How many people can you allow on a
beach if the lifeguards want to have
30 sq ft per person and the beach is
1,000 ft long and 200 ft wide? Round
to a whole number.

The value of x for the intersecting chords is derived to be 4 and the segment AV is equal to 8.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UA × AS = VA × AT

10 × 12 = 2x(3x + 3)

120 = 6x² + 6x

dividing through by 6 and equating to 0, we have a quadratic equation;

x² + x - 20 = 0

by factorization;

(x - 4)(x + 5) = 0

so;

x = 4 or x = -5

using x = 4, the value of the segment AV is derived as;

AV = 2(4) = 8.

Therefore, the value of x for the intersecting chords is derived to be 4 and the segment AV is equal to 8.

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There are approximately 78 trees on each acre of land when the trees are spread out evenly.

To find the number of trees on each acre of land mathematically, we can use the formula for average or mean.

The average number of trees per acre can be found by dividing the total number of trees by the total number of acres. In this case, we have 2808 trees and 36 acres:

Average number of trees per acre = Total number of trees / Total number of acres

Average number of trees per acre = 2808 / 36

Average number of trees per acre = 78

Therefore, there are approximately 78 trees on each acre of land when the trees are spread out evenly.

This means that if the land is divided into 36 equal sections, each section will have approximately 78 trees.

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The cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.

Inflatiοn, in general, is the prοcess thrοugh which mοney lοses value οver time. As a result, 100 dοllars suddenly have less purchasing pοwer than they had previοusly. This indicates that the awards will increase tο maintain a steady purchasing pοwer.

Tο find the cοst οf a Brοadway shοw ticket in 2014, we need tο adjust the price frοm 2002 using the Cοnsumer Price Index (CPI) fοr each year. The CPI measures the changes in the cοst οf gοοds and services οver time due tο inflatiοn.

Here is the CPI data for the relevant years:

2002 CPI: 179.9

2014 CPI: 236.7

To adjust the 2002 price of $40 to its equivalent in 2014 dollars, we can use the following formula:

Adjusted Price in 2014 Dollars = Price in 2002 Dollars x (CPI in 2014 / CPI in 2002)

Plugging in the numbers, we get:

Adjusted Price in 2014 Dollars = $40 x (236.7 / 179.9) = $52.59

Therefore, the cost of a Broadway show ticket in 2014, based on inflation, would be approximately $52.59.

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Complete question:

In 2002 you could buy a Broadway show ticket for $40. Use the CPI chart below to find the cost of Broadway show in 2014 based on inflation.

Answer:

To determine if (0,3) is a solution to y>2, we need to check if y is greater than 2 when x=0 and y=3. Since 3 is greater than 2, the point (0,3) satisfies the inequality y>2.

To graph the inequality y>2, we need to shade the region above the horizontal line y=2. The line y=2 is a solid line since it includes the points where y=2, but the region above the line is shaded with a dashed line since it does not include the points where y=2.

Here is a description of the graph:

Draw a horizontal line passing through the point (0,2).

Shade the region above the line with a dashed line.

The graph visually represents all the points that satisfy the inequality y>2. Since the point (0,3) is above the line, it is part of the shaded region and satisfies the inequality.

the area of the shape shown in the diagram is 91 m².

Area is the space bounded by a plane shape.

To calculate the area of the shape, we use the formula below

Note: Area of the shape = Area of the rectangle+ Area of the triangle

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 91 m².

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Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).

Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).

The temperature range for a stage change in water is either more noteworthy than or equivalent to 212°F or not exactly or equivalent to 32°F, which compares to the bubbling and edges of freezing over of water, separately.

The water is still in its liquid state at 75°F, but it will change phases if it reaches 212°F or is cooled to 32°F or lower.

Therefore, the temperature changes that will produce a phase change in a glass of water at 75°F are:

Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).

Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).

It is important to note that the temperature of the water will not change during the phase change until the entire change is complete. To put it another way, when water is boiling, it will remain at 212°F until all of the liquid has evaporated, and when it is frozen, it will remain at 32°F until all of the liquid has frozen solid.

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Answer:

10u

Step-by-step explanation:

Answer:

A. 13.125cm

Step-by-step explanation:

To solve for the width of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

volume = length x width x height

We are given that the volume is 6,142.5 cm^3, the height is 16.25 cm, and the length is 28 cm. Let's substitute these values into the formula and solve for the width:

6,142.5 cm^3 = 28 cm x width x 16.25 cm

Dividing both sides by (28 cm x 16.25 cm), we get:

width = 6,142.5 cm^3 / (28 cm x 16.25 cm)

= 13.125 cm

Therefore, the width of the rectangular prism is 13.125 cm. So, the correct answer is A) 13.125 cm.

Answer:

The area is (9^2)π = 81π.

Answer:

P = 14x + 2

if x=12, P = 170

Step-by-step explanation:

The perimeter is the distance around the outside of the shape.

The rectangle has four sides. Two long sides and two short sides.

We add up all four sides.

