six boys stood equally spaced on a circle of radius $40$ feet. each boy walked to all of the other non-adjacent persons on the circle, shook their hands and then returned to his original spot on the circle before the next boy started his trip to shake hands with all of the other non-adjacent boys on the circle. after all six boys had done this, what is the least distance in feet that could have been traveled? express your answer in simplest radical form.

The temperature of the pizza after 20 minutes will be 25 degrees.

the slope refers to the measure of the steepness or inclination of a line.

We can create a linear model to describe the relationship between time and temperature.

So, slope (m) = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Using the temperature and time values from the first and last data points:

m = [tex]\frac{(145 - 450)}{(16 - 0)}[/tex]

m = -305/16

Using the point-slope form of the equation of a line, we can now ascertain the equation of the line:

y - y₁ = m(x - x₁)

Using the first data point (0, 450);

y - 450 = (-305/16)(x - 0)

Simplifying, y = (-305/16)x + 450

To predict the temperature after 20 minutes, we can plug in x = 20 and solve for y:

y = (-305/16)(20) + 450

y = -950/16 + 450

y = 25

Therefore, we can predict that the temperature of the pizza after 20 minutes will be approximately 25 degrees.

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Alpha for this confidence interval is approximately 0.021 when rounded to 3 decimals.

We can follow these steps:

Determine the z-score that corresponds to the given margin of error.

Use the z-score to find the alpha level.

Step 1: Determine the z-score
We know the margin of error (M) formula is:

M = z * (population standard deviation / sqrt(sample size)).

We are given M = 0.708219250861584, population standard deviation = 1.92, and sample size = 31. We need to find the z-score.

0.708219250861584 = z * (1.92 / √(31))
To solve for z, divide both sides by (1.92 / √(31)):

z = 0.708219250861584 / (1.92 / √(31))
z ≈ 2.036

Step 2: Use the z-score to find the alpha level

A z-score of 2.036 corresponds to an alpha level of 0.042 (which you can find using a z-table). Since the confidence interval is two-tailed, we need to divide the alpha by 2:

Alpha (α) = 0.042 / 2
α ≈ 0.021

So, the alpha for this confidence interval is approximately 0.021 when rounded to 3 decimals.

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The slope of the function is 1.

The whole function is simply f(x)=x+3

Answer:

107 hamburgers

Step-by-step explanation:

Let's call hamburgers A and cheese burgers B.

We know that A + B = 321

And that the number of cheeseburgers sold was two times the number of hamburgers sold which means ->  B = 2A

So A + 2A = 321

3A = 321

Now you need to divide both sides of the equation by 3 and you get:

A= 107

The equation of the line with slope 6/5 that passes through the point (0,3) is y = (6/5)x + 3.

The equation of a line with slope m that passes through the point (x₁, y₁) is given by:

y - y₁ = m(x - x₁)

In this case, we know that the slope is 6/5 and the line passes through the point (0,3), so we can substitute these values into the equation:

y - 3 = (6/5)(x - 0)

Simplifying:

y - 3 = (6/5)x

Multiplying both sides by 5 to eliminate the fraction:

5y - 15 = 6x

Adding 15 to both sides:

5y = 6x + 15

Dividing both sides by 5 to solve for y:

y = (6/5)x + 3

Therefore, the equation of the line with slope 6/5 that passes through the point (0,3) is y = (6/5)x + 3.

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The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

What is the polynomial equation?

A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.

Assuming that the expression is 7 + 3p²:

To write the polynomial in standard form, we need to arrange the terms in descending order of degree:

3p² + 7

hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.

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Using the empirical rule, the percentage of IQ scores that are greater than 79 is 84%.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

Since we know that the mean is 96 and the standard deviation is 17, we can calculate how many standard deviations away from the mean an IQ score of 79 is:

(79 - 96) / 17 = -1

This means that an IQ score of 79 is one standard deviation below the mean. This also means that approximately 68% of the data falls between 79 and (96 + 17) = 113.

Meanwhile, approximately 32% of the data falls outside of one standard deviation. We can say that half of this 32% are scores less than 79 and the other half are scores greater than 113. So the percentage of IQ scores greater than 79 is:

100 - (1/2 of 32) = 84%

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The final amount after 2 years of compounding semiannually at 11% is $31,909.52.

First we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where

Plugging in the given values, we get:

P = $24,700

r = 0.11 (11% annual rate as a decimal)

n = 2 (compounded semiannually, or twice per year)

t = 2 (2 years)

A = $24,700(1 + 0.11/2)^(2*2)

= $31,909.52

Therefore, the final amount after 2 years of compounding semiannually at 11% is $31,909.52.

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By the Triangle Sum Theorem, x + y + a = 180° and x + y + b = 180°. By substitution, x + y + a = 180°. Subtract equal quantities from both sides to get a = b.

In Mathematics, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

x + y + b = 180°

By substitution, we have the following:

x + y + a = 180°

Next, we would subtract equation 1 from equation 2, we have:

a - b = 0

a = b (Prove).

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After answering the provided question, we can state that As a result, expression rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

An expression in mathematics is a collection of interpretations, digits, and transnational corporations that resemble a causative link or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include extension, subtraction, rapid spread, separation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Because the dot plot is not symmetrical and the distribution appears to be skewed towards higher ratings, a rating of 6 may not be a good description of the centre of this data set. The numbers 8, 9, and 10 are more common than the numbers 0-7, indicating that the data set has a right skew.

As a result, the centre of the data set may be better described by a measure of central tendency that accounts for data skewness, such as the median.

As a result, rather than a rating of 6, it would be more appropriate to use the median to describe the centre of this data set.

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Answer: In any right angled triangle , the square of the length of the hypotenuse (longest side) is equal to the sum of square of length of the other two side (i.e. adjacent leg and opposite leg)

No, the idea that water always goes down the drain counterclockwise in the northern hemisphere and clockwise in the southern hemisphere is a myth.

The direction that water drains is actually determined by the shape of the sink or toilet bowl, as well as any other factors such as the water pressure and the motion of the water before it enters the drain. The Coriolis effect, which is often cited as the cause of the supposed clockwise/counterclockwise rotation, only affects large-scale phenomena like weather patterns and ocean currents, and is not noticeable in small-scale phenomena like draining water. So, in reality, the direction that water drains is not determined by the hemisphere in which you are located.

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Complete question

Does water go down the drain counterclockwise in the northern hemisphere and clockwise in the southern hemisphere?

To find how many years Napoleon Bonaparte lived, we can subtract his year of birth from his year of death:

Years lived = Year of death - Year of birth

Years lived = 1821 - 1769

Years lived = 52

Therefore, Napoleon Bonaparte lived for 52 years.

Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

They are asking us to calculate the volume of a cycle, formed by a cylinder (The cycle is shaped like a cylinder).

To calculate the volume, we apply the formula:

We know that the height you have is 150 feet, and the radius is 35 feet, we solve:

V = 3.14 × (35 ft)² × 150 ft

V = 3.14 × 1225 ft² × 150 ft

V = 576975 ft³

Therefore, the volume of a cycle that is shaped like a cylinder with a height of 150 feet and a radius of 35 feet is 576975 ft^3.

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Answer:

Step-by-step explanation:

The Answer is 203 Fahrenheit.

(95 x 9/5) + 32 = 203

The answer is in the picture

If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, then she will pay $119.

The cοst οf anything is the sum οf mοney οr resοurces that must be used up in οrder tο acquire οr manufacture it. It is a measurement οf the cοsts incurred tο attain a specific οbjective οr result.

The expressiοn tο represent the cοst οf Karina's theme park trip wοuld be:

38 + 10 + 4h + (1/2)r

This includes the $38 entry price, the $10 lunch expense, and the $4 per hοur parking expense fοr the 72 hοurs. Given that Karina and her friend are splitting the cοst οf the hοtel rοοm, the final phrase (1/2)r denοtes Karina's pοrtiοn οf the expense.

If the hοtel rοοm fοr Karina and her friend cοsts $86 and they park fοr 7 hοurs, we can change these values intο the fοrmula tο make it simpler:

= 38 + 10 + 4(7) + (1/2)(86)

= 38 + 10 + 28 + 43

= $119

Therefοre, Karina will pay $119 fοr her theme park trip.

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Answer:

False.

Step-by-step explanation:

Use Pythagorean theorem.

919681+1022121=1067089

1941802≠1067089

so the triangle is acute, not right.

Answer:

number A

Step-by-step explanation:

Answer:

I think the answer is x= -0.66 . .. and continuous more 6's

Step-by-step explanation:

I hope this helps. Have a good day!

The minimum sample size required to ensure that the estimate has an error of at most 0.15 at the 99% level of confidence = 426

Here, the population variance is σ² = 1.44

The mean is [tex]\bar{x}[/tex] = 6

And the margin of error is  E = 0.15

The standard deviation is given by,

⇒ σ = [tex]\sqrt{1.44}[/tex]

⇒ σ = 1.2

Here, the confidence level is 99%

So, the level of signoficance would be,

⇒ α = (100 - 99)%

⇒ α = 0.01

From the normal distribution table the critical value would be,

[tex]z_{\alpha /2}[/tex] = 2.58

Now we find the sample size :

[tex]n=(\frac{z_{\alpha /2}\times \sigma}{E} )^2\\\\n=(\frac{2.58 \times 1.2}{0.15} )^2[/tex]

n = 426

Therefore, the sample size is 426

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Step-by-step explanation:

A. 7

B. 22,5

C. symmetrical, because the mean and the median are not the same

Answer:

360 adult tickets and 800 student tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve this problem.

Let x be the number of adult tickets sold, and y be the number of student tickets sold. We know that a total of 1,160 tickets were sold, so:

x + y = 1160

We also know that the total amount collected was $2,600. The amount collected from adult tickets is $5 times the number of adult tickets sold, and the amount collected from student tickets is $1 times the number of student tickets sold. So:

5x + 1y = 2600

Now we have a system of two equations:

x + y = 1160

5x + y = 2600

We can solve for one of the variables in terms of the other, and substitute into the other equation to solve for the remaining variable. For example, we can solve the first equation for y:

y = 1160 - x

Now substitute this expression for y into the second equation:

5x + (1160 - x) = 2600

Simplifying and solving for x:

4x + 1160 = 2600

4x = 1440

x = 360

So 360 adult tickets were sold. To find the number of student tickets sold, we can use either equation. Let's use the first equation:

x + y = 1160

360 + y = 1160

y = 800

So 800 student tickets were sold.

Therefore, 360 adult tickets and 800 student tickets were sold.

Therefore, the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4) is -30 degrees.

An ellipse is a geometric shape that resembles a stretched or squished circle. It can be defined as the set of all points in a plane, such that the sum of the distances from two fixed points, called the foci, is constant. An ellipse has two axes, a major axis and a minor axis, which intersect at the center of the ellipse. The length of the major axis is twice the distance from the center to one of the foci, while the length of the minor axis is twice the distance from the center to one of the points where the ellipse intersects the major axis. Ellipses have many applications in mathematics, physics, and engineering. They are used to model the orbits of planets and satellites, as well as the paths of objects in electric and magnetic fields. They are also used in optics to describe the shape of lenses and mirrors, and in statistics to model data distributions.

Here,

To determine the angle at which the ellipse x² + 3y² = 12 is seen from the point M (0,4), we first need to find the equation of the tangent line to the ellipse at the point (0,4).

To do this, we take the derivative of the equation of the ellipse with respect to x and evaluate it at the point (0,4):

d/dx (x² + 3y²) = 2x + 6y(dy/dx)

At the point (0,4), we have x = 0 and y = 4, so the equation becomes:

0 + 6(4)(dy/dx) = 0

Solving for dy/dx, we get:

dy/dx = 0

This means that the tangent line to the ellipse at the point (0,4) is a horizontal line passing through the point (0,4).

Now we can find the angle at which the ellipse is seen from the point M (0,4) by finding the angle between the horizontal tangent line and the line connecting the point M to the origin. This angle is given by:

tan θ = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) = (0,4) is the point M and (x₂, y₂) is the point where the tangent line intersects the x-axis.

Since the tangent line is horizontal, it intersects the x-axis at the point (±2√3, 4), which are the x-intercepts of the ellipse. Choosing the positive x-intercept, we have:

x₂ = 2√3

y₂ = 0

Substituting these values into the formula for the tangent, we get:

tan θ = (0 - 4)/(2√3 - 0) = -2/2√3 = -1/√3

Taking the inverse tangent of both sides, we get:

θ = -30 degrees

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The principal will be outstanding at the halfway time C) p = $3218 & P(180) = 313,722.

Principal is an amount of money borrowed or invested, on which interest is paid. It is the original sum of money that is invested or borrowed and not the interest that accumulates over time. Principal is the amount of money before any interest or other costs are added. Borrowers must pay back the principal plus interest when the loan is due. Investors can earn returns on their principal when an investment is successful.

