5. Counting problems, leave answers as expressions, e.g., 10 npr 4, 8 nCr 3 or 35 [5 pts each part]
a) A club elects a steering committee of 5. Among these 5, a chair and secretary are chosen. How many different sets of committees (including officer selection) are possible if club has 15 members? Officers are not the same as the non-officer members, so this is hybrid permutation/combination problem.
b) At an event that drew 100 people where each attendee gets one raffle ticket, there are 6 raffle prizes worth $200, $100, $50, $25, $25, $25. How many different raffle ticket winner selections are possible? Be careful, the $25 prizes are equivalent, so this is hybrid permutation and combination problem.
c)If repeats are allowed but a code cannot begin with 0, how many six-digit PIN codes can be made?
Answers
Answer:
Step-by-step explanation:
a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:
15 nCr 5 * 5 * 4 = 3,003,600
b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:
(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000
c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:
9 * 10^5 = 9,000,000
Related Questions
4 1/2 x 2 1/2 x 8 1/2 =
Answers
Answer:
\(95\frac{5}{8}\)
Step-by-step explanation:
\(4\frac{1}{2} * 2\frac{1}{2} * 8\frac{1}{2}\) = 9/2 * 5/2 * 17/2
765/8 = \(95\frac{5}{8}\)
What is the side length of the largest square that can fit into a circle with a radius of 5 units?
Answers
Answer:
7.07 Units
Step-by-step explanation:
This question has been answered previously here on Brainly. For a full and in depth explanation I would search this question up directly.
12
A paratrooper falls to the ground along a diagonal line. His fall begins 5 330 meters above the ground, and the line he follows has a slope
of 6.5. That is, he falls 6.5 meters vertically for every 1 meter he moves across horizontally. How far horizontally across the ground does
he land from his initial position in the sky?
meters
Answers
Answer:
820
Step-by-step explanation:
Using the given values you can form the equation f(x)=-6.5x+5330 to model this example. All you need to do is look to where the x intercept is and there is you answer.
Please help.
Is it no solution, one solution or infinitely many
Solution.
Answers
The median, upper and lower quartiles, fourth and seventh deciles, and fiftieth and 65th percentiles of a distribution of a continuous variable were calculated as:
63.94, 66.50, 73.67, 72.0, 60.63, 70.57 and 58.12
Identify the median, quartiles, deciles, and percentiles
Answers
Is triangle DBE similar to triangle ABC. If so, by what similarity criterion?
A) Yes and by SSA
B) Yes and by SAS
C) Yes and by AA
D) No, the triangles are not similar.
Answers
Answer:
Yes by AA.
Step-by-step explanation:
find the slope of the line. 5x-2y=7
Answers
Thus 5/2 is the slo
a punch bowl has a capacity of 8 quarts. a recipe fills the bowl 3/4 full.how many quarts does the recipe make
Answers
Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.
Here,
The quantity of punch produced by the recipe is:
If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.
=> 6 pints = 8 * 3/4.
The formula yields 6 quarts of punch as a result.
Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.
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pls help!!!! i will give brainly!!!!
Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship? (4 points)
y = 1 over 2x + 2
y = 1 over 2x + 1
y = x + 2
y = 2x + 1
Answers
9514 1404 393
Answer:
(a) y = 1/2x + 2
Step-by-step explanation:
The only equation that matches the first table entry is ...
y = 1/2x +2
3 = (1/2)(2) +2 . . . . first table entry
√2x² + 7x + 5√2 = 0
find the roots of the following quadratic equation by factorization method
PLS HELP ME FAST
Answers
Step-by-step explanation:
√2x² + 7x +√2=0
2x + 7x + √ 2 =0
√2=9x
x = o.15713484
Rich chooses a 4-digit positive integer. He erases one of the digits of this integer. The
remaining digits, in their original order, form a 3-digit positive integer. When Rich
adds this 3-digit integer to the original 4-digit integer, the result is 6031. What is the
sum of the digits of the original 4-digit integer?
Answers
Answer:
*step by step*
Step-by-step explanation:
If he erases one of the digits in a 4-digit number, then only 3 remain, not four.
If he erased the first digit, then it must have been 1-9, so the total is in the range 11 - 19
otherwise the digit could have been 0-9 in which case the total is in the range 10-19
Which of the points below correctly plots the point (−2,−5π/3)?
Select the correct answer below:
A
B
C
D
E
F
Answers
Answer: F
Step-by-step explanation:
Answer: correct answer is A
Step-by-step explanation:
Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.
Cans of soft drinks cost $0.30 in a certain vending machine. What is the expected value and variance of daily revenue (Y) from the machine, if X, the number of cans sold per day has E(X) = 125, and Var(X) = 50?
(a) E(Y) = 37.5, Var(Y) = 50
(b) E(Y) = 37.5, Var(Y) = 4.5
(c) E(Y) = 37.5, Var(Y) = 15
(d) E(Y) = 37.5, Var(Y) = 30
(e) E(Y) = 125, Var(Y) = 4.5
Answers
The correct option is (b) as the expected value and variance of daily revenue are 37.5 and 4.5 respectively.
