Complete the following items. For multiple choice items, write the letter of the correct response on your paper. For all other items, show or explain your work.Consider the expression (r³m / r^⁻m t⁴ⁿ)¹/ⁿ . (r¹/ⁿ / t²/m )^⁻m .
a. Simplify the expression so that r and t are only written once. Show your work.
Answers
The simplified expression, with r and t written only once, is:\((r^2^m t^2)^(^1^/^n^) / (t^2^m r^1^/^n^)^m\)
To simplify the given expression, let's break it down step by step:
Step 1: Simplify the numerator.
The numerator contains two terms: r³m and \(r^-^mt^4^n\). To simplify, we combine the terms with the same base, r.
r³m / \(r^-^mt^4^n\) can be rewritten as \(r^(^3^m^ -^ (^-^m^)t^4^n\), which simplifies to \(r^4^m t^4^n\).
Step 2: Simplify the denominator.
The denominator contains two terms: \(r^1^/^n and t^2^/^m.\) To simplify, we combine the terms with the same base, t which simplifies to\(r^-^m^/^n / t^-^2^m^/^m\).
Simplifying further, we have \(r^-^m^/^n / t^-^2\), which can be rewritten as \(r^-^m^/^n / 1 / t^2\), and finally as \(r^-^m^/^n t^2\).
Step 3: Combine the numerator and denominator.
We now have \((r^(^4^m^) t^(^4^n^))^(^1^/^n) / (r^(^-^m^/^n) t^2)\).
To simplify further, we can apply the exponent rule for raising a power to a power. When we raise a power to another power, we multiply the exponents.
In the numerator, \((r^(^4^m^) t^(^4^n^))^(^1^/^n^)\) simplifies to \(r^(^4^m^/^n^) t^(^4^n^/^n^)\), which becomes \(r^(^4^m^/^n^) t^4\).
In the denominator, \(r^(^-^m^/^n^) t^2\) remains the same.
Putting it all together, the simplified expression is:
\(r^(^4^m^/^n^) t^4 / (r^(^-^m^/^n^) t^2)\).
Therefore, the simplified expression with r and t written only once is \((r^2^m t^2)^(^1^/^n^) / (t^2^m r^1^/^n^)^m\)
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Related Questions
Bianca spent 1/2 of an hour playing on her phone . that used up 1/3 of her battery how long would she have to play on her phone to use the entire battery
Answers
Bianca should play with her phone for 1.5 hours to use the entire battery.
What exactly are fractions?A fraction is a portion of a whole or, to put it another way, any number of equal parts.A fraction in everyday English refers to the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.Bianca spent 1/2 of an hour playing on her phone which used up 1/3 of her phone's battery.
So, 1/3 × 3 = 3/3 = 1So, if she plays with her phone 3 times more she will use the entire battery of the phone.Then,
1/2 × 3 = 3/2 = 1.5 hoursTherefore, Bianca should play with her phone for 1.5 hours to use the entire battery.
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Look at the figure. Which ray is opposite of CD?
Answers
Consider a function that describes how a particular car’s gas mileage depends on its speed. What would be an appropriate domain for this function?
0 to 100 miles per hour
0 to 50 miles per gallon
times from 0 to 10 minutes
times from –10 to 10 minutes
Answers
Answer:
Samantha has 8 quarts of milk. The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have? x a. 1 over 32 x b. begin mathsize 16px style 1 half end style x c. 2 x d. 32
Step-by-step explanation:Samantha has 8 quarts of milk. The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have? x a. 1 over 32 x b. begin mathsize 16px style 1 half end style x c. 2 x d. 32Samantha has 8 quarts of milk. The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have? x a. 1 over 32 x b. begin mathsize 16px style 1 half end style x c. 2 x d. 32Samantha has 8 quarts of milk. The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have? x a. 1 over 32 x b. begin mathsize 16px style 1 half end style x c. 2 x d. 32
Answer:
A
Step-by-step explanation:
Got it right on Edge.