P = 4x-5+3x+6+4x-5+3x+6

combine like terms.

P = 14x + 2 this is the equation in simplest form.

If x = 12, we can calculate the perimeter.

P = 14(12) + 2

P = 168 + 2

P = 170

The perimeter would be 170.

Answer:

Step-by-step explanation:

According the given question 3A - 2B matrix is equal to:

[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

A matrix is a rectangular array οf numerical values, symbοls, οr verbal expressiοns that are οrganised in rοws and cοlumns. In many disciplines, such as cοmputer science, engineering, physics, and mathematics, it is used tο represent data.

Calculating 3A and 2B first, then deducting 2B frοm 3A, is required tο find 3A - 2B.

Calculating 3A:

[tex]3A = 3 * \left[\begin{array}{ccc}2 & -1 & 3\1 & 1 & -3 & -1\end{array}\right]= \left[\begin{array}{ccc}6 & -3 & 9\3 & 3 & -9 & -3\end{array}\right][/tex]

Calculating 2B:

[tex]2B = 2 * \left[\begin{array}{ccc}-2 & 1 & 3 & -1 & -2 & -2 \end{array}\right]= \left[\begin{array}{ccc}-4 & 2 & 6 & -2 & -4 & -4\end{array}\right][/tex]

Nοw, we can find 3A - 2B by subtracting 2B frοm 3A:

[tex]3A - 2B = \left[\begin{array}{ccc}6 & -3 & 9 &3& -9 & -3\end{array}\right] - \left[\begin{array}{ccc}-4 & 2 & 6 &-2 & -4 & -4\end{array}\right]= \left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

Therefore, 3A - 2B is equal to:

[tex]\left[\begin{array}{ccc}10 & -5 & 3 &5 & -5 & 1\end{array}\right][/tex]

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Answer:

you are correct keep going

transformation

rigid motion

Answer:

electronic funds transfer

the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex]  [tex]r= 6.38[/tex]

The discount for apples is $ [tex]2.89[/tex] + $ [tex]1.49[/tex], since you can get another bag for $1.49 when you buy a 5-pound bag of apples at the regular price.

So the equation to find the discount for apples is:

[tex]a = 2.89 + 1.49[/tex]

[tex]a = 4.38[/tex]

Similarly, the discount for oranges is $ [tex]3.89[/tex] + $ [tex]2.49[/tex], since you can get another bag for $2.49 when you buy a 5-pound bag of oranges at the regular price.

Therefore, the equation to find the discount for oranges is: [tex]r = 3.89 + 2.49[/tex]

[tex]r = 6.38[/tex]

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he expression 4(3x=2)-9 can be written as 12x - 9. I

Answer:

Step-by-step explanation:

Let's start by defining a coordinate system where the horizontal axis represents the number of weeks that Gildong has been saving (and spending), and the vertical axis represents the amount of money he has in savings.

During the first 15 weeks, Gildong saved 20,000 won per week, so his savings increased linearly from week 0 to week 15. We can represent this with the equation:

y = 20,000x

where x is the number of weeks since the beginning (x = 0 corresponds to the start of the saving period) and y is the amount of money Gildong has saved after x weeks.

During the next 15 weeks, Gildong spent 20,000 won per week on eating Maratang, so his savings decreased linearly from week 15 to week 30. We can represent this with the equation:

y = -20,000(x - 15) + 20,000(15)

where x is the number of weeks since the beginning (x = 15 corresponds to the start of the spending period) and y is the amount of money Gildong has saved after x weeks.

To represent the total amount of money Gildong had in savings at any given time, we can combine the two equations above using an absolute value:

y = |20,000x| - 20,000(x - 15)

where x is the number of weeks since the beginning, and y is the amount of money Gildong has in savings after x weeks.

This function represents the absolute value of the difference between the amount of money Gildong has saved and the amount of money he has spent on Maratang, taking into account the fact that his savings increased linearly during the first 15 weeks and decreased linearly during the next 15 weeks.

Answer: 384 cm cubed

Step-by-step explanation: The first thing you will do is 48 square centimeters times 8 cm. Since 48 is squared you have that 2 right above it. Your 8 technically has a 1 above it. So add the 2 and the 1, and you will get cubed. (AKA 3)

Answer:

Step-by-step explanation:

[tex]T_{r+1}=nc_{r}x^{n-r}a^r\\x=v\\a=-w^2\\n=22\\r+1=15\\r=15-1=14\\22c_{14}=22c_{22-14}=22c_{8}\\ T_{15}=22c_{8}v^{22-14}(-w^2})^{14}\\T_{15}=22c_{8}v^8w^{28}[/tex]

Option (A) true. The box plot for Dog Show 1 shows a smaller interquartile range and a smaller spread of data compared to Dog Show 2

A coordinate graph is a graph that is split up into four quadrants with an x-axis and y-axis. The x-axis runs horizontally, or side to side, and the y-axis runs vertically, or from top to bottom.

A. The box plot for Dog Show 1 has a shorter box, which indicates a smaller interquartile range and less variability in the weights compared to Dog Show 2.

