There are 3,997,440,000 ways to assign 12 graduate students to two triple and three double hotel rooms during a conference.
To solve the problem, we can use the concept of permutations and combinations.
First, we need to choose 2 triple hotel rooms out of the available options. This can be done in C(5, 2) ways, where C(n, r) represents the number of ways to choose r items from a set of n items without replacement. So, we have:
C(5, 2) = 5! / (2! * (5-2)!) = 10
Now, we need to assign 3 graduate students to each of the chosen triple rooms.
This can be done in P(12, 3) * P(9, 3) ways,
where P(n, r) represents the number of ways to select and arrange r items from a set of n items with replacement. So, we have:
P(12, 3) * P(9, 3) = 12! / (9! * 3!) * 9! / (6! * 3!) = 369,600
Next, we need to choose 3 double hotel rooms out of the available options. This can be done in C(3, 3) ways, which is just 1.
Now, we need to assign 2 graduate students to each of the chosen double rooms. This can be done in P(6, 2) * P(4, 2) * P(2, 2) ways, which is:
P(6, 2) * P(4, 2) * P(2, 2) = 6! / (4! * 2!) * 4! / (2! * 2!) * 2! / (1! * 1!) = 1,080
Finally, we can multiply the results of all these steps to get the total number of ways to assign the graduate students to the hotel rooms:
Total number of ways = C(5, 2) * P(12, 3) * P(9, 3) * C(3, 3) * P(6, 2) * P(4, 2) * P(2, 2)
= 10 * 369,600 * 1 * 1,080
= 3,997,440,000
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What happens to an image when it is enlarged using scale factor between 1 and 1?
When an image is enlarged using a scale factor between 1 and 1, the image does not change in size.
A scale factor of 1 means that the image is not being enlarged or reduced in size; it is remaining the same size. Therefore, the image will appear the same as it did before the enlargement.
A scale factor of less than 1 means that the image is being reduced in size, and a scale factor greater than 1 means that the image is being enlarged in size. But when it comes to scale factor between 1 and 1, the image will not change in size, it will appear the same as it was before.
It's important to note that when you're enlarging an image using a scale factor that's less than 1, the image becomes smaller but when you're using a scale factor greater than 1 the image becomes larger.
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Eric i making banana bread to erve 20 guet. He want each guet to have 1/6 of a loaf. If he bake 3 love of banan bread will eric have
No, Eric will not have enough banana bread to serve all 20 guests if he bakes only 3 loaves.
Eric is making banana bread to serve 20 guests, and he wants each guest to have 1/6 of a loaf. This means that each loaf will be divided into 6 equal portions, and each guest will receive one of these portions.
Eric plans to bake 3 loaves of banana bread. As 1 loaf can serve 6 guests with 3 loaves he can serve a total of
3×6 = 18 < 20
So only 18 guests can be served with 3 loaves of bread.
--The question is incomplete, complete question is given below--
"Eric is making banana bread to serve 20 guests. He want each guest to have 1/6 of a loaf. If he bake 3 loaves of banana bread will eric have enough banana bread to serve all 20 guests?"
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one number exceeds (is more than) another number by 6, and the sum of the two numbers is 26. find the two numbers
Answer:
10 and 16
Step-by-step explanation:
let on number be x then the other number is x + 6
sum the 2 numbers and equate to 26
x + x + 6 = 26
2x + 6 = 26 ( subtract 6 from both sides )
2x = 20 ( divide both sides by 2 )
x = 10
x + 6 = 10 + 6 = 16
the 2 numbers are 10 and 16
NEED HELP ASAP - Algebra 2 - 50 Points
Create two complex numbers a+bi, where b≠0, such that the product of your numbers is 821
The product of two complex numbers, with a result of 821, is given as follows:
(26 + 12.04i)(26 - 12.04i) = 821.
What are complex numbers?Complex numbers are numbers that are composed by a real part and by an imaginary part, and have the notation given as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.The most important complex numbers relation is given as follows:
i² = -1.
Meaning that the easiest way to obtain the desired product is multiplying complex-conjugate numbers, as follows:
(a + bi)(a - bi).
Applying the subtraction of perfect squares, we have that:
(a + bi)(a - bi) = a² - (bi)²
(a + bi)(a - bi) = a² - b²i²
(a + bi)(a - bi) = a² + b² (as i² = -1).
