Share your own multi-step combination problem
Answers
My own multi-step combination problem is given below:
Amanda was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda create?How do you solve the multi-step combination?To solve this problem, Amanda need to use the formula for combinations and it is:
nCr = n! / (r! x (n-r)!)
where:
n = total number of items to select from
r is the number of items to select.
First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:
5C3
= 5! / (3! x (5-3)!)
= 10
Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be
4C2
= 4! / (2! x (4-2)!)
= 6
Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:
3C2
= 3! / (2! x (3-2)!)
= 3
To have the total number of dinner menus, we have to multiply these three numbers together:
= 10 x 6 x 3
= 180
Therefore, one can say that Amanda have 180 different dinner menus that she can be create.
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Related Questions
simplifying expressions (3n+2) + (5n+6)
Answers
Answer:
3n + 2 + 5n + 6 = 8n + 8 = 8(n + 1)
Find the point of intersection of the pair of straight lines.
y = −10x − 3
−y = 11x + 5
(x, y) =
Answers
The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given lines,
y = −10x − 3
−y = 11x + 5 → y = -11x - 5
The value of the function at the point of intersection is always the same.
So,
−10x − 3 = -11x - 5
-10x + 11x = -5 + 3
x = -2
So,y = -10(-2) - 3 = 17
Hence "The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17)".
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write fifty and two hundreds eight thousandths as a mixed decimal
Answers
Answer:
Pretty sure it's 0.528
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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How do I find GBA and show all the work
Answers
Answer:
Angle ACB = 44°
There are two ways to solve it. Both are right
Solution number 1
From triangle ABC
angle BAC = 180°-(102° +44°) = 36°
Because BG is parallel with AC
Then angle GBA = angle BAC = 34°Another solution
The sum of angles in the shape AGBC = 360°
So angle GBC = 360 - (90 + 90 + 44 + 102) = 34°Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin
Answers
After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.
When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.
The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.
Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.
The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.
It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.
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If a perpetuity pays a cash flow (C) every time period, forever, how come it is not worth an
infinite amount of money right now? Explain.
Answers
F (p)= 2p+4/p-A and f (0)= -2 What is the value of A?
A=
Answers
9514 1404 393
Answer:
A = 2
Step-by-step explanation:
Using 0 for p, we have ...
F(0) = (2·0 +4)/(0 -A) = 4/-A
We want this to be -2, so ...
-2 = 4/-A
A = 4/(-(-2)) = 2 . . . . multiply by A/-2
A = 2
The factored form of 30.8n+8.4 is a(11n+3) . What is the value of a?
Answers
After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We are given that the factored form of 30.8n+8.4 is a(11n+3).
To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.
Expanding a(11n+3), we get:
a(11n+3) = 11an + 3a
Equating this to 30.8n+8.4, we have:
11an + 3a = 30.8n + 8.4
We can factor out an "a" from the left-hand side:
a(11n + 3) = 30.8n + 8.4
Now we can see that this is the same as the given factored form, so we can equate the two expressions:
a(11n + 3) = a(11n + 3)
This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):
a = 30.8/(11n+3)
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If a store marks up merchandise by 40% on cost, what is the markup in dollars on an item costing $80?
Answers
Solve for x: ___ degrees.
Answers
Answer:
63
Step-by-step explanation:
This is a cyclic quadrilateral, meaning that its opposite angles are supplementary. So, x=180-117=63.
What is the area of the square that measures 3.1 m on each side
Answers
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Evaluate without a calculator. If a real answer does not
Answers
a)
\(\log_3(27)=\log_3(3^3)=3\)Answer: 3
b)
\(\log_3(9)=\log_3(3^2)=2\)Answer: 2
c)
\(\log_5(1)=0\)Answer: 0
d)
\(\log_5(\frac{1}{25})=\log_5(5^{-2})=-2\)Answer: -2
-9(x+2)=54 apply the distributive property and simplify
Answers
Answer:
x = -8
Step-by-step explanation:
-9 (x+2) = 54
-9x - 18 = 54
-9x = 72
x = -8
Hope this helps :)
Let me know if there are any mistakes!!
Suppose $5000 is invested at 5.25% annual interest, compounded continually.
What will be the
amount in the account in 7 years if no money is withdrawn?
$2609.00
$7220.60
$5000.00
$5269.51
Answers
Answer:
I am sure that it is $7220.60
Step-by-step explanation:
If you invested in 5000 you would have that much in your account to withdraw
hope this works for you
50 Points! Multiple choice algebra question. Transform both sides of each equation to determine which is a polynomial identity. Photo attached. Thank you!
Answers
The only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
How to express the valueIt should be noted that to determine which equation is a polynomial identity, we need to simplify both sides of each equation and see if they are equal for all values of c and d.
(A) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c + d)
The left-hand side can be expanded using the binomial formula. The right-hand side is a polynomial of degree 3, so we can see that equation (A) is a polynomial identity.
