A hockey tournament consists of 16 teams. In the first round, every team is randomly assigned to one of 8 games (2 teams per game). Suppose exactly 3 of the teams are from Alberta. What is the probability all 3 Alberta teams are randomly assigned to different games (call this event A)?

The tangential component of the acceleration vector is given by the derivative of the velocity vector with respect to time, which is the second derivative of the position vector with respect to time.

In this case, the tangential component is obtained by taking the derivative of the velocity vector r'(t) = (5(3 − 3t^2))i + (30t)j. The normal component of the acceleration vector is obtained by taking the magnitude of the acceleration vector and subtracting the tangential component.

It represents the acceleration perpendicular to the tangent line. The magnitude of the acceleration vector is given by |a(t)| = sqrt((5(−6t))² + (30)²) = 30sqrt(t² + 1), and the normal component can be calculated as sqrt((5(−6t))² + (30)²) - |r''(t)|.

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Answer:

23

Step-by-step explanation:

It appears that you want to find the value of the expression 4x - 6 ÷ x when x = 6.  Replacing each instance of x with 6, we get:

4(6) - 6 ÷ (6)

Order of opertions rules require that we perform multiplication and division before addition or subtraction.  Thus, our

4(6) - 6 ÷ (6) becomes 24 - (6/6), or 24 - 1, or 23.

Answer:

im not sure if my answer is correct

The missing statement in the proof is; AB/BD = CB/EB

Similar triangles have the same corresponding angle measures and proportional side lengths.

The given proof is the triangle proportionality theorem which states that the segments formed by side DE are proportional.

The two column proof is presented as follows;

Statement                                           Reason

1. DE || AC                                             1. Given

2. ∠CAB ≅ ∠EDB        2. Corresponding angles formed between ║ lines

3. ΔABC ~ ΔDBE                  3. AA criterion for similarity

4. AB/BD = CB/EB                4. Corr. sides of similar Δs are prop.

5. AB = AD + DB                   5. Segment addition CB = CE + EB

6. (AD + DB)/(DB) = (CE + EB)/(EB)        6. Substitution Property of Equality

7. (AD)/(DB) + 1 = (CE)/(EB) + 1               7. Division

8. (AD)/(DB) = (CE)/(EB)                          8. Subtraction Property of Equality

Hence, the missing statement in the proof is; AB/BD = CB/EB

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Answer:

C

Step-by-step explanation:

\(12000 \times {1.05}^{4} = 14586\)

Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

A set of numbers known as coordinates describes a point or object's location in a given space or coordinate system. When representing a spot's location in a plane or three-dimensional space, coordinates are frequently expressed as x or triples in mathematics. Depending also on system being utilised, several values can be used to represent coordinates, although often, integers or real numbers are used to express them.

given

We can substitute negative values for x and solve for y to obtain three pairs of negative x and y coordinates that lie on the line y = 3x + 4.

With x = 1, y = 3(-1), plus 4, equals 1. Hence, one set of negative x and y coordinates is (-1, 1).

Y = 3(-2) + 4 = -2 when x is equal to 2. In light of this, another set of negative x- and y-coordinates is (-2, -2).

Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

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The numbers in this problem are classified as follows:

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Answer:

796 feet

Step-by-step explanation:

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

y = -3x + 4

Step-by-step explanation:

y = 4, this is where your line intersects with the y axis.

x = 1 is where your line is on the x axis (you want to include the part of the line that hits a point straight on, not one that goes past it.) So when it lands on the corner of the grids like the 4 for the y axis does, that is the point you are going to use.

Rise/Run is then your equation, so since you go down 3 and over 1 (counting from your y axis point), your slope is -3/1 or -3.

Then goes your y axis, so the final equation is

y= -3x + 4

I hope this helped!

