As a result, there are 1140 different methods to select a committee of three from a group of 20 people.
what is probability ?The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is a way to gauge how likely something is to happen. Probability is expressed as a number between 0 and 1, with 0 denoting that the occurrence won't happen and 1 denoting that it will definitely happen. By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an occurrence. Numerous disciplines, including statistics, finance, engineering, and science, use probability extensively to forecast the chance of an event happening and base decisions on that forecast.
given
The following combination formula determines how many options there are to select a committee of three from a class of 20 members:
C(20, 3) = 20! / (3! * (20-3)!) = 20 * 19 * 18 / (3 * 2 * 1) = 1140
As a result, there are 1140 different methods to select a committee of three from a group of 20 people.
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Is {A, B, C} a subset of the set of letters of the alphabet?
The set {A, B, C} is a subset of the set of letters of the alphabet.
What are sub-sets:A subset is a set that contains only elements that are also in another set, called the superset. In other words, all of the elements in the subset are also contained in the superset.
For example, suppose we have a superset S = {1, 2, 3, 4, 5}. Then, the following sets are subsets of S:
{1, 2, 3}, {2, 4, 5}, {1}, and {} etc.
Here we have
{A, B, C} a subset
As we know, the set of the alphabet = { A, B, C, D,... Z }
which also includes the elements A, B, and C
Hence,
The set {A, B, C} is a subset of the set of letters of the alphabet.
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Calculate the concentration for the following pH: pH = 2.44
The concentration οf hydrοgen ions in a sοlution with pH 2.44 is [tex]2.754\times 10-12 M[/tex]
What is the pH value?
The pH value is a measure οf the acidity or basicity of a solution. It is defined as the negative lοgarithm (base 10) of the concentration of hydrogen ions (H+) in moles per liter (mol/L) of solutiοn. The pH scale ranges from 0 to 14, where a pH of 7 is considered neutral. Solutions with a pH less than 7 are acidic, while solutiοns with a pH greater than 7 are basic οr alkaline.
a) Given pH = 2.44
We knοw pH + pOH = 14,
pOH = 14 - 2.44 = 11.56
[tex][H+] = 10^{-pH} = 10^{-2.44} = 3.63\times 10 ^{-3} M[/tex]
[tex][OH-] = 10-pOH = 10-11.56 = 2.754\times 10-12 M[/tex]
b) Given ,pOH = 10.85
and it is knοwn that pH + pOH = 14, thus pH = 14 - 10.85= 3.15
[tex][H+] = 10^{-pH} = 10^{-3.15} = 7.07\times10^{-4 M}[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-10.85} = 1.41\times10^{-11} M[/tex]
c) Given pH = -0.65
and it is knοwn that pH + pOH = 14, thus pOH = 14 +0.65 = 14.65
[tex][H+] = 10^{-pH} = 10^{0.65} = 4.466 M[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-14.65} = 2.23 \times10^{15} M[/tex]
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Complete question:
Calculate the [H+] and [OH-] concentrations for the fοllowing solutions with: (a) pH = 2.44 (b) pOH = 10.85 (c) pH = -0.65
Help help help help I really need help on this question please
Answer:60 cents per taco
Step-by-step explanation:
120/2=60
180/3=60
300/5=60
480/8=60
The final RSVP guest count is 60 people Which catering company will offer the best deal for your family? How much money will your family save by choosing that company
a) The family's best deal is with Smokey's BBG which charges $780 for 60 guests.
b) Choosing Smokey's BBG over Bennie's BBQ will save (difference) the family $40.
How is the difference or saving determined?The total cost for each company's catering services is worked out using their cost functions.
Smokey's BBG does not charge a fixed cost, unlike Bennie's BBG.
The difference between the total costs of the companies is obtained by subtraction.
The number of guests = 60
Smokey's BBQ Bennie's BBQ
Catering Fees $0 $100
Charge per person $13 $12
The total charge for 60 $780 ($13 x 60) $820 ($100 + $12 x 60)
Difference between the charges = $40 ($820 - $780)
However, using a system of equations we can determine the number of guests that makes the total cost the same for each company as 100.
Thus, comparing the total costs for the two companies shows the difference or cost savings to be gained by the family.
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Question Completion:Smokey's BBQ charges $13 per person while Bennie's BBG charges a $100 catering fee and $12 per person.
Help with part 2 please
The blanks when completes are:
The value of 6x - x² increases from 0 at x = 0 to 9 at x = 3, then decrease back at x = 6. Also, the values are 0 for x = 0...
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we can see that
The function increases from x = to to x = 3The function decreases from 3 = to to x = 5This means that the values that complete the blanks are increase, decrease and 0
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What is the value of X? HELP ME PLEASE:) THIS QUESTION IS HARD WHATS THE ANSWER
Answer:
96 because 60 plus 36 equals 96 and value means add but if your multiplying the answer would be 2160
Step-by-step explanation:
What is the eighth term of 4000, 800, 160, 32
The eighth term of 4000, 800, 160, 32... will be 0.0512.
