A circle with center O(2, 3) contains the point A(5, 11).

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=2827.43\\ h=4 \end{cases}\implies 2827.43=\pi r^2(4)\implies \cfrac{2827.43}{4\pi }=r^2 \\\\\\ \sqrt{\cfrac{2827.43}{4\pi }}=r\hspace{5em}\stackrel{\textit{twice that is the \underline{diameter}}}{2\sqrt{\cfrac{2827.43}{4\pi }}} ~~ \approx ~~ \text{\LARGE 30}[/tex]

The given statement is false.

While both the algebraic and spreadsheet approaches to linear programming aim to optimize a linear objective function subject to linear constraints, the steps involved in the two methods are different. Therefore given statement is false.

In the algebraic approach, the problem is formulated mathematically using linear equations and inequalities. The objective function and constraints are written in terms of decision variables, and the system of equations is solved using techniques such as the simplex method or graphical method.

In the spreadsheet approach, the problem is set up in a spreadsheet using cells to represent decision variables and constraints. The objective function is entered as a formula, and constraints are entered as inequalities. The solver tool is used to find the optimal solution.

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As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar

Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. To put it another way, profit is what is left over after all costs have been subtracted from revenue1.

For instance, if a business sells widgets for $100 apiece and the cost of production is $50 each widget, the profit would be $50. The business would make $10,000 in total income and incur $5,000 in total costs if it sold 100 widgets. There would be $5,000 in total profit.

Using the given equation y=-2x²+145x1051 we can utilise the procedures below to get the greatest profit the corporation may make:

1. Using the equation x = -b/2a, where a = -2 and b = 145, determine the x-coordinate of the parabola's vertex.

2. To determine the highest possible value of y, substitute this x value into the equation.

These actions result in:

x = -b/2a = -145/(2×(-2)) = 36.25

When we enter this x value into the equation, we obtain:

y = -2(36.25)² + 145(36.25) - 1051 ≈ $1,292

As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar.

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The method that uses an arithmetic mean to forecast the next period is "moving averages".

The method that uses an arithmetic mean to forecast the next period is the "moving averages" method.

In this method, the average of the past observations is calculated, and this average is used as the forecast for the next period.

The number of past observations used in the calculation of the moving average depends on the specific variant of the method being used.

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Answer:

A.) LGJ

Step-by-step explanation:

20% of the students surveyed did not choose soccer, football, or basketball as their favorite sport.

To find the percentage of students who did not choose soccer, football, or basketball as their favorite sport, we need to first find the total number of students who did not choose any of these sports.

Total number of students who chose soccer, football or basketball = 54 + 42 + 24 = 120

Number of students who did not choose any of these sports = 150 - 120 = 30

Therefore, the percentage of students who did not choose soccer, football or basketball as their favorite sport is:

(30/150) x 100% = 20%

So, 20% of the students surveyed did not choose soccer, football, or basketball as their favorite sport.

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--The complete Question is, Out of the 150 students surveyed, 54 chose soccer, 42 chose football, and 24 chose basketball. What percentage of the students surveyed did not choose soccer, football or basketball as their favorite sport? --

Answer:

[tex] \frac{ {g}^{4} {h}^{2} }{ g{h}^{6} } = \frac{ {g}^{3} }{ {h}^{4} } [/tex]

because other values are 1, and this one is less, because g<h

The function is a linear function because as x increases, the y-value changes at a constant rate . The rate of change of this equation is 2.

The difference between linear and exponential functions is that  Linear functions change at a constant rate per unit interval while an exponential function changes by a common ratio over equal intervals.

We are given the function table as:

(0, -3)

(1, -1)

(2, 1)

(3, 3)

Thus, we can see that as x increases, the y-value changes at a constant rate of  + 2.

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To convert km/h (kilometers per hour) to m/s (meters per second), we need to divide the speed by 3.6.

Therefore, 135 km/h = (135/3.6) m/s ≈ 37.5 m/s

So, 135 km/h is approximately equal to 37.5 m/s.

Step-by-step explanation:

the equation for the following graph os (-3,-5) & (1,1)

Larry cannot make exactly 23 cents using only 4-cent and/or 9-cent stamps, but he can make any amount of postage greater than or equal to 24 cents.

