If 247 players separated into 13 equal teams, how many players will be on each team?

Answer:

wait what

Step-by-step explanation:

The mass of the solid is 7π/2 units.

The task is to calculate the mass of the solid.

Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.

The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.

Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.

The density is equal to the distance from the origin, i.e. ρ = r.

The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr

The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀  π dθ= 14π/4= 7π/2 units.

The mass of the solid is 7π/2 units.

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Answer:

$250

Step-by-step explanation:

The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.

c. Responsible, Accountable, Consult & Inform matrix

The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.

The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.

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The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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(a) P(X < 1470) = 0.8849, P(X >= 950) = 0.7487, (b) the probability that the size of a single droplet is between 950 and 1470 μm is 0.6336, (c) the smallest 2% of all droplets are those smaller than 827 μm in size, and (d) the probability that at least one exceeds 1470 μm is 0.3995.

(a) To find the probability that the size of a single droplet is less than 1470 μm or at least 950 μm, we need to use the standard normal distribution table. To do this, we first need to convert the droplet size to a standard normal variable.

Let X be the droplet size. Then we have:

Z = (X - 1050)/150

The probability that the size of a single droplet is less than 1470 μm is equal to the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:

P(X < 1470) = P(Z < 1.2) = 0.8849 (rounded to four decimal places)

The probability that the size of a single droplet is at least 950 μm is equal to 1 minus the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6:

P(X >= 950) = 1 - P(Z < -0.6) = 0.7487 (rounded to four decimal places)

(b) To find the probability that the size of a single droplet is between 950 and 1470 μm, we subtract the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6 from the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:

P(950 <= X <= 1470) = P(Z <= 1.2) - P(Z <= -0.6) = 0.8849 - 0.2513 = 0.6336 (rounded to four decimal places)

(c) To find the smallest 2% of all droplets, we find the value of Z such that P(Z <= Z) = 0.02. Using the standard normal distribution table, we find that Z = -2.33. Then, we convert Z back to the original variable X:

X = Z * 150 + 1050 = -2.33 * 150 + 1050 = 827 (rounded to two decimal places)

So, the smallest 2% of all droplets are those smaller than 827 μm in size.

(d) To find the probability that at least one of five independently selected droplets exceeds 1470 μm, we use the cumulative distribution function of a binomial distribution with n = 5 and p = P(X > 1470). The cumulative distribution function of a binomial distribution with parameters n and p is given by:

1 - (1 - p)^n

Using the standard normal distribution table, we find that P(X > 1470) = 1 - P(Z < (1470 - 1050)/150) = 1 - 0.8849 = 0.1151. Then, we plug in n = 5 and p = 0.1151 into the cumulative distribution function formula:

P(at least one exceeds 1470 μm) = 1 - (1 - 0.1151)^5 = 0.3995 (rounded to four decimal places).

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The probability is 0.4647.

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Answer: (2, 6)

Step-by-step explanation:

We know that \(\overrightarrow{UM}=\overrightarrow{MT}\). From the given coordinates, \(\overrightarrow{UM}=(-1, -2)\). Therefore, the coordinates of \(T\) are \((3,8)+(-1,-2)=(2,6)\).

The mean estimation of cholesterol change  for the population of aquarobic program participants using 95% confidence falls between 8.17 and 11.83 mg/dL.

To estimate the mean cholesterol change using 95% confidence, we need to use a confidence interval. The formula for a confidence interval is:

Mean cholesterol change ± (t-value * standard error)

We can use a t-distribution with n-1 degrees of freedom, where n is the number of participants in the aquarobic program. We can assume that the sample is randomly selected and independent, and that the population of cholesterol changes follows a normal distribution.

To find the t-value, we need to use a t-table or calculator with the appropriate degrees of freedom and confidence level. For 95% confidence and n=sample size, the t-value is:

t-value = 2.306

To calculate the standard error, we can use the formula:

standard error = standard deviation / sqrt(n)

If the standard deviation is not given, we can use the sample standard deviation instead. We can assume that the sample standard deviation is a good estimate of the population standard deviation.

Once we have the standard error, we can substitute it into the confidence interval formula along with the t-value and the mean cholesterol change. This will give us the 95% confidence interval for the mean cholesterol change.

For example, if the mean cholesterol change is 10 mg/dL and the standard deviation is 3 mg/dL, and there were 20 participants in the aquarobic program, then the 95% confidence interval would be:

10 ± (2.306 * (3 / sqrt(20)))
10 ± 1.83

The confidence interval would be (8.17, 11.83). This means that we can be 95% confident that the true mean cholesterol change for the population of aquarobic program participants falls between 8.17 and 11.83 mg/dL.

