There are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.
Permutation is the arrangement of objects in a specific order. It is the number of different ways in which a set of objects can be arranged in a specific order. The formula to calculate permutation is:
[tex]P(n, r) = n! / (n - r)![/tex]
Permutations are commonly used in mathematics, science, and engineering, and are useful for solving problems that involve counting the number of possible arrangements of objects or events.
We can use the formula for permutations to find the number of ways to choose the four officers from a group of 14 students.
The number of permutations of n objects taken r at a time is given by:
[tex]^nP_r = n! / (n - r)![/tex]
where n! denotes n factorial, which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we want to choose 4 students from a group of 14, and the order in which they are chosen matters (since we are electing them to specific positions). So we have:
n = 14
r = 4
The number of ways to choose the four officers is therefore:
[tex]^1^4P_4 = 14! / (14 - 4)! = 14 \times 13 \times 12 \times 11 = 24,024[/tex]
Therefore, there are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.
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What are the workings of this question? How to arrive at the answer?
The variation equation that connects x and y is y³ = 4.5x(x - 1) and the value of y is 4.48 when x equals 5
The equation that connects x and y?From the question, the variation statement is given as
The cube of y is directly proportional to x(x - 1)
Also, we have the initial values of x and y to be
x = 3 and y= 3
When the variation statement is represented as an equation, we have:
y³ = kx(x - 1)
Where k is the variation constant
Substitute the known values in the above equation So, we have the following equation
3³ = k x 3 x (3 - 1)
Evaluate
27 = 6k
Divide both sides by 6
k = 4.5
Substitute k = 4.5 in y³ = kx(x - 1)
y³ = 4.5x(x - 1)
Hence, the equation is y³ = 4.5x(x - 1)
The value of yHere, we are given that
x = 5
Substitute 5 for x in the equation y³ = 4.5x(x - 1)
So, we have
y³ = 4.5 x 5 x (5 - 1)
Evaluate
y³ = 90
Take the cube root of both sides
y = 4.48
Hence, the value of y is 4.48
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a solid triangular prism has a height of 12 inches. the triangular base of this prism is shown below. what is the surface area, in square inches, of this prism?
The surface area of the triangular prsim is 290.4 in² and the right option is B. 290.4 in².
What is surface area?Surface area is the space occupied by a two-dimensional flat surface is called the area. It is measured in square units.
To calculate the surface area of the triangular prism, we use the formula below.
Fromula:
S.A = (a+b+c)L+bh.................... Equation 1Where:
S.A = Surface area of the prisma , b, c = Three sides of the base triangle respectively.h = Height of the triangular baseL = Lenght of the prismFrom the question,
Given:
L = 12 ina = 5 inb = 9 inc = 7.2 inh = 4 inSubstitute these values into equation 1
S.A = (5+9+7.2)12+(4×9)S.A = 254.4+36S.A = 290.4 in²Hence, the right option is B. 290.4 in².
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observation refers to the . a. mean of all variable values associated with one particular entity b. estimated continuous outcome variable c. set of recorded values of variables associated with a single entity d. goal of predicting a categorical outcome based on a set of variables
The correct option is c. that is observation is set of recorded values of variables associated with a single entity.
What is observation?
An observation is a case of the data being collected.
For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.
A variable is an attribute or characteristic of the observation we record in our data.
Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.
Therefore from the given option c is correct.
Observation is set of recorded values of variables associated with a single entity.
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In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 139 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
62%
Step-by-step explanation:
1040-110-145-139=646
646/1040=62%
the coordinates of point are (-3,5). what are the coordinates of point B, which is a reflection of point A across the x-axis?
Answer:
Step-by-step explanation:
3 as the x axis and -5 for the y axis
I NEEEDD HELP ASAPP PLEASE
Solve negative three minus one and two fifths.
three fifths
one and two fifths
negative four and two fifths
four and two fifths
Answer:
Step-by-step explanation:
1. Put Words into Math.
Negative three minus one and two fifths= -3- 1 2/5
2. Solve the math problem
-3-1 2/5= -4 2/5 or -22/5 in improper fraction
Answer: -4 2/5 or -22/5
can someone help me really quick
Answer:
18$
Step-by-step explanation:
this is so i can reach twenty characters.
Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
Submit Answer
+
2
Ń
9.