What is meant by variance?
Consider the expected value to be the average value. The expected value of X when it is a discrete random variable is the exact mean of the relevant data.
The difference between the actual numbers and the average should be viewed as the variance. A greater range of values is indicated by a higher variance. A spread of measure for a random variable distribution that quantifies how much a random variable's values deviate from its expected value is called variance. Frequently, V(X) is used to represent the variance of random variable X.
Given,
Cost of soft drink c = $0.30
Expected value of the number of cans sold per day E(X) = 125
Variance of number of cans sold per day V(X) = 50
So,
Expected value of daily revenue E(Y) = c * E(X) = 0.3 * 125 = 37.5
Variance of daily revenue V(Y) = c² * V(X) = 0.3² * 50 = 4.5
Therefore the expected value and variance of daily revenue are 37.5 and 4.5 respectively. The correct option is (b).
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The triangle is to be reduced by a ratio of 1:2.
a
Answers
Answer:
where is the triangle?
Step-by-step explanation:
3
2
1
-1
-2
-3
Determine the period.
2
4
6
8
10 12 14
Answers
The calculated period of the function is 12
How to determine the period of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
By definition, the period of the function is calculated as
Period = Difference between cycles or the length of one complete cycle
Using the above as a guide, we have the following:
Period = 13 - 1
Evaluate
Period = 12
Hence, the period of the function is 12
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1. Prove ~ (Pvq) <=> (~P^~9).
Algebra of propositional variables
2. P^ q = q^q
P v q = q v p
show that both are commutative
Answers
Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
How to explain the commutative property.It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property
From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.
In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.
Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.
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Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long
What scale factor was used to produce Figure 2 from Figure 1?
Answers
Answer:
The answer
Step-by-step explanation:
Figure 1 figure
3/4
A 0.60-kg basketball is dropped out of a window that is 6.1mabove the ground. The ball is caught by a person whose handsare 1.5m above the gound.1. How much work is done on e the ball by its weight?What is the gravitational potential energy of the basketball,relative to the ground, when it is ... 2. released and 3. caught?4. How is the change (PEf- PE0) in the ball'sgravitational potential energy related to the workdone by its weight?
Answers
The work that gravity does;
W = F.S = mgΔh
In light of the fact that gravity points downward and that displacement is also downward, their angle is 0 and their cosine 1, respectively.
W = mgΔh
g = 9.8 m/s²
Δh = 4.6 m
m = 0.60 kg
W = 0.60 x 9.80 x 4.6
W = 2.7 J
The source of gravitational potential energy in relation to the ground is;
U = mgh
The release point therefore
Ug = mgh(0)
U0 = 0.60 x 9.8 x 6.1
U0 = 35.87 J
At the point of release
U(gf) = mgh(f)
U(gf) = 0.60 x 9.80 x 1.5
U(gf) = 8.820 J
Gravitational potential energy changes are;
ΔU(g) = U(gf) - U0
ΔU(g) = 8.820 J - 35.87 J
ΔU(g) = -27.05 J
Result, we can see that the work done through gravity is the opposite of how the gravitational potential energy has changed.
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This year jake is 47 in tall. This is 4 more than he was last year. Write and solve an equation to find out how tall jake was last year site:socratic.org
Answers
Answer:
x + 4 = 47
x = 43
Step-by-step explanation:
i minus 4 from 47 to get x by its self and x = 43 do he was 43 inches last year
Which country boarders the Horn of Africa in the West?
Answers
The answer is Ethiopia.
There are 4 countries in the horn of Africa.They are Eritrea,Ethiopia,somalia and Djibouti
I know there is a very similar question already out there
but my version is requesting different functions
Cami is comparing the growth rates in the value of two items in a collection. the value of a necklace increases by 3.2% per year. the value of a ring increases by 0.33% per month.
1a) Write a function to represent the value of A of the necklace after t years, assuming the initial value of $1
1b) then write an equivalent function with a power of 12t
2a) Write a function to represent the value of B of the ring after t years with the power of 12t , assuming the initial value of $1
2b) then write an equivalent function with a power of t
so
1a) A= 1 (1+3.2/100)^t
A= $1.032
1b) ????? please help
2a) B=1 (1+0.33/100)^12t
B= $1.04
2b) ???????? please help
ty ty ty this momma is trying to help her kids and is a bit lost !
Answers
Problem 1, part (a)
t = number of years
A = value of the necklace after t years
3.2% = 3.2/100 = 0.032
If the necklace starts off being $1, then after t years, it will have this value
A = 1*(1 + 0.032)^t
A = 1.032^t
You were close, but forgot about the exponent t
------------------------------------
Problem 1, part (b)
Since t represents the number of years, this means 12t represents the number of months, because there are 12 months in a year.