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Answer: Choice D)  1 - sec^2(a) = tan^2(a) is not an identity.

================================================

Explanation:

a) is the pythagorean trig identity assuming you meant to write sin^2(a)+cos^2(a) = 1

b) is a rewritten version of tan = sin/cos. You multiply both sides by cos(a).

c) is an identity that you can find through dividing everything in equation (a) by sin^2. I'm assuming you meant to put exponent symbols before each "2".

d) is not an identity. I recommend looking at a table or graph that compares the two sides as separate functions. You should see they are not the same. The actual identity should be sec^2(a) - 1 = tan^2(a). You divide both sides of equation (a) by cos^2 and do a bit of algebra to get it into this form.

The probabilities and corresponding situations for selecting two cards from a standard deck of 52 cards, with the first card placed back in the deck before the second card is drawn:

Probability: 1/1692

Corresponding Situation: Both cards are aces

Probability: 1/13

Corresponding Situation: The first card is a spade

Probability: 3/51

Corresponding Situation: The first card is not a spade, and the second card is diamond

Probability: 1/17

Corresponding Situation: Both cards are kings

Probability: 12/51

Corresponding Situation: The first card is not a king, and the second card is spade

Probability: 1/4

Corresponding Situation: The first card is a heart, and the second card is a diamond

Probability: 4/17

Corresponding Situation: The first card is a heart, and the second card is not a heart

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Answer:

90 is ur anwser

Step-by-step explanation:

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

y = 44

Step-by-step explanation:

Slopes of parallel lines are equal.

P(15, 7)

Q(20, 14)

\(m_{PQ}\) = \(\frac{14-7}{20-15}\) = \(\frac{7}{5}\)

G(3, 2)

F(33, y)

\(m_{PQ}\) = \(m_{GF}\) = \(\frac{y-2}{33-3}\) = \(\frac{7}{5}\)

5(y - 2) = 7(30)

y - 2 = 42

y = 44

Answer:

A - 1:6

Step-by-step explanation:

Answer:

Option C. 576 in^2

Step-by-step explanation:

Given ,

Length = 8 inches

Breadth = 8 inches

Height = 14 inches

Now ,

using surface area of box (Cuboid)

= 2(l×b + b×h + l×h )

= 2(8×8 + 8×14 + 14×8)

= 2 ( 64 + 112 + 112 )

= 2 ( 288)

= 576 inches^2.

The value of x in the open interval (1, 3) that satisfies the conclusion of the Mean Value Theorem for f on the closed interval [1, 3] is x = √3.

The first derivative of a function in calculus is a different function that shows how quickly the original function is changing at each location in its domain.

As the change in the input gets closer to zero, it is described as the limit of the difference quotient.

By the Mean Value Theorem, we know that there exists a value c in the open interval (1, 3) such that:

f'(c) = (f(3) - f(1))/(3 - 1)

Substituting the given values, we have:

f'(c) = (11 - 9)/(3 - 1) = 1

Now we can solve for c by setting f'(c) equal to the given expression for f'(x) and solving for x:

f'(x) = (3x² - 6)/(x²) = 1

Multiplying both sides by x² and rearranging, we get:

3x² - x² - 6 = 0

Simplifying the left side, we have:

2x² - 6 = 0

Dividing both sides by 2, we get:

x² - 3 = 0

Taking the positive square root, we have:

x = √3

Since √3 is in the open interval (1, 3), it satisfies conclusion of the Mean Value Theorem for f on closed interval [1, 3]. The result of the Mean Value Theorem for f on the closed interval [1, 3] is thus satisfied by the value of x in the open interval (1, 3), which is x = 3.

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Answer:

What?

Step-by-step explanation:

Okay, the formula, then what?

Answer:

the answer is v=bh/3

Step-by-step explanation:

I solve for V since you didn't put what letter you wanted the question to be solved for.

hope this helps.

Systematic risk is the type of risk for which you can be rewarded with a higher expected return.

So, the correct answer is A

Systematic risk, also known as market risk or non-diversifiable risk, affects the entire market and cannot be eliminated through diversification.

Investors are compensated for taking on systematic risk through higher expected returns as they bear the fluctuations and uncertainties associated with the overall market.

In contrast, firm-specific, diversifiable, and idiosyncratic risks are specific to individual companies or industries and can be mitigated through diversification in an investment portfolio, so investors don't get rewarded with higher expected returns for these types of risks

Hence, the answer of the question is A.

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Answer:

the answer is 45/100=9/50 according to my solution

The number of room that can be painted can be determined as,

Thus, the required number of rooms is 35.

Therefore, the volume of the irregular solid in the fourth image is 243 cubic meters.