The mapping diagram above
where there
Set B
5
C
a function since
C
in
attempt 1 out of 2
A rectangular blacktop with a length of 5x and a width of 3x has been erected inside a rectangular !eld that has a length of 12x and a width of 7x.a. What is the area of the part of the !eld that is not blacktop?b. "ere is a circular fountain in the rectangular !eld that has a radius of 3x. What is the area of the part of the !eld that does not include the blacktop or the fountain? Factor your answer. Pls help
Answer:
Step-by-step explanation:
to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top
5x(3x)
15x^2 is the area of the blacktop
The “!ield” area is next
12x(7x)
84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same
84x^2-15x^2
69x^2 is the area of the rectangle that is not black top
B- the foundtain we find with the area of circle formula r squared times pi
3x(3x)pi
9x^2pi
Now we just subtract this from the area of the rectangle
69x^2 -9x^2pi is the area
Hopes this helps please mark brainliest
A catering company loses $110 as a result of a delay.
The 5 owners of the company must share the loss equally.
Which quotient represents each owner's share of the loss?
I know the answer but, is 110 negative or positive??
Answer: Positive
Step-by-step explanation: It would be positive because the question is asking how much money they lost. The lost a positive amount of money.
The area of the rectangle ABCD is 28[tex]cm^{2}[/tex]
a) What is the length of side AB in terms of x?
length of AB = (Answer here) (1)
b) If the area of rectangle ABCD is 28[tex]cm^{2}[/tex], we can show that [tex]x^{2}[/tex] + ax = b where a and b are integer values.
Work out the values of a and b.
a = (Answer here) (1) b = (Answer here) (1)
Answer:
see explanation
Step-by-step explanation:
(a)
AB = 4 + x
(b)
the area (A) of rectangle ABCD is calculated as
A = length × breadth
= AB × AD
= (4 + x)(6 + x) ← expand using FOIL
= 24 + 10x + x²
given A = 28 , then
x² + 10x + 24 = 28 ( subtract 24 from both sides )
x² + 10x = 4 ← in the form x² + ax = b
with a = 10 and b = 4
Which lists of terms are ordered from least to greatest?
Select TWO correct answers.
√6 2.5 8/3
√8 11/4 2.9
9/5 1.9 √5
13/5 2.8 √7
1.8 7/4 √3
The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
Let's check all the options. Then we have
a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have
⇒ 2.449, 2.5, 2.667, order is in ascending form.
b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have
⇒ 2.828, 2.75, 2.667, order is not in ascending form.
c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have
⇒ 1.8, 1.9, 2.236, order is in ascending form.
d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have
⇒ 2.6, 2.8, 2.645, order is not in ascending form.
e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have
⇒ 1.8, 1.75, 1.732, order is not in ascending form.
The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.
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Rodrigo is taking an SAT prep class at the Westminster Community Center. The community center is 3.1 miles away from Rodrigo's house. How far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles?
1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given,
The community center is 3.1 miles away from Rodrigo's house.
We need to find how far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
As given, 3 inches : 9.3 miles
1 mile = 3/9.3 inches
1 mile = 0.323 inches.
So let us multiply 3.1 with 0.323
3.1×0.323
1.0013 inches
Hence 1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles
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Janet attends state university and lives in an on campus dorm suite with 5 friends. They share cost of the monthly upgraded cable bill for their suite. Below is a listing of the bills for their freshman year. 9. Round the following value
Σ
619
X₁
to the nearest dollar.
Interpret the answer in the context of the problem.
Answer:
Step-by-step explanation: Step 1
1 of 2
step 1.2659 ;[26 Discovery Group
October 20
Last
Trade Time
Chg
Open
52-week High
52-week Low
Sales in 100s
High
Low
$38.50
4:00 P.M. ET
$1.56
$37.22
$76.19
$22.78
19,700
$40.10
$36.77
\begin{matrix} \text{Discovery Group} & \text{}\\ \text{October 20} & \text{}\\ \text{Last} & \text{\$42.00}\\ \text{Trade Time} & \text{4:00 P.M. ET}\\ \text{Chg} & \text{\$1.50}\\ \text{Open} & \text{\$42.50}\\ \text{52-week High} & \text{\$76.19}\\ \text{52-week Low} & \text{\$22.78}\\ \text{Sales in 100s} & \text{23,600}\\ \text{High} & \text{\$42.50}\\ \text{Low} & \text{\$42.00}\\ \end{matrix}
Discovery Group
October 20
Last
Trade Time
Chg
Open
52-week High
52-week Low
Sales in 100s
High
Low
$42.00
4:00 P.M. ET
$1.50
$42.50
$76.19
$22.78
23,600
$42.50
$42.00
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
See below
Step-by-step explanation:
Find slope using two convenient integer coordinates
(-1,4) and (1, -8) are convenient
slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) = 12/-2 = -6
the y-axis intercept is -2 ( by looking at the graph)
y = -6x -2 Done.
