TEAMS Of the 12 people in the room, only 5 will be selected to play on a team. How many different ways could the teams be formed?
Answers
There are 792 different ways the teams can be formed from a group of 12 people when selecting 5 people for each team.
To determine the number of different ways the teams can be formed, we can use the concept of combinations. In this case, we need to select 5 people out of a total of 12.
The number of ways to choose a team of 5 out of 12 people can be calculated using the formula for combinations, which is denoted as "nCr" or "C(n, r)".
The formula for combinations is:
nCr = n! / (r!(n - r)!)
Where:
n is the total number of people (12 in this case)
r is the number of people to be selected for the team (5 in this case)
! denotes the factorial function
Now let's calculate the number of different ways the teams can be formed:
12C5 = 12! / (5!(12 - 5)!)
= 12! / (5! * 7!)
= (12 * 11 * 10 * 9 * 8) / (5 * 4 * 3 * 2 * 1)
= 792
Therefore, there are 792 different ways the teams can be formed from a group of 12 people when selecting 5 people for each team.
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Related Questions
Find the equation of the line that passes through the points (1, 4) and (-2, 4).
Answers
Answer:
[tex]y=4[/tex]
Step-by-step explanation:
A circle whose center is the origin passes through the point (-5,12). Which point also lies on this circle?
Answers
The distance between the center of the circle and the given point is 13 units.
The distance between the center of the circle (0, 0) and the given point (-5, 12) should be equal to the radius of the circle.
Using the distance formula,
d= √(-5-0)² + (12-0)²
d = √25 + 144
d = √169
d = 13 unit
Therefore, the distance between the center of the circle and the given point is 13 units.
Any point on the circle will have a distance of 13 units from the center.
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I NEED HELP PLEASE ASAP
Answers
Examining the stem and leaf plot, the number of drivers that travelled below 70 miles per hour is
A. 8
What is stem and leaf plotA stem and leaf plot is a type of data display used in statistics to organize and rank data while retaining individual data points.
It is a visual representation of a frequency distribution of numerical data where each value is split into a stem (usually the leftmost digits) and a leaf usually the rightmost digit).
Using the information we can write out the speed of drivers that drove below 70 miles per hour
54, 56, 59, 62, 62, 63, 64, and 68
This gives 8
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how to calculate quantity produced from fabrication and finishing hours stoneage surfboards question
Answers
To calculate the quantity produced from fabrication and finishing hours for Stoneage Surfboards, you would need to have additional information such as the production rate or efficiency of the fabrication and finishing processes. Without specific data on the production rate, it is not possible to determine the exact quantity produced.
However, if you have the production rate, you can use the following formula:
Quantity Produced = Production Rate × Fabrication and Finishing Hours
For example, if the production rate is 5 surfboards per hour and you have 8 hours of fabrication and finishing time, the calculation would be:
Quantity Produced = 5 surfboards/hour × 8 hours = 40 surfboards
Remember to adjust the units and variables based on the specific information and units of measurement used in Stoneage Surfboards' production processes.
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PLS HELP AND EXPLAIN ASAP
Sphere A has a radius twice that of sphere B, and sphere B has a volume of 16pi. What is the volume of sphere A? A.) 16 pi B.) 128 pi C.) 144 pi D.) 32 pi
Answers
The value of the volume of Sphere A is expressed as: 128π
How to find the volume of the sphere?The formula to calculate the volume of a sphere is given as:
V = ⁴/₃πr³
Where:
V is volume
r is radius
The radius of sphere A is: r_A = 2r_b
Radius of Sphere B is: r_B
Volume of sphere B = 16π
Thus:
⁴/₃πr_B³ = 16π
r_B³ = 12
r_b = ∛12
V_A = ⁴/₃π(2 * ∛12)³
V_A = ⁴/₃π * 8 * 12
= 128π
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Solve each of the following equations. Show its solution set on a number line. |5-4r|=17
Answers
Answer:
Step-by-step explanation:
To solve the equation |5-4r| = 17, we need to consider two cases:Case 1: 5 - 4r is positiveIf 5 - 4r is positive, then we have:5 - 4r = 17Subtracting 5 from both sides, we get:-4r = 12Dividing both sides by -4, we get:r = -3So if 5 - 4r is positive, then the solution to the equation is r = -3.Case 2: 5 - 4r is negativeIf 5 - 4r is negative, then we have:-(5 - 4r) = 17Simplifying the left side by distributing the negative sign, we get:-5 + 4r = 17Adding 5 to both sides, we get:4r = 22Dividing both sides by 4, we get:r = 5.5So if 5 - 4r is negative, then the solution to the equation is r = 5.5.Therefore, the solution set of the equation |5-4r| = 17 is {-3, 5.5}.To show this solution set on a number line, we can draw a number line and mark the points -3 and 5.5 with open circles, since these values are not included in the solution set. Then, we shade the part of the number line between -3 and 5.5, since any value of r in this interval satisfies the equation. The resulting number line looks like this:
So the solution set of the equation is the interval (-3, 5.5).
