the mathcounts international airport had 738,114 departures in 2001. if these were distributed uniformly throughout each 24-hour period, what is the mean number of seconds between each departure time? express your answer to the nearest whole number.

The two plans will cost the same when Lucy has driven 550miles. ($55 + $0.50 x 550)= $330

(0.6*550)=$330

The difference between both the trip rate is .10$

and the difference between initial fee is 55$

so after 1 mile the difference is .10$

the 55$can be earn after

55*10=550 mile.

Divide the overall distance traveled by the time period to find the average speed. An someone traveling at an average speed of 40 miles divided by 40 minutes, or 1 mile per minute, would be driving 20 miles north and then 20 miles south to arrive at the same location (60 mph)

The overall distance traveled by an object over the total amount of time is the thing's average speed. The average speed v of an object during a motion that covers a total distance of d and a total duration of t can be estimated using the formula v = d t.

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The matrix representation of t with respect to the basis is {(1,0,0), (1,1,0), (1,1,1).

T: 1R^3 -> IR^3 activated by

T(x1 y1 z1) = (x+y+z, y+z, 0)

(1,0,0), (0,1,0), (0,0,1) be standard basis of IR^3

Therefore T(1,0,0) = (1,0,0)

(1,0,0) is 1st column of matrix of T

T(0,1,0) = (1,1,0)

(1,1,0) is 2nd column of matrix of T

T(0,0,1) = (1,1,0)

(1,1,0) is 3rd column of matrix of T

Therefore Matrix representation of T with respect to standard basis of IR^3 is

A = 1,1,1    0,1,1    0,0,0

2. Nullspace of T = kennel T

KerT = {(x,y,z)E IR^3/T(x,y,z,) = (0,0,0)}

KerT = {(x,y,z)E IR^3/(x+y+z, y+z,0) = (0,0,0)}

KerT = {(x,y,z)E IR^3/(x+y+z = 0, y+z,0)

KerT = {(x,y,x) EIR^3/x = 0, y = -2}

KerT = {(0,-z,z)}

KerT = {z(0,-1,1)} = Multiple of T

As it contains only one linear independent rectors = nullity = 1

3. Range T = {T(x,y,z)/(x,y,x) EIR^3}

= {(x+y+z, y+z,0)}

Range T = {(x+y+z)(1,0,0) + (y+z)(0,1,0)}

As range contains only two linear independent rectors = Rank = 2

4. T(x,y,z) = (x+y+z, y+z,0)

consider basis, B = {(1,0,0), (1,1,0), (1,1,1)}

T(1,0,0) = (1,0,0)

(1,0,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(1,0,0) = (a+b+c, b+c, c)

a+b+c = 1, b+c = 0, c = 0

b = 0, a = 1

Therefore above of a,b,c gives first column matrix

Now,

T(1,1,0) = (2,1,0)

consider (2,1,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(2,1,0) =  (a+b+c, b+c, c)

a+b+c = 2, b+c = 1, c = 0

b = 1, a = 1

Therefore above values of a,b,c gives 2nd column of matrix

Now,

T(1,1,1) = (3,2,0)

(3,2,0) = a(1,0,0) + b(1,1,0) + c(1,1,1)

(3,2,0) = (a+b+c, b+c, c)

a+b+c = 3, b+c = 2, c = 0

b = 2, a = 1

Therefore above values of a,b,c gives 3rd column of matrix

Hence the answer is the matrix representation of t with respect to the basis is {(1,0,0), (1,1,0), (1,1,1).

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If a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

Reflecting a point over the x-axis negates the y-coordinate, while leaving the x-coordinate unchanged.

Therefore, reflecting (-1,4) over the x-axis gives us the point (-1,-4).

Translating a point up 3 units means adding 3 to the y-coordinate. Therefore, translating (-1,-4) up 3 units gives us the point:

(-1, -4 + 3) = (-1, -1)

So the final point is (-1,-1).

