Final answer:
There can be a total of 11,175 two-person conversations at the party.
Explanation:
In a party with 150 people, the number of two-person conversations that can occur can be calculated using the formula for combinations. Since each conversation involves two people, we need to choose 2 people from the total of 150. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of people and r is the number of people we need to choose. Plugging in the values, we have:
C(150, 2) = 150! / (2!(150-2)!)
C(150, 2) = (150 ×149) / (2 ×1)
C(150, 2) = 11175
Therefore, there can be a total of 11,175 two-person conversations at the party.
Final answer:
At a party with 150 people, there can be 11175 unique two-person conversations, calculated using the combination formula 150C2.
Explanation:
The question is asking how many two-person conversations can occur at a party with 150 people. This is a classic combination problem where we need to calculate the number of unique pairs that can be made from 150 people. Since the order in which the pair is chosen does not matter, we use the combination formula nCr = n! / (r!(n-r)!), where 'n' is the total number of people and 'r' is the group size (in this case, 2 for a two-person conversation).
For 150 people, the calculation is:
150C2 = 150! / (2!(150-2)!) = 150! / (2! x 148!) = (150 x 149) / (2 x 1) = 11175.
Therefore, there can be 11175 unique two-person conversations at a party with 150 people.
How does finding the square root of a number compare to finidng the cubic root of a number?
Final answer:
Square rooting and cube rooting are processes to find a number that, when raised to the second or third power respectively, equals the original number. Square roots are related to squares, and cube roots are related to cubes; both functions are essential in solving various mathematical problems, including equilibrium and Pythagorean Theorem problems.
Explanation:
Finding the square root of a number is the process of determining a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 squared (5²) is 25. This can be expressed using exponents as x¹⁄₂ = √x.
On the other hand, finding the cube root of a number involves determining a number which, when multiplied by itself twice (or cubed), results in the original number. For instance, the cube root of 27 is 3, since 3 cubed (3³) equals 27. The formula for a simple equilibrium problem that involves cubic roots is a³ = M₁ × P², where you would then find the cube root of the result to solve for 'a'.
Both operations are inverse functions: square rooting is the inverse of squaring, and cube rooting is the inverse of cubing. When dealing with equilibrium problems or Pythagorean Theorem applications, it's important to know how to perform these operations, often requiring a calculator. Make sure you are comfortable with your calculator's functions for these operations, or seek assistance from your instructor if needed.
How to solve more complex problems involving angles the backwards Method
In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.
m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.
From the figure attached,
JK and JL are equal sides of the triangle.m(∠J) = 23x - 4m(∠K) = 4x - 1m(∠L) = 9x - 31Since, two sides JK and JL of ΔJKL are equal in measure,
Therefore, ΔJKL is an isosceles triangle.
By the property of an isosceles triangle, opposite angles of the equal sides are equal.
Therefore, m(∠K) = m(∠L)
4x - 1 = 9x - 31
9x - 4x = 31 - 1
5x = 30
x = 6
By substituting the value of 'x' in the measures of each angle,
m(∠J) = 23x - 4
= 23(6) - 4
= 138 - 4
= 134°
m(∠K) = 4x - 1
= 4(6) - 1
= 24 - 1
= 23°
m(∠L) = 9x - 31
= 9(6) - 31
= 23°
Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.
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Solve 4(c + 2) < 4c + 10.
Write an additional word problem in which the estimated sum is 14,000
The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.
Explanation:The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?
First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.
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The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].
Answer:
(a) 324 solutions are possible
(b) (6 - s)(6 - w)(9 - r)
(c) 198/78
Step-by-step explanation:
Just a pure guess and also give brainliest to the other person
Please help asap!!! I will mark brainliest!
Estimate 27.89 • 10.3 divided by 4.37 using compatible numbers
Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work.
Find the specific formula for the sequence. [−3,1,5,9,13,...]
x+4 is the specific formula for sequence [−3,1,5,9,13,...]
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is
−3,1,5,9,13,...
-3+4=1
1+4=5
5+4=9
9+4=13
As we can see above, to get from one number to the next it is simply adding 4. So the formula for sequence is x + 4.
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What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.
What is the Perimeter of a Polygon?
Perimeter = sum of all sides of the polygon.