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Systolic Blood Pressure (SBP) of 13 workers follows normal distribution with standard deviation 10. SBP are as follows: 129, 134, 142, 114, 120, 116, 133, 142, 138, 148 , 129, 133, 140_ Find the 99%0 confidence interval for the mean SBP level: (124.84 (129.84 (126.84 (125.84 139.16) 139.16) 137.16) 138.16)
Answers
Answer:The 99% confidence interval is
To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:
CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)
Where:
Mean is the sample mean of SBP
Z is the Z-score corresponding to the desired confidence level
Standard Deviation is the population standard deviation
Explanation:
Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.
First, we calculate the sample mean:
Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13
= 1724 / 13
≈ 132.62
Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.
Now, we can calculate the confidence interval:
Confidence Interval = 132.62 ± 2.576 * (10 / √13)
132.62 ± 2.576 * (10 / 3.6056)
≈ 132.62 ± 2.576 * 2.771
≈ 132.62 ± 7.147
Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).
The present age of Joshua's father is four times that of Joshua. After 3 and 1/6
years, the difference in their age is 34 years. Find their present ages.
(Estimate the solution to the nearest whole number).
Answers
Father = 45 years
Joshua = 11 years
See the image I have shared.
Round off at the end
9 + 15m
factorisation of algebraic expression that contain common factor
Answers
Answer:3(3+5m)
Step-by-step explanation:
I need the volume of that figure
Answers
Answer:
708π in³ = 2224.25 in.³
Step-by-step explanation:
The composite solid is made up of a cone, a cylinder, and a half sphere.
Recall the volume formulas:
cone: πr²h/3
cylinder: πr²h
sphere: 4πr³/3
half sphere: (1/2) × 4πr³/3
We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.
h = √(10² - 6²) = 8
total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3
total volume = π(96 in.³ + 468 in.³ + 144 in.³)
total volume = 708π in³ = 2224.25 in.³
or, 2x+y-5=0 ple 7 Find the co-ordinates of the foot of the perpendicuair drawn from (1, 5) to the line segment joining (1, 1) and (5, 5).
Answers
For the given coordinates, the equation of line is y = 1, The coordinates of foot of perpendicular will be (0, 5)
What is the formula for the foot of a perpendicular?Assume that ax + by + c = 0. is a continuous line. If a perpendicular line is drawn from any point on the plane to the provided straight line, the intersection of the two lines is referred to as the foot of the matching perpendicular.
How many feet does the perpendicular reach from the point?Because a perpendicular line is created from point P to the y-axis, the distance between its intersection with the x-z plane remains constant.
Given,
the points of line are - (1, 1) and (5, 5).
equation of line = (y - yo) = m (x - xo)
⇒ y - 1 = \(\frac{5 - 1}{5 - 1}\) (x - 1)
⇒ y = 1. is the equation of the line,
Let us consider the point (a,b) such that it is the foot of the perpendicular,
Now, as the line line joining the points (1,5) and (a,b) will be perpendicular to each other,
⇒ y - 1 = b - 5 / a - 1 (x - 1)
The slope of one line is the negative inverse of other line,
⇒ b - 5 / a -1 = 0
⇒ b = 5
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Consider the vectors: a=(1,1,2),b=(5,3,λ),c=(4,4,0),d=(2,4), and e=(4k,3k)
Part(a) [3 points] Find k such that the area of the parallelogram determined by d and e equals 10 Part(b) [4 points] Find the volume of the parallelepiped determined by vectors a,b and c. Part(c) [5 points] Find the vector component of a+c orthogonal to c.
Answers
The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).
a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.
We have,
d=(2,4)
and e=(4k,3k)
Then,
d×e= (2 * 3k) - (4 * 4k) = -10k
Area of parallelogram = |d×e|
= |-10k|
= 10
As we know, area of parallelogram can also be given as,
|d×e| = |d||e| sin θ
where, θ is the angle between the two vectors.
Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ
⇒ 10 = √20 √25k^2 sin θ
⇒ 10 = 10k sin θ
∴ k sin θ = 1
Therefore, sin θ = 1/k
Hence, the value of k is 1.
Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,
| a . (b × c)|
Here, a=(1,1,2),
b=(5,3,λ), and
c=(4,4,0)
Therefore,
b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k
= -4i + 4λj + 8k
Now,| a . (b × c)|=| (1,1,2) .
(-4,4λ,8) |=| (-4 + 4λ + 16) |
=| 12 + 4λ |
Therefore, the volume of the parallelepiped is 12 + 4λ.
Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].
Here, a=(1,1,2) and
c=(4,4,0).
Then, a + c = (1+4, 1+4, 2+0)
= (5, 5, 2)
Now, projecting (a+c) onto c, we get,
projc(a+c) = [(a+c).c / |c|^2] c
= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)
= (4,4,0.5)
Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)
= (1,1,1.5)
Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).
Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).
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F(x)=-4x^2+10x-8
What is the value of the discriminating of f
Answers
Answer:
f(x)=-4x^2+10x-8
Step-by-step explanation:
well x normally equals 1 so replace all X's with 1 and solve
4*1=4 to the power of 2 is 16
10*1=10 subtract 8 equals 2 so
16-2= 14
F(x) is 14
the Y would be 14
Answer:
Here are Both Anwsers
Step-by-step explanation:
WILL GIVE BRAINLIST TO BEST ANSWER
Find the value of x that makes lines u and v parallel
Answers
If those two angles = 180, then lines u and v are parallel.
90 + (x+102) = 180
192 + x = 180
x = 180-192
x = -12
So if x = -12, then lines u and v are parallel.
Answer:
x = -12
Step-by-step explanation:
We know that the right angle measuring 90° on line u and the (x + 102)° angle are both same side interior angles. When two lines are parallel, the measure of their same interior angles are always equal to 180. Thus, we can solve for x by making the sum of the 90° right angle and the (x + 102)° angle equal to 180:90 + x + 102 = 180
192 + x = 180
x = -12
Therefore, in order for lines u and v to be parallel, the value of x must be -12
Find 5 less than 17.
Answers
The swim team manager needs to purchase award ribbons for competitions. The table shows the sizes of packages he can purchase.
For a package of 500 ribbons, what is the cost per ribbon?
A.
$0.15
B.
$0.21
C.
$0.67
D.
$0.07
Answers
I really need help with part a and b, please help. Incorrect answers will be downvoted, correct answers will be upvoted. 1. The army is interested in characterizing the acoustic signature of a helicopter. The following data show measurements of acoustic pressure (made dimensionless) for a two-bladed helicopter rotor through of a rotor revolution. The data points are equally spaced in time, and the period of the data collection is of a second. p=00.00040.0015 0.0028 0.0040 0.0048 0.0057 0.0071 0.0095 0.0134 0.0185 0.02420.0302 0.0364 0.0447 0.0577 0.0776 0.0955 0.0907 -0.0477 -0.0812 -0.0563 -0.0329 -0.0127 0.0032 0.0147 0.0221 0.0256 0.0255 0.0222 0.0170 0.0112 0.0064 0.0035 0.0023 0.0020 0.0019 0.0016 0.0009 0.0002 a) Find the real discrete Fourier transform for this data set. (b) Any term in the Fourier series can be written: ak Cos(kwt)+bk sin(kwt) =ck Cos(kwt+$k) ak Find the ck's and plot their amplitude on a bar graph vs. k to illustrate the relative size of each term in the series. Explain the significance of the plot
Answers
(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.
(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.
To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.
Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.
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Add the following military times:
0645 + 0745 =
Answers
Answer:
2316
Step-by-step explanation:
use a calculator
Answer:
0645+0745= 1390 but there are not 90 mins in an hour so you roll over 60 over those min to get 1430
2:30
explanation:
he defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3-sigma control chart limits are:
ucl = (enter your response as a number between 0 and 1, rounded to four decimal places).
Answers
The defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3-sigma The upper control limit (UCL) is approximately 0.0450.