Then, attributing a = 26, the value of b is obtained as follows:
a² + b² = 821
26² + b² = 821
[tex]b = \sqrt{821 - 26^2}[/tex]
b = 12.04.
Meaning that the product is given as follows:
(26 + 12.04i)(26 - 12.04i) = 821.
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(dy/dx) = e^(3x+2y)
solve the differential equation by separation of variables
A reflective pronoun is a pronoun
formed with -self or -selves that is used for emphasis.
formed with -self or -selves that refers to the subject.
that is not formed with -self or -selves.
that is not plural or possessive.
A reflective pronoun is a pronoun formed with -self or -selves that refers to the subject. Hence, option B is correct.
What is reflective pronoun?When a pronoun is used to refer to the same noun as both the subject and the object of a verb, it is known as a reflexive pronoun. The pronouns that in English finish in "self" or "selves" are things like "himself," "myself," "ourselves," etc.
Words like myself, you, him, her, it, ourselves, ourselves, and yourselves are examples of reflexive pronouns. They make a reference to someone or something. When the subject and the object of a verb are the same, reflexive pronouns are frequently used. I cut myself yesterday night while preparing dinner.
Thus, option B is correct.
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What are substitution reactions How are they classified give one example of each?
A substitution reaction is a reaction in which one group of molecules gets replaced by another group of molecules in an aqueous medium.
The substitution reactions are classified into three groups,
nucleophilic substitution electrophilic substitution homolytic substitution.In the nucleophilic reactions the atom is said to be rich in electron , whereas, in the electrophilic reaction, the atom is known to be an electron-deficient species.
The primary difference between substitution and elimination reactions is that substitution reactions replace one group with another, whereas elimination reactions merely remove the group. The main distinction between the groups is the number of stages involved in the reaction.
Example , R-Br + OH− → R-OH + Br−
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Based on the information provided in the graph, for which of the following situations could you expect to have the greatest increase in salary?
On solving the provided question we can say that based on the provided graph obtaining a doctorate after earning a master's degree.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things.
so here,
based on the provided graph obtaining a doctorate after earning a master's degree.
High education is generally highly valued by employers. People with greater education tend to be seen as candidates with a larger variety of skill sets than other candidates with lower level of education, which would positively affect their income level (although this may not always be the case).
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The correct question is -
Based on the information provided in the graph, for which of the following situations could you expect to have the greatest increase in salary? a. Having a high school diploma and going to college for a year. b. Having an associate’s degree and getting a bachelor’s degree. c. Having a bachelors degree and getting a master’s degree. d. Having a master’s degree and getting a doctorate degree.
2. Examine the figure and answer the questions to determine whether or not the triangles shown are similar. What can
you conclude about the relationship between A ABC and A AB'C'. Explain your reasoning
On solving the provided question, we can say that we have two triangle, in which only one angle is same and all other angles and sides are not equal, so they are not similar.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
we have two triangle,
in which only one angle is same and all other angles and sides are not equal, so they are not similar.
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How do you learn 4x tables?
When you multiply 4 with any number, you can use the doubling-up trick (that's the one you used for the two times table) twice. Here is an example: 2 x 4 is the same as 2 + 2 = 4 and then 4 + 4 = 8. So, 2 x 4 = 8.
Here is next double, double example are: 5 x 4 is the same as 5 + 5 = 10, so then 10 + 10 = 20. So, the answer is 5 x 4 = 20.
Here, is the table of four.
4×1=4
4×2=8
4×3=12
4×4=16
4×5=20
4×6=24
4×7=28
4×8=32
4×9=36
4×10=40
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What is the answer for this I need help pls
Answer: the total spent on the meal is $88.25875.
Step-by-step explanation:
The total spent on the meal can be calculated by adding the cost of the meal, the tax, and the tip.
First, we need to calculate the cost of the tax: 72.5 x 0.0675 = 4.88375
Then we need to calculate the cost of the tip: 72.5 x 0.15 = 10.875
Finally, we add the cost of the meal (72.5), the tax (4.88375) and the tip (10.875) to find the total cost of the meal: 72.5 + 4.88375 + 10.875 = 88.25875
Therefore, the total spent on the meal is $88.25875.
What are the 5 methods of factoring polynomials?