Name the vertices as follows:
A(−2, 1)B(−2, 4)C(2, 7)D(6, 4) E(6, 1)Perimeter of the polygon = AB + BC + CD + DE + EA
Use the distance formula, [tex]d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find the length of each segment:
AB = |1 - 4| = 3 units
BC = √[(2−(−2))² + (7−4)²]
BC = 5 units
CD = √[(2−6)² + (7−4)²
CD = 5 units
DE = |4 - 1| = 3 units
EA = |6 - (-2)| = 8 units
Perimeter of the polygon = 3 + 5 + 5 + 3 + 8
Perimeter of the polygon = 24 units
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Not sure how to do this. (I'm aware this is wrong lol)
Bill weighs 120 lbs and is gaining ten lbs each month. Phil weighs 150 lbs and is gaining four lbs each month. How many months will it take for bill to wiegh the same as phil?
Algebraic equations are equations that contain variables that are unknown. These unknown variables are represented by any letters of the Alphabet.
it will take 5 months for Bill to weigh the same as Phil.
Let's represent the number of months they gain extra weight as: m
Step 1
Bill weighs 120 lbs and is gaining ten lbs each month. The algebraic equation for the above statement is :
120 ib + 10 ib x m
120 + 10m ........Equation 1
Phil weighs 150 lbs and is gaining four lbs each month. The algebraic equation for the above statement is :
150 ib + 4 ib x m
150 + 4m ........Equation 2
Step 2
We equate equations 1 and 2 to each other
Equation 1 = Equation 2
120 + 10m = 150 + 4m
Collect like terms
10m - 4m = 150 - 120
6m = 30
Divide both sides by 6
6m/6 = 30/6
m = 5
Therefore, it will take 5 months for Bill to weigh the same as Phil
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The three interior angle measures of this triangle are x = °, y = °, and z = °.
Answer:
30-70-80
Step-by-step explanation:
What is a security deposit
Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35kg. Write an equation to determine the weight, w ww, of each of Carl's checked bags. Find the weight of each of his checked bags.
Answer:
15.5 kg (each)
Step-by-step explanation:
Let [tex]w[/tex] be the weight of each checked bag (there are 2). Thus, we can write, from the information given:
[tex]w+w+4=35\\2w+4=35[/tex]
Now we solve this equation for [tex]w[/tex] to find weight of each checked bag:
[tex]2w+4=35\\2w=35-4\\2w=31\\w=\frac{31}{2}\\w=15.5[/tex]
So, the weight of each of his checked bags is 15.5 kg.
The volume of a cone is 1004.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.)
64
32
8
4
If 15% of x is 42, what is x?
Write a function g in terms of f so that the statement is true.
The graph of g is a reflection in the y-axis of the graph of f
g(x)=
The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a point across the y-axis, we change the sign of the x-coordinate. So, to reflect the graph of f(x) across the y-axis, we need to change the sign of f(x). This can be achieved by multiplying f(x) by -1, giving us g(x) = -f(x).
For example, if f(x) = 2x+3, then g(x) = -(2x+3) = -2x-3.
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The function g(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a graph in the y-axis, we replace each x-coordinate with its opposite (negative value) while keeping the y-coordinate unchanged. In this case, since g is the reflection of f in the y-axis, the function g(x) will have the same y-values as f(x), but the x-values will be their negatives.
For example, if f(x) = 2x + 3, then g(x) = -f(x) would be g(x) = -2x - 3, where the graph of g(x) is the reflection of f(x) across the y-axis.
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Determine the axis of symmetry the vertex and the x-and y intercepts f(x)=x2+2x-3
Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.
Given:
∠C, ∠F are rt.∠'s; AC = DF; BC = EF
Answer:
LA
Step-by-step explanation:
Odyssey
The profits of a company are found by subtracting the company's costs from its revenue. If a company's cost can be modeled by 14x + 120,000 and its revenue can be modeled by 40x - 0.0002x^2, what is an expression for the profit?
The profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
To find the expression for the profit, we need to subtract the cost function from the revenue function.
Given:
Cost function: [tex]\( C(x) = 14x + 120,000 \)[/tex]
Revenue function: [tex]\( R(x) = 40x - 0.0002x^2 \)[/tex]
The profit function, ( P(x) ), is given by:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substitute the given functions into the profit function:
[tex]\[ P(x) = (40x - 0.0002x^2) - (14x + 120,000) \][/tex]
Now, let's simplify:
[tex]\[ P(x) = 40x - 0.0002x^2 - 14x - 120,000 \][/tex]
[tex]\[ P(x) = 26x - 0.0002x^2 - 120,000 \][/tex]
This is the expression for the profit:
[tex]\[ {P(x) = -0.0002x^2 + 26x - 120,000} \][/tex]
So, the profit function is given by [tex]\( P(x) = -0.0002x^2 + 26x - 120,000 \).[/tex]
Write the following statement as a conditional. All flowers are beautiful.
