The volume of a right cylinder is found by the formula V equals pi r squared h. Two cylinders both have a height of 10 centimeters. One has a volume of 2009.6 cubic centimeters. The other has a volume of 196.25 cubic centimeters. What is the radius of each cylinder? (Use 3.14 as an approximation of pi.)

Answer:

axis of symmetry : x = 4

coordinates of the vertex : (4, 28)

Step-by-step explanation:

Before we start solving, let's define what the coefficients of this quadratic equation is.

[tex]y = ax^2 + bx + c[/tex]

[tex]y = -x^2 + 8x + 12[/tex]

a = -1

b = 8

c = 12

⭐What is the axis of symmetry?

To find the axis of symmetry, we need to find the x-coordinate of the vertex.

Equation for the x-coordinate of the vertex:

[tex]x = \frac{-b}{2a}[/tex]

Substitute the values of a, b, and c into this equation and compute.

[tex]x = \frac{-(8)}{2(-1)}[/tex]

[tex]x = \frac{-8}{-2}[/tex]

[tex]x = 4[/tex]

∴ The axis of symmetry is x = 4

⭐What is the vertex of a parabola?

To find the x-coordinate of the vertex, you can use the formula: [tex]x = \frac{-b}{2a}[/tex].

To find the y-coordinate of the vertex, substitute the x-coordinate of the vertex and compute.

x-coordinate: 4

y-coordinate:

[tex]y = -x^2 + 8x + 12[/tex]

[tex]y = -(4)^2 + 8(4) + 12[/tex]

[tex]y = -(16) + 32 + 12[/tex]

[tex]y = -16 + 44[/tex]

[tex]y = 28[/tex]

y-coordinate: 28

∴ The coordinates of the vertex is (4,28)

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The law of sines uses only two sides and the angles that are opposite them, while the law of cosines uses all three sides and only one of the sides opposite an angle

An angle's cosine and sine are equal to each other, with the sine of an angle equal to the cosine of its complementary angle.

The law of cosines uses all three sides and only one of the sides that are opposite an angle, whereas the law of sines only uses two sides and the angles that are opposite them. The sine ratio is used by the law of sines, and the cosine ratio is used by the law of cosines.

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Complete question

What is the difference between the law of sines and the law of cosines

The given linear equation (1/3)x+ y=2 in the slope-intercept form is

y=(-1/3)x+2.

Where m is the slope and b is the y-intercept, the slope-intercept form is represented as y = mx+ b. By utilizing y=mx+ b, a line is typically simple to graph. The point-slope form and standard form of linear equations are further types. Example 1: A line with a slope of 1/2 and a y-axis crossing at (0, -3). Calculate the line's equation. It is y = x/2 - 3 that determines the line's equation. Example 2: Determine the equation utilizing the y-y-intercept axis's and the horizontal line's slope intercept formula (0, 8).

Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+ b allow us to build an equation for that line.

Given linear equation is:

(1/3)x+ y=2

The following is the slope-intercept form of the given linear equation:

y=(-1/3)x+2

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No. Tom is not correct.

If the money were split equally everyone would've gotten £200.

But, if everyone went by the mentioned distribution, then,

Rachel would get = 2/5 x 600 = £280

Remainder money = 600 - 280 = £320

Samina would get = 1/4 x 320 = £80

Tom would get the remaining money = 600 - (280 + 80)

                                                              = 600 - 360

                                                              =  £240      

Since, £240 > £200, Tom would be incorrect in saying he would have had more money if he had split the money equally.

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The possible solutions of the inequality expression given as 20y < -5 + 18y are (c) y < -5/2, y < -2.5 and (d) -2.5 > y

From the question, we have the following parameters that can be used in our computation:

20y < -5 + 18y.

To start with, we need to collect the like terms of both sides

Using the above as a guide, we have the following:

20y -18y < -5

Next, we need to evaluate the like terms of both sides

Using the above as a guide, we have the following:

2y < -5

Lastly, we divide both sides by 2

y < -5/2

Express as decimal

y < -2.5

Switch the positions

-2.5 > y

Hence, the solutions are y < -5/2, y < -2.5 and -2.5 > y

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The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

Step-by-step explanation:

It is easier to graph using a free online graphing utility, such as DESMOS.  See the attached graph.  If the goal is to make a graph with pencil and graph paper, then select a few values of x  and put them into the equation to find y.

A talble of a few random values is attached.  

The graph includes both the generated DEMOS line (a downwards parabola) and the calculated points from the attached table.  Add the points to a blank graph and draw a line as best you can that connects all the points.  It is clear that a few more points with negative values of x would help with the line drawing.

Answer: 9d

Step-by-step explanation:

10d+d-2d = 9d

An increasing exponential function is modeled as follows:

A(t) = A(0)(1 + r)^t.

The parameters of the exponential function are given as follows:

She borrows 12,000 at 12% annual percentage rate, hence the initial value and the growth rate are given as follows:

A(0) = 12,000, r = 0.12.

Then the function that describes her loan is given as follows:

A(t) = 12000(1.12)^t.