Therefore , the solution of polynomials problem is Grouping technique using the greatest common factor (GCF) and others given below.
What are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
There are several methods for factoring polynomials, but the most common methods are:
Grouping: This method involves grouping the first two and last two terms of a polynomial and factoring out the greatest common factor (GCF) from each group.Factoring by GroupingFactoring by grouping is a method of factoring polynomials that is similar to factoring by grouping. The idea behind factoring by grouping is to group together the first two and last two terms of a polynomial and then factor out the greatest common factor (GCF) from each group.Factoring by Inspection: This method involves looking at a polynomial and seeing if it can be factored into two binomials of the form (x + a) or (x - a).Factoring by using the synthetic Division: This method involves dividing a polynomial by a linear factor using synthetic division, which can reveal a linear factor in the polynomial.Factoring by using the quadratic formula: This method involves factoring a polynomial of degree 2 by using the quadratic formula.Factoring by using the difference of squares: This method involves factoring a polynomial that is a difference of squares.Factoring by using the sum and difference of cubes: This method involves factoring a polynomial that is a sum or difference of cubes.To know more about polynomials visit:
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Solve the inequality for x.
-8+2x>4
By solving the given inequality in question, i.e -8+2x>4 , the solution obtained is x>6, which means the inequality satisfies for all the values of x that are greater than 6.
What is inequality?An inequality is a statement that compares two values and asserts that one value is greater than, less than, or not equal to the other value. Inequalities are used to describe a range of values that a variable can take on. The most common symbols used to express inequalities are ">", "<", "≥" and "≤", which represent "greater than", "less than", "greater than or equal to" and "less than or equal to" respectively.
Give an example of inequality?An example for inequality can be , the inequality x > 2 , which states that x is greater than 2, which means that any value of x that is greater than 2 satisfies the inequality.
Inequality can be solved either graphically or algebraically. The solution of an inequality is the set of all values that make the inequality true.
To solve the inequality -8 + 2x > 4, you can follow these steps:
Add 8 to both sides of the inequality: -8 + 2x > 4 becomes 2x > 12Divide both sides of the inequality by 2 : 2x > 12 becomes x > 6So the solution of the inequality is x > 6.
This means that x is greater than 6. So any value of x that is greater than 6 satisfies the inequality.
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What is the following simplified product? Assume x ≥ 0.
(√6x² +4√8x³)(√x-x√√5x5
O3x√6x+x4√30x
+24x² √2x+8x5 √/10x
3x√6x+x4√30x +24x² √√2+8x5/10
3x6x-x√30x+24x²
√2-8x5 10
3x√6x-x√30x +24x² √√2x-8x5 /10x
Answer:
(c) 3x√(6x) -x⁴√(30x) +24x²√2 -8x⁵√10
Step-by-step explanation:
You want to simplify the product ...
[tex](\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})[/tex]
ChoicesAs with a lot of problems of this type, the correct answer choice can be selected by examining a term or two.
Multiplying the last two terms of the binomials, we get ...
[tex]4\sqrt{8x^3}\cdot (-x\sqrt{5x^5})=-4x\sqrt{40x^8}=-4x\sqrt{10(2x^4)^2}=\boxed{-8x^5\sqrt{10}}[/tex]
This term is only found in choice C.
__
Additional comment
The expression is simplified by making use of the radical relations ...
(√a)(√b) = √(ab)
√(a²b) = a√b
The given expression can be rewritten with squares taken out of the radicals as ...
(x√6 +8x√(2x))·(3√x -x³√(5x))
Then, using FOIL or the distributive property, we have ...
= 3x√(6x) +24x²√2 -x⁴√(30x) -8x⁵√10 . . . . . matches C
Which rule describes the translation?
(x, y) → (x-8, y-3)
(x, y) → (x-3, y + 8)
(x, y) → (x+8, y - 3)
(x,y) → (x+3, y + 8)
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Answer: 1,176 miles
Step-by-step explanation:
490 / 5 = 98 miles
98 mph X 12 hours is 1,176
Let C2(R) be the linear pace of all function from R to R that have two continuou
derivative and let Sf be the et of olution u(x) ∈ C2(R) of the differential
equation
u′′ u = f (x)
In mathematics, a differential equation is an equation involving one or more functions and their derivatives. The derivative of a function defines the rate of change of the function at some point.