Hence, if a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)

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Answer:

No, he is wrong

Step-by-step explanation:

To find that probability, the first thing we need to know is the total number of coins present.

Mathematically, that would be 3 + 2 + 3 = 8

Since there are 8 coins, the probability of selecting a dime is number of dimes/total number of coins = 2/8 = 1/4

The probability we want to work with is that the two selections are dimes, let’s say with replacement.

That means; first selection is a dime and second selection is also a dime

Mathematically in probability, the term and means that we have to multiply our results.

So the probability that both are dimes would be 1/4 * 1/4 = 1/16

And this makes his answer wrong

Answer:

Dividend: 3 1/2

Divisor: 1 3/4

To solve this problem, we can convert both mixed numbers to improper fractions:

Dividend: 7/2

Divisor: 7/4

Then we can divide the two fractions:

(7/2) ÷ (7/4) = (7/2) x (4/7) = 2

So the quotient is 2, which is a whole number. Therefore, the division problem 3 1/2 ÷ 1 3/4 = 2 has been solved.

Answer:

A. 14 nickles

Step-by-step explanation:

Answer:

55.9%

Step-by-step explanation:

To find the percentage of girls in the class, we can use the following formula:

Percentage = (Number of girls / Total number of students) * 100

Number of girls = 19

Total number of students = 34

Percentage = (19 / 34) * 100

                   = 55.88235 % ≈ 55.9 % ( rounded off to one decimal place)

1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.

[(40 km /h) / (50 km / h)] = t / 20 min

4 / 5 = t / 20

t = 80 / 5

t = 14 min

El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:

r = [(50 km / h) / (90 km / h)] × 100 %

r = 55.556 %

La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

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Answer:

3,6have you are not the same as the one that is why

Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

107

Step-by-step explanation:

Answer:

well instead of being the value of 50 it would be the value of 5.

Step-by-step explanation:

It's being moved to the ones place

Answer:

it would be 5, if it moves to the right it takes the place of the 6

In the context of your experiment comparing the effectiveness of two treatments using a randomized block design, the following must be true:

1. The subjects are divided into two blocks based on their age: under 40 years and 40 years or older.
2. Randomization is used within each block to assign subjects to one of the two treatments. This ensures that each treatment group within a block has a random mix of subjects, reducing potential biases.
3. The purpose of blocking by age is to control for any confounding variables or potential effects that age might have on the treatment outcomes. By blocking, researchers can more accurately measure the differences between the two treatments.
4. The experiment is well-designed, which means it should minimize potential sources of error, include sufficient sample size, and ensure proper randomization and data collection.
5. To analyze the results, researchers will compare the treatment outcomes within each age block and then combine the results to get an overall measure of the effectiveness of the two treatments.

By using a randomized block design in this experiment, researchers can control for age-related factors and obtain a more accurate comparison of the treatment effectiveness.

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Answer:

D, because parallel lines never have a solution.

Step-by-step explanation:

The graphs which show no solution is required.

Option D has no solution.

When a system of linear equations have a solution means that the lines intersect each.

This means for a given \(x\) value of both equations there exists the same \(y\) value.

Options A, B and C all have lines that intersect each other at some point.

In option D the lines are parallel to each other.

So, option D has no solution.

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By following these steps, you can choose a suitable container shape, calculate the volume and surface area of the donuts and the container, and ensure the two donuts fit comfortably without being squished together.

To find a suitable container for two Dunkin Donuts, you need to consider the size of the donuts and ensure they fit without being squished together. Here's a step-by-step process:

Research the dimensions of a Dunkin Donut: Find the average diameter and height of a single donut. Let's say the diameter is 8 cm, and the height is 2 cm.

Determine the shape of the container: Since you want to minimize the size, a cylinder might be a good choice due to its efficiency in utilizing space.

Calculate the volume of the donuts: The volume of a single donut can be calculated using the formula V = πr²h, where r is the radius (half of the diameter) and h is the height. Calculate the volume of two donuts.