The annual growth rate is 3.2%, which converts to 0.032
Divide this over 12 and we get the approximate value 0.032/12 = 0.00267
So we get this new equivalent function
A = 1*(1+0.00267)^(12t)
A = 1.00267^(12t)
=========================================================
Problem 2, part (a)
t = number of years
12t = number of months
The ring's value goes at a rate of 0.33% per month, which converts to the decimal form 0.0033
The value of the ring is
B = 1*(1 + 0.0033)^(12t)
B = 1.0033^(12t)
------------------------------------
Problem 2, part (b)
We'll take the reverse approach in what we did with part (b) of the previous problem. There we divided by 12 to go from an annual rate to a monthly rate.
We'll multiply by 12 to go from the monthly growth rate to the annual growth rate.
The monthly growth rate of 0.33% turns into the annual growth rate of 12*0.33% = 3.96%, and that turns into the decimal form 0.0396
So,
B = 1*(1+0.0396)^t
B = 1.0396^t
represents the value of the ring after t years.
Find the distance covered by a wheel of radius 1.4 m, if it makes 250 revolutions. show working too
Answers
Answer:
The distance covered by a wheel is given by the formula:
distance = circumference of the wheel x number of revolutions
The circumference of the wheel can be found using the formula:
circumference = 2πr
where r is the radius of the wheel.
Substituting the given values, we get:
circumference = 2π(1.4) = 2π(1.4) = 2(22/7)(1.4) = 8.8 meters
Therefore, the distance covered by the wheel in 250 revolutions is:
distance = 8.8 x 250 = 2200 meters
So, the wheel covers a distance of 2200 meters if it makes 250 revolutions.
Answer:
\(\text{Radius} = 1.4 m\)
\(\text{Distance covered in One revolution} = 2\pi r\)
\(2\pi r =\)
\(2\times22=\dfrac{1.4}{7}\)
\(= 8.8 \ \text{m}\)
\(\text{Distance covered in 250 revolutions}\)
\(= 8.8 \ \text{m}\times 250\)
\(\bold{= 2200 \ m}\)
\(\it{Hope \ this \ is \ the \ answer \ you \ were \ looking \ for.}\)
if the slope of one line is 13/8 what is the slope of the line that is perpendicular to it ?
Answers
Answer:
\(-\frac{8}{13}\)
Step-by-step explanation:
To find the slope of the line that is perpendicular to a line with a given slope, we simply take the negative reciprocal of the given slope.
The given slope is: \(\frac{13}{8}\)
The reciprocal is obtained by swapping the numerator and the denominator.
The negative reciprocal of the slope is: \(-\frac{8}{13}\)
in a popular shopping Centre waiting time for an ABC bank ATM machine is found to be uniformly distributed between 1 and 5 minutes what is the probability of waiting between 2 and 4 minutes to use the ATM
Answers
so here we get two outcomes one is 2 and other is 4.
so there is total 2 outcomes.
total no. of possibility is 5
so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.
what are your thoughts about the choice of music style and genre in hamilton? Give reasons for your answer (write a paragraph with a few lines) please don’t waste my points because i really need this i’ll also give brainliest.
Answers
Style is quite a fun quirky music style in my opinion I also feel as if the music genre has a story behind it. Tell me if you need more lines
a number is taken away from 13 and the result is 4 what is the number?
Answers
Answer:
9
Step-by-step explanation:
13-9= 4
The difference between two positive integers is 60. One integer is three times as great
as the other. Find the integers.
Answers
Answer:
a = 90, b = 30
Step-by-step explanation:
If one is three times as great, it must be the bigger number
a - b = 60
a = 3b
-b = 60 - 3b
b = 3b - 60
b - 3b = -60
-2b = -60
2b = 60
b = 30
a - b = 60
a - 30 = 60
a = 60 + 30
a = 90
X-1 3/4= 3/4
I do not understand it pls help I need the working to
Answers
Answer:
2 1/2
Step-by-step explanation:
To Find x It the same things as 1 3/4 + 3/4 = x.
Look in the picture for the work or below:
Add \(\frac{7}{4}\) to both sides of the equation
\(x-\frac{7}{4}+\frac{7}{4}=\frac{3}{4}+\frac{7}{4}\)
Simplify
\(\frac{5}{2}\)
\(\frac{5}{2}=2\frac{1}{2}\)
Answer:
\(x = 2\frac{1}{2}\) or \(2.5\)Step-by-step explanation:
\(x - 1\frac{3}{4} =\frac{3}{4}\)
\(x =\frac{3}{4} + 1\frac{3}{4}\)
\(x =\frac{3}{4} + \frac{7}{4}\)
\(x = \frac{3+7}{4}\)
\(x=\frac{10}{4}\)
\(x = \frac{5}{2}\)
\(x = 2\frac{1}{2}\) or \(2.5\)
To make a trail mix you must have 4 cups of pretzels
and 2 cups of bread chips. What is the ratio of
pretzels to bread chips?
Someone please help
Answers
Answer:
1:2
Step-by-step explanation:
You do 4:2 then divide 2 on each side which is 1:2
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Answers
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour