interval is given by:

=(2 * Margin of error)

From the above formulae, it can be inferred that the width of the confidence interval is directly connected to the margin of error, which in turn is directly related to the confidence level or Z-score. Hence, if we change the 95% confidence interval estimate to a 99% confidence interval, the size of the confidence interval will increase.

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The complete question is:

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect:

A. the size of the confidence interval to decrease.

B. the sample size to increase.

C. the size of the confidence interval to increase.

D. the size of the confidence interval to remain the same.

The width of the two paths is 5 m.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

Let the width of the two paths be x.

Thus, the total area covered by the paths is = (30×x) + (40×x) - x²

The total area covered by the paths is 325 m².

Equate both of them.

⇒ (30×x) + (40×x) - x² = 325

⇒ 30x + 40x  - x² = 325

⇒ x² -70x + 325 = 0

Solving the above equation, we get

x = 65 or x = 5

The valid solution is x = 5.

Thus, the width of the two paths is 5 m.

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The value of z at the end of the procedure is 84.

The term procedure in math is defined as a sequence of mathematical operations carried out in order.

Here we have given that if x was 20 and y was 2.

And here we need to find the value of z.

Here let us consider the the equation of z can be written according to the theorem it can be written as,

=> z = 4x + y²

Here we know the values of x and y then the value of z is calculated as,

=> z  = 4(20) + 2²

When we simplify the equation, then we get,

=> z = 80 +  4

=> z = 84.

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The true statements are 0.04b +  0.05s = 320, b + s = 7000, and Amber invests $3,000 in bonds and $4,000 in stocks. Then the correct options are A, C, and F.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Amber invests $7,000 in bonds and stocks.

Then the equation is given as,

b × 0.04 + s × 0.05 = $320

0.04b +  0.05s = 320         ...1

b + s = 7000                       ...2

From equations 1 and 2, then we have

0.04(7000 - s) + 0.05s = 320

0.01s = 40

s = 4000

Then the value of 'b' is given as,

4000 + b = 7000

b = 3000

The true statements are 0.04b +  0.05s = 320, b + s = 7000, and Amber invests $3,000 in bonds and $4,000 in stocks. Then the correct options are A, C, and F.

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The complete question is attached below.

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

What is radian ?

A radian is a unit of measurement for angles. It is defined as the ratio of the length of an arc of a circle to the radius of that circle. One radian is approximately 57.3 degrees. Radians are often used in mathematics, physics, and engineering because they allow for a more natural way of measuring angles and help simplify certain calculations.

To find the bearing, we can use the formula ,

Bearing = atan2(East, North)

Where East is the number of miles east of the airport and North is the number of miles north of the airport.

The atan2 function is a variation of the arctangent function, which returns the angle (in radians) whose tangent is the quotient of its two arguments. This function is defined for all real arguments and returns a value between -π and π.

So you can convert the bearing from radians to degrees using the formula ,

degrees = bearing * (180/π)

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

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Answer:

3[tex]x^{2}[/tex](3+1)

Step-by-step explanation:

The HCF is 3[tex]x^{2}[/tex] hence it will go outside the brackets.

Answer:

3x^2(3+1)

^2 means squared or two to the exponential power.

Step-by-step explanation:

The two games are different as Honduran futbolito is typically played on a small, concrete court.

Honduran futbolito and foosball in the United States are both games that mimic soccer, but they have some key differences. Honduran futbolito is typically played on a small, concrete court with walls that the ball can be played off of.

The game is usually played with a smaller, harder ball than a standard soccer ball. Foosball, on the other hand, is played on a table with miniature figures mounted on rods that players use to strike the ball. The game is usually played with a small, lightweight ball. Both games can be played with teams or individually, but Foosball is more common as a table-top game, while Futbolito is a street game.

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The total number of possible outcomes when a coin is tossed ten times is 2^10 = 1024. To find the number of outcomes that have at least three heads, we can use the principle of complementary counting. We can find the number of outcomes that have fewer than three heads and subtract it from the total number of outcomes.

There are two cases to consider:

Outcomes with two or fewer heads: There are 10 ways to choose the position of the first head, 9 ways to choose the position of the second head (assuming it's not in the same position as the first head), and 8 ways to choose the position of the third head (assuming it's not in the same position as the first two heads). This gives 10 x 9 x 8 = 720 ways to have two or fewer heads.

Outcomes with zero or one head: There are 10 ways to choose the position of the first head, and 9 ways to choose the position of the second head (assuming it's not in the same position as the first head). This gives 10 x 9 = 90 ways to have zero or one head.