The problem of finding the largest number of cents that Larry cannot make exactly using only 4-cent and/or 9-cent stamps is a classic example of the Frobenius coin problem. This problem arises in many areas of mathematics, including number theory and combinatorics.

To solve the problem, we can use the coin-changing algorithm, which is a general method for finding the largest amount that cannot be formed from any combination of two coin denominations. The algorithm states that the largest amount N that cannot be formed using denominations a and b is given by:

N = ab - a - b

In this case, a = 4 cents and b = 9 cents, so we have:

N = 4 x 9 - 4 - 9 = 23

Therefore, the largest amount of postage that Larry cannot make exactly using only 4-cent and/or 9-cent stamps is 23 cents. This means that he can make any amount of postage greater than or equal to 24 cents using these stamps.

The Frobenius coin problem has many practical applications, such as in currency systems, vending machines, and computer algorithms for making change. It also has connections to other areas of mathematics, such as group theory and geometry.

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The surface area of the given cylinder is 368π square centimeter.

What is a cylinder?

The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

We are given a cylinder with following dimensions:

Radius (r) = 8 cm

Height (h) = 15 cm

Now, using the formula, we get

⇒ S = 2πrh + 2π[tex]r^{2}[/tex]

⇒ S = 2π * 8 * 15 + 2 * π * [tex]8^{2}[/tex]

⇒ S = 2π * 120 + 2 * π * 64

⇒ S = 240π + 128π

⇒ S = 368π

Hence, the surface area of the given cylinder is 368π square centimeter.

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Since, there are multiple questions so, the question answered above is attached below.

Question: Find the surface area of the given figure. Writh the answer in terms of pi.

The mean is 120

The mode is 126
The median is 123
The range is 21

How to calculate the mean, mode, median and range?

Mean= 126 + 128 + 107 + 113 + 120 + 126/6

= 720/6

= 120

Mode= 126

Median= 120 + 126/2

= 246/2

= 123

Range= Highest-lowest

= 128-107

= 21

Hence the mean is 120, the mode is 126, the median is 123 and the range is 21

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Answer:

3/20

Step-by-step explanation:

0.150= 150/1000

Find the highest common denominator, which is 5

150/50= 3

1000/50= 20

3/20

0.150 in fraction for equals 3/20

i think its 1.45in^2

Answer:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

Answer:

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:

(

3

,

0

)

Focus:

(

3

,

1

4

)

Axis of Symmetry:

x

=

3

Directrix:

y

=

−

1

4

x

y

1

4

2

1

3

0

4

1

5

4

Tap to view steps...

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.

Plugging in these values, we get:

average rate of change = (f(65) - f(9)) / (65 - 9)

average rate of change = (3√64 + 2 - 3√8 - 2) / 56

average rate of change = (3(4) + 2 - 3(2) - 2) / 56

average rate of change = (12 - 4) / 56

average rate of change = 8 / 56

average rate of change = 1 / 7

Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.

Charles Darwin was a naturalist who proposed the concept of evolution via natural selection.

He discovered that versions exist inside species, and that those variations can be inherited via offspring. Darwin theorized that over the years, sure variations might be more positive for survival in a specific surroundings, and people developments could be more likely to be surpassed directly to the subsequent technology.

This method, which he called "natural selection," would lead to the evolution of latest species over long intervals of time. Darwin's concept of evolution thru herbal choice changed into a groundbreaking idea that challenged conventional ideals about the origins and diversity of lifestyles in the world, and it is still a important concept inside the fields of biology and ecology.

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The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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The total area in the image is 288 square metres.

    Figures can be divided into rectangles and triangles.

    The rectangle has a base of 18 m and a height of 8 m, giving it an area of ​​18 x 8 = 144 m2. The triangle has a base of 12 m (18 - 6) and a height of 8m, giving it an area of ​​0.5 x 12 x 8 = 48 m2.

    Adding the area of ​​rectangles and triangles gives us a total land area of ​​144 + 48 = 288 m2.

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Answer:

Step-by-step explanation:

You want to know the number of cubic meters in a cube that is 10^3 meters on each side, and whether that volume amounts to a pond, lake, or ocean.

The volume of a cube is given by ...

  V = s³

where s is the edge length.

The volume of interest is ...

  V = (10³ m)³ = 10⁹ m³

The volume of oil is 10⁹ cubic meters.