What is geometric progression?
A geometric progression is also known as the geometric sequence which is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
We are given, 4000, 800, 160, 32, ....
a is the first term = 4000
The terms are in reducing order of 1/5 at each stage.
So, 5th term = 32/5 = 6.4
6th term = 6.4/5 = 1.28
7th term = 1.28/5 = 0.256
And 8th term = 0.256/5 = 0.0512
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Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). Mark this and return
The variable y is directly proportional to x, which is the definition of direct variation.
What is coordinate geometry?The intersection of two perpendicular lines, the x-axis and the y-axis, results in a 2D plane known as a coordinate plane. In geometry, a coordinate system is a method for calculating the positions of the points using one or more integers or coordinates.
The graph that represents a function with direct variation is a coordinate plane with a line passing through (0, 0) and some other point that is not the origin.
Out of the given options, the graph that represents a function with direct variation is the coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).
This is because the equation of this line can be written in the form y = mx, where m is the slope of the line. In this case, the slope is:
m = (0 - (-2)) / (-4 - 0) = 1/2
So the equation of the line is y = (1/2)x - 2, which is in the form of y = kx, where k = 1/2. This means that y is directly proportional to x, which is the definition of direct variation.
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Please Help!
Solve each inequality:
1) P=a+b+2c
2) y=2ab-C
We can write the expression for {P} as -
P = a + b + 4ab - 2y
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
Given are the expressions as -
P = a + b + 2c
y = 2ab - C
We can write -
C = 2ab - y
Putting the values in the equation -
P = a + b + 2c
P = a + b + 2(2ab - y)
P = a + b + 4ab - 2y
Therefore, we can write the expression for {P} as -
P = a + b + 4ab - 2y
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5,10,15,20,25 is this an arithmetic or geometric sequence
Because of the common difference of 5, this series is math because it has a common difference of 5.
What in mathematics is an arithmetic sequence?An arithmetic series is one in which each term grows by adding or removing a certain number, k. In a geometric series, each term grows by dividing by or increasing by a certain constant k. For instance, a1 = 25 and a(n) Equals a(n-1) Plus 5.
This is a list of numbers.
Each term in an arithmetic series is created by adding a fixed difference to the term before it. The distance between successive words in this order is 5:
10 - 5 = 5
15 - 10 = 5
20 - 15 = 5
25 - 20 = 5
Therefore, this sequence has a common difference of 5, which means it is an arithmetic sequence.
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30 gallons= 114 liters
Answer: 113.56235 Liters
Step-by-step explanation:
A researcher watches popular television shows and records every time someone interrupts a speaker. She wants to understand the frequency of interruption on television.
Answer:
the frequency of someone interru
Step-by-step explanation:
The correct answer is (d) noise. Unwanted sound that is regarded loud, unpleasant, or disruptive to hearing is called noise.
What is noise?Even if the label "unwanted" is arbitrary, some sounds are frequently regarded as noise. A sound pressure level, expressed in decibels, is used to measure or anticipate noise (dB).
here, we have,
The measurements and noise meter used depend on the application; different noise metrics can account for magnitude, frequency, and time in different ways.
and, we have,
Another illustration is workplace noise, where the effect of noise on hearing loss is of utmost importance.
To offer a degree of exposure that can be associated to the possibility of hearing loss in employees exposed to the sound during the course of exposure, both the intensity and duration of sound are combined.
Hence, The correct answer is (d) noise. Unwanted sound that is regarded loud, unpleasant, or disruptive to hearing is called noise.
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Complete question:
ivan is trying to understand the concern of an angry customer, but several employees keep interrupting the conversion. these interruptions are an example of
3.
1
A decorative wooden piece is made up of four rectangles as shown to the
right. The smallest rectangle measures 4 inches by 7 inches. If 2
inches are added to each dimension as the rectangles get larger, what is
the total area of the entire piece?
The total area of the rectangle with the provided figures will be equal to 280 inches.
How to obtain the area of the rectanglesNote that the area of a rectangle is length * width.
So, given this formula:
The area of the smallest rectangle will be: 4 * 7 = 28
The area of the next rectangle will be: (4 + 2) * (7 + 2)
= 6 * 9
= 54
The area of the next rectangle will be: (6 + 2) * (9 + 2)
= 8 * 11
= 88
The area of the fourth and largest rectangle will be: (8 + 2) * (11 + 2)
10 * 11
= 110
The total area of the angles will be: 28 + 54 + 88 + 110
= 280.
