USE A MODEL The Newton City Park has 11 basketball courts, which are all in use. There are 54 people playing basketball. Some are playing one-on-one, and some are playing in teams. A one-on-one game requires 2 players, and a team game requires 10 players. a. Select a system of equations that represents the number of one-on-one and team games being played. Let x be one-on-one games and y be team games A)x+ 10゠11;2x+y=54 B) x+y=54;x+ 10y=11 C)x+y = 11; 2x + 10y= 54 D) x+2y = 11; 10x+2y= 54

The net of a cylinder is a 2-dimensional representation of a 3-dimensional cylinder that has been "unwrapped" and laid flat. The net consists of two circles (representing the top and bottom of the cylinder) and a rectangle (representing the side of the cylinder).

The length of the base of the rectangle in the net of a cylinder represents the circumference of the cylinder, which is the distance around the circular base of the cylinder. The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In the net of a cylinder, the base of the rectangle is the same as the circumference of the circles because it is equal to the distance around the circular base of the cylinder. The width of the rectangle represents the height of the cylinder, which is the same as the distance between the top and bottom circles.

Answer:

Therefore, the length of the base of a rectangle in the net of a cylinder is the same as the circumference of the circles because it represents the distance around the circular base of the cylinder.

The measure of the largest exterior angle of the polygon in discuss is; 100°.

It follows from the task content that the measure of the largest exterior angle of the polygon be determined.

Since the sum of all exterior angles of a polygon is equal to 360°;

x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°

36x° = 360°

x = 10

Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.

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The data described, the numbers of cases of flu treated at a certain hospital in different years, are quantitative data.

Quantitative data is any data that can be measured or expressed in numerical terms. In this case, the data is expressed as the number of cases of flu treated at the hospital in different years. This type of data can be analyzed using mathematical and statistical methods to obtain insights and patterns.

The information provided, specifically the numbers of flu cases treated at a certain hospital in various years, is quantitative information because it is expressed numerically.

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Answer:

≅20.9%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.

The formula for percent decrease is:

percent decrease = ((old value - new value) / old value) x 100%

Substituting the given values, we get:

percent decrease = ((349 - 276) / 349) x 100%

percent decrease = (73 / 349) x 100%

percent decrease = 20.92%

Rounding to the nearest tenth of a percent, we get:

percent decrease ≈ 20.9%

Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]

Casey's number is given as follows:

36.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods are given as follows:

The least common factor of 4 and 6 is obtained as follows:

4 - 6|2

2 - 3|2

1 - 3|3

1

Hence:

lcm(2,3) = 2² x 3 = 12.

This means that one in 12 customers receive both the free cookie and the free muffin. Casey is the third customer to receive both of them, hence the number is given as follows:

3 x 12 = 36.

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The solution to the inequality is any value of X that is less than or equal to -36

What is Inequality?

An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

The inequality X/(-3) ≥ 12 can be solved as follows:

We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:

X ≤ -36

Therefore, the solution to the inequality is any value of X that is less than or equal to -36.

In interval notation, we can write the solution as:

(-∞, -36]

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Answer:

ok what is the question to your math equation then..?

Answer:study

Step-by-step explanation:

-120x^8y^7

To simplify the expression, you can use the product rule of exponents, which states that when you multiply two terms with the same base, you add the exponents.

Here, we have:

-12x^5y^2y(10x^3y^4)

= -12 * 10 * x^5 * x^3 * y^2 * y^5 (using the product rule to simplify y^2 * y^4 to y^6)

= -120x^8y^7 (using the product rule to simplify x^5 * x^3 to x^8)

Therefore, the simplified expression is -120x^8y^7.

Answer:

k = 11.7

Step-by-step explanation:

Constant of Proportionality

When two quantities y and x are proportional to each other, they are related by the proportionality equation
y = kx
where k is known as the constant of proportionality

The y axis is Money earned in $

x axis is time worked in hours

The relationship is y = kx and we are asked to find k

The constant of proportionality for this graph is nothing but the slope of the graph.