Answer:
w
Step-by-step explanation:
linear equation
4(-8x +5)=-30x-26
Answers
Answer:
x=23
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
have a great day and thx for your inquiry :)
Janet is at an arcade where she is bowling with her friends. She has a 25% chance of winning. She wants to know the probability of it taking at least six games for her to win. Which simulation can best be used to compute the probability?
Answers
The simulation that can best be used to compute the probability would be one that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation.
Probability imulation problemA simulation that randomly generates a large number of outcomes and records the number of games it takes for Janet to win in each simulation can be used to compute the probability of it taking at least six games for her to win.
By running the simulation many times and calculating the proportion of simulations in which Janet wins after six or more games, an estimate of the probability can be obtained.
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Local Municipality Residential Water Tariff (Excluding VAT) Approved Indigents (free 6kl) 1-6 kl 7-15 kl 16-30 kl 31-45 kl 46-60 kl 61 and Above Mogale City Approved Tariffs July (2020/2021) RO R17 R22 R28 R32 R35 R39 Mogale City Approved Tariffs July (2021/2022) RO R18 R24 R29 R34 R37 R41 Other consumers: Government Schools, NGOs and Hospitals per kl (Excluding Private Schools & Private Hospitals) 1 - 200 kl Above 200 kl R25 R40 R26 R43 Source: www.mogalecity.gov.za *The registered Indigent will receive the allocated 6 kl free basic water per month on a daily pro- basis. Use the information in the table to answer the questions that follow. 3.1 Mrs Mabaspacked is a registered resident and she used 14 kt of water for the month of August 2022 calculate her water bill excluding VAT. municipality 2021 tariff for prepaid electricity appears
Answers
The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be R144.
How to calculate the valueMrs Mabaspacked is a registered resident and she used 14 kt of water for the month of August 2022. The first 6 kl of water is free for registered residents, so she will only be charged for the remaining 8 kl. The water tariff for Mogale City in August 2022 is R18 per kl, so her water bill excluding VAT will be 8 kl x R18/kl = R144.
Water used: 14 kl
Free water: 6 kl
Water used after deduction of free water: 14 kl - 6 kl = 8 kl
Water tariff: R18 per kl
Water bill excluding VAT: 8 kl x R18/kl = R144
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Gary's car gets about 20 miles per gallon. About how many miles can Gary drive on
9.9 gallons of gas? At $2.90 a gallon, about how much would that amount of
gas cost?
Gary can drive about
miles on 9.9 gallons of gas, which would cost about $.
Answers
If Gary's car gets about 20 miles per gallon.
a. Gary can drive about 198 miles on 9.9 gallons of gas.
b. the cost of 9.9 gallons of gas at $2.90 per gallon would be $28.71.
What is the miles?a. Number of miles
Miles = Gallons * Miles per gallon
Miles = 9.9 gallons * 20 miles/gallon
Miles = 198 miles
Therefore Gary can drive about 198 miles on 9.9 gallons of gas.
b. Cost of the gas
Cost = Price per gallon * Gallons
Cost = $2.90/gallon * 9.9 gallons
Cost = $28.71
Therefore the cost of 9.9 gallons of gas at $2.90 per gallon is $28.71.
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Consider a political discussion group consisting of 7 Democrats, 4 Republicans, and 5 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two Independents
Answers
Answer:
1/16
Step-by-step explanation:
The probability of selecting an Independent on the first draw is 5/16, since there are 5 Independents out of 16 total members.