Simplify the expression (20-14)^2 divided by 12
A)1
B)3
C)17
D)0.5
Answer:
The correct option is B) 3.
Step-by-step explanation:
Consider the provided expression.
(20-14)^2 divided by 12
The above statement can be written as:
[tex]\frac{(20-14)^2}{12}[/tex]
[tex]\frac{(6)^2}{12}[/tex]
[tex]\frac{6\times 6}{12}[/tex]
[tex]\frac{36}{12}[/tex]
3 times 12 is 36,
[tex]3[/tex]
Hence, the simplified form of the provided expression is 3.
Therefore, the correct option is B) 3.
Which inequality will have a shaded area above its graph?
a
x − 9y ≤ 1
b
4x + 3y < 6
c
2x − y ≥ 4
d
x − 3y > 4
Help
simply. this math problem
- 4 1/5 = -21/5 = -42/10
-13 1/10 = -131/10
-42/10 - -131/10=
-42/10 + 131/10 = 89/10 = 8 9/10
answer is A
Divide. 42/−8 Enter your answer as a mixed number, in simplified form, in the box.
Markus receives dollar bills from his grandfather for one week on the first day he received $1 on the second day he received $2 on the third day he received $4 and on the fourth day he received $8 if this continues how much money will Marcos have by the end of the week
Answer:
127
Step-by-step explanation:
It gas geometric sequence,
We has a sequence: 1, 2, 4, 8, 16, 32, 64.
It can be solved by two method either sum these digits individually or use formula of sum of geometric sequence
We have formula: [tex]S_n=\frac{a_1(1-r^n)}{(1-r)}[/tex]
Here r = Common Ratio = 2 ÷ 1 = 4÷2 = 2
and a = First term = 1
⇒ [tex]S_n= \frac{1\times(1-2^7)}{(1-2)} \\\Rightarrow S_n=\frac{(1-128)}{-1}\\ \Rightarrow S_n=127[/tex]
Deshawn has several dimes and quarters that total $2.05. he has 3 fewer quarters than dimes. how many of each doe he have
For what values of x does 25^x = 5^x^2-3?
The values of x that satisfy the given equation are -1 and 3
What is an indical equation?From the question, we are to determine the values of x that satisfy the given equation
The given equation is
25^x = 5^x^2-3
The can be written as
[tex]25^{x} =5^{x^{2} -3}[/tex]
Expressing 25 in index form, we get
[tex]5^{2x} =5^{x^{2}-3 }[/tex]
Now, equate the powers (since the bases are equal)
[tex]2x =x^{2}-3[/tex]
Then, we have that
[tex]x^{2} -2x-3 =0[/tex]
Solve quadratically
Using the factorization method, we get
[tex]x^{2} -2x-3 =0[/tex]
[tex]x^{2} -3x+x-3 =0[/tex]
[tex]x(x-3)+1(x-3)=0[/tex]
[tex](x+1)(x-3) =0[/tex]
∴ x+1 = 0 OR x-3 = 0
x = -1 OR x = 3
Hence, the values of x that satisfy the given equation are -1 and 3.
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Sharon is twice as old as brian, and in 5 years the sum of their ages will be 25 years. find their present ages.
Answer:
sharon=10
Step-by-step explanation:
The present age of Sharon and Brain is 10 years old and 5 years old.
Given,
Sharon is twice as old as brian.
In 5 years the sum of their ages will be 25 years.
We need to find their present ages.
What are the important terms in solving age problems?Some of the terms are:
In x years - add x years to the present age
x years ago - Subtract x years with the present age
Before x years - subtract x years to the present age
After x years - add x years to the present age
Find the present age of Sharon and Brain.
Let the present age of:
Sharon - S
Brain - B
Now,
Sharon is twice as old as brian.
We can write this as:
S = 2B ____(1)
In 5 years the sum of their ages will be 25 years.
It can be written as:
(S + 5) + (B + 5) = 25
S + B + 10 = 25
S + B = 25 - 10
S + B = 15 _____(2)
From (1)
We get,
2B + B = 15
3B = 15
B = 5. ______(3)
Putting (3) in (2)
S + 5 = 15
S = 15 - 5
S = 10
We have,
B = 5 and S = 10
Thus the present age of Sharon and Brain is 10 years old and 5 years old.
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