(B) (c+d) = c + d³ + 3cd(c + d)
= d³ + c³ + 3cd(c + d) + c + d - c³
= d³ + c³ + 3cd(c + d) + c + d
The right-hand side can be simplified, but it is not equal to the left-hand side for all values of c and d. Therefore, equation (B) is not a polynomial identity.
(C) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ + d³ + 3cd(c + d) + cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (C) is not a polynomial identity.
(D) (c+d)³ = c³ + 3c²d + 3cd² + d³
= c³ - d³ + 3cd(c - d) + c³ + d³
= 2c³ + 3cd(c - d)
The right-hand side is not equal to the left-hand side for all values of c and d, so equation (D) is not a polynomial identity.
Therefore, the only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).
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Solve the inequality.
|4x - 1| ≥ 23
I need some help if anyone knows it!
Answers
The value of the inequality |4x - 1| ≥ 23 will be
x ≥ 6.
How to calculate the inequality?It should be noted that the inequality given is expressed as:
|4x - 1| ≥ 23
This will be
|4x - 1| ≥ 23
4x ≥ 23 + 1
4x ≥ 24
Divide
4x/4 ≥ 24/4
x ≥ 6
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A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class. Write an equation that represents the total cost of the membership.
Answers
The equation that represents the total cost of the membership will be y = 5x + 265.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.
Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,
y = 5x + 265
The equation that represents the total cost of the membership will be y = 5x + 265.
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Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Answers
25% = 75/x
To solve for x, we can cross-multiply:
0.25x = 75
Then, we can divide both sides by 0.25:
x = 300
Therefore, there are 300 6th-grade students in total.
14. A photograph measures eight inches wide and ten inches long. The picture is enlarged to fit on a wall. If the new larger picture is 208 inches wide, how long is it?
Answers
Answer:
The file contains the solution to the question
Which of the equations below could be the equation of this parabola?
OA y--¹x²
OB. x--²
C. x-²
D. y - x²
10
(0,0)
Vertex
10
Answers
An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).
How to determine the equation of a parabola?In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:
x = a(y - k)² + h.
Where:
h and k represent the vertex.a represent the leading coefficient.By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:
h = 0
k = 0
a = positive.
x = a(y - k)² + h.
x = a(y - 0)² + 0.
x = ay²
Therefore, a possible equation is x = 1/12(y²).
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Water is filling a conical tank at a rate of 3 pi cubic feet per second. However, the water level is only increasing at a rate of 1/2 pi feet per second. There must be a leak in the tankout the rate water is out of the tank when the water level is 5 feet from the bottom of the tank. The tank is 10 feet in height and has a radius at the top of 2 feet.
Answers
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
Answers
The psi that the TPMS would trigger a warning for this car is = 23.36 psi
Calculation of tire pressureThe target tire pressure of the car is = 32 psi (pounds per square inch.)
The Tire pressure monitoring systems (TPMS) warns the car below 27% of 32psi
That is , 27/100 × 32
= 864/100
= 8.64psi
Therefore, 32 - 8.64 = 23.36. When the car is below 23.36psi, TPMS would trigger a warning for this car.
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Complete question:
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is above or below?
Kay solves the following system of equations using the substitution method.
y=-4x+2
3x-y=9
What is the single variable equation she solves after substituting
Answers
Step-by-step explanation:
Substitute y=-4x+2 into 3x-y=9
3x-(-4x+2)=9
3x+4x-2=9
This is the single variable equation she solves after substituting.
(Note: It could be either of the bolded it depends if you want it distributed already or not)
What is the value of x
Answers
Answer:
5"
root4square+3square=root25
=5
pls help will give brainliest
Given f(x)=2/x^2+3x-10, which of the following is true?
A. f(x) is positive for all x<-5
B. f(x) is negative for all x<-5
C. f(x) is positive for all x<2
D. f(x) is positive for all x>2
Answers
The only true statement about the domain of the given function is:
B. f(x) is negative for all x < -5
How to solve for the domain of the function?The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).
Now, we are given the function as:
f(x) = \(\frac{2}{x^{2} } + 3x - 10\)
When x < -5, we have:
f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)
f(-4) = -21.875
This suggests that for all values below x = -5 will result in negative values
When x > 2
f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)
f(3) = -0.78
Thus, it will get positive for higher values but it can also be negative as seen here.
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Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount?
A. 12%
B. 25%
C. 50%
D. 60%
Answers
Differentiate cos 5x
Answers
Answer
\( - 5 \sin(5x) \)
Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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The length of a man's shadow is directly proportional with his height.
At the same time of day, a man who is 1.8 meters tall casts a 25.2
meter shadow and his son casts a 21 meter shadow. What is the
height of the man's son, in meters? If necessary, round to the nearest
tenth.
Answers
Answer:
The man's son height is 1.5m
Step-by-step explanation:
\(\frac{x}{21} =\frac{1.8}{25.2}\)
\(\frac{21x1.8}{25.2}\)
21x1.8= 37.8
37.8 ÷ 25.2= 1.5
Hope this helps
sorry if i got it wrong