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The net of a triangular prism and its dimensions are shown below. What is the total surface area of the prism? The net of a triangular prism and its dimensions are shown below.
What is the total surface area of the prism?
The total surface area of the prism is equal to 74 m².
How to calculate the total surface area of the triangular prism?In Mathematics, the total surface area of a triangular prism can be calculated by using this mathematical expression:
Total surface area of triangular prism = (Perimeter of the base × Length of the prism) + (2 × Base area)
Total surface area of triangular prism = (S₁ + S₂ + S₃)L + bh
where:
b is the bottom edge of the base triangle.h is the height of the base triangle.L is the length of the triangular prism.S₁, S₂, and S₃ represent the three sides (edges) of the base triangle.By substituting the given parameters, we have:
Total surface area of triangular prism = 4 + (5 × 4)3.5
Total surface area of triangular prism = 4 + (20)3.5
Total surface area of triangular prism = 74 m².
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Write the equation of a rational function that has been translated left 2 units and shifted up 1 unit.
The equation of a rational function that has been translated left 2 units and shifted up 1 unit is; f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
What is the equation after transformation?A relation is defined as a function in the event that it possesses only One y-value with a corresponding x-value.
A general form of how a rational function is represented is:
f(x) = (ax + b) / (cx + d)
To translate this function left 2 units, we need to replace x with x + 2. This gives us:
f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)
To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:
f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)
Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
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PLEASE HELP IM SO LOST !!
The function has domain = {2, , 5, - 4, - 5} and rangle = {1, 4, 5, 3, - 6} and it is not a function.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
From the given coordinate plots the ordered pairs are,
(2, 1), (2, 4), (5, 5), (- 4, 3), and (- 5, - 6).
We know a relation is not a function when two distinct ordered pairs have the same x-coordinate.
In this case (2, 1) and (2, 4) have the same x-coordinate and hence it is not a function.
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10. You are painting a room that is 18 feet long, 14 feet wide and 8 feet high. If the paint costs $6.50 a gallon and each gallon covers 128 square feet, how much will it cost to paint the room?
The total cost to paint the room is, $102.375.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, A room that is 18 feet long, 14 feet wide, and 8 feet high.
Therefore, The surface area of the room is,
= 18×14×8 aq feet.
= 2016 sq feet.
Now, Paint costs $6.50 a gallon and each gallon covers 128 square feet.
Therefore, The number of gallons of paint required is,
= (2016/128) gallons.
= 15.75 gallons.
So, The total cost of painting is,
= $15.75×6.50.
= $102.375.
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if the dilation of K(-2,4) equals K'(1,-2), the scale factor used for the dilation is
Answer:
-1/2
Step-by-step explanation:
We know
The dilation of K(-2,4) equals K'(1,-2)
To get from -2 to 1, we time -1/2
To get from 4 to -2, we time -1/2
So, the scale factor used for the dilation is -1/2
1.1 PQR is a tangent to circle QABCD. AB is parallel to QD and CD = CB. Ĉ= 110°; D3= 70° and ₂= 100°. P Cloo Determine with reasons the sizes of the following: 1.1.1 B₁ (3) 1.1.2 ABC (4) 1.1.3 D₂ (2) 1.1.4 A₂
Answer: Unfortunately, the given information is not sufficient to answer the questions 1.1.1, 1.1.2, 1.1.3, and 1.1.4. However, I can provide some insights based on the given information.
1.1.1: B₁ is not defined in the given information. Without knowing what B₁ represents, we cannot determine its size.
1.1.2: We know that AB is parallel to QD, and CD = CB. Also, angle Ĉ = 110°. However, we don't know the location of point P, so we cannot determine the size of angle ABC.
1.1.3: We know that angle D₃ = 70°, but we don't know the location of point P, so we cannot determine the size of angle D₂.
1.1.4: We know that angle ₂ = 100°, but we don't know the location of point P, so we cannot determine the size of angle A₂.
Step-by-step explanation:
Find the slope of the line shown below?
MATH I WILL GIVE BRAINLIEST!
d ≥ 4, The family must travel at least four days.
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is replaced by less than (or less than or equal to), more than (or greater than or equal to), or not.
Given:
The family drives 350 miles per day.
they need to travel at least 1400 miles
let the number of day taken to travel 1400 miles.
So, the Inequality of the Situation as
350d ≥ 1400
d≥ 1400/350
d≥ 140/ 35
d ≥ 4
So, the family must travel at least four days.
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please help, need help understanding step by step.
we will need at least 96 bags of sand to cover the base of the circular pool.
what is circle?
A circle is a two-dimensional geometric shape consisting of all the points that are equidistant from a given point, called the center.
The area of a circular pool with a diameter of 22 feet can be calculated using the formula:
A = πr^2
where A is the area of the circle, π is a constant (approximately equal to 3.14), and r is the radius of the circle (which is half the diameter).
