Determine the number of three letter arrangements using the letters of the word METAPHORa. 336b. 40 320 512c. 512d. 56
Answers
Given:
The word, "METAPHOR".
To find:
The number of three letter arrangements.
Explanation:
There are 8 letters.
Therefore, n = 8.
Out of 8 letters, we need to select 3 letters.
So, r = 3.
Using the permutation,
\(\begin{gathered} ^8P_3=\frac{8!}{(8-3)!} \\ =\frac{8!}{5!} \\ =\frac{5!\times6\times7\times8}{5!} \\ =336 \end{gathered}\)Therefore, the number of three-letter arrangements is 336.
Final answer:
The number of three-letter arrangements is 336.
Related Questions
How many terms are in this expression? 2s²+u²
Answers
Answer:
2 terms
Step-by-step explanation:
Given
\(2s^2 + u^2\)
Required
Determine the number of terms
In an expression, the terms are represented as:
\(Term_1 \± Term_2 \± Term_3 +.......\±Term_n\)
Using that logic:
\(2s^2 + u^2\) has 2 terms i.e. \(2s^2\) and \(u^2\)
Which statement is not always true for a parallelogram?
Answers
Answer:
A.
Step-by-step explanation:
The angles are not always congruent as the only way for them to all be congruent is if it were to be a square, and not all parallelograms are squares.
What is the value of f(-2)?
Answers
Answer:
-2f
Step-by-step explanation:
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 8ft Find the area of the shaded region.
Use the value 3.14 for PI , and do not round your answer. Be sure to include the correct unit in your answer.
it wont let me paste the picture but please help
Answers
Answer: 6.88 cm sq.
1. Find the area of the rectangle
A=l *w
L=8cm
the width=the radius of the semicircle
Width=8/2=4
8*4=32
A=32cm sq
2. find area of the semicircle
area=pi times the radius squared divided by 2
r=4cm
A=(3.14)*4^2/2. The area =25.12 cm sq.
Area of the shaded region=32-25.12=6.88cm sq.
Simplify the product. 7(–9)
Answers
Any time there is a number directly outside another in parentheses, that means multiply!
So, you must multiply 7 and -9. Remember a positive times a negative is always a negative.
7*-9= -63
Answer:-63
Hope this helped! Comment if you have questions :)
Answer:
have a great day
god is great
PLEASE HELP ASAPPPPP!!!!!!!
For the infinite geometric series below, identify whether the series is convergent or divergent. If convergent, find the number where the sum converges.
5 + 5/2 +5/4 + ......
Answers
Answer:
10
Step-by-step explanation:
This is an infinite geometric series with first term 5 and common ratio 1/2.
\(\frac{5}{1-\frac{1}{2}}=10\)
A rectangular tank of length 22 cm, width 9 cm and height 16 cm is filled with water. The water is poured into a cylindrical container of radius 6 cm. Calculate the i) volume of the rectangular tank. ii) depth of water in the cylindrical container. [Take pi = 22/7]
Answers
Given: Length of rectangular tank = 22 cm, Width of rectangular tank = 9 cm, Height of rectangular tank = 16 cm, Radius of cylindrical container = 6 cm. So, the depth of water in the cylindrical container is 3.6 cm.
The volume of the rectangular tank = length × width × height
The volume of rectangular tank = 22 cm × 9 cm × 16 cm
The volume of rectangular tank = 3,168 cm³
Depth of water in cylindrical container, We know that the volume of water poured from the rectangular tank is equal to the volume of cylindrical container.
The volume of cylindrical container = πr²h, Where, r is the radius of the cylindrical container, and h is the height of the water poured into the container.Let the height of water poured into the container be h.
The volume of the cylindrical container = πr²h
The volume of cylindrical container = (22/7) × 6 cm × 6 cm × h
The volume of cylindrical container = 36 × (22/7) × h cm³
We know that volume of water poured from the rectangular tank is equal to the volume of the cylindrical container.
The volume of water in rectangular tank = Volume of cylindrical container3,168 = 36 × (22/7) × h∴ h = 3.6 cmHence, the depth of water in the cylindrical container is 3.6 cm.
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Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
Answers
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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Lisa is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25 . If the flight is on time, the probability that her luggage will make the connecting flight is 0.8 , but if the flight is delayed, the probability that the luggage will make it is only 0.65. Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that her first flight was delayed?
Answers
Answer:
The probability is 0.33
Step-by-step explanation:
Please find the attachment for detail
Which is a solution of 1/4+x=0 0.25, 3/4, -3/4, or -0.25.