The upper control limit (UCL) for a 3-sigma control chart is given by:
\(\[UCL\) = defect rate + 3 * sqrt((defect rate * (1 - defect rate)) / sample size)
Substituting the values, where the defect rate is 1.50% (0.015) and the sample size is 200, we get:
\(\[UCL = 0.015 + 3 \times \sqrt{\frac{0.015 \times (1 - 0.015)}{200}}\]\)
Calculating this expression, we find:
\(\[UCL \approx 0.0450\]\)
Therefore, the upper control limit (UCL) is approximately 0.0450.
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Solve for Enter the solutions from least to greatest . (2x - 1)(x + 4) = 0 lesser x = greater x=
Answers
:)))) hope this helped
Answer:
lesser x =-4
greater x =1/2
y = x² + 4x - 5 1. Transpose the c-value to the left side of the equation. 2. Complete the square of the expression on the right side of the equation to get a perfect square trinomial. Add the resulting term to both sides. 3. Add the numbers on the left and factor the trinomial on the right. 4. Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k. 5. Make sure the addition and subtraction signs are correct to give the proper vertex form.
Answers
The vertex is at (-2, -9).
How to find the vertex form
From the equation:
y = x² + 4x - 5
Transpose the c-value to the left side of the equation:
y + 5 = x² + 4x
Complete the square of the expression on the right side of the equation to get a perfect square trinomial:
y + 5 = x² + 4x + 4 - 4
by adding and subtracting 4 to the right side of the equation to maintain its balance.
Add the numbers on the left and factor the trinomial on the right:
y + 9 = (x + 2)²
Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:
y = (x + 2)² - 9
Make sure the addition and subtraction signs are correct to give the proper vertex form.
Here, the vertex is at (-2, -9).
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Given:-
y = x² + 4x - 5 .To find:-
The vertex form following the given steps .Answer:-
1) Firstly we are told to transpose the c value to LHS .
With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;
\(\implies y + 5 = x^2 + 4x\\\)
w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .
\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)
\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)
The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,
\(\implies y + 5 = (x +2)^2 - 4 \\\)
\(\implies y + 5 + 4 = (x+2)^2 \\\)
3) Next we have to add the number on the left and factor the trinomial on right as ,
\(\implies y + 9 = (x+2)^2 \\\)
4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .
\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)
This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;
\(\implies vertex = ( -2,-9) \\\)
and we are done!
5. The circumference of the earth is about 24,855miles. Find the surface area of the Western Hemisphere of Earth.
Answers
Answer:
oh my answer is in the explanation
Step-by-step explanation:
it
is
quite
big
what is 6(x+4)+1 what is the answer
Answers
Answer:
6x-23
Step-by-step explanation:
6(x+4)+1
Distribute:
=(6)(x)+(6)(4)+1
=6x+24+1
Combine Like Terms:
=6x+24+1
=(6x)+(24+1)
=6x+25
Find perimeter of ABDE
Answers
Step-by-step explanation:
(10 x 6)/2 = 30 + 47 = 77
Someone please do this!
Answers
Answer:
£518.42
Step-by-step explanation:
It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box
which holds 15 cups of sugar. Double the dimensions of the box. Approximately how
much paint would the new box need? How much sugar would it hold?
Answers
Answer:
120 cups of sugar
8 ounces of paint
Step-by-step explanation:
Given that :
To cover all sides of the rectangular prism with paint, that is the surface area.
The amount of sugar held by the prism is function of its volume.
Hence, doubling the dimension :
The surface area, in unit² is a obtained by
Initial paint required * 2^2
2 * 2² = 2 * 4 = 8 ounces of paint.
For sugar :
It has to do with volume, unit³
Initial * double³
15 * 2³
15 * (8) = 120 cups of sugar
Evaluate f (x) = 4x-5, find f (2x+3)
Answers
Answer:
8x + 7
Step-by-step explanation:
To evaluate f(2x + 3) , substitute x = 2x + 3 into f(x) , that is
f(2x + 3) = 4(2x + 3) - 5 = 8x + 12 - 5 = 8x + 7
Answer:
8x+9
Step-by-step explanation:
f(x)=4x-5
f(2x+3)=4(2x+3)-5
=8x+12-5
=8x+9
this is your answer.I hope this will help you
Choose a company with your option and explain how
that company can create a business model? There are 8 steps in the
business module, explain each step based on the company which you
have chosen.