Assuming that the first person selected is an Independent, there are now 4 Independents left out of 15 total members for the second draw. So the probability of selecting a second Independent given that the first person selected was an Independent is 4/15.
Therefore, the probability of selecting two Independents in succession is:
(5/16) * (4/15) = 1/16
So the probability of selecting two Independents is 1/16 or approximately 0.0625.
In the study of logic, p q is to be understood in the exclusive sense, whereby if "p" and "q" are both true, the compound claim pvq is, as a whole claim, true. True False
Answers
The statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.
This principle is known as the exclusive disjunction, which means that the truth value of p v q is only true if either p or q is true, but not both.
In other words, if both p and q are true, then the statement p v q is still considered true because only one of them needs to be true for the whole statement to be true. This concept is essential in the study of logic as it helps to clarify the relationship between different statements and propositions.
Furthermore, this principle is often used in mathematics, computer science, and other fields that rely heavily on logical reasoning. It enables us to make accurate predictions and draw valid conclusions from a set of given premises or statements.
In conclusion, the exclusive disjunction is a crucial concept in the study of logic that helps us understand the truth value of compound claims. Therefore, the statement "In the study of logic, p q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim pvq is, as a whole claim, true" is true.
In the study of logic, the statement "p ∨ q is to be understood in the exclusive sense, whereby if 'p' and 'q' are both true, the compound claim p ∨ q is, as a whole claim, true" is actually false. This is because the given description refers to the "inclusive" sense of the disjunction (OR) operator, rather than the exclusive sense.
In logic, there are two types of disjunctions: inclusive and exclusive. The inclusive disjunction, represented by p ∨ q, is true when at least one of p or q is true. This means that if both p and q are true, the compound claim p ∨ q is also true, which matches the given description in the question.
On the other hand, the exclusive disjunction, represented by p ⊕ q or p XOR q, is true only when either p or q is true, but not when both are true. If p and q are both true, then the compound claim p ⊕ q is false.
So, the statement in the question actually describes the inclusive disjunction, not the exclusive disjunction, and is therefore false.
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you decide to hike up a tall mountain, and you want to know the gradient of the trail you are hiking. the elevation at the mountain's trail head is 645ft, and the elevation at the summit is 6,849ft. the entire trail is 8.2 mi long from beginning to end. what is the gradient of this trail in ft/mi? round to the tenths place.
Answers
The gradient of the trail you hiked up is approximately 754.6 ft/mi. This means that for every mile you hiked horizontally, the elevation increased by about 754.6 feet.
The gradient of the trail is essentially the steepness of the trail, or the rate at which the elevation changes per unit of horizontal distance. To find the gradient in ft/mi, we need to calculate the total change in elevation and divide it by the total horizontal distance.
The total change in elevation is the difference between the elevation at the summit and the elevation at the trail head, which is:
6,849 ft - 645 ft = 6,204 ft
The total horizontal distance of the trail is 8.2 mi. To convert the total change in elevation to ft/mi, we divide it by the total horizontal distance
6,204 ft / 8.2 mi = 754.63 ft/mi
Rounding this to the tenths place gives us:
Gradient = 754.6 ft/mi
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pls help <3 Which is the correct expansion of (x+4y)^3 using the binomial theorem?
a.(x+4y)^3=(3/0)(x)^3(4y)^0+(3/1)(x)^2(4y)^1+(3/2)(x)^1(4y)^2+(3/3)(x)^0(4y)^3
b.(x+4y)^3=(4y)^0+(x)^2(4y)^1+(x)^1(4y)^2+(x)^0(4y)^3
c.(x+4y)^3=(3/0)(4y)^3(x)^0+(3/1)(4y)^2(x)^1+(3/2)(4y)^1(x)^2+(3/3)(4y)^0(x)^3
d.(x+4y)^3=(x)^0(4y)^0+(x)^1(4y)^1+(x)^2(4y)^2+(x)^3(4y)^3
Answers
The correct expansion of (x + 4y)³ using the binomial theorem is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³
Calculating the correct expansion using the binomial theorem
From the question, we have the following parameters that can be used in our computation:
(x + 4y)³
The binomial theorem of expansion states that
Given that an expression is (a + b)ⁿ, the current term is
ⁿCₓ * (a)ˣ * (b)ⁿ ⁻ ˣ
Using the above as a guide, we have the following:
(x + 4y)³ = ³C₀ (x)⁰(4y)³ +³C₁ (x)¹(4y)² + ³C₂ (x)²(4y)¹ + ³C₃ (x)³(4y)⁰
Rewrite as
(x + 4y)³ = [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³
This means that the correct expansion is (c) [tex]\left[\begin{array}{c}3&0\end{array}\right][/tex] (4y)³(x)⁰ + [tex]\left[\begin{array}{c}3&1\end{array}\right][/tex] (4y)²(x)¹ + [tex]\left[\begin{array}{c}3&2\end{array}\right][/tex] (4y)¹(x)² + [tex]\left[\begin{array}{c}3&3\end{array}\right][/tex] (4y)⁰(x)³
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PLEASE ANSWER ASAPP
TYSM :))
(giving all my points.. 20 pts..)