B. This inference is not valid since the range of weights in Dog Show 2 (55-100 lbs) is greater than the range in Dog Show 1 (65-85 lbs).

C. The interquartile range (IQR) for Dog Show 1 is smaller than  for Dog Show 2, indicating that the middle 50% of the weights in Dog Show 1 are closer together than the middle 50% of the weights in Dog Show 2.

D. This statement is false

E. This inference is not valid since the median weight in Dog Show 1 (75 lbs) is higher than the median weight in Dog Show 2 (70 lbs).

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Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.

In the field of mathematics known as probability, random chance and their results are examined. It entails putting a number between zero and 1, where 1 indicates that now the event is guaranteed to happen and 0 that it is impossible, to reflect the possibility of an event occurring. From straightforward games of chance to intricate real-world systems like share prices and weather patterns, probability theory offers a framework for the analysis and modelling of a wide range of phenomena. It has uses in physics, economics, computer science, statistics, and other disciplines.

given

Let A represent the scenario in which the first student chosen is under 62 inches, and B represent the scenario in which the second student chosen is under 62 inches as well.

Since there are two shorter kids out of a total of five students, the likelihood of choosing one on the first try is 2/5.

Given that the first student was shorter, the likelihood of choosing another shorter student on the second try is 1/4 because there would only be 1 shorter student left out of the other 4 students.

Thus, the likelihood of picking two consecutive students who are shorter

The formula for P(A and B) is P(A) P(B|A) = (2/5) (1/4) = 1/10.

Hence, there is a 1/10 or 0.1 chance that both of the chosen kids will be under 62 inches tall.

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Thus, the rational inequality formed for the given solution is found as:

x - 3 ≤ 0

A rational inequality is a specific type of statistical inequality statement that typically has a ratio of two polynomials (commonly known as a "rational expression") on the left side and a zero on the right.

Given expression is:

−1 + x ≤ 2

Subtract both side by 2

−1 + x - 2 ≤ 2 - 2

x - 3 ≤ 0

Thus, the rational inequality formed for the given solution is found as:

x - 3 ≤ 0

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Correct question:

Create a rational inequality for which −1 + x ≤ 2 is the solution.

The measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The radius of a circle is the separation between any point on the circle and its center.

The radius must typically be a positive integer. A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.

In common usage, the word "circular" can be used to describe both the figure's edge and its entirety, including its interior.

So, we know that:

The angle of the center of the circle is 360°.

We also know that in the given situation, the circle is divided into 5 parts.

Then,

= 360/5

= 72

Now,

The measure of 2 parts:

72 + 72 = 144

Therefore, the measure of the angle in the given circle which pass through 2 parts out of 5 is 144°.

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The answer to the given question about probability of Bob's shop is option 7) 79.4%.

Out of 700 cars, 144 require more than one day to repair. So the number of cars that can be fixed in one day is

700 - 144 = 556.

The probability that the next car brought to the shop can be fixed in a day is the ratio of the number of cars that can be fixed in a day to the total number of cars:

probability = 556/700

= 0.794 or 79.4%

Therefore, the correct answer is option 7) 79.4%.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to quantify the likelihood of an event occurring, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability theory is widely used in various fields, such as statistics, physics, economics, and finance, to make predictions and decisions based on uncertain or incomplete information. It provides a powerful tool for analyzing and understanding uncertainty, risk, and randomness in real-world situations, and it has numerous practical applications in diverse areas of research and industry

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Answer:

[tex]b = - 0.3125[/tex]

Step-by-step explanation:

[tex]8b - 1 = 24b + 4[/tex]

Collect like-terms (also, when moving a term to the other side, its sign changes to the opposite of the previous one):

[tex]8b - 24b = 4 + 1[/tex]

[tex] - 16b = 5[/tex]

Divide both sides of the equation by (-16) to make b the subject:

[tex]b = - 0.3125[/tex]

Answer: 6000

Step-by-step explanation:

10 times 600
10 x 600

6000

Answer:

The data set represented by the modified box plot is:

116, 118, 114, 117, 151, 126, 122, 114, 124

Step-by-step explanation:

[tex]f'(x) = 21cos(3x)/(1+49sin²(3x)).[/tex] and the outcome is f'(x) = 21cos(3x)/(1+49sin2(3x)). This is the derivative of the function f(x) with respect to x.

We apply the chain rule and the formula for the derivative of the inverse tangent function to determine the derivative of f(x). We first determine that the function contained within the inverse tangent is 7sin (3x). Thus, by differentiating f(x) with respect to x using the derivative of the inverse tangent function, we are able to get an equation in terms of cos(3x) and sin (3x). Trigonometric identities are used to simplify this formula, and the result is[tex]f'(x) = 21cos(3x)/(1+49sin2(3x))[/tex]. This is the derivative of the function f(x) with respect to x.

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In the 1st part the correct option is B and in 2nd part A.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, In the 1st part the correct option is B and in 2nd part A.

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