How many distinguishable letter codes can be formed from the word PREPARED if every letter is used? In how many ways can a committee of 4 students be formed from a pool of 31 stadents? CHCH Express the number of ways, N, that the students can be selected for the commitioe ning appropriate counting notation. Use the torm,P, to represent the number of permutations of n distinct opschs ban tata time or C to represent the number of combinations of a distinct objects saen at a time N A hand in a card game consists of nine cards dealt without replacement from a standard deck of ty two cands
Answers
There are 7,015 ways to form a committee of 4 students from a pool of 31 students.
.
To determine the number of distinguishable letter codes that can be formed from the word "PREPARED" where every letter is used, we need to consider the repetition of certain letters.
In the word "PREPARED," we have the following letters:
P occurs twice
R occurs twice
E occurs twice
A occurs once
D occurs once
To calculate the number of distinguishable letter codes, we can use the concept of permutations. The total number of permutations can be calculated as follows:
Total Permutations = (Total letters)! / (Repetitions1! * Repetitions2! * ... * Repetitionn!)
In this case, the total number of permutations would be:
Total Permutations = 9! / (2! * 2! * 2!)
Simplifying the expression:
Total Permutations = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1 * 2 * 1)
Total Permutations = 362,880 / 8
Total Permutations = 45,360
Therefore, there are 45,360 distinguishable letter codes that can be formed from the word "PREPARED" where every letter is used.
Now let's move on to the second question regarding the formation of a committee of 4 students from a pool of 31 students.
To calculate the number of ways a committee can be formed, we can use the concept of combinations. The formula for calculating combinations is:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have 31 students to choose from, and we want to select a committee of 4 students. So the calculation would be:
C(31, 4) = 31! / (4! * (31 - 4)!)
C(31, 4) = 31! / (4! * 27!)
Simplifying the expression:
C(31, 4) = (31 * 30 * 29 * 28) / (4 * 3 * 2 * 1)
C(31, 4) = 7,015
Therefore, there are 7,015 ways to form a committee of 4 students from a pool of 31 students.
.
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Related Questions
What is the slope of the line that passes through the points (-10, –4) and (10, -29)? Write your answer in simplest form. Answer: Submit Answer undefined attempt i out of
Answers
Answer:
-5/4
Step-by-step explanation:
Leonardo knows it is 42 days until summer break. how many weeks is it until Leonardos summer break?
Answers
Answer: 6 weeks
Step-by-step explanation: 42 days in weeks would be 6 weeks
HELP PLEASE PLEASEEEEEEE
Answers
Answer:
about 1854.55 miles (rounded to the hundredth)
Step-by-step explanation:
1.
\( \frac{44}{100} = \frac{816}{x} \)
The first fraction represent the percentage of the distance.
The second one represent the number of 816 miles out of x
2. 100 × 816 = 44 × x
3. You'll get 81,600 = 44x
4. and then you divided both side by 44 to solve for x
which of the number 285, 627, 5490, 7290, 7295, 15780, 43695 are divisible by 5 but not 3
Answers
Answer:
Step-by-step explanation:
They all end in 0 or 5 except 627, so all but 627 are divisible by 5.
The following are divisible by 3
285
627 is divisible by 3 (but not 5)
5490 is divisible by 3
7290 is divisible by 3
15780
43695
===============
So your answer is
7295
I think that's the only one divisible by 5 but not 3.
===============
There's a quick way to divide by 3. Just add the digits. If the sum is divisible by 3 then the whole number is divisible by 3
For example 285
2 + 8 + 5 = 15.
15 is divisible by 3 so 285 is divisible by 3.
==================
7295 = 7 + 2 + 9 +5. Anything adding up to 9 you can cast out.
7 + 2 = 9 Cast it out
9 = 9 Cast it out
5 is not divisible by 3, so 7295 is not divisible by 3
43. Last year 1,320,000 people visited the state fair. This year 1,544,400 visited. What percentage increase or decrease was this, to the nearest whole percent?