According to the given Question:
Differential equation:
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, a function generally represents a physical quantity, a derivative its rate of change, and a differential equation defines the relationship between the two. Such relationships are common. Therefore, differential equations play an important role in many fields such as engineering, physics, economics and biology.
The study of differential equations consists primarily of studying their solutions (the set of functions that satisfy each equation) and the properties of those solutions. Only the simplest differential equations can be solved with explicit formulas. However, many properties of solutions to particular differential equations can be determined without exact computation. In many cases, when a closed formula for the solution is not available, the solution can be approximated numerically using a computer. Although the theory of dynamical systems focuses on qualitative analysis of systems described by differential equations, many numerical methods have been developed to determine solutions with some degree of accuracy.
A first-order linear differential equation is an equation that can be written in the form y0 + p(x)y = q(x). where p and q are continuous functions on the interval I. The second-order linear differential equation has a similar form.
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What logarithmic function represents the data in the table?
X f(x)
25 2
125 3
625 4
The antithesis of an exponential function is a logarithmic function. A logarithmic function and an exponential function both use the same base.
What is logarithm function?Writing y = log2 x or f(x) = log2 x represents the logarithmic function for the equation x = 2y. Even today, the base is still 2. Y equals log base b of x, or more simply, "y equals log to the base b of x," is how y = logb x is typically read. Similarly to exponential functions, b > 0 and b 1.
Consequently, the table's data is represented by the logarithmic function f(x) = log3(x).
Table provided:
x f(x)
25 2
125 3
625 4
We can write x in this case as powers of 5, so that
[tex]$25=5^2$$125=5^3$$625=5^4$$\Rightarrow f(x)=5^{f(x)}$[/tex]
After dividing the log in half, we now have
[tex]$\log x=\log 5^{f(x)}$$\Rightarrow \log x=f(x) \log 5 \ldots .\left[\log (a)^m=m \log (a)\right]$[/tex]
[tex]$\Rightarrow f(x)=\frac{\log x}{\log 5}$$\Rightarrow f(x)=\log _5 x \ldots \ldots\left[\log _a b=\frac{\log b}{\log a}\right]$[/tex]
A base-log function [tex]$f(x)=\log _5 x$[/tex], then, reflects the data in the table.
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HELP ASAP ( 15 POINTS)
The constant of proportionality, given that this is a proportional relationship, is 11. 7
How to find the constant of proportionality?To find the constant of proportionality, the following formula is used :
= Y value / Corresponding x value
The constant of proportionality can only be found for proportional relationships.
In this instance, we have x and y of ( 7, 81. 9 ).
The constant of proportionality is:
= 81 .9 / 7
= 11. 7
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Complete the conversion 2.5 T Lb
Answer:
2.5 Tons to lb
1 ton = 2,000 lb
2.5 tons x 2000 lb = 5,000 lb
What is the domain of the graph?
The domain of the graphed function in this problem is given as follows:
2 <= x <= 5.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
On the graph, the domain of the function is given by the values of x.
For this problem, the values of x are a closed interval between x = 2 and x = 5, hence the domain of the function is defined by the interval presented as follows:
2 <= x <= 5.
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Use the vertical line test to determine whether the relation is a function. If not, identify two points a vertical
line would pass through.
Answer:
It is a function
Step-by-step explanation:
The vertical line test proves that it’s is a function because there is no place on the graph where a vertical line would pass through two points.
HELPPPPPPP Answer 5 questions and get lots of Points
Tell whether the ratios form a proportion.
16/12 & 26/ 22
The ratios _____ (do or do not) form a proportion. The cross products are _____ (state the cross product or state "not equal")
Response:
Answer: The ratios do form a proportion. The cross products are equal (16 * 22 = 26 * 12)
Step-by-step explanation:
Circle all perfect squares:
49
32
2
9
42
16
Tyrone has $95 to spend. He already bought pants for $22. How many $5 t-shirts can he buy if he wants to have at least $15 left over?
