There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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If 2X = 25 then X = 5, true are false.
Answer:
False
Step-by-step explanation:
The reason for it being false is because 2X = 25 should be divided to by 2 to get to X, which should be half of 25.
therefore X should equal 12.5
x+2y=5
4x+8y=20
I need help asap
Answer:
(x, -1/2x + 5/2) or infinitely many solutions
Step-by-step explanation:
We can solve the system of equations using substitution. We can start by isolating x in the first equation. Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:
Isolating:
x = -2y + 5
Plugging in and solving for y:
4(-2y + 5) + 8y = 20
-8y + 20 + 8y = 20
20 = 20
We see that we get a constant equal to another constant. Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:
y = -1/2x + 5/2
Thus, the general rule for the solution to the system of equations is
(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions
You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation. Let's try 4 for x and 0 for x:
4 for x in first equation:
4 + 2(-1/2(4) + 5/2) = 5
4 + 2(0.5) = 5
4 + 1 = 5
5 = 5
4 for x in the second equation
4(4) + 8(-1/2(4) + 5/2) = 20
16 + 8(0.5) = 20
16 +4 = 20
20 = 20
0 for x in the first equation:
0 + 2(-1/2(0) + 5/2) = 5
0 + 2(2.5) = 5
5 = 5
0 for x in the second equation:
4(0) + 8(-1/2(0) + 5/2) = 20
0 + 8(2.5) = 20
20 = 20
Find the volume of the solid obtained by rotating the region underneath the graph of the function over the given interval about
the y-axis.
f(x)=√x² +9, [0,2]
(Use symbolic notation and fractions where needed.)
The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³
Given data ,
The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis
The formula for Area under definite integral is
∫ₐᵇ f ( x ) = f ( b ) - f ( a )
Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x
The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)
Using these expressions for r and h, we can write the volume of each cylindrical shell as:
V(x) = 2πx[f(x + Δx) - f(x)]Δx
V = ∫₀² 2πx[f(x + Δx) - f(x)]dx
As Δx approaches zero, this integral becomes:
V = ∫₀² 2πx√(1 + (f'(x))²) dx
where f'(x) is the derivative of f(x), which is:
f'(x) = x/√(x² + 9)
Substituting this expression for f'(x) into the integral, we get:
V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx
This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:
V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx
V = [4/5 π(x² + 9)^(5/2)]₉¹³
V = 44.46 units³
Hence , the volume of the solid is 44.46 units³
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Please help me with this question
Answer:
Your answer is E) 1/2 , -6 , 5
Step-by-step explanation:
Find the slope between (-6,5) then simplify and you will get 1/2
The graph shows the total weight of a fish tank, y, as a function of the amount of water in the tank, x
What is the weight of an empty tank?
The weight of the empty tank is given as follows:
4 pounds.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The weight of the empty tank is the intercept of the function, which is of b = 4, hence:
4 pounds.
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Solve 8 • w ≤ 72. Graph the solution.
Please help
Answer:
w≤9
Step-by-step explanation:
8w ≤ 72
Divide by 8 on both sides
w ≤ 9
For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.
what are the answers to these questions?
a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.
b) The domain of V is [0, 3) in interval notation.
c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.
d) The maximum volume is 160/27 cm³.
(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.
Since the height of the box is x cm, the volume of the box can be expressed as
V = x(20-2x)(6-2x) cm³.
(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.
(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get
dV/dx = 4x³ - 52x² + 120x.
Setting dV/dx = 0, we get
x = 0 or x = 3 or x = 10/3.
Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.
We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get
V(0) = V(3) = 0
and
V(10/3) = 160/27.
(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.
So, the length of the box is
20-2(10/3)
= 40/3 cm,
the width of the box is
6-2(10/3)
= 2/3 cm, and
the height of the box is 10/3 cm.
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tamara. Find the sum of two number cubes rolled at the same time. The chart below shows all possible sums from 36 possible combinations how many times should tamara expect the sum of two cubes to be equal to five if she rolls the cubes 180 times
Answer:
Step-by-step explanation:
There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.