A. 15 B. 16 C. 17 D. 18
Answers
Answer: 17% increase
Step-by-step explanation:
Percentage increase/decrease = (final value - initial value) / initial value x 100
% change = (1,544,400 - 1,320,000) / 1,320,000 x 100
% change = 224,400 / 1,320,000 x 100
% change = 0.17 x 100
% change = 17% increase
23. If the cube and rectangular box have the same volume, which equation can you use to find the height (h) of the box? (1) 63 = 6 x 12 xh (2) 62 = 6 x 12 xh (3) 63 = 6 + 12 + h (4) 6 = (6 x 12)h (5) h = 6 x 6 x 12
Answers
We are given two figure, i) Cube, ii) rectangular box
The volume of any shape is calculated by multiplying height, width, length.
Volume = height x length x width
In the case of a cube, all the dimensions are the same. So volume would be = length x length x length
here, length = 6
So,
V(cube) = 6^3
For a rectangular box:
V(rect) = height x length x width
V(rect) = h x 12 x 6
As given, V(cube) = V(rect). Therefore,
6^3 = h x 12 x 6
Hence, the first option is correct.
-5pq x - 3p x 6q find the product
Answers
\(\\ \sf\longmapsto -5pq(3p)(6q)\)
\(\\ \sf\longmapsto -5pq(18pq\)
\(\\ \sf\longmapsto -90(pq)^2\)
\(\\ \sf\longmapsto -90p^2q^2\)
what is the major restriction in linear regression forecasting?
Answers
Linear regression forecasting is an algorithm used for identifying and predicting the future values of a dependent variable based on the independent variable.
The major restriction in linear regression forecasting is that it only takes into account the linear relationship between the dependent and independent variables.
The model assumes that the relationship between the dependent and independent variable is linear and not nonlinear. This assumption may not always be true because there might be cases where the relationship between the variables is non-linear, which can result in inaccuracies in the forecast.
The model's reliability is also based on the quality of the data used for regression analysis. If the data is incorrect, outdated, or incomplete, the accuracy of the model can be negatively affected. Another limitation is that the model assumes that the relationship between the dependent and independent variables is constant over time, which may not be true in the real world.
Also, linear regression is a parametric method that requires certain assumptions about the data, including the normality of the residuals and constant variance of the errors.Linear regression forecasts require data to be independent and unbiased and may not work well if data contains outliers or noise.
Linear regression cannot identify causality or differentiate between correlation and causality. Hence, it is recommended to use linear regression along with other techniques for better accuracy.
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WILL MARK BRAINLIEST IF CORRECT!
Two experiments are conducted to determine the mass of an object.
-In Experiment 1, you place the object on an electronic balance and read the object's weight.
-In Experiment 2, you apply a constant force to pull the object along a horizontal surface, while using a motion detector to measure the object's speed as it is pulled.
All frictional forces for both experiments are considered to be negligible. Which of the two experiments, if either, could be used to determine the gravitational mass of the object?
a. Experiment 2 only
b. Experiment 1 only
c. Neither experiment
d. Both experiments
Answers
Answer:
b I think is the right answer.
PLEASE HELP
what is the max or min value of
2x^2-12 − 14
Answers
Answer:
-22
Step-by-step explanation:
ASAP WHO EVER ANSWER THESE WILL BE MARKED BRANLIEST
Answers
Answer:
i dont know honestly
Step-by-step explanation:
The volume of a cube is 27 in.. How long is each side?
Answers
Answer:
6.75
Step-by-step explanation:
Answer:
Hi there!!
Your answer is:
Each side is 3 inches.
Step-by-step explanation:
The volume of a cube is equal to l×w×h. All sides of a cube are the same size!
If x^3 = 27, then work backwards!
1: Take the cubed root of 27.
The cubed root of 27= 3!
2: Check your work!
If the length, width, and height is all 3 units, plug in 3 and solve. If both sides equal each other, you are correct
3×3×3 = 27 ?
9×3 = 27 ?
27= 27 ✓
please help me with this
Answers
Answer:
0.40
Step-by-step explanation:
Sin(T) is Opposite over Hypotenuse, which is RS/ST.
ST = sqrt(43) so we can plug that in.
