A catering service offers 12 appetizers, 9 main courses, and 7 desserts. A customer is to select 10 appetizers, 3 main courses, and 5 desserts for a banquet. In how many ways can this be done?
Answers
There are 112224 ways in which the required selection can be made.
Using the concept of CombinationFor the appetizers, we need to choose 10 out of the available 12 options. We can calculate this using the formula for combinations:
C(12, 10) = 12! / (10! * (12 - 10)!)
= 12! / (10! * 2!)
= (12 * 11 * 10!) / (10! * 2)
= (12 * 11) / 2
= 132 / 2
= 66
So, there are 66 ways to select 10 appetizers.
For the main courses, we need to choose 3 out of the available 9 options:
C(9, 3) = 9! / (3! * (9 - 3)!)
= 9! / (3! * 6!)
= (9 * 8 * 7 * 6!) / (3 * 2 * 1 * 6!)
= (9 * 8 * 7) / (3 * 2 * 1)
= 504 / 6
= 84
So, there are 84 ways to select 3 main courses.
For the desserts, we need to choose 5 out of the available 7 options:
C(7, 5) = 7! / (5! * (7 - 5)!)
= 7! / (5! * 2!)
= (7 * 6 * 5!) / (5! * 2)
= (7 * 6) / 2
= 42 / 2
= 21
So, there are 21 ways to select 5 desserts.
To calculate the total number of ways to make the selections, we can multiply the number of options for each category together:
Total number of ways = Number of ways to select appetizers * Number of ways to select main courses * Number of ways to select desserts
= 66 * 84 * 21
= 112,224
Therefore, there are 112,224 ways to make the selections for the banquet.
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Related Questions
What is the Definition of Math?
Answers
Answer:
mathematics
Step-by-step explanation:
Example....
"She teaches math and science" .
Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3). Find the coordinates of G.
The coordinates of G are
Answers
Answer:
Coordinates of G = \((2,0)\)
Step-by-step explanation:
Given: Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3).
To find: coordinates of G
Solution:
Midpoints of a side joining points \((a,b),\,(c,d)\) are given by \((\frac{a+c}{2},\frac{b+d}{2})\)
Diagonals of a parallelogram bisect each other.
So,
Midpoint of DF = Midpoint of EG
Midpoint of DF = \((\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})\)
Midpoint of EG = \((\frac{-3+x}{2},\frac{1+y}{2})\)
Let coordinates of G be \((x,y)\)
Therefore,
\((\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0\)
So,
Coordinates of G = \((2,0)\)
In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, & the first aid station, F. The campground is 0.35 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular.
If the path from the park ranger station to the campground is 0.65 mile, determine and state, to the nearest
hundredth of a mile,
a. Find the length of PL
Answers
Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.
How to calculate the valueIt should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:
= ✓(0.35² + 0.65²)
= 0.76 miles.
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Which graph represents the function f(x) = -|x| − 3?
Answers
A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.
The function f(x) = -|x| − 3 can be graphed by following these steps:
To begin, draw a regular x and y-axis and mark it off with an appropriate scale. Then, mark off the negative values on the y-axis and both negative and positive values on the x-axis. After that, we will begin graphing the function f(x) = -|x| − 3, which is a reflection of the absolute value of x over the y-axis and shifted three units down the y-axis. Since the function f(x) = -|x| − 3 is a reflection of the absolute value of x over the y-axis, the graph should be symmetrical. This means that each point to the left of the y-axis is a reflection of the point to the right of the y-axis. Then, we will plot the vertex (0, -3), which is three units down from the origin. Next, we can plot other points using a table of values. We can select values for x that are both negative and positive, such as -2, -1, 0, 1, and 2, and then evaluate them to find the corresponding y values. Then, plot these points on the graph. Finally, we connect the points with a smooth curve, which will form the graph of the function f(x) = -|x| − 3. The graph will be in the shape of a V that opens downwards.Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.
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If the square below has an area of 50, what is the value of x
Answers
Answer:
10
Step-by-step explanation:
A= L²
50 = L² (do opposite operation to find L)
L = 7.07
x²= L²+ L²
x²= 7.07² + 7.07²
x² = 100 ( do opposite operation to make x the subject)
x = 10
Note: opposite operation of square is square root
The point P (5, -1) is rotated 270° counterclockwise around the origin.
What are the coordinates of the resulting point P prime?
Answers
Answer:
(-1,-5) Hopes this helps you :)
Step-by-step explanation:
Given that f(x)=2x+1 and g(x)=x^3 , find (fog)(-2)
Answers
36.66 is 47% of what number?
