In how many ways Can the word COMMITTEE be arranged
Answers
Answer:
43200
Step-by-step explanation:
There are total 9 letters in the word COMMITTEE, had they been all unique letters then total permutations = 9! = 362880
Now, we have 2M's, 2T's and 2E's, so the total permutations of COMMITTEE will be (9!)/(2! * 2! * 2!) = 362880/8 = 45360
There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts, so the permutations = (6!)/(2! * 2!) = 720/4 = 180
In the 180 arrangements, the 4 vowels O,I,E,E remain together and can be arranged in (4!)/(2!) ways = 24/2 = 12
So, the number of ways in which the four vowels always come together = 180 x 12 = 2160.
Hence, the required number of ways in which the four vowels do not come together = 45360 - 2160 = 43200
Sorry if it's wrong.
There are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.
The number of ways in which 9 letters can be arranged = 9 !/( 2!2!2!) = 45360
There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in 6 !/(2! × 2!) = 180 ways. In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in 4 !/2 ! = 12 ways.
The number of ways in which the four vowels always come together = 180 x 12 = 2160
No of possible arrangement = 45360 - 2160 = 43200
Related Questions
air is pumped into a spherical balloon, so the balloon expands. the volume of a sphere of radius r is . if the radius of the sphere after seconds is centimeters, at what rate is air being pumped in when ?
Answers
The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.
The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.
At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.
Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.
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Angle R and angle S are supplementary angles. If angle R measures 28
degrees, what is the measure of angle S?
Answers
Answer:
c
Step-by-step explanation:
cause R+S=180 which is supplementary then we subtract from both side R and it will be S=180-28=152
Answer:
C. 152º
Step-by-step explanation:
Supplementary angles add up to 180º
so that means...
Angle R + Angle S = 180
28 + x = 180
When we do 180 - 28 = 152º
Therefore the final answer is C, 152º
x^3x^5=x^p, where p=
Answers
Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.
Therefore,
\(x^(3+5) = x^8\)
Now,
\(x^(3+5) = x^8\)
is of the form:
\(x^b = x^p\)
When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,
p = 8
There we have it. The value of p is 8. The full solution is shown below:
\(x^3 × x^5 \\= x^px^8\\ = x^p\)
We can see that the base of the exponential expression on either side is equal.
Therefore, the power of the base must be equal as well. In other words
,p = 8.
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Evaluate the function rule for the given value. y = 6 ∙ 2x for x = –2
–24
3
3/2
3/4
Answers
What is the domain and range of this function?
Answers
I think
Move words to the blanks and equations to the boxes to prove that vertical angles 21 and 23 are congruent.
Because linear pairs of angles are
and
Because angles that are
to the same angle are
it can be concluded that 21 23.
congruent
m21 +m22 = 180°
supplementary
m22 + m23 = 180°
m2l + m23 = 180°
Answers
Answer:
Because linear pairs of angles are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.
Step-by-step explanation:
The correct question is attached.
Linear pairs angles are angles which are formed from the intersection of two lines and they are adjacent to each other. Linear pair angles are supplementary.
If angles are supplementary to the same angle, then they are congruent.
∠1 and ∠3 are vertical angles
∠1 and ∠2 form linear pairs while ∠2 and ∠3 form linear pairs. Therefore:
m∠1 + m∠2 = 180° (linear pair angles are supplementary)
m∠2 + m∠3 = 180° (linear pair angles are supplementary)
Hence using transitive property of equality:
m∠1 + m∠2 = m∠2 + m∠3
Using subtraction property of equality by subtracting m∠2 from both sides gives:
m∠1 = m∠3
∠1 ≅ ∠3 (vertical angles are congruent)
Because linear pairs of angles are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.
PLZ HELP
How many solutions does the equation −5a + 5a + 8 = 8 have? (5 points)
a
None
b
One
c
Two
d
Infinitely many
Answers
Answer:
d) Infinitely many
Step-by-step explanation:
−5a + 5a + 8 = 8
8 = 8
Since this is an identity solution, that means it's infinitely many.
Answer:
a none
Step-by-step explanation:
please mark this answer as brainliest
sketch a graph of x = − 2 cos ( t ) , y = − 1 sin ( t ) , 0 ≤ t < 2 π .
Answers
The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.
To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.
1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.
2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.
3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.
4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.
The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.
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(Help!) I need somebody (Help!) Not just anybody (Help!) You know I need someone (Help!). Algebra question :)
Answers
Step-by-step explanation:
meetcome on (Help!) You know I need someone (Help!). Algebra question :)
Answer:
the 1st, 3rd, 6th and last one
Step-by-step explanation:
just use square roots
What is the total surface area of the square pyramid below?
14 cm
10 cm
10 cm
O 100 cm
O 200 cm
O 280 cm?