Answers
x/-7 +14 >/ 16
show your work
include a number line
Answers
9514 1404 393
Answer:
x ≤ -14
Step-by-step explanation:
We assume you want to solve ...
x/(-7) +14 ≥ 16
Subtract 14, then multiply by -7.
x/(-7) ≥ 2 . . . . subtract 14
x ≤ -14 . . . . . . multiplying by a negative number reverses the inequality
The solution is shown on the number line below.
The points (0,2), (1,3), (2,6), and (3,11) are on the graph of a function. Which of the following equations represents that function?
A.h(x)=x^2+2
B.h(x)=0.5x^2+1.5
C.h(x)=2x^2
D.h(x)=x+2
Answers
Given:
The points (0,2), (1,3), (2,6), and (3,11) are on the graph of a function.
To find:
The function.
Solution:
In option A,
\(h(x)=x^2+2\)
Putting x=0, 1, 2, 3 respectively, we get
\(h(0)=(0)^2+2=2\)
\(h(1)=(1)^2+2=3\)
\(h(2)=(2)^2+2=6\)
\(h(3)=(3)^2+2=11\)
The function passes through the points (0,2), (1,3), (2,6), and (3,11). So, \(h(x)=x^2+2\) is the required function.
In option B,
\(h(x)=0.5x^2+1.5\)
At x=0,
\(h(0)=0.5(0)^2+1.5=1.5\neq 2\)
So, option B is incorrect.
In option C,
\(h(x)=2x^2\)
At x=0,
\(h(0)=2(0)^2=0\neq 2\)
So, option C is incorrect.
In option D,
\(h(x)=x+2\)
At x=2,
\(h(2)=(2)+2=4\neq 6\)
So, option D is incorrect.
Therefore, the correct option is A.
In a class of 33 students, there are 19 females. What is the ratio of makes to females in the class?
Answers
Answer:
14:19
Step-by-step explanation:
33-19=14
hope this helps :3
if it did pls mark brainliest
Step-by-by-step explanation
Which expression does not have a solution of 12, if w = 4?
3 w
w + 8
4 w
16 - w
Answers
Answer:
8 w
Step-by-step explanation:
yes
Answer:
4 w
Step-by-step explanation:
So first, let's check,
Substitute 4(w=4) for each expression and then evaluate
3(4)=12
4+8=12
4(4)=16
16-4=12
16 is not equal to 12, so the answer is 4 w
What is the awnser please!! -5r + 6 < -5(r + 2)
Answers
The equation z = 30x represents a(n) _____ variation.
a. direct
b. joint
c. inverse
d. combined
Answers
The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.
Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.
In the case of the given equation, as x increases, z also increases proportionally.
Similarly, if x decreases, z will also decrease proportionally.
Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.
In the given equation, we can see that z is the dependent variable, and x is the independent variable.
We can rewrite the equation as z = kx, where k = 30.
To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.
Here, the cost of buying apples is directly proportional to the number of apples purchased.
For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.
Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.
Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.
The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.
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Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
What is the image point of (3,3)(3,3) after the transformation D_{5}\circ T_{0,-1}D
5
∘T
0,−1
?
Answers
The coordinates of image point is (15, 20)
How to determine the image pointA dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
The transformation is given as
T<0, 1>D5
Mathematically, this
(x, y) = 5(x, y + 1)
So the image point is
(x, y) = 5(3, 3 + 1)
(x, y) = (15, 20)
So the image point of is (15, 20)
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If x and y vary inversely, and x = 8 when y = 1/4, what is y when x = -4?
Answers
\(y \propto \dfrac 1x\\\\\implies y = \dfrac kx \\\\\implies \dfrac 14 = \dfrac k{8}\\\\\implies k=2\\\\\text{When}~ x =-4\\\\y = \dfrac{k}{x} = \dfrac{2}{-4}= -\dfrac 12\)
Determine the amount of taxes owed on a taxable income of $51, 100.
A) $5,310.00
B) $6,919.00
C) $11,682.00
D) $12,744.40
Answers
The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.
What is the taxable amount?To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.
For the tax year 2021, the federal income tax brackets and rates for single filers are:
10% on taxable income from $0 to $9,950
12% on taxable income from $9,951 to $40,525
22% on taxable income from $40,526 to $86,375
24% on taxable income from $86,376 to $164,925
32% on taxable income from $164,926 to $209,425
35% on taxable income from $209,426 to $523,600
37% on taxable income over $523,600
To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.
Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.
Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.
Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.