Answers
Answer:
78
Explanation:
Let the number = n
So, we say that:
\(47\%\text{ of n}=36.66\)We then write this mathematically as:
\(\begin{gathered} \frac{47}{100}\times n=36.66 \\ 47n=36.66\times100 \end{gathered}\)Divide both sides of the equation by 47:
\(\begin{gathered} \frac{47n}{47}=\frac{36.66\times100}{47} \\ n=\frac{3666}{47} \\ n=78 \end{gathered}\)Thus, 36.66 is 47% of 78.
someone help me.... if u guys geniussssss
Answers
Answer: For a) the Factor is (x+2) (x+1)
Step-by-step explanation: Because (x+2) multiplied by (x+1) gives you x2 + 3x +2.
I don't know your language so I don't know if that was the question or what the other questions were asking, but that's the best I can do
For what values of a and b is x^64 + ax^b +25 a perfect square for all integer values of x?
Answers
For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)
To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.
A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.
Let's examine the given expression: \(x^64 + ax^b\) + 25
For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.
So we have:\(x^64 + ax^64 + 25\)
Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)
By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)
Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)
From the second equation, we know that k = 25.
Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)
To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.
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Put the following
numbers in order
from greatest to
least :
1/3. 0.13
13.3% 3
Answers
Answer:
Step-by-step explanation:
3, 13.3% 0.13, 1/3
if a₁=3 and aₙ=5aₙ-₁ then find the value of a₅
Answers
Answer:
The value of a₅ is 1875.
Step-by-step explanation:
Given:
a₁ = 3
aₙ = 5aₙ₋₁
To find the value of a₅, we can apply the recursive formula to compute each term successively:
Step 1: Compute a₂
a₂ = 5a₁ = 5(3) = 15
Step 2: Compute a₃
a₃ = 5a₂ = 5(15) = 75
Step 3: Compute a₄
a₄ = 5a₃ = 5(75) = 375
Step 4: Compute a₅
a₅ = 5a₄ = 5(375) = 1875
PLEASE HELP WITH FACTORING PROBLEM/SHOW WORK!
Answers
Answer:
(3x+2)(x-5)
Step-by-step explanation:
Factor by grouping
\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)
A bacteria population is tripling every hour. By what factor does the population change in 1/2 hour? Select all that apply.
Answers
Answer:
B but there might be more, look below. I didn't have time to calculate the other answers.
Step-by-step explanation:
Well, it is growing x3 each hour, so each half hour it's 1.5...
So whichever is equal to 1.5 is the answer, like B. There might be more.
figure below represents a floor covered with white tiles and gray tiles. KEY = 1 square unit Which expression could be used to find the area, in square units, of the entire floor? A (12+7) x (12+7) B (12 × 7) + (12 × 7) X (10+7) x (2+7) (10 × 7) + (2 × 7)
Answers
the area of the given fig will be (12 × 7) +(12 × 7)
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
a floor covered with white tiles and gray tiles.
the area of the given figure will be
(12 × 7) and another (12 × 7)
So the total area will be (12 × 7) +(12 × 7)
Hence the area of the given fig will be (12 × 7) +(12 × 7)
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HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
help din HDKE EJFNQKEHWHQODBEHQVEIFNFJRNSJEBSG
Step-by-step explanation:
di ko din alam e AHAHAHAHAHAHAHAHAHA NSKFBWJF S DJEBEJS
JSHEBEJS IF JENSKS.DJWKW
SBWUKWVEUEBJQBRJDNDJXBDJDBDKW
EBEJE KD DJWKQKQBWHS
Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6.7 % interest, bonds pay 2.5 % interest, and CDs pay 5.75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977.5 , how much was invested in each account?
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Answers
Answer:
stocks: $45000bonds: $55000CDs: $45000Step-by-step explanation:
You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.
SetupWe can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...
s + b + c = 145000b - c = 100000.067s +0.025b +0.0575c = 6977.50SolutionThese equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.
We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...
stocks: $45000bonds: $55000CDs: $45000__
Additional comment
Using b = c +10000, the two remaining equations are ...
s +2c = 1350000.067s +0.0825c = 6727.50<95141404393>
Please help!!!! I will give brainliest
Answers
Answer:
Top one (A)
Step-by-step explanation:
X >/ -4 Means that the number is "true" as long as it is -4, or larger in amount.
find an area of a circle
Answers
The area of a circle is pi times the radius squared (A = π r²).
3) Ms. Jamison and her niece, Sarah go on a hike. Sarah's backpack weighs 25 pounds. Ms. Jamison tells her niece that her pack is 7 pounds less than twice as heavy as her pack. Use the equation 2p - 7 =25 to find the weight of Ms. Jamison's backpack
Answers
Solution
From the given equation
2p - 7 =25
By collecting like the term
2p = 25 + 7
2p = 32
p = 32/2
p = 16
Which of the following is NOT a linear factor of the polynomial function?
f (x) = x^3 – 5x^2 - 4x + 20
F. (x + 5)
G. (x - 2)
H. (x - 5)
J. (x + 2)
Answers
Answer:
Among the four choices, \((x + 5)\) is the only one that is not a linear factor of this polynomial function.