In this case, the diameter is 22 feet, so the radius is:
r = d/2 = 22/2 = 11 feet
Now we can calculate the area of the circle:
A = πr^2 = 3.14 x 11^2 = 379.94 square feet (rounded to 2 decimal places)
To cover this area with sand, we need to know how many bags of sand are required. We are told that one bag of sand covers about 4 square feet, so we can calculate the number of bags of sand required as follows:
Number of bags = Area of pool / Area covered by one bag
Number of bags = 379.94 square feet / 4 square feet per bag
Number of bags ≈ 95 bags
Since we need to round up to a whole number of bags, we will need at least 96 bags of sand to cover the base of the circular pool.
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2/7
of the 140 students in a contest gave their speeches. How many students gave their speeches?
Yesterday,
Write your answer in simplest form.
Answer:40
140/7=20
20x2=40
40 is the same as two-sevenths of 140
Fins the center of the radius circle.
(x-1)^2 + (y-5)^2=4
Answer:
the radius is 1
Step-by-step explanation:
how many solutions are in 16 (3x − 6) = 18 (4x + 8).
Answer:
alot
Step-by-step explanation:
Answer:
One solution, x = -10
Step-by-step explanation:
16 (3x − 6) = 18 (4x + 8)
48x - 96 = 72x + 144
-24x = 240
x = - 10
number that multiply to 375 but adds to -10
The two numbers that multiply to 375 and add to -10 are -25 and 15.
How to find two numbers that multiply ?To find two numbers that multiply to 375 but add to -10, we can use a system of equations.
Let's call the two numbers we're looking for x and y. Then we have:
xy = 375 (since they multiply to 375)
x + y = -10 (since they add to -10)
We can use the second equation to solve for one variable in terms of the other. For example, if we solve for y, we get:
y = -x - 10
Now we can substitute this expression for y into the first equation:
x(-x - 10) = 375
Expanding the left side gives:
-x^2 - 10x = 375
Bringing everything to one side gives:
x^2 + 10x - 375 = 0
We can factor this quadratic equation as:
(x + 25)(x - 15) = 0
This gives us two possible values for x: x = -25 or x = 15.
If x = -25, then y = -10 - (-25) = 15.
If x = 15, then y = -10 - 15 = -25.
So, The two numbers that multiply to 375 and add to -10 are -25 and 15.
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David has 6 pounds of dried fruit to make snack bags. He separates each pound of dried fruit into fourths and wants to use 1 fourth for each bag. How many snack bags can he make with all of the dried fruit?
Answer: 24
Step-by-step explanation: 6*4=24
i did 6*4 because there are 4 fourths in each pound
Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $120, or she is able to buy 2 shirts and 4 sweaters for $160. How many dollars does a shirt cost? How many dollars does a sweater cost?
Answer:
Shirt = $20
Sweater = 30
Step-by-step explanation:
3sh + 2sw = 120
2sh + 4sw = 160
Multiply (3sh + 2sw = 120) by -2
-6sh + -4sw = -240 -> -6sh -4sw = -240
Add the two equations -6sh -4sw = -240 and 2sh + 4sw = 160 together. -4sh = -80
Shirt = 20
Substitude in 20
3 x 20 = 60 120 - 60 = 60 60/2=30
Solve:
|3x|=9
x= 3
x= 1 and x=-2
x=3 and x=-3
x= 0 and x= 7
The required solutions of the equation |3x| = 9 are x = 3 and x = -3.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
We can solve the given equation by isolating the absolute value on one side and simplifying it.
|3x| = 9
| x | = 3
Now, we need to solve two separate equations for x:
When x is positive:
|x| = 3
=> x = 3 (since x is positive)
When x is negative:
|x| = 3
-x = 3 (since x is negative)
x = -3
Therefore, the solutions of the equation |3x| = 9 are x = 3 and x = -3.
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These lists show the ages of attendees in a yoga class and a dance class.
Yoga: 18, 31, 17, 44, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Which statement about attendees in the two classes is true?
A. The median age of the attendees in the yoga class is greater than the median age of
the attendees in the dance class.
B. The median age of the attendees in the dance class is greater than the median age of
the attendees in the yoga class.
C. The median age of the attendees in the yoga class is the same as the median age of the
attendees in the dance class.
D. The median age of the attendees in the yoga class is 44 years and the median age of
the attendees in the dance class is 47.
The true statement is the median age of the attendees in the yoga class is greater than the median age of the attendees in the dance class. (option A).
What is the true statement?
Median is the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
Ages of Yoga students arranged in ascending order: 18, 17, 20, 31, 33, 36, 44
Median = 31
Ages of Dance students arranged in ascending order: 20, 23, 26, 30, 38, 42, 47
Median = 30
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