Answers
35 and 7 books would not follow trend of this scatter plot. 20 books is the obvious choice as it lies in the middle of the positive trend.
What is the equation of the line that passes through (0,2) and (-3,14) in slope intercept form?
Answers
Answer: y = -4x + 2
Step-by-step explanation:
Can you guys help me pleasse
Answers
Answer:
c
Step-by-step explanation:
Looking at Jen's slope, we can see that the slope is steeper, but has a higher starting point, meaning that while she can hold more gas, she burns through her gas quicker.
On the other hand, DJ's car starts at a lower point on the graph, meaning their car holds less gas, But has a less steep slope, meaning their car has better mileage.
This means the answer is c: Jen's car holds more gasoline, but DJ's car gets better gas mileage
La escala en un plano de una casa indica que 6 centímetros representan 3 metros. ¿Cuántos centímetros en el plano representan una distancia real de 27 metros?
Answers
A real distance of 27 meters will be represented by a distance of 54 centimeters on the plane.
How many centimeters representa real distance of 27 meters?We know that the scale factor of the plane is:
6cm to 3m
Then each meter on the plane will be represented by:
1m = (6cm/3) = 2cm
So each meter in the real world is represented by 2 centimeters on the plane.
Then a real distance of 27 meters will be reprsented by:
27m = 27*(2cm) = 54cm
That distance is represented by 54 centimeters.
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A
B
D
C
If m/ABD = 110°, and m/DBC = 35⁰,
then m/ABC = [ ? ]°
Answers
m/ABC = 235° + 2(180° - 35°) - 2(110°)
a 5 foot ladder leaning against a wall is slipping down the wall at 1 foot per minute. how fast is the base of the ladder moving away from the wall when the top of the ladder is 4 feet from the ground?
Answers
So the base of the ladder is moving away from the wall at a rate of 3/4 feet per minute when the top of the ladder is 4 feet from the ground.
We can use the Pythagorean Theorem to relate the ladder's length to the distance it is from the wall. Let's call the distance from the wall "x", and the length of the ladder "y". Then:
x^2 + y^2 = 5^2
We can take the derivative with respect to time of both sides of this equation, using implicit differentiation:
2x(dx/dt) + 2y(dy/dt) = 0
Now we can plug in the values we know and solve for the rate at which the base of the ladder is moving away from the wall (which is the same as the rate at which x is increasing):
x = sqrt(5^2 - 4^2) = 3
y = 4
dx/dt = 1 (given)
dy/dt = ?
Plugging in these values, we get:
2(3)(1) + 2(4)(dy/dt) = 0
Simplifying:
6 + 8(dy/dt) = 0
Solving for dy/dt:
dy/dt = -6/8 = -3/4
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Characteristics that are harmful to a species tend
to decrease in frequency from generation to
generation because these characteristics usually
(1) have a high survival value for the species
(2) have a low survival value for the species
(3) are inherited by more individuals
(4) affect only the older members of the population
Answers
Characteristics that are harmful to a species tend to decrease in frequency from generation to generation because these characteristics usually have a low survival value for the species.
Option 2.
What are characteristics that are harmful to a species?Characteristics that are harmful to a species are numerous and some of them affect species in many ways.
Some of the harmful characteristics to species include the following;
Poor genetic diversity - species that are not diverse will not survive long the nearest future as tend to go into extinct.
Poor habitat ; species with limited habitation will not survive long.