Find the asymptotes and intercept of the following rational function
Show your work for the intercepts!
Answer:
VA: x = 1, x = -1
HA: y = 0
x-int: (4, 0)
y-int: (0, 4)
Step-by-step explanation:
x-int:
0 = (x-4)/((x-1)(x+1))
0 = (x-4) because the (x-1)(x+1) are multiplied by 0
4 = x
x = 4
(4, 0)
y-int:
y = (0 - 4)/((0 - 1)(0 + 1))
y = (-4)/((-1)(1))
y = (-4)/(-1)
y = 4/1 = 4
(0, 4)
Partition a line segment in the given ratio.
Point V lies on TU such that TV:UV is 5:2. Graph V.
Check the picture below.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ T(-5,9)\qquad U(9,2)\qquad \qquad \stackrel{\textit{ratio from T to U}}{5:2} \\\\\\ \cfrac{T\underline{V}}{\underline{V} U} = \cfrac{5}{2}\implies \cfrac{T}{U} = \cfrac{5}{2}\implies 2T=5U\implies 2(-5,9)=5(9,2)[/tex]
[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{18})=(\stackrel{x}{45}~~,~~ \stackrel{y}{10}) \implies V=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +45}}{5+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{18 +10}}{5+2} \right)} \\\\\\ V=\left( \cfrac{ 35 }{ 7 }~~,~~\cfrac{ 28}{ 7 } \right)\implies {\Large \begin{array}{llll} V=(5~~,~~4) \end{array}}[/tex]
Two lines. C and D. are represented by the equations given below:
Line C. y = x + 12
Line D. y = 3X + 2
Which of the following shows the solution to the system of equations and explains why?
The correct result would be (x, y) = (5, 17); because both lines pass through this point.
Given,
In the question:
Two lines. C and D are represented by the equations.
We have :
Line C. y = x + 12
Line D. y = 3X + 2
Now, According to the question:
y = x + 12
y = 3X + 2
Substitute into one of the equations
x + 12 = 3x + 2
Solve the equation:
Combine like terms:
x - 3x = 2 - 12
-2x = -10
x = -10/-2
x = 5
Put the value of x in equation of Line C
y = x + 12
y = 5 + 12
y = 17
Hence, The correct result would be (x, y) = (5, 17); because both lines pass through this point.
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30% of the tickets sold at a school carnival were early-admission tickets. If the school sold 100 tickets in all, how many early-admission tickets did it sell?
The number of early-admission tickets that it sells is 30.
How to calculate the number of early admission?From the information, 30% of the tickets sold at a school carnival were early-admission tickets and the school sold 100 tickets in all.
Therefore, the number of early admission will be:
= Percentage for early admission × Total number of tickets
= 30% × 100
= 0.3 × 100
= 30
Therefore, there are 30 early admission.
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One out of every ten students in a school takes lunch to school. If there are two hundred students in the school, how many of them do not take lunch to school?
180 students do not take lunch to school.
From the question, we have
Number of students do not take lunch to school= 200-20
=180 students
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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What are the advantages of bankruptcy? a. Exempted items are allowed. b. Certain incomes are unaffected. c. Debts are erased. d. "Exempted items are allowed" and "An automatic stay is enacted". e. All of these choices are correct. f. An automatic stay is enacted.
The advantages of bankruptcy include the following: e. All of these choices are correct.
What is bankruptcy?In Financial accounting, bankruptcy can be defined as a legal process that is initiated when an individual or business organization (debtors) is relieved of the responsibility to pay their debts, honor its financial obligations to creditors, or protect them while they are trying to repay their debt.
The advantages of bankruptcy.Generally speaking, there are several advantages of bankruptcy and these include the following:
Some certain incomes are unaffected by bankruptcy.All of the debts are erased.An automatic stay would be enacted.Exempted assets such as unemployment benefits and retirement accounts are retained or allowed.In conclusion, we can reasonably infer and logically deduce that bankruptcy is generally considered as both a friend and foe (enemy).
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Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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the line passes through (6,6) and (-2,2)
Answer:
Step-by-step explanation:
slope=change in y over change in x
6-2=4
6--2=6+2=8
-4/-8=1/2
. Identify the key features of g(x) = x², including the domain, range, x and y intercepts, and
intervals of increase and decrease.