After six years, the value of the loan is calculated as follows:

A(6) = 12000(1.12)^6 = $23,686.

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The values of x is x = 6 Or x = - 4 when the expression - 3x² + 6x + 72 will be zero.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Here in the problem, we have to find the roots of the quadratic equation

- 3x² + 6x + 72 = 0.

3x² - 6x - 72 = 0.

x² - 2x - 24 = 0.

x² - 6x + 4x - 24 = 0.

x(x - 6) + 4(x - 6) = 0.

(x - 6)(x + 4) = 0.

x = 6 Or x = - 4 are the values of x when the expression will be zero.

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The dilated figure is plotted and attached and the coordinates is written as

preimage            image

A (-4, 3)               A; (-8, 6)

B (3, 2)                B' (6, 4)

C (-4, 0)               C' (-8, 0)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                           image

A (-4, 3)   → (-4 * 2, 3 * 2) →   A' (-8, 6)

B (3, 2)    → (3 * 2, 2 * 2)  →    B' (6, 4)  

C (-4, 0)  → (-4 * 2, 0 * 2) →    C' (-8, 0)

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By solving a linear equation, it can be calculated that-

The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet

What is a linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, the linear equation is

Let the time taken by the airplane to meet the same altitude be t minutes

An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.

So altitude of the first airplane after t minutes = 55800 - 3500t

At the same​ airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.

Altitude of second airplane = 2700t

By the problem,

The linear equation is

55800 - 3500t = 2700t

2700t + 3500t = 55800

6200t = 55800

t = 9 minutes

Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet

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The college graduate's new net worth is given as follows:

$13,833.

The net worth of a company or of a person is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts of the person.

The assets if the student are given as follows:

The liabilities of the student are given as follows:

Thus the student's net worth is calculated as follows:

(10000 + 14278 + 4337 + 14950 + 11774) - (3250 + 5129 + 33097) = $13,863.

Which is closest to the third option among those given.

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Answer:

the correct answer is 12057

Step-by-step explanation:

in order to calculate net worth, add up the assets, and then subtract the debt. be sure to pay attention to details

heres an UNRELATED TO THE QUESTION example:

i have...

$500 in my savings

$20 in my wallet

but im $200 deep in credit card debt..

(add 500 + 20, then subtract 200)

net worth: 320

The total cost of the rental if Dana drives the car for 15 miles is $90.2

From the question, we have the following parameters that can be used in our computation:

C = 73.25 + 1.13m

Where

m = number of miles

This means that

m = 15

SO, we have the following equation

C = 73.25 + 1.13 * 15

Evaluate

C = 90.2

Hence, the total cost is $90.2

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"Dana and her family are going to Six Flags Great America the sum- mer after her Sophomore year. She is excited, because she will be doing all driving: After doing some complicated analysis, she calcu; lates that it will cost a certain amount per mile to pick up everyone and drive to the park, plus flat amount for everyone's admission tickets. The equation below models the total cost, €,and the variable m represents the number of miles driven: C = 73.25 + 1.13m

Answer: The probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%.

Step-by-step explanation:

We can use the formula for combinations, which is:

n! / (r! * (n - r)!)

In this case, n is the total number of tosses (4) and r is the number of successes we want to count (4 heads). Plugging these values into the formula, we get:

4! / (4! * (4 - 4)!) = 4! / (4! * 0!) = 4! / (4! * 1) = 1 / 1 = 1

The probability of getting exactly 4 heads in 4 tosses of a fair coin is therefore 1, or 100%. However, this is assuming that the coin is not fair and always lands on heads. If the coin is fair, the probability of getting 4 heads in 4 tosses is actually much lower.

To find the probability of getting 4 heads in 4 tosses of a fair coin, we need to use the formula for binomial probability, which is:

(n! / (r! * (n - r)!) * p^r * (1 - p)^(n - r)

In this case, p is the probability of getting a head in a single toss of the coin (0.5), r is the number of successes we want to count (4 heads), and n is the total number of tosses (4). Plugging these values into the formula, we get:

(4! / (4! * (4 - 4)!) * 0.5^4 * (1 - 0.5)^(4 - 4) = 1 * 0.5^4 * (1 - 0.5)^0 = 0.5^4 * 1 = 0.0625

Thus, the probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%, to the nearest thousandth.

The points (x, y) lie in the 2nd quadrant when x<0 and y>0.

Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.

The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.

These areas include coordinates or positive and negative values of the x- and y-axes.

So, refer to the graph attached below.

Now, we know that:

Quadrant 1: x>0, y>0

Quadrant 2: x<0, y>0

Quadrant 3 x<0, y<0

Quadrant 4: x>0, y<0

We are given: x<0 and y>0

We can say that when x<0 and y>0 the point (x, y) lies on the 2nd quadrant.

Therefore, the points (x, y) lie in the 2nd quadrant when x<0 and y>0.

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Answer:

Step-by-step explanation:

Rocio ha gastado mas. El cubo de Jaime esta mas lleno.