Calculate the volume of the container: Determine the dimensions of the cylinder that can accommodate the two donuts. Adjust the radius and height to ensure the volume of the container is slightly larger than the volume of the donuts.

Calculate the surface area of the container: Find the surface area of the cylinder using the formula SA = 2πrh + 2πr².

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Step-by-step explanation:

Check the above photos....

Volume is a three-dimensional scalar quantity. The volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a cone with a base radius of 4 ft. and height of 8 ft. can be written as,

Volume = (π/3)×(Radius)²×Height

             = (π/3)×(4)²×8

             = 134.0412 ft³ ≈ 134 ft³

Hence, the volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.

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a. The formula B = 703w/h^2 can be solved for w by rearranging the equation as w = B * h^2 / 703.
b. For a person who is 64 inches tall and has a body mass index of 21.45, the weight can be calculated by substituting the values into the formula w = B * h^2 / 703, where B is 21.45 and h is 64 inches.

a. To solve the formula B = 703w/h^2 for w, we can rearrange the equation to isolate w on one side of the equation. Multiply both sides of the equation by h^2, then divide both sides by 703. The resulting equation is w = B * h^2 / 703.
b. To find the weight of a person who is 64 inches tall and has a body mass index of 21.45, we can substitute the values into the formula w = B * h^2 / 703. In this case, B is 21.45 and h is 64 inches. Plugging these values into the equation, we get w = 21.45 * 64^2 / 703. Evaluating this expression will give us the weight in pounds.

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Answer:

6000 seconds.

Step-by-step explanation:

Given:

A car covers a distance of 14.75km in 20 minutes.

find:

In how many seconds, will it cover a distance of 73.75km

solution:

the idea is ratio and proportion to get the time based on 73.75 km from 14.75km./20min. in seconds.

 14.75 km.    =  73.75 km    --------> cross multiply

   20 min.              t

14.75 (t) = 73.75 (20)

14.75 (t) = 1475

t =    1475  

      14.75

t = 100 min.  -----------> convert min to seconds.

100 min. x   60 secs.      =          6000 seconds

                      1 min.

therefore,

the time in seconds to travel a distance of 73.75 km is 6000 seconds.

Answer:

The probability is 1/6

Step-by-step explanation:

Firstly, we need to get the total number of coins

that would be the sum of all the coins present

We have this as;

8 + 10 + 4 + 2 = 24 coins

The number of nickels is 4

So the probability of selecting a nickel is the number of nickels divided by the total number of coins

We have this as;

4/24 = 1/6

Answer:

Step-by-step explanation:

Required function is:

The capacity of Supercut in customers per hour is 18.

The capacity of Supercut is the total number of customers served by three stylists in an hour, considering the average time it takes each stylist to serve one customer. This capacity calculation helps Supercut in keeping up with demand and avoiding long waiting periods, which could discourage clients.

The given data: Supercut salon has three stylists. The average time each stylist takes to serve one customer is 10 minutes. According to the data provided, it takes 10 minutes for each stylist to serve one customer, and there are three stylists. So, in 1 hour (60 minutes), each stylist will have the capacity to serve six clients.

Supercut's total capacity in an hour is calculated by adding up the capacity of each stylist. Therefore, the capacity of Supercut is: Capacity of Supercut = Capacity of each stylist * Number of Stylists= 6 customers * 3 stylists= 18 customers. Therefore, the capacity of the Supercut salon in customers per hour is 18.

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Answer:

SSS

Step-by-step explanation:

It would be SSS.

XY is congruent to ZY.

XW is congruent to ZW.

YW is congruent to WY.

Hope this helps!

So let's check:

So as we can see all are sides make the triangle congruent so option D is correct ie SSS (side,side,side)

Answer:

the independent variable goes on the x-axis (the bottom, horizontal one) and the dependent variable goes on the y-axis (the left side, vertical one).

Step-by-step explanation:

The normalization constant, N, is given by:

\(N = \sqrt{Z / (8 * a_0)}\)

To calculate the normalization constant, N, for the given wavefunction, we need to integrate the square of the wavefunction over all space and set it equal to 1.

