What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 18 yd 9 yd​

Number of tickets one can purchase from 56 dollars is 7.

Given that, 4 football tickets costs $32.

So, the cost of one football ticket = Total cost/Number of tickets

= 32/4

= $8

Number of tickets purchased for $56 = 56/8

= 7

Using variation

4:32::x:56

32x=56×4

x=7

Therefore, there are 7 tickets one can purchase from 56 dollars.

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The difference of two positive integers is never negative.

Through definition, a positive integer is any whole number greater than zero, and subtraction is the operation used to find the difference among two numbers.

When subtracting a smaller number from a larger number the end result is constantly a non-negative number or 0.

This is because the subtraction operation measures the distance between the two numbers, and distance is usually a positive value.

For instance, the difference among 7 and 3 is 4, that's a positive value. consequently, the difference of positive integers is always a non-negative number.

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The average value of f(x) over the interval [-14, 14] is 0.

The average value of the function f(x) = 14 - |x| over the interval [-14, 14] we need to use the formula:

[tex]f_{ave[/tex] = (1/(b-a)) × integral(a to b) f(x) dx

a and b are the limits of integration.

a = -14 and b = 14.

So we have:

[tex]f_{ave[/tex] = (1/(14 - (-14))) × integral(-14 to 14) (14 - |x|) dx

Simplifying the integral get:

[tex]f_{ave[/tex] = (1/28) × integral(-14 to 0) (14 + x) dx + (1/28) × integral(0 to 14) (14 - x) dx

Evaluating the integrals get:

[tex]f_{ave[/tex] = (1/28) × [(14x + (x²)/2)|(-14 to 0) + (-14x + (x²)/2)|(0 to 14)]

[tex]f_{ave[/tex] = (1/28) × [(0 + 98) + (-196 + 98)]

[tex]f_{ave[/tex] = (1/28) × 0

f_ave = 0

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The required standard error of the mean is 2.4 units.

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 36 units and the sample size is 225. Therefore, the standard error of the mean is:

SE = σ / √n = 36 / √225
     = 36 / 15 = 2.4 units

Therefore, the standard error of the mean is 2.4 units.

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The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:

Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:

Domain: Not specified

Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:

Range: Not specified

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The value of f(2) is 40.5

The given function is f(x) = 1/x + 5[tex]x^3[/tex], and we need to find the value of f(2).

To do this, we substitute x=2 into the function and simplify:

f(2) = 1/2 + 5([tex]2^3[/tex])

= 1/2 + 5(8)

= 1/2 + 40

= 40.5

Therefore, the value of f(2) is 40.5.

The function f(x) has two parts: 1/x and 5[tex]x^3[/tex]. The first part of the function, 1/x, is a decreasing function that approaches zero as x gets larger. The second part of the function, 5[tex]x^3[/tex], is an increasing function that grows rapidly as x gets larger.

When we substitute x=2 in the function f(x), we get f(2) = 1/2 + 5([tex]2^3[/tex]) = 40.5. This means that at x=2, the value of the function is 40.5.

This result tells us that the function f(x) has a positive value at x=2. Moreover, since the second part of the function grows faster than the first part, the value of the function f(x) will increase as x gets larger. This means that as x increases, the value of f(x) will increase more and more rapidly.

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The conversion of 2553 base 10 to base 7 is 10305 base 7.

We are given that;

The value= 2553 base 10

Now,

To convert 2553 base 10 to base 7, we need to divide 2553 by 7 repeatedly and write down the remainders. The final answer will be the remainders read from bottom to top. Here are the steps:

Divide 2553 by 7. The quotient is 364 and the remainder is 5. Write down 5.

Divide 364 by 7. The quotient is 52 and the remainder is 0. Write down 0 below 5.

Divide 52 by 7. The quotient is 7 and the remainder is 3. Write down 3 below 0.

Divide 7 by 7. The quotient is 1 and the remainder is 0. Write down 0 below 3.

Divide 1 by 7. The quotient is 0 and the remainder is 1. Write down 1 below 0.

Therefore, by conversion the answer will be 10305 base 7.

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Answer:

0.34

Step-by-step explanation:

4 or below go down low

5 or above fly like a dove

so the 33 part is lower than 50 so round down

A transformation that would take Figure A to Figure B include the following: D. A counterclockwise rotation of 90° about the origin.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:

(x, y)                               →                (-y, x)

Ordered pair (-4, 9)        →           Ordered pair (-9, -4)

In conclusion, we can logically deduce that a rotation of 90° counterclockwise around the origin is a type of transformation that would take Figure A to Figure B.

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The box plot contains a median of 9, Q1 as 7, and Q3 as 12.

The Smallest: value is 5 and the largest value is 15.

Option B is the correct answer.

We have,

To find the median, we need to arrange the numbers in order:

5, 6, 8, 9, 9, 11, 11, 13, 15

The median is the middle number, which is 9.