So the total number of outcomes with two or fewer heads is 720 + 90 = 810. To find the number of outcomes with at least three heads, we subtract this from the total number of outcomes:

1024 - 810 = 214

So there are 214 possible outcomes that have at least three heads when a coin is tossed ten times and the result, heads or tails, is recorded for each toss.

I hope this helps :)

Answer:

the answer is the middle one

Domain: [-2, 2]

Range: [-4, 3]

Property which represents the one half of the figure exactly same as the rest half of the same figure is known as the line of symmetry.

As given in the question,

Therefore, property used to define the one half of the figure is exactly same as the other half is known as line of symmetry.

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Answer:

160

Step-by-step explanation:

.4x = 256  Divide both sides by .4

[tex]\frac{.4x}{.4}[/tex] = [tex]\frac{256}{.4}[/tex]

x = 640

What is 25% of 640

.25(640) = 160

Answer:

160

Step-by-step explanation:

The formula for expected value is E(p) = Σ [p(x) * x] where x are the possible values of p and p(x) is the probability of x.

Without the probability distribution of p, it is impossible to determine the expected value of p.

The expected value (also known as the mathematical expectation or mean) of a random variable is a measure of the central tendency of the variable's possible values. The expected value of a discrete random variable p is the sum of the product of each possible value of the variable and its corresponding probability.

To find the expected value of p, you would need to know the probability distribution of the variable, which tells you the likelihood of each possible value of p. The probability distribution would typically be provided in a problem statement, or can be determined through experimentation or survey data.

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Answer:

Step-by-step explanation:

No, the ordered pair (-2, 3) is not a solution to the system of linear equations. When substituted into the equations, the values do not result in the equations being true. For the first equation, 5(-2) + 3 = -7, which is not true. Similarly, for the second equation, -3(-2) + 2(3) = 0, which is also not true. Therefore, the ordered pair (-2, 3) is not a solution to the system of linear equations.

The standard error of the mean is approximately for 225 elements with variance of 900 is 1.4847.

In contrast to range and interquartile range, variance is a measure of dispersion that considers the spread of all data points in a data collection. It is the most commonly used measure of dispersion, along with the standard deviation, which is essentially the square root of the variance. The calculations for variance are listed below. Variance can be stated as follows for ungrouped data: Population (Xi X)2N is the variance for a population of size N. The variance is calculated as the total of the squared departures from the mean. The variance of population data is denoted by 2 (read as sigma squared), whereas the variance of sample data is marked by s2.

Here,

For 225 items with a variation of 900, the standard error of the mean is roughly 1.4847.

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High mean with High standard Deviation is the data outcome of stock prices would best support the idea that there is more risk with that stock.

Stock Price:

The stock price is the price of one share out of the number of shares available for sale in the company. Simply put, stock price is the maximum amount someone is willing to buy a stock, or the minimum amount someone is willing to buy.

High mean with High standard Deviation:

A high standard deviation literally means a large mean deviation from the mean. For example, a good dart his player can throw darts on the dartboard and group the darts across the bullseye. A poor darts player will hit the entire board with the darts and even miss the board completely and hit the wall. A good darts player has a smaller average distance from the bullseye to the dart, and therefore a lower standard deviation. Bad darts players have a higher standard deviation because the average distance of their darts from the bullseye is greater.

There are no objective criteria for small and large standard deviations. We can only determine whether the mean deviation is small or large, depending on the context and what is being measured. For example, when throwing a dart, being one foot away from the target is a large deviation, but when swinging a wrecking ball against a wall, it is a small deviation. It has a different purpose than darts.

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If a hotel has 260 rooms, where the singles cost $35 and the doubles cost $60, then there are 64 single rooms and 196 double rooms.

This is a system of equations problem. Let x be the number of single rooms and y be the number of double rooms. We know that

as the total number of rooms is 260

x + y = 260

Also as the total sales for the single and double rooms is $14,000 where the singles cost $35 and the doubles cost $60

35x + 60y = 14,000

To solve for x and y, we can use either substitution or elimination method.

Using substitution:

x + y = 260

x = 260 - y

35(260 - y) + 60y = 14,000

9,100 - 35y + 60y = 14,000

25y = 4,900

y = 196

So there are 196 double rooms.

Therefore, x = 260 - y

x = 260 - 196

x = 64

So there are 64 single rooms

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Answer: [tex](x+1)^2+y^2=117[/tex]

Step-by-step explanation:

The radius of the circle is [tex]\sqrt{(-1-(-4))^2 +(\sqrt{108}-0)^2}=\sqrt{117}[/tex].