Slope can be found by taking any two points on the graph, determining the difference in y values and dividing by the difference in corresponding x values;

Two points have been chosen for us:
(3, 35.1) and (7, 81.9)

Difference in y values = 81.9 - 35.1 = 46.8 (also known as rise)

Difference in x values = 7 - 3 = 4 (also known as run)

Slope = k = rise/run = 46.8/4 = 11.7

Therefore k = 11.7

Answer: k = 11.7

Step-by-step explanation: hope this helps0^0

Answer:

The value of y is 10 cm

Answer:

Below

Step-by-step explanation:

1/81    *    27^5   =

1/(3^4)   *   (3^3)^5 =

3^-4    *    3^(3 *5)

3^-4    *   3^15

3^(-4 + 15)

3^11

The expression  1/81 * 27⁵ can be written as a power of 3 as 3¹¹.

Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.

Given expression is,

1/81 × 27⁵

We have to write the expression as a power of 3.

Write each term as a power of 3.

81 can be written as 3⁴.

27 can be written as 3³.

1/81 × 27⁵ = (1 / 3⁴) × (3³)⁵

We can use two rules here, 1/aᵇ = a⁻ᵇ and (xᵃ)ᵇ = xᵃᵇ.

1/81 × 27⁵ = 3⁻⁴ × 3¹⁵

Multiplication rule of exponent states that xᵃ × xᵇ = xᵃ⁺ᵇ.

1/81 × 27⁵ = 3⁻⁴⁺¹⁵

                = 3¹¹

Hence the expression can be written as 3¹¹.

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The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

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The expression when evaluated is 1.25

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

1.25*0.9-1.25*0.3+1.25*0.4

Evaluate the products in the expression

So, we have the following representation

1.25*0.9-1.25*0.3+1.25*0.4 = 1.125 - 0.375 + 0.5

Evaluate the like terms

1.25*0.9-1.25*0.3+1.25*0.4 = 1.25

Hence the solution is 1.25

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The required value of X is 14

The probability that the basketball player makes 0 shots out of 3 is 0.343, or 34.3%. This can be calculated by using the binomial probability formula.

To calculate the probability of any outcome of a binomial experiment, use the formula: P(x) = nCx * px * (1-p)n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in any one trial.

The Binomial Probability formula is

In this case, n = 3, x = 0, p = 0.39, and (1-p) = 0.61. Plugging these values into the formula, we get

P(x) = 3C0 * [tex]0.39^0[/tex] * 0.61³

= 0.343.

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The image of the polygon after the rotation is added as an attachment

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

(1, 0), (2, 0), (0, 2) and (2, 2)

The location of point G is

G = (3, -1)

To rotate about point G, we start by subtracting the points from G

So, we have

[(1, 0), (2, 0), (0, 2) and (2, 2)] - (3, -1)

This gives

(-2, 1), (-1, 1), (-3, 3) and (-1, 3)

The rule is 90 degrees clockwise rotation

This is represented as

(x, y) ⇒ (y, -x)

So, we have

(-2, 1), (-1, 1), (-3, 3) and (-1, 3) ⇒ (1, 2), (1, 1), (3, 3) and (3, 1)

Next, we plot (1, 2), (1, 1), (3, 3) and (3, 1)

See attachment for the image of the transformation

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Part A. The calculated correlation coefficient is incorrect.

Part B. A causal relationship for strawberries picked on the farm is the relationship between rainfall and number of strawberries picked.

Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system. The independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.

Given,

Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated.

Observing the scatter-plot, the data is moderately correlated,  as the days increase, the number of strawberries also increase, following upward trend,

r = 0.01 means that 1% of the variation in y is explained by the variation in x.

that means both quantities are very weakly correlated.

but the scatter-plot shows otherwise, so r = 0.01 is not an accurate value for the data.

Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm.

A causal relationship exists when one variable in a data set has a direct influence on another variable. Thus, one event triggers the occurrence of another event. A causal relationship is also referred to as cause and effect.

Here, rainfall could be reasonable variable that can effect the number of strawberries picked. when there is heavy rainfall, strawberries picked will be less.