a. Write an inequality that demonstrates this situation
b. solve your inequality
c. Explain what your answer means to Tyrone
Answer:
a. Write an inequality that demonstrates this situation
Let x be the number of $5 t-shirts Tyrone can buy
The inequality that demonstrates this situation is:
x*5 + 22 <= 95 - 15
b. solve your inequality
x5 + 22 <= 80
x5 <= 58
x <= 11.6
x <= 11
c. Explain what your answer means to Tyrone
Tyrone has $95 to spend, he already bought pants for $22, so he has $95-22 = $73 left to spend. He wants to have at least $15 left over after buying t-shirts, so he can buy up to $73-15 = $58 worth of t-shirts. Each t-shirt costs $5, so he can buy a maximum of 11 t-shirts (58/5=11.6) with no remainder. So Tyrone can buy 11 t-shirts and he will have $73-11*5 = $18 left. This means that Tyrone can buy 11 t-shirts and still have $18 left over.
Step-by-step explanation:
Please help for geometry here the photo
Answer:f = 57 g = 33
Step-by-step explanation:
Add f and g together and make them equal 90 and then solve for x and plug x back in to both angles 57 and 33
Answer:
m<F + m<G + m<H=180°[Sum of angles of traingle is Supplementary]
or,90°+(4x +13)°+(2x +11)°=180°
or,6x + 24°=180°-90°
or,6x=90°-24°
or,X=66°/6
:.X=11°
Now,
m<F=(4x+13)°=(4×11+13)°=57°
m<G=(2x+11)=(2×11+11)°=33°
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please help with trigonometry hw
Answer: ok what is it
Step-by-step explanation:
Determine the power and the rms value for each of the following signals:
a) 5 + 10cos(10t + π/3)
b) 10cos(100t + π/3) + 16 sin(150t + π/5)
c) (10 + 2 sin (3t)) cos 10t
d) 10 cos(5t)cos(10t)
e) 10 sin(5t)cos(10t)
f) e^(jαt) cos(w0t)
The power and the r m s value for each of the following signals are a)p=50w and r m s =7.07 b)p=178w, r m s =√178 c)p=51w, r m s =√51
d)p=25w, r m s =√25 e)p=25w, r m s =√25 and f)p=1/2, r m s =√1/2.
(a) 5+10cos(100t+π/3)
=A cos(w0t+θ)
power of the signal
P=10^ 2/2=100/2=50w
p=50w
r m s value of the signal
=√50
=7.07
b) 10cos(100t+π/3)+16sin(150t+π/5)
power of the signal.
p=10^ 2/2+16^ 2/2
p=178w
r m s value of the signal=√178
c) (10+2sin(3t)cos10t
=10cos10t+2sin3tcos210t
=2sin3tcos10t
=1/2(sin(3+10)+sin(3-10))
(sin a cos b=1/2(sin(a + b)+sin(a-b))
=2x1/2(sin13t-sin7t)
=sin13t-sin7t
=10cos10t+sin13t-sin7t
power of the signal is
p=10^ 2/2+1^ 2/2+1^ 2/2
p=51w
r m s value of the signal=√51
d) 10 cos(5t)cos(10t)
=10(cos(5+10)T+ cos (5-10)t/2
(cos a cos b=1/2(cos a+ cos b)+cos(a-b))
=10(cos(15)t+ cos (-5)t/2
=5cos15t-5cost
power value of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the signal=√25
e) 10 sin(5t)cos(10t)
=10(sin(5+10)t+ sin(5-10)t/2
=10/2(sin15t-sin5t)
=5sin15t-5sin5t
power of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the =√25
F) f) e^(jαt) cos(w0t)
=e jαt cos wot
=(cosαt+ cos wot+jsin2tcoswot
=(cos(α+wo)t+ cos(α-wo)t/2+j(sin(2+wo)t+ sin cos-wot/2
=1/2cos(α+wo)T+1/2cos(α-wo)T
power of the signal
p=(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2
p=1/2
r m s value=√1/2
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[tex]\pi[/tex]
Go step by step to reduce the radical sqrt 162
The final solution after reducing the given number radical is; 9√2
How to simply a number radical?
The radical of a number is defined in the same way we define the root of a number. The root can be a square root, fourth root or even cube root, up to the nth root.
Now, we are given the number radical as; √162
Now, 162 can be broken down into its' factors as √(81 * 2)
We know from properties of surds that;
√(a * b) = √a * √b
Thus, we now have;
√162 = √81 * √2
This can be simplified further to get;
9√2
Thus, that is the final solution to the number radical simplification.
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