O 380 cm?
a
Answers
Answer:
D
Step-by-step explanation:
380
Figure A is a scale image of Figure B. What is the value of x?
please answer asap!
Answers
Answer:
\(\huge \boxed{x=30}\)
Step-by-step explanation:
\(\sf We \ can \ use \ ratios \ to \ solve.\)
\(\displaystyle \frac{45}{27} =\frac{x}{18}\)
\(\sf Multiply \ both \ sides \ by \ 18.\)
\(\displaystyle \frac{45}{27}(18) =\frac{x}{18}(18)\)
\(\sf Simplify \ the \ equation.\)
\(\displaystyle \frac{810}{27} =x\)
\(30=x\)
Darnell collected data from two different sales teams in his department, each with four employees the results of the study, based on each workers age and sales, are listed in the tables below. Which of the following is a true statement
Answers
The correct statement states that the sales range for team 2 is greater than the sales range for team 1.
What is the range?The range is defined as the difference between the maximum value to the minimum value.
Team 1
Worker's Age Sales
25 30,000
27 29,000
28 32,000
33 35,500
Team 2
Worker's Age Sales
25 35,000
28 37,000
29 38,000
31 65,000
Range Team 1 = 38000 - 30000 = 8000
Range Team 2 = 65000 - 29000 = 36000
Thus, The sales range for team 2 is greater than the sales range for team 1.
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What is 400 x 29 can you please solve thank you
Answers
Answer:
11,600
Step-by-step explanation:
calculated
Answer: 400 x 29= 11,600
A standard yield sign is an equilateral triangle with sides measuring 36
inches. The height of the triangle is approximately 40.5 inches. What is
the area of a standard yield sign?
Answers
Answer:
729 sq in
Step-by-step explanation:
Area = 1/2bh
1/2 * 36 * 40.5 = 729 sq in
Angelina has 5 cakes. She wants to cut them into 2/5 pieces. How many pieces will she be able to cut? Answer without units.
Answers
Answer:12.5 pieces
Step-by-step explanation:2/5 as a decimal is .4.
5/.4=12.5
What are three ways in which stereotypical views of gender could negatively affect progressive growth of society
Answers
Jacob has 17 yards of fabric. He uses 1 third of it to make a cape. How many yards of fabric does Jacob use for the cape? zearn m4L7
Answers
Answer:
5 2/3
You multiply.
3) Simplify:
\( {12x}^{2} - 27 \\ 4 - (2x + 1)\)
Answers
Answer:
4+ \(\frac{3}{5}\)
Step-by-step explanation:
Answer:
\(3(4x^2-9)\)
Step-by-step explanation:
First, we can start by factoring \(12x^2-27\) so that we get:
\(3(4x^2-9)\)
Second Question:
Answer:
Step-by-step explanation:
We can get rid of the parentheses by multiplying the minus inside:
\(4-(2x+1)=4-2x-1 \text{ Now, we see that -1+4=3, and that we have:}\\3+2x \text{ as our final answer }\)
3. Consider the following system: →0.85→0.85→ Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) b. Each system component has a backup with a probability of .85 and a switch that is 100 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places. c. Each system component has a backup with a probability of .85 and a switch that is 90 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Answers
a. The probability that the system will operate as shown is approximately 0.6141.
b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141
The probability that the system will operate as shown is approximately 0.6141.
b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:
Probability = 0.85 × 0.90 × 0.85
Probability ≈ 0.6485
The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
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Molly's school is selling tickets to a play. On the first day of ticket sales the school sold 7 senior citizen tickets and 11 student tickets for a total of $125. The school took in $180 on the second day by selling 14 senior citizen tickets and 8 student tickets. What is the price each of one senior citizen ticket and one student ticket?
Answers
Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.
Step-by-step explanation:
Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.
According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:
7s + 11t = 125 ---(1)
On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:
14s + 8t = 180 ---(2)
We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.
Multiplying equation (1) by 8 and equation (2) by 11, we get:
56s + 88t = 1000 ---(3)
154s + 88t = 1980 ---(4)
Subtracting equation (3) from equation (4) eliminates 't':
(154s + 88t) - (56s + 88t) = 1980 - 1000
98s = 980
s = 980 / 98
s = 10
Substituting the value of 's' back into equation (1), we can solve for 't':
7s + 11t = 125
7(10) + 11t = 125
70 + 11t = 125
11t = 125 - 70
11t = 55
t = 55 / 11
t = 5
Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.
62% of all bald eagles survive their first year of life. if 45 bald eagles are randomly selected, find the probability that
Answers
This results in a probability of approximately 0.044, or 4.4%. the probability of any number of eagles surviving their first year can be calculated using the binomial probability formula.
