Answer:
1485120
Step-by-step explanation:
Since the order of arrangement does not matter, we use combination :
Recall :
nCr = n! ÷ (n-r)!r!
For administrator : 1 out of 5 :
5C1 = 5! ÷ (5-1)!1!
For faculty members : 3 out of 14 :
14C3 = 14! ÷ (14 - 3)!3!
For students : 3 out of 18 :
18C3 = 18! ÷ (18 - 3)!3!
5C1 * 14C3 * 18C3 = 1485120
Type the correct answer in each box. Use numerals instead of words.
Answer:
First box: 35 Negative Result
Second box : 60 Positive Result
Step-by-step explanation:
Contains organic matter
Sample size : 700
95% positive means [tex]\frac{95}{100} \times 700 = 665\\[/tex]
5% negative means [tex]\frac{5}{100}\times 700 = 35[/tex]
Does not contain organic matter
Sample size : 300
20% positive means [tex]\frac{20}{100} \times 300 = 60[/tex]
80% negative means [tex]\frac{80}{100}\times 300 = 240[/tex]
Answer:
Just subtract the less no by greater one .you get the answer.
Positive result of sample test gives a positive result than it is 665/1000*100*=66.5% likely that the soil sample contains organic matter.
Members from 6 different school organizations decorated floats for the homecoming parade. How many different ways can first, second, and third prize be awarded?
=======================================================
Explanation:
There are...
6 ways to select the first place winner5 ways to pick the second place winner4 ways to pick the third place winnerWe start with 6, and count down by 1 each time we fill up a slot. We stop once the third slot is filled or accounted for. The countdown is to ensure that we don't pick the same person twice. From here, multiply those values: 6*5*4 = 30*4 = 120
Interestingly, this is equal to 5! = 5*4*3*2*1 = 120 because the 3*2 becomes 6 and that *1 at the end doesn't affect things. Though usually results of permutation problems don't always end up like this. The order matters because a result like ABC is different from BAC, where A,B,C,D,E,F are the six school organizations.
As a slightly longer way to do the problem, you can use the nPr formula which is [tex]_nP_r = \frac{n!}{(n-r)!}[/tex] where n = 6 and r = 3 in this case. The exclamation marks indicate factorial. If you go this route, you should find that one of the steps will involve 6*5*4.
Find the equilibrium solutions. Enter your answer as a list of ordered pairs (A,L), where A is the number of aphids and L the number of ladybugs. For example, if you found three equilibrium solutions, one with 100 aphids and 10 ladybugs, one with 200 aphids and 20 ladybugs, and one with 300 aphids and 30 ladybugs, you would enter (100,10),(200,20),(300,30). Do not round fractional answers to the nearest integer.
The Required equilibrium solution are (400, 40) (500, 50) (600,60).
To find the equilibrium solutions and to enter answer as a list of ordered pairs (A,L), where A is the number of aphids and L the number of ladybugs.
equation is the relationship between variable and represented as y =ax+b is example of polynomial equation.
since the equilibrium solution given by the expression
L = 10A
where A is the number of aphids and L the number of ladybugs.
And ordered pairs with equilibrium solution of one with 400 aphids and 40 ladybugs, one with 500 aphids and 60 ladybugs and one with 600 aphids and 60 ladybugs are (400, 40) (500, 50) (600,60).
Thus, The Required equilibrium solution are (400, 40) (500, 50) (600,60).
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If P(E) = 0.41, P(A) = 0.52, and P(E and ) = 0.35, calculate P(E or F).
how many different California license plates can be made if there has to be one number followed by three letters followed by three more numbers
Answer:
175,760,000 different California license plates can be made.
Step-by-step explanation:
Possible outcomes for each number of letter:
10 numbers(from 0 to 9) and 26 letters.
Format of the plate:
Number - letter - letter - letter - number - number - number
The numbers of possible outcomes are:
10 - 26 - 26 - 26 - 10 - 10 -10
How many different plates?
We multiply these values. So
10*26*26*26*10*10*10 = 175,760,000
175,760,000 different California license plates can be made.
Alice and Bob play a game by taking turns removing 1 or 2 stones from a pile that initially has n stones. The person that removes the last stone wins the game. Alice plays always first.
(a) Prove by induction that if n is a multiple of 3 then Bob has a wining strategy.
(b) Prove that if n is not a multiple of 3 then Alice has a wining strategy.
Answer:
Step-by-step explanation:
(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.
Let n=3
It is given that Alice always plays first.
Then, for the first move, Alice has a choice of removing 1 or 2 stones.
Case 1:
Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.
Case 2:
Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.
Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)
Now, let us assume that Bob has a winning strategy for n=3p.
We will now check if Bob has a winning strategy for n=3p+3
It is given that Alice plays first.
Case 1:
Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.
Case 2:
Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.
Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)
Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.
(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.
If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.
We will prove the given fact for both the forms simultaneously
Let m=0, i.e., n=1 or n=2
Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)
Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2
Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5
Let n=3k+4
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Let n=3k+5
Since Alice plays first, she has a choice to remove 1 or 2 stones.
Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.
Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.
Case 1:
Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.
Case 2:
Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.
Thus, in either case, Alice has a winning strategy.
Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)
Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.
Which could be a binomial expansion of (4x + y)?
Answer:
It's D
Step-by-step explanation:
100%
A 2-pound bag of broccoli costs $4.48. What is the price per ounce?
Need help with the answer??
angle B is teh answer
100% sure !
Plz mark me brainliest
x^2log2x+secx differential equation plz solve the question and give ans
Answer:
only 5 points
Step-by-step explanation:
HELP
Which equation has no real solution A. B2 + 3b = -3
B. 2c2 + 4c = 9
C. -5c2 – c= -2
D.7g +1 + 3g2 = 0
Answer:
A.
[tex] {b}^{2} + 3b - 3 = 0[/tex]
Step-by-step explanation:
[tex] {b}^{2} + 3b - 3 = 0 \\ because \: \: {b}^{2} < 4ac \\ {b}^{2} = {3}^{2} = 9 \\ 4ac = 4 \times 1 \times - 3 = - 12 \\ hence : {b}^{2} < 4ac[/tex]
WILL GIVE BRAINLIST
MATH
CONVERT EACH MEASUREMENT
25FT TO YARDS
SHOW STEPS ALL HOW YOU GOT THE ANSWER
Answer:
8.333... Yards.
Step-by-step explanation:
To convert feet to yards, divide the feet by 3.
[tex]\frac{25}{3} = \frac{25}{3}/8.333...[/tex]
To check work
Multiply 8.333... by 3.
8.333 · 3 = 24.999...
It Is Not Exactly 25 Because The 3 Is Infinite But It Is Enough To Prove Your Answer.
To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 35 specimens are buried in soil for an extended period. The maximum penetration (in mils) is then measured for each specimen, yielding a sample mean penetration of 52.7 and a sample standard deviation of 4.8. The conduits were manufactured with the specification that true average penetration be at most 50 mils. Does the sample data indicate that specifications have not been met
Answer:
t(s) > t(c) then t(s) is in the rejection region for H₀.
We reject H₀ we support the claim that the mean penetration is bigger than that of the specifications
Step-by-step explanation:
Sample Information:
sample size n = 35
sample mean x = 52.7
sample standard deviation s = 4.8
spec. true average = 50
Test Hypothesis:
Null Hypothesis H₀ x = 50
Alternative Hypothesis Hₐ x > 50
The standarddeviation of the population is unknown therefore even though we assume distribution is normal we have to use t-student distribution
The alternative hypothesis indicates that the test is a one-tail test, we will test at significance level α = 5 % CI = 95 %
for α = 0.05 t(c) is from t-student -table and with df = 35 - 1
df = 34 t(c) = 1.69
t(s) = ( x - μ ) / s/√n
t(s) = ( 52.7 - 50 ) / 4.8/√35
t(s) = 2.7 * 5.92 / 4.8
t(s) = 3.33
Comparing t(s) and t(c)
t(s) > t(c) then t(s) is in the rejection region for H₀.
We reject H₀ we support the claim that the mean penetration is bigger than that of the specifications
What is the approximate volume of the cylinder use 22/7 for 3.14 round to the nearest whole number
Answer:
the formula for a cylinder is πr^2•h
Step-by-step explanation:
just plug in the numbers, and you can change π to 3.14 for an approximate answer!
hopefully this helps you!
[tex]\pi {r}^{2} h \\ 22 \div 7 \times {r}^{2} h[/tex]
What will be the coordinates of vertex N' of the image?
(-2, 4)
O (-2, 6)
O (-4,4)
O (-4, 8)
Answer:
N'(-2,6)
Noting Else To Put
Answer: The correct answer is B (-2,6)
Step-by-step explanation: it is show down below
Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour. How fast was Cathy driving?
Answer:
Cathy was driving at a speed of 67 miles per hour.
Step-by-step explanation:
Fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $105.
We solve this using a rule of three.
1 mile - $15
x miles - $105
Applying cross multiplication:
15x = 105
x = 105/5 = 7.
Cathy was 7 miles above the speed limit.
How fast was Cathy driving?
7 miles above the speed limit of 60 miles per hour, so 60 + 7 = 67 miles per hour.
Cathy was driving at a speed of 67 miles per hour.
10 m
10 m
Please help quick :(
I guess you need to find the area :
Area of the figure = Square area + half of
circle area
A = ( length )^2 + 1/2 × pie × ( radius)^2
A = ( 10 )^2 + 1/2 × pie × ( 10/2 )^2
A = 100 + 1/2 × pie × 25
A = 100 + 12.5 pie
____________________________
If pie = 3 : | If pie = 3.14 :
|
A = 100 + 12.5 × 3 | A = 100 + 12.5 × 3.14
|
A = 100 + 37.5 | A = 100 + 39.25
|
A = 137.5 m^2 | A = 139.25 m^2
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
O A. -
B. -4
O c.
O D. 4
Please help
Answer:
Slope = 1/4
Step-by-step explanation:
[tex]slope = \frac{y2-y1}{x2-x1} \\m=\frac{3-2}{3--1} \\m=1/4[/tex]
Find the measure of angle x.
X
X =
[?]
/20
Answer:
it is 20
Step-by-step explanation:
well the angles looks the same
Answer:
x=20[vertically opposite angle are equal]
write equation of the line containing the points (1,2) and (3, 4)
Answer:
y = x + 1
Step-by-step explanation:
Answer:
y = x + 1
Step-by-step explanation:
(1,2) and (3, 4)
y = mx + b
y = x + 1
thanks
33) Solve the equation.
r^3 = 49r
Answer:
r = 7
Step-by-step explanation:
This is how you solve the equation...
[tex]r^{3} = 49r\\r^{3} / r= 49r / r\\r^{2} = 49\\r = \sqrt{49} \\r = 7[/tex]
Answer:
r = 7 is the answer
brainliestt for answerrrrrrrrrrrr fast
Answer:
1/9 ÷ 2
= 1/9 × 1/2
= 1/18
Step-by-step explanation:
THAT IS MY ANSWER HOPE IT HELPS
Juan drank 3 quarts of water. Alfred drank 8 quarts. How many cups of water did they drink altogether?(no links will get brainliest)
Answer: 44 Us Cups
Step-by-step explanation:
plz plz plz plz help me plz it is due in 1 hour and no links plz
Answer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden
Let
tenth of a degree.
tan W = 3.52
Answer:
(d) above [tex]74.1^o[/tex]
Step-by-step explanation:
Given
[tex]\tan w = 3.52[/tex]
Required
Determine w, using a calculator
We have:
[tex]\tan w = 3.52[/tex]
Take arctan of both sides
[tex]w = \tan^{-1}(3.52)[/tex]
Using a calculator, we have:
[tex]w \approx 74.1^o[/tex]
From the given options, (d) is true
What is the equivalent of (n+4)^3 ?
A. n^3 +64
B. n^3 +6n² +24n+32
C. n^3+12n^2 + 48n + 64
D. n^3 +12n^2 +48n +32
E. n^3 +24n^2 +48n+64
Answer:
C)
Step-by-step explanation:
(n+4)(n+4) = n² + 4n + 4n + 16
this can be simplified to get:
n² + 8n + 16
now multiply the above by (n+4)
(n²+8n+16)(n+4) by multiplying each of the three terms in the first set of parentheses by each of the two terms in the second set to get:
n³ + 4n² + 8n² + 32n + 16n + 64 [Now look to combine 'like terms']
n³ + 12n² + 48n + 64 [this is option C]
Solve number 3 please, with explanation
Answer:
97,655
Step-by-step explanation:
5(5)^(n-1) = 78,125
5^n = 78,125
n = 7
=> S7 = 5(5^7 -1) / (5-1)
= 5/4 (78, 125 -1)
= 5/4 (78 124) = 97,655
Thare are 2 yellow 3 pink and 5 blue. What is the possibility of drawing two pink marbles if the first one is placed back in the bag before the second draw?
Answer:
3/10
Step-by-step explanation:
a model truck is 13.5 inches long 7.5 inches wide. the original truck was 12 feet long. how wide was the truck?
Answer:
w = 6ft 8in
Step-by-step explanation:
the proportions will be the same
w/7.5 = 12/13.5
multiply both sides by 7.5
w = 12/13.5 * 7.5
w = 6.6666666667ft
w = 6ft 8in
The original truck was 6.67 feet wide.
What is ratio?"It is a comparison of two or more numbers that indicates their sizes in relation to each other."
What is proportion?"It is an equation in which two ratios are set equal to each other."
For given example,
A model truck is 13.5 inches long 7.5 inches wide.
The ratio of length to width of a model truck would be,
13.5 : 7.5 ...........................(1)
The original truck was 12 feet long.
This means the original truck was 144 inches long.
Let 'x' be the width (in inches) of the original truck.
So, the ratio of the length to the width of the original truck would be,
144 : x .................................(2)
Also, the ratios given by (1) and (2) must be in proportion.
[tex]\Rightarrow \frac{13.5}{7.5} = \frac{144}{x} \\\\\Rightarrow 13.5 \times x = 144 \times 7.5\\\\\Rightarrow \bold{x=80~inches}\\\\\Rightarrow \bold{x=6.67~feet}[/tex]
Therefore, the original truck was 6.67 feet wide.
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TT is an unending decimal. Find the
circumference of the circle below using
exact TT.
C = [?]TT
8
c=
2r
Answer:
C = 16 pi
Step-by-step explanation:
The circumference is given by
C = 2*pi*r
C = 2* pi*8
C = 16 pi
Answer:
Solution given:
radius [r]=8
Now
we have
circumference of circle=2πr=2*8*π=16π
16 is a required answer.