The sizes of ponds and lakes vary, but we might consider a pond to be a body of water larger than about 150 square meters and less than 6 meters in depth. On the other hand, a lake will generally be larger than about 4000 square meters. An average size lake may be about 10 meters in depth.

If we put the given amount of volume in a space with a depth of 40 meters, it would cover an area of about 25 million square meters, roughly 6000 acres. That is the area of a circle about 7 km in diameter. This might be considered a medium-sized lake.

The oil would fill a medium-sized lake.

__

Additional comment

A "lake" is generally a body of water upwards of an acre in area. While an average lake in some areas is about 10 m deep, worldwide, the average is just over 40 m in depth. Some lakes are well over 20,000 acres in area.

A "pond" may be larger than a "lake", but will generally be smaller than 500 acres.

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For quadrilateral ABCD x=85 and angle B= 23°.

A quadrilateral is a polygon with four sides and four angles. It is a closed figure and can have different shapes and sizes, depending on the length of its sides and the angles between them.

(a) Supplementary equation used to solve for x:

∠A + ∠C = 180°

(b) All math used to calculate for x:

∠A + ∠C = 180°

(x - 5) + (x + 15) = 180 (substitute the given values for ∠A, ∠C)

2x - 10 = 180

2x = 170

x = 85

(c) Correct value for x:

x = 85

(d) Plugging x into expressions for angles A, C, D:

∠A = x - 5 = 2(85) - 5 = 165

∠C = x + 15 = 85 + 15 = 100

∠D = x - 13 = 85 - 13 = 72

(e) All math used to calculate the measures of angles A, C, D:

∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)

165 + ∠B + 100 + 72 = 360

∠B = 23

Therefore, the measures of the angles are:

∠A = 165°

∠B = 23°

∠C = 100°

∠D = 72°

(f) All math used to calculate the measure of angle B:

∠B = 360 - ∠A - ∠C - ∠D

∠B = 360 - 165 - 100 - 72

∠B = 23°

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The main topic is the split-half reliability test used in psychological research to assess the internal consistency of a scale.

In psychological research, reliability is a crucial aspect of measuring constructs or attributes. One commonly used method for assessing the reliability of a scale is the split-half reliability test.

In this test, the scale questions are divided into two parts equally, and the resulting scores of both parts are correlated against one another.

For example, if a scale had 20 items, the items could be randomly split into two groups of 10 items each.

Scores are then calculated for each group, and the scores are correlated with each other to determine the degree of consistency between the two halves.

The correlation coefficient obtained from this analysis provides an estimate of the internal consistency of the scale.

A high correlation coefficient indicates a high level of internal consistency, indicating that the two halves of the scale are measuring the same construct or attribute.

Conversely, a low correlation coefficient suggests that the two halves of the scale are not measuring the same construct or attribute, and the scale may need to be revised or abandoned.

Overall, the split-half reliability test provides a quick and efficient method for evaluating the reliability of a scale.

However, it is important to note that this method does have some limitations, such as the possibility of unequal difficulty or discrimination of the items in each half of the scale.

Therefore, researchers often use other methods, such as Cronbach's alpha, in conjunction with the split-half reliability test to provide a more comprehensive assessment of the reliability of a scale

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Answer:

Step-by-step explanation:

jill has 4 one dollar bills, and Mark has 3 one dollar bills so 3 of them would cancel out, so jill would have one more dollar. And then we also know that Jill has 4 dimes, and Mark also has 4 dimes. So they cancel out. And Jill has 3 pennies, and Mark has 2, so Mark has one more penny than Mark. And lastly we know that Jill has 3 quarters. So know we add it all up Jill has 1 dollar, 3 quarters and 1 penny. Which is $1.76.

Answer:

Step-by-step explanation:

Jill's money:

4 one dollar bills- 4 x 1 = 4

3 quarters: 3 x 0.25 = 0.75

4 dimes: 4 x 0.10 = 0.4

3 pennies: 3 x 0.01 = 0.03

4 + 0.75 + 0.4 + 0.03 = $5.18

Jill has $5.18

Mark's Money:

3 one dollar bills: 3 x 1 = 3

4 dimes: 4 x 0.10 = 0.4

2 pennies: 2 x 0.01 = 0.02

3 + 0.4 + 0.02 = $3.42

Mark has $3.42

To find the difference between these values, we subtract.