Answer:

n = 9

Step-by-step explanation:

2n - 41 = - 23

2n = - 23 + 41

n = 18/2

Answer:

Step-by-step explanation:

5 3/4 + 2 1/2

Add the whole numbers first

5 + 2

Add the fractions next

3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 and 1/4

The total is

7 + 1 1/4 = 8 1/4

Step-by-step explanation:

solution given:

\(5 \times \frac{3}{4} + 2 \times \frac{1}{2} \\ \frac{23}{4} + \frac{5}{2} \\ \frac{23 + 10}{4} \\ \frac{33}{4} \\ is your answer\)

Answer:

67

Step-by-step explanation:

we are given adjacent and opposite sides. thus tan^-1 would be used to determine the angle

opposite side = 665 - 5 = 660

adjacent side = 280

tan = opposite / adjacent

\(tan^{-1}\) (660/280) = 67

Answer:

67

Step-by-step explanation:

I took it on EDG

Answer:

3,724 cubic inches

Step-by-step explanation:

All you have to do is multiply 19•14•14

The required mean absolute deviation of the number of goals is 0.8.

The mean of the values is the ratio of the total sum of values to the number of values.

The mean absolute deviation of the number of goals is a measure of how far the individual scores deviate from the mean (average) score.

To find the mean (average) score:

Mean = (2 + 3 + 5 + 3 + 2) ÷ 5 = 15 ÷ 5 = 3

Next, we find the absolute deviation for each score:

Absolute deviation for score 2: |2 - 3| = 1

Absolute deviation for score 3: |3 - 3| = 0

Absolute deviation for score 5: |5 - 3| = 2

Absolute deviation for score 3: |3 - 3| = 0

Absolute deviation for score 2: |2 - 3| = 1

Mean absolute deviation is given as,
= (1 + 0 + 2 + 0 + 1) ÷ 5 = 4 ÷ 5 = 0.8

So, the mean absolute deviation of the number of goals is 0.8.

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Answer:

y intercept = -3

the slope of the line is 1

Step-by-step explanation:

y intercept is the value of y when x = 0

x = 0 when y = -3

Answer:

x=3

Step-by-step explanation:

3x-5x+25= 5x+4

-2x+25=5x+4

+2x.      +2x

25=7x+4

-4.      -4

21=7x

/7. /7

3=x

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

3x - 5(x -5) = - 3 + 5x + 7

3x - 5x + 25 = 4 + 5x

3x - 5x -5x = 4 - 25

-7x = -21

x = -21 : (-7)

x = 3

The population of rabbits on a farm grows by 12% each year. The sequence starts with r0 = 30.

(a) A mathematical expression for r12 is r12 = (1 + 0.12)r11 = \((1 + 0.12)(1 + 0.12)^{10}(30)\) = \((1 + 0.12)^{11}(30)\)

(b) If each rabbit consumes 10 pounds of rabbit food each year, then rabbit food consumed in 10 years is 10(r0(1 - \((1 + 0.12)^{10})\) / -0.12) = \(10(30(1 - (1 + 0.12)^{10})\) / -0.12)

To define the sequence {rn}, we can use the formula:
rn = (1 + 0.12)rn-1
where rn-1 is the rabbit population at the end of the previous year.
Starting with r0 = 30, we can calculate the population at the end of each year:
r1 = (1 + 0.12)r0 = 33.6
r2 = (1 + 0.12)r1 = 37.632
r3 = (1 + 0.12)r2 = 42.150144
...
rn = (1 + 0.12)rn-1
(a) To find a mathematical expression for r12, we can use the formula:
r12 = (1 + 0.12)r11
where r11 is the rabbit population at the end of the 11th year:
r11 = (1 + 0.12)r10 = \((1 + 0.12)^{10}r0\)
Substituting r0 = 30, we get:
r11 = \((1 + 0.12)^{10}(30)\)
Therefore, the mathematical expression for r12 is:
r12 = (1 + 0.12)r11 = \((1 + 0.12)(1 + 0.12)^{10}(30)\) = \((1 + 0.12)^{11}(30)\)
(b) The total amount of rabbit food consumed in 10 years can be expressed as:
10(r0 + r1 + r2 + ... + r9)10
To simplify the expression, we can use the formula for the sum of a geometric sequence:
r0\((1 - (1 + 0.12)^{10})\) / (1 - (1 + 0.12)) = r0\((1 - (1 + 0.12)^{10})\) / -0.12
Substituting r0 = 30, we get:
10(r0 + r1 + r2 + ... + r9) = \(10(r0(1 - (1 + 0.12)^{10})\) / -0.12)
Therefore, the closed-form mathematical expression for the amount of rabbit food consumed in 10 years is:
10(r0(1 - \((1 + 0.12)^{10})\) / -0.12) = \(10(30(1 - (1 + 0.12)^{10})\) / -0.12)

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Answer:

There are 40 multiples of 5.