Step-by-step explanation:
Let \(a\) denote some constant. A linear factor of the form \((x - a)\) is a factor of a polynomial \(f(x)\) if and only if \(f(a) = 0\) (that is: replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(a\!\) would give this polynomial a value of \(0\).)
For example, in the second linear factor \((x - 2)\), the value of the constant is \(a = 2\). Verify that the value of \(f(2)\) is indeed \(0\). (In other words, replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(2\) should give this polynomial a value of \(0\!\).)
\(\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}\).
Hence, \((x - 2)\) is indeed a linear factor of polynomial \(f(x)\).
Similarly, it could be verified that \((x - 5)\) and \((x + 2)\) are also linear factors of this polynomial function.
Rewrite the first linear factor \((x + 5)\) in the form \((x - a)\) for some constant \(a\): \((x + 5) = (x - (-5))\), where \(a = -5\).
Calculate the value of \(f(5)\).
\(\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}\).
\(f(5) \ne 0\) implies that \((x - (-5))\) (which is equivalent to \((x + 5)\)) isn't a linear factor of this polynomial function.
PLEASE HELPPPPPPPPPP
Answers
180-113
x=67
Find the area of the figure. Type your answer as just a number, without units.
Answers
After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.
Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point E, this allows the two diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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3|3x+4|-7=5 please help
Answers
Answer:
\(x = 0\)
Step-by-step explanation:
\(3 |3x + 4| - 7 = 5\)
Add 7\(3 |3x + 4 | = 12\)
Divide by 3.\( |3x + 4| = 4\)
Remove the absolute value signs and left with:\(3x + 4 = 4\)
Subtract\(3x = 0\)
\(x = 0\)
El perímetro de un rectángulo es de 72 cm. Halla el área del rectángulo si su largo es el 25% más grande que su ancho
Answers
Answer:
Las dimensiones del rectángulo son:
ancho = 16 cm
largo = 20 cm
Step-by-step explanation:
Consideración:
La formula del perímetro de un rectángulo es:
perímetro = 2(largo + ancho)
25% más grande = 125% = 125/100 = 1.25
Planteamiento:
2(a+b) = 72
b = 1.25a
a = longitud del ancho
b = longitud del largo
Desarrollo:
de la primer ecuación del planteamiento:
a+b = 72/2
a+b = 36
b = 36 - a Ec. 3
Igualando la segunda ecuación del planteamiento con la Ec. 3:
1.25a = 36 - a
1.25a + a = 36
2.25 a = 36
a = 36/2.25
a = 16
de la Ec. 3:
b = 36 - a
b = 36 - 16
b = 20
Comprobación:
de la primera ecuación del planteamiento:
2(a+b) = 72
2(16+20) = 72
2*36 = 72
Why people with different levels of income pay different amounts of taxes
Answers
Answer:
bc if you have more to give
Step-by-step explanation:
Complete the two-way frequency table.
Type of Fruit
Food
Vegetable
Total
Child
15.5%
44.4%
%
Age
Adult (18+)
28.9%
55.6%
%
Total
57.8%
%
%
Answers
The values in the missing places are 26, 52, 14, 40 and 50
What is a frequency table?A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.
Given is a frequency table with some missing places,
For every missing places, we just need to add or subtract from the total.
Types of food Age
child adult (18+) Total
Fruit 26 26 52
Vegetable 14 24 38
Total 40 50 90
First missing place = 50-24 = 26
Second missing place = 26+26 = 52
Third missing place = 38-24 = 14
Fourth missing place = 26+14 = 40
Fifth missing place = 90-40 = 50
Hence, The values in the missing places are 26, 52, 14, 40 and 50
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Evaluate the expression For d=4
-d + 7 =
Answers
Answer:
3
Step-by-step explanation:
-(4)+7=3
plug in 4 for d and since it is -d it would be -4
7-4=3
how to graph y = 3x - 6?
Answers
Answer:
you have to start at the zero figure number which would be (-6) and go up 3 but sideways only once each time if that makes scene.
Step-by-step explanation:
Answer:
y
=
3
x
−
6
Use the slope-intercept form to find the slope and y-intercept.
Tap for more steps...
Slope:
3
y-intercept:
−
6
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
1
−
3
2
0
Graph the line using the slope and the y-intercept, or the points.
Slope:
3
y-intercept:
−
6
x
y
1
−
3
2
0
Step-by-step explanation:
A dairy farmer wants to mix 35% protein supplement in a standard 10% protein ration to make 1300 pounds of high grades 25% protein ration how many pounds of each should he use
Answers
Answer:
Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.
Step-by-step explanation:
The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.
The equation from the fourth column is:
0.35x + 0.10(1300 - x) = 0.25(1300)
Solving for x, we get:
x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600