To find the quartiles, we first need to find the median of the lower half and upper half of the data.

Lower half: 5, 6, 8, 9, 9

Upper half: 11, 11, 13, 15

To find Q1, we find the median of the lower half:

(6 + 8)/2 = 7

To find Q3, we find the median of the upper half:

(11 + 13)/2 = 12

The smallest number is 5 and the largest number is 15.

Therefore,

Median: 9

Q1: 7

Q3: 12

Smallest: 5

Largest: 15

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(a) The distribution of X ~ N(7.08, 2.29)

(b) The probability of a patron's lunch cost is 0.049

(b) The probability of a group patron's lunch cost is 0.049

(d) The assumption of normal distribution is not necessary

Given that

Mean = 7.08

Standard deviation = 2.29

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(7.08, 2.29)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (6.9379  - 7.08)/2.29 and z = (7.2186 - 7.08)/2.29

Evaluate

z = -0.062 and z = 0.061

So, we have

P = P(-0.062 < z < 0.061)

Evaluate

P = 0.049039

Approximate

P = 0.049

This is same as part (b)

i.e. the probability that the average lunch is between $6.9379 and $7.2186 is 0.049

No, the assumption is not necessary

This is because

The distribution has a sample size less than 25 as required by the central limit theorem

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Using iterations, the solution to the above equation  6⁽⁻ˣ⁾ +4 = 3x -1 is Option C  = 27/16. See the graph attached.

The question requires you to state the solution of the equation. On the graph, this would be the point of intersection of both curves.

To solve for x, we'll continue using an iterative method called the fixed-point iteration ..

Rewrite the equation in the form x = g(x):

g(x) = (6⁽⁻ˣ⁾ + 5) / 3

Start with an initial guess, let's say x0 = 1.

Iterate using the formula x(n+1) = g( x(n )) until convergence, where n is the iteration number:

x (1) = g(x 0)

x (2 ) = g (x(1))

x( 3) = g(x (2))

Let's perform three iterations to approximate the solution

Iteration 1

x (1) = g( x0) = (6⁻¹ + 5) / 3

= (1/ 6 +5) / 3

= (1 /6 + 30/6) / 3

= 31/18

≈ 1.7222

Second iteration is

x(2) = g(x (1)) = ([tex]6^{1.72222}[/tex] + 5) / 3 ≈ 1.6806

Iteration 3:

x(3) = g(x (2)) = ([tex]6^-1.6806[/tex] + 5) / 3 ≈ 1.6875

After three iterations, the approximate solution to the equation 6⁽⁻ˣ⁾ + 4 = 3x - 1 is x ≈ 1.6875, which can also be expressed as the fraction 27/16.

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The probability that a person's favorite pastime is cooking is 0.125 (or 12.5%).

To find the probability that a person's favorite pastime is cooking, we need to divide the number of people whose favorite pastime is cooking by the total number of people.

Given the following pastimes,

Reading = 25

Sports = 40

Crafts = 20

Cooking = 15

Others = 20

Since 15 people listed cooking as their favorite pastime. To find the total number of people, we can add up the number of people who listed each pastime:

Total = Reading + Sports + Crafts + Cooking + Others

Total = 25 + 40 + 20 + 15 + 20 = 120

Therefore, the probability that a person's favorite pastime is cooking is:

P(cooking) = Cooking  / Total

           = 15 / 120

           = 0.125 or 12.5%

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Answer:

x= 0•5

Step-by-step explanation:

x÷2/3=3/4

3/2x=3/4

x= 3/4 ÷2/3

Answer:

16 in

Step-by-step explanation:

50 ft x 12 in/ft = 600 in

Scale factor:  2 : 600 = 1 : 300

x = length of island on the map

400 ft = 4800 in

1/300 = x/4800

x = 4800/300 = 16 in

The end behavior of the quadratic function is f(x) = (x + 5)² - 2

We have the table of values which represents a quadratic function f(x).

A quadratic equation is represented as;

f(x) = a(x - h)² + k

Where, Vertex = (h, k)

If we plot the graph according to the given table, the vertex will be,

(h, k) = (-5, -2)

Substitute, (h, k) = (-5, -2) in f(x) = a(x - h)² + k

we have, f(x) = a(x + 5)² - 2

Also, the graph, we have the point (0, 23)

This means that

a(0 + 5)² - 2 = 23

25a = 25

a = 1

Substitute a = 1 in f(x) = a(x + 5)² - 2

f(x) = (x + 5)² - 2

Hence, the equation is polynomial f(x) = (x + 5)² - 2

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Answer:

(2x + 1) (x - 4)

Step-by-step explanation:

2x² - 7x - 4.

need two number that add up to -7, but that multiply together to get -4.