Thus, the scenario could be:

Amount of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

      50                                                      40

      25                                                      80

     12.5                                                    160

     6.25                                                   320

The amount of rainfall is a cause that affect the number of strawberries picked.

Hence,

The calculated correlation coefficient is false.

Another causal relationship for strawberries picked on the farm can be of rainfall in mm and number of strawberries picked on the farm.

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After 2 hours, the Serenity and Mystic sailboats will be 68 miles apart. To determine how far apart the Serenity and Mystic sailboats will be after 2 hours, we need to calculate the total distance each boat will travel in that time.

The distance that the Serenity travels is:

distance = rate x time = 13 mph x 2 hours = 26 miles

The distance that the Mystic travels is:

Distance = rate x time = 21 mph x 2 hours = 42 miles

To use this formula, you need to know the rate at which the object is traveling and the time it has been traveling.

Simply multiply the rate by the time to calculate the distance traveled.

Since they are traveling in opposite directions, we can add these distances to find the total distance between them:

total distance = distance traveled by Serenity + distance traveled by Mystic

total distance = 26 miles + 42 miles

total distance = 68 miles

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Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

A function,

f(x) = 3 sec 2θ - 2.

The standard form of the function is,

a sec(bx - c) + d.

Here, c is a phase shift and d is a vertical shift.

So, by comparison, we get,

Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Therefore, the graph is given in the attached image.

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Answer:

1) y = -1x+-1 and 2) y = -1x+-1

Step-by-step explanation:

Slope Intercept Form: y = mx+b (m is slope and b is y-intercept)

1) 8x+8y=-8

8y = -8x+-8

y = -1x+-1

2) 3x+3y =-3

3y = -3x+-3

y = -1x+-1

Answer:

3

Step-by-step explanation:

9-7=2

2*3=6

6*2=12

75/5=15

15-12=3

Answer:

Therefore, the value of the expression 75÷5−[(9−7)×3]×2 is 138.

Step-by-step explanation:

Using the order of operations (also known as PEMDAS), we simplify the expression as follows:

First, we solve the parentheses: (9-7) = 2.

Next, we multiply 2 by 3: 2 x 3 = 6.

Then, we subtract 6 from 75: 75 - 6 = 69.

Finally, we multiply 69 by 2: 69 x 2 = 138.

Therefore, the value of the expression 75÷5−[(9−7)×3]×2 is 138.

The midpoint of the line segment is (0.5, -6.5).

A line segment is a part of a line that is bounded by two distinct endpoints. It is a finite portion of a line and has a specific length. The length of a line segment is the distance between its two endpoints, which can be calculated using the distance formula.

A line segment can be named by its two endpoints, such as AB or CD. The order of the endpoints is important, as AB and BA refer to two different line segments.

Line segments are often used in geometry and in applications such as computer graphics and image processing. They are important in many mathematical and scientific disciplines, as well as in engineering and design.

To find the midpoint of the line segment joining the pair of points (0, -10) and (1, -3), we need to find the average of their x-coordinates and the average of their y-coordinates.

Average of x-coordinates = (0 + 1)/2 = 0.5

Average of y-coordinates = (-10 + (-3))/2 = -6.5

Therefore, the midpoint of the line segment is (0.5, -6.5).

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The required real diameter of the tin is 250 mm.

Diameter is a measurement of the length of a straight line that passes through the center of a circular object, such as a circle or a sphere. It is the distance between two points on the object's edge that are furthest from each other and that pass through the center of the object.

Here,
If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:

Actual Diameter = 2.5 x Picture Diameter
Actual Diameter = 2.5 x 10 cm
Actual Diameter = 25 cm

To convert the actual diameter to millimeters (mm), we can multiply by 10:

Actual Diameter in mm = Actual Diameter x 10
Actual Diameter in mm = 25 cm x 10
Actual Diameter in mm = 250 mm

Therefore, the real diameter of the tin is 250 mm.