The payment for a 30 year $400,000 mortgage at 9% compounded monthly is calculated using the following formula:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^⁻³⁶⁰))
Plugging in the given values, we get:
p = (400000 * (1 + (0.09/12))³⁶⁰)/(360 * (1 - (1 + (0.09/12))^-360)) = $3218
The amount of principal outstanding at the halfway time (180 payments) is calculated using the following formula:
P(180) = 400000 - (p * 180)
Plugging in the given values, we get:
P(180) = 400000 - (3218 * 180) = 313,722
Therefore, the answer is C) p = $3218 & P(180) = 313,722.

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If You take a 30 year $400,000 mortgage at 9% compounded monthy. the paynebt will be $3218 and P(180) = 317,322.  The correct answer is A) p = $3218 & P(180) = 317,322.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves the measurement of the likelihood or chance of an event occurring, based on the ratio of the number of favorable outcomes to the total number of possible outcomes.

To calculate the monthly payment for the mortgage, we can use the formula:

P = A / ((1 - (1 + r)^(-n)) / r)

where P is the monthly payment, A is the loan amount ($400,000), r is the monthly interest rate (9%/12 = 0.0075), and n is the total number of payments (30 years x 12 months/year = 360 payments).

P = 400000 / ((1 - (1 + 0.0075)^(-360)) / 0.0075)

P = $3,219.64 (rounded to the nearest cent)

Therefore, the monthly payment is $3,219.

To find the outstanding principal balance at the halfway time (180 payments), we can use the formula for the remaining balance of a loan after t payments:

P(t) = A * ((1 + r)^t - 1) / (r * (1 + r)^t)

where P(t) is the remaining principal balance after t payments.

P(180) = 400000 * ((1 + 0.0075)^180 - 1) / (0.0075 * (1 + 0.0075)^180)

P(180) = $313,721.87 (rounded to the nearest dollar)

Therefore, the correct answer is A) p = $3218 & P(180) = 317,322.

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Answer: It costs 23.75 for 5 bags of cat food.

Step-by-step explanation: If 3 bags of cat food costs 14.25 to figure out how much it costs. First thing to do is, divide the known number (14.25) or the costs by the amount of bags that made up to this price.

14.25 divided by 3 equals 4.75.

4.75 is the costs of 1 bag of cat foods. Now for the final step, multiply the cost of 1 bag (4.75) by 5 because we’re trying to see how much it costs for 5 bags of cat food.

4.75

x 5

= 23.75!

you’re welcome!!

Since no specific figure or measurements were provided in the student question, it's important to follow these steps for any given 3-dimensional shape.

To find the volume and surface area of a figure, follow these steps:
Identify the type of figure
Determine the shape of the figure, whether it's a sphere, cube, cylinder, or another 3-dimensional shape.
Determine the necessary measurements
Depending on the figure, gather measurements like the length, width, height, or radius.
Calculate the volume
Use the appropriate formula for the figure's volume:
- Cube: [tex]V = L^3[/tex](L = length)
- Rectangular prism: V = L * W * H (L = length, W = width, H = height)
- Sphere: V = (4/3) * π * [tex]r^3[/tex](r = radius)
- Cylinder: V = π *[tex]r^2[/tex] * h (r = radius, h = height)
Calculate the surface area
Use the appropriate formula for the figure's surface area:
- Cube: SA = 6 *[tex]L^2[/tex] (L = length)
- Rectangular prism: SA = 2 * (L * W + L * H + W * H) (L = length, W = width, H = height)
- Sphere: SA = 4 * π * [tex]r^2[/tex] (r = radius)
- Cylinder: SA = 2 * π * r * (r + h) (r = radius, h = height)
Round your answers to the nearest hundredth, if necessary
Use standard rounding rules to round the calculated volume and surface area to the nearest hundredth.

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Answer:

x = 2 and x = 1/2.

Step-by-step explanation:

To solve (x-2)(2x-1) = 0, we need to find the values of x that make the left side of the equation equal to 0.

Using the zero product property, we know that if the product of two factors is equal to 0, then at least one of the factors must be equal to 0.

Therefore, we have two possible solutions:

1.x - 2 = 0, which gives us x = 2

2.2x - 1 = 0, which gives us x = 1/2

So, the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

After answering the presented question, we can conclude that As a equation result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

y = x/10 is the provided equation.

If a residence uses 0 kWh of power (x=0), the cost of electricity is as follows:

y = x/10 = 0/10 = $0 per kWh.

As a result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

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