Adding these three amounts together, we get the total tax owed:
$995 + $3,384.48 + $2,312.72 = $6,692.20
Therefore, the closest answer choice is B) $6,919.00.
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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).
What is an income?An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.
Define tax?Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.
=$51100* 22/100
=$11242
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Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)
A grocery store manager notices that this month her store sold a total of 571 gallons of ice cream, which represents a decrease of 18% from last month. How much ice cream did the store sell last month? Round your answer to the nearest integer.
The store sold ____________ gallons of ice cream last month.
Answers
Answer:
673.8
Step-by-step explanation:
helppppppp!!! pleaseeeeeeeee
Answers
Answer:
62,400 J
Step-by-step explanation:
As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.
SetupFor x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.
The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:
\(\displaystyle W = \int_0^{40}(3x+1500)\,dx\)
SolutionThe value of the integral is ...
\(\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}\)
The work done to lift the cable and weight is 62,400 joules.
__
Additional comment
One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).
This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.
Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.
The senior classes at Snellville High and General High planned separate trips to the water park. The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?
Answers
Answer:
133 Students
Step-by-step explanation:
Let the number of student in a van=v
Let the number of student in a bus=b
The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.
Therefore: 12v+14b=796
General High rented and filled 14 vans and 12 buses with 738 students.
Therefore: 14v+12b=738
We solve the two resulting equations simultaneously
12v+14b=796
14v+12b=738
Multiply equation 1 by 12 and equation 2 by 14 to eliminate b
144v+168b=9552
196v+168b=10332
Subtract
-52v=-780
Divide both sides by -52
v=15
We substitute v=15 to obtain b in any of the equations
12v+14b=796
12(15)+14b=796
14b=796-180
14b=616
Divide both sides by 14
b=44
Therefore a bus contains 44 Students and a Van contains 15 students.
Number of Students who would fill 2 buses and 3 vans
=2b+3v
=2(44)+3(15)
=133 Students
F. Why would a linear function describing an investment made at a bank have a minimum
value but no maximum value? Explain your reasoning.
Answers
Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.
Step-by-step explanation:
Using Compound Interest, calculate the principle and interest earned (final
balance/principal
and interest) if:
Principle=$2,000
Interest Rate=8.5%
Time=10 years
Interest Calculated Quarterly
Answers
Answer: 20,085
Step-by-step explanation: 2,000x10=20,000. 8.5x10=85. 20,000+85=20,085.
I hope I got this right and if I did it right.
What is the length of each leg in the right triangle shown?
45
7sqrt2
45°
Answers
Answer:
Below
Step-by-step explanation:
It is an isosceles right triangle ( the two legs are equal length).
Use Pythagorean Theorem
(7 sqrt2)^2 = L^2 + L^2
98 = 2 L^2
49 = L^2
L = 7
find the area!!! help please!!!
Answers
Answer:569.4 os the answear
Step-by-step explanation:
When you multiply 12 times 12 it is that hope this helps
A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.
a) Substitute the values into the vertical motion formula h(t) = -16t2 + vt + h, where v represents the rocket’s initial velocity and h represents the rocket’s initial height.
t?
Answers
Answer:
ball-x2-y2-z2-r2--n-dimensions-represent-ball-hypersphere-s-q7037775 ... -feet-rectangular-field-divide-half-fence-middle-pa-q7037837 0.8 2015-06-26 ... -thrown-vertically-upward-initial-velocity-v-original-position-s-height-h-time-t- ...
Step-by-step explanation:
If the odds are against Deborah winning first prize in a chess tournament and the odds are 3 to 5, what is the probability of the event that she will win first prize? the probability that Deborah will win first place is ____. (type an integer or a fraction).
Answers
Given:The odds are from 3 to 5 ,that is, 3,5.
We have to find the probability of the event that Deborah will win first prize.
The probability of the odds that are against Deborah winning first prize will be:
\(=\frac{\text{Number of favorable outcomes}}{nu\text{mber of possible outcomes}}\)Here, number of possible outcomes to get odd from 3 to 5 are 3,4,5 that is 3.
Number of favourable outcomes to get odd are 3,5 that is 2
So, probability of odds will be:
\(=\frac{2}{3}\)Now, the probability that she will win first prize will be:
= 1- P(the odds are winning)
\(=1-\frac{2}{3}\)\(=\frac{1}{3}\)So, the probability that Deborah will win first prize is 1/3.
Find the value of x when 5 - x = 12x + 4
Answers
Answer:
5-4=12x+x
1=13x
1/13=×