To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:
(1/36) x 180 = 5
So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.
Mr Tan calculated the average amount of money collected by all the students in his class during a fund-raising event. If three of his students each collected $32 less, the average amount of money collected would be $146. If eight of his students each collected $18 more, the average amount of money collected would be $156. How many students were there in Mr Tan's class?
There were 56 students in Mr Tan's class.
To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:
nx = sum of all amounts collected
Now, if three students each collected $32 less, the new sum of amounts collected would be:
(nx - 3*32) = (n-3)(x-32)
And the new average would be:
(n-3)(x-32) / n = 146
Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:
(nx + 8*18) = (n+8)(x+18)
And the new average would be:
(n+8)(x+18) / n = 156
Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:
n = 56 and x = 104
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if there are 15 people from the bronx, brooklyn, manhattan queens and staten island and each borough has 3 people, if the people from each borough insist on standing together, how many possible ways are there to stand
There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.
If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.
The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer
5! × (3!)⁵ = 120 × 3⁵ = 10,080
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In complex numbers what is the multiplicative inverse of 2i
To find the multiplicative inverse of 2i, we need to find a complex number z such that:
(2i) * z = 1
Multiplying both sides by -i, we get:
z = -i/2
Therefore, the multiplicative inverse of 2i is -i/2.
pls answer asap
A traveler has 9 pieces of luggage.
How many ways can the traveler select 3 pieces of luggage for a trip?
Responses
84
84
504
504
60,480
60,480
362,880
Answer:
84
Step-by-step explanation:
Trust me
Answer:
84
Step-by-step explanation:
There are 9 pieces of luggage.
We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left. The third piece can be selected 7 different ways.
9*8*7
504
But order doesn't matter since we are taking 3 pieces.
Divide by (3*2*1)
504/6 = 84
There are 84 different combinations of luggage
Determine the solution to the equation shown below.
3.2 - 1/2 (x+4) = 4.8x + 2 - 5.2x
Answer:x=-8
Step-by-step explanation:
3.2+(−1/2)x−2=4.8x+2−5.2x
−0.1x=0.8
x=-8
Answer:
x=-8
Step-by-step explanation:
x=-8
Help please!!!!
Whoever answers right gets brainliest!
The simplified form of given expression a³/a⁶b⁻¹ is b/a³.
Hence, the correct option is C.
Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.
In the given expression, a³/a⁶b⁻¹
We can apply the rules of exponents, and we get
= a³⁻⁶/b⁻¹
= a⁻³/b⁻¹
= b/a³
Hence, the correct option is C.
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Rewrite the quadratic function as a product of linear factors.
f(x) = 16x^2 - 3
help pls
Answer: (4x - √3)(4x + √3).
Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.
So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).
Which statements are true about a decagonal (10-sided) pyramid? Select 3 options.
It has one face that is a decagon.
It has two faces that are decagons.
It has 11 faces.
It has 20 edges.
It has 20 vertices.
The correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
What is decagonal pyramid?
A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.
Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.
We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.
Hence the correct statements are,
B)It has two faces that are decagons.
C)It has 11 faces.
D)It has 20 edges.
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WY is a midsegment of AVXZ.
If VZ = 5t + 51 and WY = 11t, what is VZ?
VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
what is midsegment ?
A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.
In the given question,
Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.
Let's call the length of AX as L. Then, we have:
WY = 11t = 1/2 L
Multiplying both sides by 2, we get:
22t = L
Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:
WV = VZ
Substituting WV = L/2 and VZ = 5t + 51, we get:
L/2 = 5t + 51
Substituting L = 22t, we get:
22t/2 = 5t + 51
11t = 5t + 51
6t = 51
t = 8.5
Substituting t = 8.5 in the equation for VZ, we get:
VZ = 5t + 51 = 5(8.5) + 51 = 92.5
Therefore, VZ is 92.5.