Answers
Company: Amazon, 8 Steps in the Business Model: Define the value proposition. What value does Amazon offer its customers? Amazon offers a convenient and affordable way to shop for a wide variety of products.
Identify the target market. Who are Amazon's customers? Amazon's target market is people who want to buy products online.
Determine the revenue streams. How does Amazon make money? Amazon makes money through product sales, advertising, and subscription fees.
Assess the cost structure. What are Amazon's costs? Amazon's costs include salaries, rent, and marketing.
Develop a marketing plan. How will Amazon reach its target market? Amazon's marketing plan includes online advertising, search engine optimization, and social media marketing.
Create a sales strategy. How will Amazon sell its products? Amazon's sales strategy includes a focus on customer service and convenience.
Build a team. What skills and experience does Amazon need to build a successful business? Amazon needs a team with a variety of skills, including product development, marketing, and sales.
Continuously improve. How will Amazon ensure that its business model is successful? Amazon will continuously improve its business model by listening to customer feedback and adapting to changes in the market.
The 8 steps in the business model are essential for any company that wants to be successful. By following these steps, companies can ensure that they are offering a valuable product or service to the right customers, and that they are able to make money.
In the case of Amazon, the company has clearly defined its value proposition, target market, and revenue streams.
Amazon's marketing plan is also effective, and the company has built a team with the skills and experience necessary to be successful. Finally, Amazon is committed to continuous improvement, which is why the company has been so successful over the years.
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1.100 ′
with a standard deviation of 0.010 ∘
. Caleulate the capability index ciftiss process. The Coy of this process is (round your response to two decimal places).
Answers
The question seems to have a typographical error, as the term "ciftiss process" is unclear. If you meant "Cp for this process," then the capability index can be calculated using the provided information of a target value of 1.100 degrees and a standard deviation of 0.010 degrees. However, if you intended to ask about a different process or acronym, please provide further clarification.
The capability index, Cp, is a measure of process capability that compares the width of the process spread to the width of the specification limits. It helps assess whether a process is capable of meeting the desired specifications. Cp is calculated by dividing the tolerance range by six times the standard deviation.
In this case, the question provides a target value of 1.100 degrees and a standard deviation of 0.010 degrees. However, it does not specify the tolerance range or the specification limits of the process. Without the tolerance range, we cannot calculate the exact Cp value.
To calculate the Cp, we need the upper and lower specification limits or the tolerance range. Without this information, we cannot determine the Cp or assess the process capability accurately.
Therefore, without the tolerance range or specification limits, we cannot calculate the capability index Cp or determine the capability of the process. It is essential to have complete information regarding the specification limits to evaluate process capability accurately.
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Write the point-slope form of the glven line that passes through the points (0,-3) and (4,1). Identity (x, y) as (0, -3).
Include your work in your final answer. Type your answer in the box provided to submit your solution.
Answers
-3 is slope intercept
1 is slope
Find the price of each product after a discount is applied. A game system costs 199.75 with a discount rate of 18%.
Answers
The original price is 100%
Then the price after a 18% discount is
Tell me as a percentage
Answer:
about $163.80
Step-by-step explanation:
The actual full answer (not rounded) is $163.795
A cylinder has a diameter of 5 inches. Which equation can be used to find V, the volume of the cylinder in cubic inches?
Answers
Answer:
V= π*2.5^2*h
Step-by-step explanation:
Given data
Diameter d= 5 in
radius=d/2= 5/2= 2.5in
We know that the formula for the cylinder volume is given as
V= πr^2h
substitute
V= π*2.5^2*h
Hence the expression for the volume with a given height is
V= π*2.5^2*h
An icecream shop has 10 flavors. One can choose 4 different
flavors. What is the total number of possible flavor
combinations?
a.
252
b.
462
c.
120
d.
330
e.
210
2.
Answers
An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.
In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.
Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors
.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).
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