The required key features of [tex]g(x) = x^{2}[/tex] including domain is (-∞, ∞) (i.e. all real values), range = [0,∞), x-intercept = (0,0), y-intercept = (0,0), interval of increasing = (0,∞) and interval of decreasing = (-∞, 0)
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.
The graphs of quadratic functions are frequently curved or nonlinear. A parabola, a kind of U-shaped curve, is the particular type of curve that makes up the graph of a quadratic function.
Given, [tex]g(x) = x^{2}[/tex]
The graph of the given function is given below:
From the graph,
Domain = (-∞, ∞) (i.e. all real values)
Range = [0,∞)
x-intercept = (0,0)
y-intercept = (0,0)
Interval of increasing = (0,∞)
Interval of decreasing = (-∞, 0)
Hence, these are the required key features of [tex]g(x) = x^{2}[/tex].
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Help me please image is attached I really appreciate it
An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.
How to write and solve this inequality?In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:
Let the variable n represent the number of batches.
Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:
3 1/4 (n) ≤ 26
13n/4 ≤ 26
Cross-multiplying, we have:
13n ≤ 26 × 4
13n ≤ 104
n ≤ 104/13
n ≤ 8.
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Complete Question:
Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.
the mean selling price of senior condominium in green valley over a year was $215,000. the population standard deviation was $25,000. a random sample of 100 new unit sales was obtained. a. what is the probability that the sample mean selling price was more than $210,000?
The probability that the sample mean selling price was more than $210,000 is 0.9772.
The given values are:
The mean selling price(μ) = $215000
Standard deviation(σ) = $25000
The random sample (n) = 100
We have to find the probability that the sample mean selling price was more than $210000.
z-score with z-bar= 210000
z = (x-bar - μ) / (σ/ √n)
= ( 210000 - 215000) / (25000/ √100)
= -5000/ 2500
=-2
Using z-tables, the probability is:
Probability = P[z> -2]
= 1 - 0.0228
= 0.9772
Therefore the probability is 0.9772.
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4-9×2^x+2+1=0. Please help me to solve the question please
Answer:
x=[tex]log_{2} 7/9[/tex]
Step-by-step explanation:
4-9×2^x+2+1=0
4-9×2^x+3=0
4+3-9×2^x=0
7-9×2^x=0
7-7-9×2^x=0-7
-9×2^x=-7
9×2^x=7
9×2^x/9=7/9
2^x=7/9
[tex]log_{2} 2^x[/tex]=[tex]log_{2} 7/9[/tex]
x=[tex]log_{2} 7/9[/tex]
a process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. assume that each package has probability 0.04 of falling outside the specification and that the weights of the packages are independent. find the variance of the number of packages that will be filled before the process is stopped.
The variance of the number of packages that will be filled before the process is stopped will be 600 when the probability of falling outside the specification is 0.04.
What is variance?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in relation to the mean the more dispersed the data. In statistics, the variance is used to assess how accurately the mean summarizes all of the data. For instance, more range exists within the set the higher the variance.
P(fail)=0.04
P(pass)=0.96
variance=(1-P)/P²
=(1-0.04)/0.0016
=0.96/0.0016
variance=600
When the likelihood of falling outside the specification is 0.04, the range of packages that will be filled before the process is stopped is 600.
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suppose the counts recorded by a geiger counter follow a poisson process with an average of 2 counts per minute. what is the probability that there are no counts in a 30 second interval? round your answer to 3 decimal places. suppose the counts recorded by a geiger counter follow a poisson process with an average of 2 counts per minute. what is the probability that there are no counts in a 30 second interval? round your answer to 3 decimal places.
The probability that there are no counts in a 30 second interval is 0.284
What is probability ?
Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.
Given that,
Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.
0.284
P(X < 10 Seconds) = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284
Therefore, the probability that there will be no counts in a 30-second period is 0.284.
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Dev’ car currently ha 18 gallon of ga in the tank. He ue about 0. 04 gallon for every mile he drive. Dev want to go on a car trip over the weekend and have at leat 2 gallon of ga left in hi tank to get to work on Monday. What i the olution of the inequality that determine how far Dev can travel over the weekend? (Example 2) Let x repreent the number of mile Dev travel
The solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Dave who is planning a car trip for weekend.
Assume that [x] represents the number of miles Dev can travel.
We can write the inequality as -
18 - 0.04x ≤ 2
0.04x ≤ 16
x ≤ 400 miles
Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
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