Step-by-step explanation:

You take 10000 and subtract 8000 = 2000.

Then divide 2000 by 5.

Answer:

5 times

Step-by-step explanation:

The tank holds 0.72 gallons, and burn 13 gallons every time. Which means 0.72 divided by 0.13 would be the amount of times you would trim the weeds without refilling the tank. Which in this case the answer is 5.538... so if you round it u would get 5.

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Tip #1: Find the right string trimmer for you.

A few different string trimmers exist to meet the needs of you and your lawn:

Electric string trimmers tend to use lithium-ion batteries at 40 to 80 volts and are clean, quiet, and light. The uncorded versions add mobility to your work; however, corded electric string trimmers don’t require recharge time and are lighter.

Gas string trimmers use gas engines that provide more power than their electric counterparts. These trimmers are cordless and mobile, but you must regularly refuel for continued use. Some gas trimmers require a pull-start to crank, while other models come with an automatic crank.

String trimmer mowers, or walk-behind trimmers, resemble traditional lawnmowers without the size or the spinning blade. String trimmer mowers offer an in-between range for those lawn sections too big or too small for conventional mowers and trimmers.

Tip #2: Take safety precautions when using your string trimmer.

Like lawnmowers, string trimmers use a spinning motion to cut grass and thin wooden plants. For example, trimmers cutting in a counter clockwise spin will eject cut debris in a leftward direction.

Acknowledge the direction of your string trimmer’s spin and position yourself appropriately to avoid harmful debris hitting your body, like rock, glass, plastic, or any other small objects that can go flying when hit by the trimmer’s filament line. Additionally, keep children and pets indoors, or otherwise keep them and others on the opposite side of the eject direction.

Tip #3: Take advantage of spin direction when using your string trimmer.

Though you must heed the spin direction of your string trimmer for safety, the spin direction also commands the best use of your string trimmer. Ensure that your string trimmer ejects material away from your cut path to avoid working over piles of cut material, which drastically reduces the efficiency of your tool and encourages an uneven lawn trimming.

Tip #4: Use a cutting technique that fits the circumstance of your yard.

You accomplish a well-trimmed lawn by handling your string trimmer with precision. String trimmers seem clunky at best, but you can use a few different techniques to get that even cut you want. Mark Clement from Popular Mechanics suggests these methods:

Tapering: To cut along the boundaries of your lawn, angle the string trimmer so that the line cuts somewhat at an angle. You get your best cut toward the tip of the line, Clement explains, so tilting the trimmer slightly down helps cut smaller, more manageable portions while allowing the line to strike at its strongest point.

Edging: This method is useful when you need to cut grass at the edge of a parallel surface, such as a driveway or sidewalk. Instead of tilting the trimmer down, hold the tool so that the line cuts vertically. Clement notes that edging may uproot rocks and dirt and suggests easing these portions of your lawn into the right cut over time if you haven’t edged before.

Scything: Gently swing your string trimmer in a U-shaped pattern to navigate a difficult or obstructed area of the lawn. This method provides manageable trimming, and by overlapping the pattern, you’ll get the even cut you want.

Screeding: Clement explains that this method of using your string trimmer helps cut grass and weeds growing out of sidewalks, driveways, and other paved areas. Angle your string trimmer so that the line tip is hitting the pavement but the rest is slicing close to the base of the weed or grass.

Tip #5: Take care of your string trimmer.

Not unlike other tools, maintaining your string trimmer will keep it operable for years to come. After every use, wipe off grass and dirt debris from the line or replace it when necessary. String replacement is common, especially if you are using your string trimmer frequently. For gas-powered string trimmers, replace the spark plug every three to four months. Finally, empty the gas tank of the trimmer before long-term storage.