Poor reproductive rate - this factor does not favour species wide spread and fast growth
Predators - this factor kill and reduce the number of available species
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How many solutions does the equation 5z + 1 = -5z + 10 have?
1
2
Infinite
Answers
Answer:
infinite
Step-by-step explanation:
because if you were to graph it or something 1 could go to 10 like 1 could fit into ten without exeeding the limit going to low or to high
Use the diagram below to classify ABCD. Select all that apply.
Answer please rn
Answers
Answer: A and D
Step-by-step explanation: Its obvious.
Answer:
Square
Parallelogram
Step-by-step explanation:
Inner diagonals are all right angles and both diagonals are congruent.
Also, a square must be a parallelogram.
Find the distance between the points A and B given below.
(That is, find the length of the segment connecting A and B.)
Round your answer to the nearest hundredth.
Answers
The distance between the points A (3, 3) and B (6, 6) include the following: 4.24 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Each interval on the coordinate plane represent 1 unit.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(6 - 3)² + (6 - 3)²]
Distance = √[(3)² + (3)²]
Distance = √[9 + 9]
Distance = √18
Distance AB = 4.24 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
When we subtract a velocity vector from another velocity vector, the result is:
A. an acceleration.
B. another velocity.
C. a scalar.
D. a displacement.
Answers
When we subtract a velocity vector from another velocity vector, the result is B. another velocity.
When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.
It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.
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Write an equation that can be used to determine the angle measure, in degrees, of Angle WBK. Let b represent the measure of Angle WBK. Then determine the measure of b.
Answers
The measure of Angle WBK, the angles are supplementary,
complementary, adjacent, vertical, or part of a triangle.
The measure of Angle WBK (represented by b).
1. Identify the relationships between the angles: the angles are supplementary, complementary, adjacent, vertical, or part of a triangle or other polygon.
2. Write an equation using the angle relationships: if two angles are supplementary, the sum of their measures is 180 degrees. If Angle WBK is supplementary to Angle WBL, we would write the equation b + m(WBL) = 180, where m(WBL) represents the measure of Angle WBL.
3. Solve the equation: the values into the equation and solve for b, the measure of Angle WBK.
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Two gears are connected and rotating at the same time. The smaller gear completes 1 3/4 rotations every time the larger gear completes 1/4 of a rotation. How many rotations does the smaller gear complete when the larger gear completes 1 rotation? Drag and drop the correct value into the box.
A. 1/7
B. 7/8
C.5 1/2
D.7
Answers
Answer: Which Option do You Drag and Drop into the Box?
Step-by-step explanation:
Let's call the number of rotations of the larger gear "L" and the number of rotations of the smaller gear "S". We know that when the larger gear completes 1 rotation, the smaller gear completes 1 3/4 rotations.
We can set up a proportion to solve for S:
S/1 3/4 = L/1/4
Simplifying the right side of the equation, we get:
S/1 3/4 = 4L
Multiplying both sides by 7/4 to get rid of the fraction on the left side, we get:
S = 28/4 L
Simplifying, we get:
S = 7L
This means that the smaller gear completes 7 rotations every time the larger gear completes 1 rotation.
Therefore, the correct value to drag and drop into the box is 7.
{Hope This Helps! :)}
(2x+5)a + (x+3)b = 2x+4 calcule (a-b)^2
Answers
Answer:
Step-by-step explanation:
Let's first expand the left side of the given equation:
(2x+5)a + (x+3)b = 2x+4
2xa + 5a + xb + 3b = 2x + 4
Now, let's group the terms with x and the terms without x:
(2a + b)x + (5a + 3b) = 2x + 4
We can see that the coefficients of x are equal on both sides, so we can equate the coefficients of x and the constant terms separately:
2a + b = 2 (1)
5a + 3b = 4 (2)
Solving these two equations, we get:
a = 2/7
b = 8/7
Now, we can substitute these values of a and b into the expression (a-b)^2 and simplify:
(a-b)^2 = (2/7 - 8/7)^2
= (-6/7)^2
= 36/49
Therefore, the value of (a-b)^2 is 36/49.
can you help me with math
Answers
In the question it ask for a slope of -6 so the answer is D.
¿Cuál es la masa que tienen 700 ml de un líquido que posee una densidad de 855 kg/m°?
Answers
Explicación : La fórmula para encontrar la masa es masa = densidad x volumen.