The probability of a bald eagle surviving its first year of life is 62%. If 45 bald eagles are randomly selected, we can use the binomial probability formula to calculate the probability of a certain number of eagles surviving their first year.
P(x=k) = (n choose k) * p^k * (1-p)^(n-k)
Where n is the total number of trials (45), k is the number of successes (surviving eagles), p is the probability of success (0.62), and (n choose k) is the binomial coefficient.
To find the probability that exactly 20 eagles survive their first year, we plug in the values:
P(x=20) = (45 choose 20) * 0.62^20 * 0.38^25
This results in a probability of approximately 0.044, or 4.4%.
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Grace at 6 berries. levi at 2 times more berries tham grace. how many berries did levi eat
Answers
Using multiplication operation, we can say that 12 berries did levi eat.
According to the question
Grace ate 6 berries.
Levi at 2 times more berries than grace.
To find out the number of berries did levi eat, multiply the grace eaten berries with 2.
Here we can write the mathematical form
= 2 × 6
= 12
Therefore,
12 berries did levi eat.
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Find the value of x using the diagram below. Will give Brainly.
Answers
Answer:
120
Step-by-step explanation:
A virus is spreading around Kingwood. At the moment, 368 people are infected. If the virus is spreading at a rate of 6% each day, how many people in all will have caught the virus in 5 days?
Answers
Answer:
478 / 479
Step-by-step explanation:
6% of 368 is 22.08.
5 days = 6% x 5 = 30%.
30% of 368 = 110.4
110.4 + 368 = 478.4
492 people will be infected with the virus in 5 days.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
We have,
Number of people infected = 368
Rate of spreading = 6%
We can make an equation for the number of people infected in x days.
y = 368 x \((106/100)^x\)
y = 368 x \(1.06^x\)
Substitute x = 5
y = 368 x \(1.06^5\)
y = 492.467
y = 492
Thus,
492 people will be infected with the virus in 5 days.
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• Determine the value of x6 when x = 51/3
Answers
x=51/3
This means that c is equivalent to 51 divided by 3. This means that x is equivalent to 17.
Then, since we know that x is 17 and we need 6x, we do 6 x 17. This will result to 102.
In conclusion, the value of 6x if x = 51/3 is 102.
The value of 6x is 102.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x=51/3
For 6x put x= 51/3 we get
6x = 6 x 51/3
6x = 2 x 51
6x = 102
Or, \(x^6\) = \((51/3)^6\)
\(x^6\) = 17,596,287,801 / 531,441
Hence, the value of 6x = 102.
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Which of the following is a correct equation of the linear model?
Answers
The correct model for the linear equation is y = mx + b
Given data ,
To find the correct equation of a linear model, you need to have two pieces of information: the slope of the line (often represented by the variable "m") and the y-intercept of the line (often represented by the variable "b").
Now , the slope-intercept form of the equation for a line, which is:
y = mx + b
where "y" is the dependent variable (often representing the output or response), "x" is the independent variable (often representing the input or predictor), "m" is the slope, and "b" is the y-intercept.
Hence , the equation of linear model is y = mx + b
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There are 24 men and 25 women running a race. What is the ratio of the number of female runners to the total number of runners?
Answers
Answer:
5/9 In fraction form. In decimal form 0.51 and in percentage form %51
Step-by-step explanation:
To find the ratio of the number of female runners to the total number of runners, we can divide the number of female runners by the total number of runners and express the result as a fraction. There are 25 female runners, and there are a total of 24 men + 25 women = 49 runners. Therefore, the ratio of the number of female runners to the total number of runners is 25/49. This fraction can be reduced to 5/9.
The line 1 has equation 5x + 6y + 30 = 0. Given
that P is the point (3, -1), find
(i) the coordinates of the point where l crosses the
x-axis,
(ii) the coordinates of the point of intersection
of l with the line x = 2,
(iii) the equation of the line passing through P
and having the same gradient as I,
(iv) the equation of the line passing through P
and having a gradient of 0.
w through the points ACO 3).
pls help
Answers
Find The Area Of The Region. Interior Of R = 9 + 7 Sin Θ (Below The Polar Axis) 2) Find The Area Of The Region. Two Petals Of R = 8 Sin(3θ) 3) Find Dy/Dx.
1) Find the area of the region.
Interior of r = 9 + 7 sin θ (below the polar axis)
2) Find the area of the region.
Two petals of r = 8 sin(3θ)
3) Find dy/dx.
x=\sqrt[3]{t}
y=3-t
Answers
To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.
To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.
To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.
The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).
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A.4x+2=6−x
b.5x+2=6
1) How can we get Equation BBB from Equation AAA?
Answers
Step-by-step explanation:
simply add x to both side
4x + x + 2 = 6 - x + x
5x + 2 = 6
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