If you buy the right string trimmer for your needs, keep it properly maintained, and remember cutting direction for safety and a good cut, you’ll be using your string trimmer like a pro in no time.

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Answer:

13

Step-by-step explanation:

\(DE=.5*BC=.5*26=13\)

Answer:

Below

Step-by-step explanation:

Realize  ----    Angle 3 = Angle 7

  from this , you should be able to see that angle 3 and angle 6 are supplementary ( they add to 180 degrees....straight line)

Answer:

1024

Step-by-step explanation:

Assuming you mean \(4^{5}\) , then

\(4^{5}\) = 4 × 4 × 4 × 4 × 4 ( 4 multiplied by itself 5 times )

  = 16 × 16 × 4

   = 256 × 4

   = 1024

Answer:

3, 7

Step-by-step explanation:

-5 - (-9) = 4

The common difference is 4.

Add 4 to a term to find the next term.

-1 + 4 = 3

3 + 4 = 7

Answer: 3, 7

Answer:

\(35\)

Step-by-step explanation:

One is given the following function (\(y=3x+5\)). The given problem asks one to find the output of the function when the input is (10). Keep in mind, a general rule for dealing with functions is that, when present, the variable (x) represents the input. Whereas the variable (y) represents the output. Thus, if one were to substitute (10) in place of (x), and simplify: the result one would get is the output. Apply this idea to the given scenario:

\(y=3x+5\)

\(y=3(10)+5\)

\(y=30+5\)

\(y=35\)

If the correlation between two variables in a sample is r=1, the best description of the resulting scatterplot is that the points lie perfectly on a straight line with a positive slope.

A correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. When the correlation coefficient is 1,

it indicates a perfect positive linear relationship between the variables. In this case, every data point in the scatterplot falls precisely on a straight line with a positive slope.

The scatterplot represents the relationship between the two variables, with each data point plotted based on its corresponding values for the two variables.

With a correlation coefficient of 1, all the data points in the scatterplot align exactly on a straight line. This implies that as one variable increases, the other variable also increases in a consistent and proportional manner.

The scatterplot will exhibit a tight, upward-sloping pattern, where there is no variability or scatter around the line.

This indicates a strong and predictable relationship between the variables. Each point in the scatterplot will have the same x and y values, resulting in a perfect positive correlation.

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The correct answer to the given question is "it is inverse."

One of the most essential characteristics of the normal distribution is that it is bell-shaped.

This implies that it is symmetrical, with the highest point at the mean or center and the curve declining on either side of the mean.

Normal distribution is a crucial concept in statistics and is widely utilized in research and decision-making processes.

It is a probability distribution that is commonly used to describe the distribution of a set of data.

The normal distribution has several characteristics that distinguish it from other probability distributions.

The normal distribution is not inverse, meaning that the tails do not approach the x-axis as they extend.

Rather,

The normal distribution has a gradual decline, with the tails diminishing in size but never reaching zero.

It is also asymptotic, which means that the tails of the distribution continue indefinitely without ever touching the x-axis, although they become increasingly small as they move away from the mean.

Normal distribution is not skewed, which means that it is symmetrical around the mean.

A skewed distribution is one in which the mean, median, and mode are not equal, indicating that one side of the curve is longer than the other.

The normal distribution's symmetry is one of its most important features since it indicates that the mean, median, and mode are all equivalent, and the data is uniformly distributed on either side of the mean. Therefore, the correct answer to the given question is "it is inverse."

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James takes about 120 steps per minute and each step is 2.75 feet long. To find his walking speed in miles per hour, James should use the following calculation.

Convert 120 steps/min to steps/hour by multiplying by 60 (minutes in an hour):120 x 60 = 7,200 steps/hour Convert 2.75 feet to miles by dividing by 5,280 (feet in a mile):2.75 ÷ 5,280 = 0.000520833 miles/step Multiply the distance per step by the number of steps per hour to get the total distance walked in one hour:0.000520833 x 7,200 = 3.75 miles/hour Therefore, James' walking speed is 3.75 miles per hour.

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