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Answer:

⁷

Step-by-step explanation:

questions 1 and

The volume of the largest right circular cone that can be inscribed in a sphere of radius 18 cm is approximately 11622.85 cubic centimeters.

To find the largest right circular cone that can be inscribed in a sphere of radius 18 cm, we need to find the cone with the largest possible volume that can fit inside the sphere.

Let's assume that the apex of the cone is at the center of the sphere. Since the cone is a right circular cone, the base of the cone will lie on the surface of the sphere, forming a circle with radius equal to the radius of the sphere, which is 18 cm.

Let's call the height of the cone "h" and the radius of the base of the cone "r". Then we can use the Pythagorean theorem to relate the height, radius, and slant height (which is equal to the radius of the sphere):

r^2 + h^2 = (18 cm)^2

The volume of a cone can be expressed as V = (1/3)πr^2h. We want to maximize this expression subject to the constraint above. We can use the constraint to eliminate one of the variables in the volume expression, then differentiate with respect to the remaining variable and set the derivative equal to zero to find the maximum.

From the constraint, we can solve for h^2:

h^2 = (18 cm)^2 - r^2

Substituting into the volume expression, we get:

V = (1/3)πr^2(18 cm - sqrt(r^2 + h^2))

Simplifying this expression, we get:

V = (1/3)πr^2(18 cm - sqrt((18 cm)^2 - r^2))

Differentiating with respect to r, we get:

dV/dr = (1/3)π(36 cm)r - (1/3)πr^3/sqrt((18 cm)^2 - r^2)

Setting this equal to zero and solving for r, we get:

r = (18 cm)/sqrt(2)

Substituting this value of r back into the expression for h, we get:

h = (18 cm)/sqrt(2)

Finally, substituting these values of r and h into the expression for the volume, we get:

V = (1/3)π((18 cm)/sqrt(2))^2((18 cm) - sqrt(((18 cm)/sqrt(2))^2 + ((18 cm)/sqrt(2))^2))

Simplifying this expression, we get:

V ≈ 11622.85 cubic centimeters

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The quadratic formula can be used to resolve the equation x2 - 2x - 3 = 0.

x=(-b sqrt(b2 - 4ac)) / 2a

x = (2 ± sqrt(4 + 12)) / 2

If we simplify, we get:

x = (2 ± 2sqrt(4)) / 2

x = 1 ± sqrt (4)

As a result, x = 1 + 2 and x = 1 - 2 are the solutions.

The following are the answers, separated by commas:

3, -1

[tex]x^2 + 5x + 6 = 0[/tex]

[tex]x^2 + 5x + 6 = 0[/tex]

We can factor this equation into: to find its solution.

(x + 2)(x + 3) = 0

The following answers can therefore be determined using the zero product attribute: x + 2 = 0 or x + 3 = 0.

x = -2 or x = -3

The following are the solutions, each separated by a comma:

-2, -3

36. We can factor the equation to find the solution to x2 + 3x - 4 = 0.

(x + 4)(x - 1) = 0

We can calculate x + 4 = 0 or x - 1 = 0 using the zero product property.

We obtain the following results when we solve for x: x = -4 or x = 1.

Hence, the answers are x = -4 and x = 1.

Solution: -4, 1.

37. We can factor the equation to find the solution to x2 - 6x + 5 = 0.

(x - 5)(x - 1) = 0

We can calculate x - 5 = 0 or x - 1 = 0 using the zero product condition.

We obtain x = 5 or x = 1 when we solve for x.

Hence, the answers are x = 5 and x = 1.

Respondents: 5

38. We can apply the quadratic formula x = (-b (b2 - 4ac)) / 2 to solve 6x2 + 5x + 1 = 0. (2a)

We obtain the following equation by plugging in the variables a = 6, b = 5, and c = 1: x = (-5 (25 - 24)) / 12 x = (-5 1) / 12

We obtain x = -2/3 or x = -1/2 by simplifying.

The answers are therefore x = -2/3 and x = -1/2.