Rocio gasto otro poco mas porque 3 esta mas grande que 2

The price of the chair in the furniture store is $94.

Given that the wholesale price for a chair is $169 and that a certain furniture store marks up the wholesale price by 16%.

The price of the chair in the furniture store will be:

= $169 + (16% × $169)

= $169 + $27.04

= $196

The price is $194.

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A sample's accuracy is determined by how well it captures the genuine characteristics of the population it represents true

Accuracy is a measure of how closely a sample reflects the true values of the population it is representing. A sample that is accurate is one that accurately reflects the characteristics of the population it is representing. For example, if a sample is taken from a population of 1000 people, the sample should represent the diversity of the population, such as age, gender, race, and other characteristics. If the sample accurately reflects these characteristics, then it can be said to be accurate. The accuracy of a sample can be determined by comparing it to the population it is representing, either through surveys, interviews, or other data collection methods. If the sample closely matches the true values of the population, then it can be said to be accurate. If there are discrepancies between the sample and the population, then the sample is not accurate.

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the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

2x + 3y + 4z = 30

3x + 4y + 5z = 45

5x + 6y + 7z = 75

The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.

The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.

The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.

Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

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Answer:

d. Orthocenter

Step-by-step explanation:

⭐What is an orthocenter?

⭐What is an altitude?

We can see that point O is the point of concurrency of the altitudes of this given triangle because there are 90° formed by the perpendicular lines.

Thus, O is referred to as the orthocenter.

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The domain is set of all real numbers and the range is y ≥ -4

From the question, we have the following parameters that can be used in our computation:

The equation is given as

g(x) = |x + 4|

The domain

The above equation is an absolute value equation

An absolute value equation can take any value as its input

This means that the domain is the set of all real numbers

When represented as an interval, we have

The domain is (-∝, ∝)

Also, we have

-∝ < x < ∝

Hence, the domain is the set of all real numbers

The range

Here, we have

g(x) = |x + 4|

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-4, 0)

Remove the x value

y = -4

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

[-4, ∝)

Another representation is

y ≥ -4

So, the range is y ≥ -4

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The length of the diagonal path that leads to the original position of the moth that travels 2 meters down and, 3 meters along a wall, then 4 meters along a perpendicular wall, representing the dimensions of a rectangular prism is √(29) meters

The diagonal of a rectangular prism is a segment that stretches from one corner of the prism to the opposite corner of the prism, passing through the center of the prism.

The distance down the wall the moth crawled = 2 meters

The distance along the same wall the moth crawled = 3 meters

The distance the moth crawled along the adjoining wall = 4 meters

Angle at which the walls join = 90°

The distance distance traveled by the moth when flying in a straight line back to its original position is a diagonal of a rectangular prism of height, h = 2 meters, width, w = 3 meters, and length, l = 4 meters

The length of the diagonal of a rectangle that has height, h, width, w, and length, l, is found using the following formula;

d = √(h² + w² + l²)

The length of the diagonal along which the moth flies is therefore;

d = √(2² + 3² + 4²) = √(29)

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Answer: -90

Step-by-step explanation: To solve this equation for y, we need to isolate the variable y on one side of the equation. To do this, we can multiply both sides of the equation by -5 to get rid of the fraction on the right side:

18 = y / -5

18 * -5 = y / -5 * -5

-90 = y

Therefore, the value of y that satisfies the equation is -90.

Answer:

Step-by-step explanation:

You want equations of lines parallel and perpendicular to y = 2x -1 through the point (-7, 2).

The given equation is written in slope-intercept form:

  y = mx + b

where m = 2, and b = -1.

The slope of the line is m, the x-coefficient. For the given line, the slope is 2.

A parallel line will have the same slope: 2.

A perpendicular line will have the opposite reciprocal slope: -1/2.

When you have a point and slope, it is useful to use the point-slope form of the equation for a line:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

For both of the desired lines, the point is (h, k) = (-7, 2). Using this point and the above slopes, we have ...

Answer:greater

Step-by-step explanation:

Answer:

972 is greater than 792.

Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.

Limited respondent selections, a lack of knowledge, difficulty assessing intensity, and lack of interest in political matters are just a few of the factors that might make a poll unreliable.

Survey mistake, fewer respondent alternatives, a lack of knowledge, problems assessing intensity, and a lack of interest in political matters are some potential polling weaknesses.

The drawback of polling is that if there are too many devices to check, it may take longer to service an I/O device than it does to poll all of the devices.

Instrumental, environmental, procedural, and human errors are frequent causes. Depending on how they affect the outcomes, each of these errors can either be random or systematic.

Therefore,

Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.

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The number of bears living in the area after 17 years is; 22555

We are given the function;

f(t) = 103/(1 + 26e^(-0.31t))

Where f(t) is a function that models the number of bears living in the area after t period of years.

Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;

f(17) = 103/(1 + 26e^(-0.31*17))

f(17) = 103/0.00456653759

f(17) ≈ 22555 bears

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Answer:

42

Step-by-step explanation:

150+102=252

252/6=42