Volume is a measure of the amount of space occupied by a three-dimensional object or solid. It is usually expressed in cubic units such as cubic centimeters (cm³), cubic meters (m³), or cubic feet (ft³). The formula for finding the volume of a regular solid depends on its shape. For example, the volume of a cube is found by cubing the length of one of its sides, while the volume of a cylinder is found by multiplying the area of its base by its height.

Here,

1. To find the area of the irregular shape in the first image, we can divide it into two rectangles and one right triangle, as shown below:

+--------+ 4 cm

|        |

|        |

+--------+

   2 cm

   5 cm

+--------+

|        |

|        |

+--------+

   2 cm

The area of the shape is then the sum of the areas of these smaller shapes:

Area = (4 cm x 2 cm) + (5 cm x 2 cm) + (1/2 x 5 cm x 2 cm)

= 8 cm² + 10 cm² + 5 cm²

= 23 cm²

Therefore, the area of the irregular shape in the first image is 23 cm².

2. To find the area of the irregular shape in the second image, we can divide it into two triangles and one parallelogram, as shown below:

+-----------------+

|        /        |

|    5 /          | 2 cm

|    /            |

|  /              |

+-----------------+

      5 cm

The area of the shape is then the sum of the areas of these smaller shapes:

Area = (1/2 x 5 cm x 5 cm) + (1/2 x 5 cm x 2 cm) + (5 cm x 2 cm)

= 12.5 cm² + 5 cm² + 10 cm²

= 27.5 cm²

Therefore, the area of the irregular shape in the second image is 27.5 cm².

3. To find the volume of the irregular solid in the third image, we can use the formula V = L x W x H, where L is the length, W is the width, and H is the height.

V = 6 ft x 25 ft x 16 ft

= 2400 cubic feet

Therefore, the volume of the irregular solid in the third image is 2400 cubic feet.

4. To find the volume of the irregular solid in the fourth image, we can divide it into a rectangular prism and a pyramid, as shown below:

+-----------------+

|                 |

|   +---------+   | 3 m

|   |         |   |

|   |         |   | 1 m

|   +---------+   |

|                 |

+-----------------+

    4 m   19 m

The volume of the rectangular prism is V1 = L x W x H

= 4 m x 19 m x 3 m

= 228 cubic meters.

The volume of the pyramid is V2 = (1/3) x B x H, where B is the base area and H is the height of the pyramid. We can find the base area by multiplying the length and width of the rectangle:

B = L x W

= 5 m x 3 m

= 15 square meters

The height of the pyramid is the same as the height of the rectangular prism:

H = 3 m

Therefore, the volume of the pyramid is V2 = (1/3) x 15 square meters x 3 m

= 15 cubic meters.

The total volume of the irregular solid is then the sum of the volumes of the rectangular prism and the pyramid:

V = V1 + V2

= 228 cubic meters + 15 cubic meters

= 243 cubic meters

Therefore, the volume of the irregular solid in the fourth image is 243 cubic meters.

6. When an irregular shape has a complex or irregular form, one way to find its area or volume is by breaking it down into smaller shapes or solids that are easier to calculate. By dividing the irregular shape into smaller, regular shapes, we can add up the individual areas or volumes to get the total area or volume of the larger shape or solid. This method is commonly used when working with irregular shapes in geometry, as well as with complex solids in calculus and physics.

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Answer:

208

Step-by-step explanation:

the formula is:

2*(width*lenght+height*lenght+height*width)

2*(6*8+4*8+4*6)

208

Answer:

\( \: \)

Step-by-step explanation:

In the given figure, it is given a net of cuboid where, the length is 8m, the breadth is 6m and the height is 4m and we have to find the surface area of the cuboid.

So, the formula for finding the surface area is ;

\(\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Surface\: area_{(cuboid)}=2(lb + bh + lh )}}}}}} \: \: \bigstar \\ \\\)

Now, we'll substitute the values in the formula :

\(\\{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(8.6 + 6.4 + 8.4 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(48 + 24 + 32 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(104 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ { \pmb{ \frak{ { \: Surface\: area_{(cuboid)}=208 }}}}}}\: \: \\ \\\)

Therefore,

Answer:

40

Step-by-step explanation:

\( \frac{x}{80} = sin(30) = \frac{1}{2} \)

if you don't know about sinuous and trigonometry, the opposite side of 30 degree angle in a rectangular triangle is the half of its hypotenuse.

The measure of x is 40.

Given,

A 30-60-90 triangle.

We need to find the measure of x.

SinФ = perpendicular / hypotenuse

We have,

A right-angles triangle with hypotenus = 80 and base = x.

We also see that the upper angle is 30°.

So,

sin 30° = x / 80

1/2 = x/80

x = 80/2 = 40

We have,

x = 40

Thus the measure of x is 40.

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