Using the center-radius form for the equation of a circle, the equation is [tex](x+1)^2+y^2=117[/tex].

Answer:

[tex](x+1)^2+y^2=117[/tex]

Step-by-step explanation:

Equation of the circle: (x - h)² + (y - k)² = r²

(x, y) – any point in the circle

(h, k) – the center of the circle

r – the radius of the circle

(-4, √108) – (x , y)

(-1, 0) – (h, k)

r – ?

[tex](x-h)^2+(y-k)^2=r^2\\\\((-4)-(-1))^2+((\sqrt{108})-(0))^2=r^2\\\\(-4+1)^2+(\sqrt{108}-0 )^2=r^2\\\\(-3)^2+(\sqrt{108} )^2=r^2\\\\9+108=r^2\\\\r^2=117\\\\r^2=9*13\\\\\sqrt{r^2}=\sqrt{9*13} \\\\r=3\sqrt{13}[/tex]

Now that we know what's the r value:

[tex](x - (-1))^2+(y-0)^2=(3\sqrt{13} )^2\\\\(x+1)^2+y^2=9*13\\\\(x+1)^2+y^2=117[/tex]

The scale factor of the dilation used to transform trapezoid MNOP to RSTU obtained by the  ratio of the corresponding sides is 1.5

A dilation transformation is one in which the lengths of the sides of the original figure are multiplied by a constant known as the scale factor of the dilation.

Part of the question includes the diagram of the trapezoids.

Please find attached diagrams of two similar trapezoids that can be used to illustrate the problem created with MS Word.

The corresponding sides of the trapezoids are;

Side OP in trapezoid MNOP is the corresponding side to side ST in trapezoid RSTU

The ratio of the corresponding side in the trapezoids indicates the scale factor of the dilation as follows;

The scale factor, s.f. used to transform trapezoid MNOP to trapezoid RSTU obtained from the ratio of the corresponding sides is; s.f. = ST/OP

ST = 15

OP = 10

Therefore; s.f. = 15/10 = 1.5

The scale factor of dilation used to transform trapezoid MNOP to trapezoid RSTU, s.f. is 1.5

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The general solution of the given differential equation is: y = c_1 e^x + (1/x)∫xe^x dx.

A general solution is a comprehensive approach that is applicable to a wide variety of situations and problems. It is usually used to solve complex problems that have multiple variables and factors. General solutions often involve a combination of strategies, techniques, and processes that can be adapted to fit a particular context. In some cases, general solutions may require a combination of both traditional and modern methods. The goal of a general solution is to provide an effective, efficient, and sustainable solution to an issue.

The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution, so the answer is NONE.

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We can see from the graph that Plan B is less expensive for the range [0, 4], however Plan A is superior if you watch 4 or more movies per month.

We know that plan A costs $14 per month plus $2 per movie, so if you watch x movies, the cost is:

C₁(x) = $14 + $2*x

Plan B costs $20 per month plus $1 per movie, so if you watch x movies, the cost is:

C₂(x) = $20 + $1*x

You can see in the graph that the blue line is behind the green one between x = 0 and x = 4. Plan B is therefore less expensive in the range [0, 4].

The green line is underneath the blue one for x > 4, hence you should select plan A for x > 4.

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Answer: I think it is the first one

Step-by-step explanation:

Answer:

I'm pretty sure it's x^2 - 4x

Step-by-step explanation:

Answer:

h = 6/7

Step-by-step explanation:

h minus four sevenths equals two sevenths

minus means -

equals means =

h - four sevenths = two sevenths

four sevenths means 4/7

two sevenths = 2/7

h - 4/7 = 2/7

add 4/7 to both sides to isolate h

h = 6/7

Answer: h =6/7

Step-by-step explanation: 4/7 + 2/7 = 6/7 so h - 4/7 = 2/7 h = 6/7

Answer: 55%

Step-by-step explanation:

The question says that Toronto FC lost 12 of 40 games and drew in 15% of the total games they played. To find the percentage of the games they won, you need to subtract the percentage of games they lost and the percentage of games they drew from 1 since all possibilities add up to 1.

% of games won = 1 - (% of games lost + % of games drawn)

First, Toronto FC lost 12 of 40 games. This means that they lost 12/40 of all games, and this can be simplified to be

3/10

Which is 0.3, or 30%.

Now the questions said that Toronto FC drew in 15% of all games, which means that using the equation from earlier, we can find the percentage of games won.

% of games won = 1 - (30%+15%)

= 1-0.45

= 0.55

Therefore, Toronto FC won in 55% of their games.