To find RS, use the Pythagorean theorem, so, 6^2+ (RS)^2= 43.
36 + (RS)^2 = 43
RS^2 = 7
RS = sqrt(7)
Thus, Sin(T) = sqrt(7/43) or 0.40
Which of the following is a solution to the inequality, y + −8 >−2.5. Select all that apply. A 5.255.25 B 5.55.5 C 5.65.6 D 5.755.75 E 66
Answers
The solutions to the inequality are:
C) 5.6
D) 5.75
E) 6
To solve the inequality y + (-8) > -2.5, we can isolate the variable y by adding 8 to both sides:
y + (-8) + 8 > -2.5 + 8
y > 5.5
Therefore, any value of y that is greater than 5.5 will satisfy the inequality.
From the options given:
A) 5.25 is not greater than 5.5, so it is not a solution.
B) 5.5 is equal to 5.5, and we need values greater than 5.5, so it is not a solution.
C) 5.6 is greater than 5.5, so it is a solution.
D) 5.75 is greater than 5.5, so it is a solution.
E) 6 is greater than 5.5, so it is a solution.
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What is 2 times 2? It would be really helpful.
Answers
Answer:
2*2=4
Step-by-step explanation:
Which function has an inverse that is also a function?
o f(x) = 4x + 7
Oh (2) = 17
O j(x) = 3cº
O g(x) = 2 – 3
Answers
Answer:
G(x) = 2x - 3 has a linear inverse which is a function.
k(x) = -9x2 has a square root inverse that is a function on only the interval x < 0.
Step-by-step explanation:
The inverse of a function is a reflection across the y=x line. This results in switching the values of the input and output or (x,y) points to become (y,x). This can be done algebraically in an equation as well. Begin by switching the x and y in the equation then solve for y.
x = 2y - 3 -------> y = x/2 + 3/2 is linear and a function.
-9y2 = x --------> y = √(-x/9) is a square root that is a function on only the interval x < 0.
Absolute value does not have an inverse function.
x = -20 is a vertical line which is not a function.
Brainliest please?
What is the formula for radius when given circumference?
Answers
Then rearrange to find r on its own
So it would be
r = circumference given / 2 π
Your net salary is 5000 per year (paid at the end of each year). Because you live in your parents' basement, you have no expenses and invest all of you salary in Dogecoin, which yields a constant rate of 12% per year (effective). What is the total value of your investments after exactly 5 years (immediately after you receive the 5th year of salary and invest it)? Answer: You must create a team of four people, formed of: one General, one Captain, and two Admin Staff (whose roles are exactly identical). There are 10 individuals available, and they can all do every role. How many different teams are possible? Answer: A loan of amount 3000 is to be repaid with one single payment of 7500, exactly 8 years from now. What is the continuously compounded interest rate (8) in place? Select one: a. 0.1145 O b. 0.1875 OC. 0.1214 O d. 0.0923 0.1043 e.
Answers
In this case, interest rate r = 12% or 0.12. The total value of your investments after exactly 5 years will be $9800.
To calculate the total value of your investments after 5 years, we can use the formula for compound interest. Since you invest your entire salary at the end of each year, the interest is compounded annually.
Let's denote the initial salary as S and the interest rate as r. In this case, S = $5000 and r = 12% or 0.12.
After the first year, your investment will grow by S * r = $5000 * 0.12 = $600.
At the end of the second year, the investment will have grown by another $600, resulting in a total value of $5000 + $600 + $600 = $6200.
Following the same pattern, at the end of the third year, the total value will be $6200 + $600 + $600 = $7400.
Continuing this process, at the end of the fourth year, the total value will be $7400 + $600 + $600 = $8600.
Finally, at the end of the fifth year, the total value will be $8600 + $600 + $600 = $9800.
Therefore, the total value of your investments after exactly 5 years will be $9800.
By following these steps, you can determine the total value of your investments after 5 years.