5.18 - 3.42 = $1.72

The difference between Jill's money and Mark's money is $1.72

$1.72 is your answer.

Answer: w = ±7

Step-by-step explanation:

To get rid of the square on w, we square root both sides of the equation.

The square root of w^2 is w, and the square root of 49 is ±7.

±7 is your answer.

The 90% confidence interval for the probability of flipping a head with this coin is approximately b. [0.339, 0.501], which corresponds to option b). [0.339, 0.501].

Calculate the sample proportion (p-hat):

p-hat = number of heads / total flips = 42/100 = 0.42

Determine the confidence level, which is 90% in this case.

Find the corresponding z-score for the confidence level.

For a 90% confidence level, the z-score is approximately 1.645.

Calculate the standard error:

[tex]SE = \sqrt{(p-hat \times (1 - p-hat) / n)}  = \sqrt{ (0.42 \times 0.58 / 100)} = 0.0496[/tex]

Calculate the margin of error:

ME = z-score × SE = 1.645 × 0.0496 ≈ 0.0816

Determine the confidence interval:

CI = (p-hat - ME, p-hat + ME)

= (0.42 - 0.0816, 0.42 + 0.0816)

= (0.3384, 0.5016)

Therefore, option b.[0.339, 0.501] is correct.

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The five number summary for the test scores and other measures are:

To find the mean test score, sum up all the test scores and divide by the total number of students:

mean = (42 + 68 + 70 + 72 + 74 + 75 + 79 + 80 + 82 + 83 + 84 + 85 + 86 + 87 + 91 + 92 + 94 + 95 + 97 + 98) / 20

mean = 1628 / 20

mean = 81.4

To find the median test score, find the middle value(s) of the ordered scores.

median = (83 + 84) / 2

median = 167 / 2

median = 83.5

The mode is the score that appears most frequently. In this case, there is no mode, as all scores appear only once.

To calculate the Mean Absolute Deviation (MAD), find the mean of the absolute differences between each score and the mean score:

MAD = (|42-81.4| + |68-81.4| + ... + |98-81.4|) / 20

MAD = 246.6 / 20

MAD = 12.33

To calculate the range, subtract the smallest score from the largest score:

range = 98 - 42

range = 56

To find Q1 (the first quartile), find the median of the lower half of the data.

Q1 = median of (42, 68, 70, 72, 74, 75, 79, 80, 82, 83)

Q1 = (74 + 75) / 2

Q1 = 74.5

To find Q3 (the third quartile), find the median of the upper half of the data.

Q3 = median of (84, 85, 86, 87, 91, 92, 94, 95, 97, 98)

Q3 = (91 + 92) / 2

Q3 = 91.5

To calculate the Interquartile Range (IQR), subtract Q1 from Q3:

IQR = Q3 - Q1

IQR = 91.5 - 74.5

IQR = 17

The only score outside the lower bound (below 49) is 42. There are no scores above the upper bound (117). So, the only outlier in the data set is the score of 42.

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Answer:

  A: description: graph of f(x) shifted left 3 units. Domain: (-∞, ∞); range: [0, ∞); vertex: (-3, 0).

  B: description: graph of f(x) shifted down 2 units. Range: [-2, ∞); vertex: (0, -2).

Step-by-step explanation:

Given parent function f(x) = |x|, you want descriptions of g(x) = |x+3| and h(x) = |x| -2, including the vertex, domain, and range.

This question is concerned with translations of functions. The translations of interest are ...

The function f(x) = |x| is defined for all values of x. Its domain is all real numbers: (-∞, ∞). Shifting the function left or right does not affect the domain.

The vertex of the function is at (0, 0), and is a minimum. That means the range of the function is all non-negative numbers: [0, ∞). Shifting the function up or down affects the range by the same amount.

The function g(x) = |x+3| is equivalent to g(x) = f(x+3). Comparing to the transformations above, we see h = -3. So the graph of f(x) will be shifted left 3 units to make the graph of g(x).

The function h(x) = |x| -2 is equivalent to h(x) = f(x) -2. Comparing to the transformations above, we see k = -2. So the graph of f(x) wil be shifted down 2 units to make the graph of h(x).

The sample space is {1, 2, 3, 4, 5, 6}.

The probability of each sample outcome is 1/6.

The probability of the event that the roll is even is 1/2.