(2x + 1) (x - 4) = 2x² - 4(2x) + x - 4 = 2x²  - 8x + x - 4 = 2x²  - 7x - 4

The  Linear function is y equals negative one third times x plus 1

A linear function is a function that has a constant rate of change, meaning that as one variable (usually x) increases or decreases by a certain amount, the other variable (usually y) also changes by a constant amount.

Out of the four given equations, the only one that represents a linear function is the third one:

y equals negative one third times x plus 1

This is because the equation has a constant rate of change of -1/3 for any change in x. For example, if we increase x by 3, y will decrease by 1 (because 3*(-1/3) = -1). Similarly, if we decrease x by 3, y will increase by 1. This constant rate of change is what makes the equation represent a straight line when graphed.

The other three equations do not represent linear functions.

The first equation, x = 3, is not a function at all because there are multiple possible y values for the given x value of 3.

The second equation, y = 3x2, is a quadratic function because it contains an x2 term, which means that the rate of change of y with respect to x is not constant.

The fourth equation, 3x - 4 = 7, is a linear equation but not a function because for any given x, there is only one corresponding value of y. However, when the equation is solved for y, it becomes y = 3x - 3, which represents a linear function with a constant rate of change of 3.

The  linear function is y equals negative one third times x plus 1

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There are no intersecting points.

The given equations are

y = (2x)² - 6x+5   ....(i)

2y + x =4 ....(ii)

Since we know that,

Degree of equation (i)  = 2

Therefore,

equation (i) is a quadratic equation.,

And equation (ii) has degree 1,

So it is a equation of line,

To find the intersection,

First of we have to plot both graphs,

Then find the coordinate of the intersection of the given line and curve.

After plotting graph,

We can see that,

The given curve and line are not intersecting,

Therefore,

There are no intersecting points.

Hence we can not find the required equation of line.

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The probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.

Calculating the standard error of the mean (SE) using the formula:

SE = σ / sqrt(n)

where σ is the standard deviation and n is the sample size.

SE = 1.02 / sqrt(45) ≈ 0.1522

We can calculate the z-score using the formula:

z = (x - μ) / SE

where x is the observed mean and μ is the claimed mean.

z = (1.73 - 1.8) / 0.1522 ≈ -0.4582

Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.3231.

Therefore, the probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.

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The probability of just thunder is 0.196.

We have,

The probability of rain P(A) = 1/2

The probability of thunder and raining P(A ∩ B) = 1/3

The probability of rain and thunder P(A U B) = 11/30

Now,

Using the addition rule of probability.

P(A U B) = P(A) + P(B) - P(A∩B)

Substituting.

11/30 = 1/2 + P(B) - 1/3

11/30 - 1/2 + 1/3 = P(B)

P(B) = 0.196

The probability of just thunder is 0.196.

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The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

The equation can be simplified to XXX × YV=1335.

If both sides of the equation are divided by 3, X × YV = 445.

If now all the X's is replaced with 5's, 5 × YV = 445.

This gives the following equation:

5 × YV = 445

Now multiply both sides of the equation by Y, to get 5Y = 445.

This gives us the following equation:

5Y = 445

Finally, divide both sides of the equation by 5, to get Y=89.

Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.

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The value of x using Tangent - Secant theorem is: 16

The tangent-secant theorem states that when a tangent and secant possess a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.

We are given:

internal part of the secant = (x + 9),

external part of the secant = 9,

tangent = 15,

According  to Tangent-secant Theorem:

(x + 9) * 9 = 15²

9x + 81 = 225

9x = 144

x = 144/9

x = 16

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The radius of the circle is [tex]\sqrt{59[/tex] and the coordinates are (6,8).

The given equation of the circle is:

[tex]x^2+Y^2-12x-16y+51=0[/tex]

To find the center and radius of the given circle, we need to rewrite the equation in the standard form [tex](x-a)^2 + (y-b)^2 = r^2[/tex],

where (a,b) is the center of the circle and r is the radius.

We can start by completing the square for the x and y terms. For the x terms, we add and subtract (12/2)² = 36 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y = -51 + 36 + 0[/tex]

Similarly, for the y terms, we add and subtract (16/2)² = 64 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y + 64 = -51 + 36 + 64[/tex]

Simplifying:

[tex](x - 6)^2 + (y - 8)^2 = 59[/tex]

Now we can see that the center of the circle is at (6, 8), and the radius is [tex]\sqrt{59[/tex].

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Answer:

98 is a whole number

Step-by-step explanation:

0.86 is a decimal

2/5 is a fraction

35% is a percentage

(5, 55) is the range of the given curve.

The given graph is similar to a quadratic graph. The range of a function is defined as the values of the function that lies along the y-coordinate.

From the given graph, the range will lie between the initial point on the graph top the vertex.

The initial point is (0, 5) while the vertex is (1, 55). The equivalent y-coordinate values will form the values for the range.

Hence the range of the given graph is (5, 55)

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