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if the mean of 3 2 x 11 13 14 is 8 find the value of x
Answers
Answer:
x=5
Step-by-step explanation:
To find the mean, add up all the numbers and then divide by the number of numbers
(3+ 2+x+ 11+ 13+14)/6 = 8
Multiply each side by 6
(3+ 2+x+ 11+ 13+14) = 48
Combine like terms
43+x = 48
Subtract 43 from each side
x =5
Answer:
\(\huge \boxed{{x=5}}\)
Step-by-step explanation:
The mean is the average value of a data set.
\(\displaystyle \sf mean = \frac{sum \ of \ terms}{number \ of \ terms}\)
The mean is given solve for x.
\(\displaystyle 8 = \frac{3+2+x+11+13+14}{6}\)
Multiply both sides by 6.
\(\displaystyle 8(6) = \frac{3+2+x+11+13+14}{6} \times (6)\)
\(48=3+2+x+11+13+14\)
Combine the numbers on the right side of the equation.
\(48=x+43\)
Subtract 43 from both sides.
\(48-43=x+43-43\)
\(5=x\)
In the Acronym WKU, what does each letter represent?
Answers
Answer:
Western Kentucky University
Step-by-step explanation:
Western Kentucky University is a public university in Bowling Green, Kentucky. It was founded by the Commonwealth of Kentucky in 1906, though its roots reach back a quarter-century earlier. It operates regional campuses in Glasgow, Elizabethtown-Fort Knox, and Owensboro.
Answer: Western Kentucky University
Step-by-step explanation:
A new car costs $23,649. The dealer
has an end-of-the-year sale, and the
car will be priced at $22,399. How
much money can a customer save by
purchasing the car on sale?
Answers
Answer:
$1250
Step-by-step explanation:
subtract $22399 from $23649 which is $1250
HELP ME PLEASE 30 POINTS ON THE LINE
Answers
Answer:
88
Step-by-step explanation:
First we do what is inside the parenthesis:
(6+2)=8
Then we do:
\(8^{2}\)=64
So:
\(14+[64 + 10]\)
Then we do brackets:
14+{74}
Then we add:
88
Answer: 88
Step-by-step explanation:
14 + ((6 + 2^)2 + 10)
Remove parentheses.
14 + (6 + 2)^2 + 10
Simplify each term.
Add 6 and 2.
14 + 8^2 + 10
Raise 8 to the power of 2.
14 + 64 + 10
Simplify by adding numbers.
Add 14 and 64.
78 + 10
Add 78 and 10.
88
Select the expression that is equivalent to x + x + y × y × y. Question options: 2x + 3y x2 + 3y x2 + y3 2x + y3
Answers
Answer:
D) 2x + y³---------------------
Adding same values results in multiplication.
Multiplication of same values results in exponents.
Find the equivalent expression with the given:
x + x + y × y × y = 2x + y³This is same as the last answer choice.
plz.help me do this question
Answers
I'll solve for half circle.
Perimeter = πr + 2r
r = 7cm
P = π*7 + 2*7
P = 35.9 cm
solve 15 2x = 36. round to the nearest ten-thousandth.
Answers
To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.
* You have a dog that can run 5 km/hr. How fast can she run in mi/hr? (i.e. convert the rate to miles per hour) (1.6 km=1mi) DO NOT JUST TYPE THIS INTO A CONVERTER ONLINE. YOU WILL NOT GET THE ANSWER RIGHT. Express your answer as decimal, rounded to the nearest thousandth (three decimal places) in mi/hr - no spaces EXAMPLE: 78.345mi/hr
Answers
The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.
To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.
However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.
Therefore, the dog can run at approximately 3.125 mi/hr.
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Read the picture please
Answers
Answer:
1100
Step-by-step explanation:
After rounding,
3200 - 2100 = 1100
In the relation (a+c)^2=t make C the subject
Answers
Answer:
See below
Step-by-step explanation:
(a+c)^2 = t
(a+c) = sqrt t
c = sqrt(t) - a
What makes an equation with an inequality symbol true?
Answers
Answer:
In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥. ... If the statement is true, the number is a solution to the equation or inequality.
Step-by-step explanation:
Find the missing side
Answers
Answer:
B
Step-by-step explanation:
cos(35)=x/15
15cos(35)=x
x=12.3