Solution: -2/3, -1/2

39. The equation 4x2 + 15x + 9 = 0 can be factored as follows:

(4x + 3)(x + 3) = 0

In response to the zero product property, we get either 4x + 3 = 0 or x + 3 = 0.

When we solve for x, we have x = -3/4 or -3.

Hence, x = -3/4 and x = -3 are the answers.

Response: -3/4, -3

[tex]40. x^2 - 36 = 0[/tex]

This problem can be solved by adding 36 to both sides to obtain:

x^2 = 36

The square root of both sides can then be calculated as follows:

x = ±6

As a result, the answers are x = 6 and x = -6.

The following are the answers, separated by commas:

6, -6

[tex]41. x^2 + 12x + 36 = 0[/tex]

We can factor this equation into: to find its solution.

(x + 6)(x + 6) = 0

The zero product attribute can then be used to identify the answers:

x + 6 = 0

x = -6

Hence, the answer is x = -6. There is just one solution because both components in the factored form are identical.

The answer is: -6.

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The equilibrium price and quantity in the milk market are $37.5 and $15.75

When you combine the supply and demand curves, there is a point where they intersect; this point is called the market equilibrium. The price at this intersection is the equilibrium price, and the quantity is the equilibrium quantity.

Given that, the equations for that the supply and demand for milk:

Supply of Milk: Q = 0.50P - 3

Demand for Milk: Q = 27 - 0.30P

We need to find the equilibrium price and quantity in the milk market.

Market equilibrium is struck when:

Market Demand = Market supply

Therefore,

Market equilibrium =

0.50P - 3 = 27 - 0.30P

0.50P + 0.30P = 30

0.80P = 30

P = 37.5

Equilibrium price = 37.5

Put P = 37.5 in equation 0.50P - 3,

0.50(37.5)-3 = 15.75

Equilibrium quantity = 15.75

Hence, the equilibrium price and quantity in the milk market are $37.5 and $15.75

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The value of x for the given equation is x = e³² - 4 / 2.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 103, its logarithm in base 10 is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.

The given equation is log(x) +log(x+4)=(32).

Raise both sides of the equation to the power of e:

[tex]e^{\log x} + e^{\log (x+4)} = e^{32}[/tex]

x + x+ 4 = e³²

2x = e³² - 4

x = e³² - 4 / 2

Hence, the value of x for the given equation is x = e³² - 4 / 2.

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Answer:

The online price with 25% off is $17.25.

The original price is $21.56

To find the original price, you will multiply the discount price by 25%, or 0.25.

0.25 * 17.25 = 4.3125 or 4.31

Now you will ad that to the discount price to find the original price:

4.31 + 17.25 = 21.56

The original price was $21.56.

Step-by-step explanation:

Hope it helps! =D

Answer:

$21.56

Step-by-step explanation:

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve this, we can multiply the price by 1.25.

We multiply by 1.25 because in order to solve for the original price of an object that was 25% off, we have to add that 25% back. The reason we don't multiply by 0.25 is because if we were to do so, the price would be getting smaller, not larger.

Therefore, the original price is $21.56

Answer:

Step-by-step explanation:

If a square pen is made using four posts on each side, then the total number of posts used can be found by multiplying the number of sides by the number of posts per side. Since there are four sides to a square, we can multiply 4 by 4 to get:

4 x 4 = 16

Therefore, 16 posts were used to make the square pen.

The length of the hypotenuse of the triangle is 6√3 inches

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The given parameters are:

Angle, θ = 60°

Shortest side = 3√3

The attached diagram illustrates the right triangle, From the diagram, we have:

cos(θ) = Shortest/Hypotenuse

This gives

cos(60°) = 3√3/Hypotenuse

This gives

Hypotenuse = 3√3/cos(60°)

Evaluate cos(60°)

Hypotenuse = 3√3/0.5

Evaluate the quotient

Hypotenuse = 6√3

Hence, the length of the hypotenuse of the triangle is 6√3 inches

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The complete question is given below.

The shortest side of a right triangle measures 3V3 inches. One angle of the triangle measures 60°. What is the length in inches, of the hypotenuse of the triangle?