The given wavefunction is:

ψ(r) = N * (2/Z * a₀)^(3/2) * exp(-r/Z * a₀)

where:

N: Normalization constant

Z: Atomic number

a₀: Bohr radius

r: Radial distance from the nucleus

To calculate the normalization constant, we need to integrate the square of the wavefunction, ψ(r)², over all space and set it equal to 1. Since the wavefunction only depends on the radial distance, we will integrate with respect to r.

∫[0,∞] |ψ(r)|² * r² * dr = 1

Let's start by calculating |ψ(r)|²:

|ψ(r)|² = |N * (2/Z * a₀)^(3/2) * exp(-r/Z * a₀)|²

= N² * (2/Z * a₀)³ * exp(-2r/Z * a₀)

Now, we substitute this back into the integral:

∫[0,∞] N² * (2/Z * a₀)³ * exp(-2r/Z * a₀) * r² * dr = 1

To solve this integral, we can separate it into three parts: the exponential term, the radial term, and the constant term.

∫[0,∞] exp(-2r/Z * a₀) * r² * dr = I₁ (say)

∫[0,∞] I₁ * N² * (2/Z * a₀)³ * dr = I₂ (say)

I₂ = N² * (2/Z * a₀)³ * I₁

To calculate I₁, we can perform a change of variables. Let u = -2r/Z * a₀:

∫[0,∞] exp(u) * (Z/2a₀)³ * (-Z/2a₀) * du

= (-Z/2a₀)⁴ ∫[0,∞] exp(u) * du

= (-Z/2a₀)⁴ * [exp(u)] from 0 to ∞

= (-Z/2a₀)⁴ * [exp(-2r/Z * a₀)] from 0 to ∞

= (-Z/2a₀)⁴ * [0 - 1]

= (-Z/2a₀)⁴ * (-1)

= (Z/2a₀)⁴

Substituting this value back into I₂:

I₂ = N² * (2/Z * a₀)³ * (Z/2a₀)⁴

= N² * 8 * a₀ / Z

Now, we can set I₂ equal to 1 and solve for N:

1 = N² * 8 * a₀ / Z

N² = Z / (8 * a₀)

Therefore, the normalization constant, N, is given by:

\(N = \sqrt{Z / (8 * a_0)}\)

Note: In the given question, there seems to be a duplication of the normalization constant, N, in the wavefunction. It appears as N * N, which is not necessary. The correct wavefunction should be:

ψ(r) = N * (2/Z * a₀)^(3/2) * exp(-r/Z * a₀)

with a single N term.

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An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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Answer:

42.42 in³ volume of juice

Step-by-step explanation:

Jim is making frozen juice treats that are in the shape of a cone.

The volume of a cone = πr²h/3

From the above question:

h = 3 inches

Diameter = 3 inches

Radius = Diameter/2

= 3/2

= 1.5 inches

The volume for 1 frozen treat =

= π × 1.5² × 3/3

= 7.07 in³

The approximate volume of juice needed for Jim to make 6 juice treats

is calculated as:

1 juice treat = 7.07 in³

6 juice treats = x

Cross Multiply

x = 6 × 7.07 in³

x = 42.42 in³

Answer:

varied

square root of number never result negative number

Step-by-step explanation:

There will only be one real solution.

If \(x\) is a real number, the square root function \(\sqrt x\) will only have real solutions when \(x\ge0\).

For \(x<0\), we get imaginary solutions.

Also, when \(\sqrt x> 0\), \(x>0\)

In other words, when the square root of \(x\) is a positive real number,  \(x\) will be a unique positive number.

We can see this when trying to solve the equation given in the question

So, the equation

\(\sqrt x=c\)

where \(c>0\), when solved, will give

\(\sqrt x=c\\(\sqrt x)^2=c^2\\x=c^2\)

We will have a unique solution because squaring a positive real number gives a single result.

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