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what is – 7n + –3 – 6n + 3 + 5 is simpified
Answer:
-13n + 5
Step-by-step explanation:
Give:
– 7n + –3 – 6n + 3 + 5
To Find:
simplify
Explanation:
– 7n + –3 – 6n + 3 + 5
= (-7n - 6n) + (-3 + 3 + 5)
= - 13n + 0 + 5
= -13n + 5
Final Answer:
-13n + 5
2. How does making tables help you
identify relationships between terms in
patterns?
Answer:
Step-by-step explanation:
well if you know the term than you know the pattern
Express each of the following as (i)Percentage (ii)Decimal :
a) 3¾ (b) 6½/50
NEED HELP ASAP! (10POINTS)
The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.
How to find the printing fee ?To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.
The printing fee is:
= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )
= ( 607.50 - 600 ) / ( 43 - 40 )
= 7. 50 / 3
= $ 2. 50
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A graph is shown.
6987654321
10
0 1 2 3 4 5 6 7 8 9 10
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function?
An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);
3 → 1
1 → 1
In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is k? k - 9 < - 6
Answer:
Step-by-step explanation:
2
2-9=-7
In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.
Answer:
[tex]\mathrm{k < 3}[/tex]Step-by-step explanation:
[tex]\mathrm{ k - 9 < - 6}[/tex]
Add both sides by 9 :-
[tex]\mathrm{ k - 9+6 < - 6+6}[/tex]Simplify :-
[tex]\mathrm{k < -6+9}[/tex][tex]\mathrm{k < 3}[/tex]___________________
Hope this helps!
the front of a refrigerator with a freezer on the bottom . The freezer part on the bottom has a height of 2 feet. The top part has a height of 5 feet.Explain how you find the total area of the front of the frig
The total area of the front of the figure is 21 [tex]feet^{2}[/tex].
What is the area?
The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.
To find the total area we need to add the area of the refrigerator and the area of the freezer.
The top part i.e refrigerator has a height of 5 feet and 3 feet width
Area of the refrigerator section = height * width
= 5 * 3
= 15 [tex]feet^{2}[/tex]
The bottom part i.e freezer has a height of 2 feet and 3 feet width
Area of the refrigerator section = height * width
= 2 * 3
= 6 [tex]feet^{2}[/tex]
The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section
= 15 + 6 = 21[tex]feet^{2}[/tex]
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How to solve -10(x-1.7)=-3 by expanding first
To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.
Expanding -10(x-1.7), we get
-10x + 17 = -3
Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation
-10x + 17 + 10x = -3 + 10x
Simplifying, we get
17 = 10x - 3
Next, we add 3 to both sides of the equation
17 + 3 = 10x - 3 + 3
Simplifying, we get
20 = 10x
Finally, we divide both sides of the equation by 10 to isolate x
20/10 = 10x/10
Simplifying, we get
2 = x
Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.
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Can you please help me with this please please
Answer:
a. 14:8
b. 6:14
Step-by-step explanation:
all books on the shelf = 6+8=14
a. 14:8
b. 6:14
Prove the following this:The number of left cosets of a subgroup is equal to the number of its right cosets?
To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.
Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.
First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.
Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.
Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.
What is the equation through the points: (6, 5), (8, -2)
ASAP please
The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values:
m = (-2 - 5) / (8 - 6)
m = -7/2
Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.
Let's use the point (6, 5):
y - y₁ = m(x - x₁)
[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]
Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].
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C & J Realty has received 16 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any two of the firm's real estate agents if each agent handles eight inquiries?
There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.
What is combinations?
Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.
We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.
The number of ways to choose 8 inquiries out of 16 is:
C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870
This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:
12870 ÷2 = 6435
Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.
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A triangle has side lengths of (6.1w + 7.8) centimeters, (1.4w + 8.1) centimeters
and (8.7x + 2.5) centimeters. Which expression represents the perimeter, in
centimeters,
of the triangle?
The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:
(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)
Simplifying and combining like terms, we get:
7.5w + 11.2x + 18.4
Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.
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