Answers
==================================================
Explanation:
Let's say we had the slots A,B,C,D,E,F. Each slot represents where a flower would go.
For slot A, we have 15 different flowers to pick from.
Then slot B has 15-1 = 14 choices
C has 15-2 = 13 choices
and so on. We count our way down until we fill up slot F.
The count down looks like this: 15, 14, 13, 12, 11, 10
Multiply out those values: 15*14*13*12*11*10 = 3,603,600
If order mattered, then this represents the number of ways to select 6 flowers from a pool of 15 total.
However, order does not matter in this case. All that matters is the group overall.
For any group of 6 items, we have 6! = 6*5*4*3*2*1 = 720 different arrangements. That means the value 3,603,600 is too large exactly by a factor of 720.
We divide by 720 to get to (3,603,600)/720 = 5005 which is the final answer
It's the number of combinations where we select 6 from a pool of 15.
-------------------------------
As you can guess, you could use the nCr combination formula as an alternative route. Plug in n = 15 and r = 6 like so
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{15} C _{6} = \frac{15!}{6!*(15-6)!}\\\\_{15} C _{6} = \frac{15!}{6!*9!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10*9!}{6!*9!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10}{6!}\\\\_{15} C _{6} = \frac{15*14*13*12*11*10}{6*5*4*3*2*1}\\\\_{15} C _{6} = \frac{3,603,600}{720}\\\\_{15} C _{6} = 5005\\\\[/tex]
In the third to last step, notice how we have the 15*14*13*12*11*10 up top and 6*5*4*3*2*1 down below.
This value 5005 can be found in Pascal's Triangle. Look in the row that has 1, 15, ... and count out 7 spaces from the left. You should arrive at 5005. However, you'll need a fairly large Pascal's Triangle to use this method.
Given:
Total number of flower cuts = 15 different flowers
Number of flowers Jeanine Baker wants to use = 6 flowers
To find:
Total number of ways 6 flowers can be chosen
Steps:
In this question, we need to find the total number of outcomes of choosing 6 random flowers from a total of 15 flowers
Let's give each flowers a letter, so there will be A, B, C, D, E, F, G, H, I, J, K, L, M, N and O.
Now let's find all the outcomes
Outcomes= ABCDEF, ABCDEG, ABCDEH, ABCDEI, ABCDEJ, ABCDEK, ABCDEL, ABCDEM, ABCDEN, ABCDEO.....
This method will take a lot of time so, i am going to use the formula
[tex]No.outcomes = \frac{n!}{r!(n-r)!}[/tex]
Here n = total number of items, and r = number of items chosen
Also the '!' means factorial, or the product of all positive numbers less then or equal to the number, so n! = n * (n-1) * (n-2) ..... * 1
So, now substituting the formula
[tex]No.outcomes = \frac{15!}{6! * (n-r)!}[/tex]
[tex]No.outcomes=\frac{15!}{6! * 9!}[/tex]
[tex]No.outcomes = \frac{15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*9*8*7*6*5*4*3*2*1}[/tex]
[tex]No.outcomes=\frac{15*14*13*12*11*10}{6*5*4*3*2*1}[/tex] (cutting same numbers)
[tex]No.outcomes = \frac{7*13*3*11*10}{6}[/tex] (simplifying)
[tex]No.outcomes = \frac{30030}{6}[/tex]
[tex]No.outcomes=5005[/tex]
Therefore, the total number of ways the 6 flowers can be chosen is 5005 ways
Happy to help :)
If u need help in this topic feel free to ask
Related Questions
SOMEONE HELP ME PLEASE
How many people worked in service jobs?
A. 1,898.40
B. 18,984
C. 189,840
D. 1,898,400
E. 18,984,000
Answers
Answer:
number of people work in service jobs
[tex]949 \: 200 \times \frac{20}{100} \\ 189 840[/tex]
answer is option C
Joseph is 5 feet 9 inches tall, and Roberto is
6 feet 4.5 inches tall. What is the difference in
height, in inches, between Roberto and
Joseph?
Answers
Answer:
7.5 inches
Step-by-step explanation:
If he is 5 feet 9 inches tall and Roberto is 6 foot 4.5 inches tall just count the inches until you get to 6"4
Page
1) In which quadrant do the following point lie?
1) (-5,4), (ii)(4,-2) (iii) 7,2) (iv) (-3,-7)
Answers
Answer:
Step-by-step explanation:
(-5,4)=since x coordinate is negative and y coordinate is positive it lies on 2 nd quadrant.
(4,-2)=x coordinate is positive and y coordinate is negative so it lies on 4 th quadrant
(7,2)=both x coordinate and y coordinate are positive so they lie in 1 st quadrant.
(-3,-7) =both x and y coordinate are negative so they lie on 3 nd quadrant
PLLEASEEE HELPPP!!! ILL BRAINLIST.
2) Using Pythagoras’ Theorem, which is the correct statement (A, B or C)
that describes the relationship between the three side lengths in this
triangle? Explain your choice.
A 262 = x2 + 242 B 242 = x2 + 262 C x2 = 242 + 262
Answers
Answer:
The answer is most likely C.
Step-by-step explanation:
Using the Pythagoras' Theorem, c^2 = a^2 + b^2
I'm not sure if 242 and 262 were 24^2 and 26^2 respectively but I'm using 24^2 and 26^2 for this answer.
The c^2 is in fact x^2 where x is the hypotenuse.
However, the answer could be A if x has to be whole number. In this case, x^2 + 24^2 = 26^2
x^2 = 26^2 - 24^2 = 100
x = sqrt (100) = 10
Find the area of each figure
Answers
Answer:
92
Step-by-step explanation:
this figure can be "split" into 3 sub-figures.
one rectangle in the middle, one triangle to the right, and one triangle on top.
these areas we can calculate very easily. and then we simply sum up all 3 of them and we have the answer.
it is clear, the area of a rectangle is length×width.
and the area of triangle is baseline×height/2.
where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.
the rectangle
R = 10×6 = 60
the triangle to the right
T1 = (14-10)×6/2 = 12
the triangle on the top
T2 = 10×(10-6)/2 = 20
so, the total area is
60+12+20 = 92
The area of the given figure is 92.
This figure contained 3 sub-figures.
One rectangle in the middle, one triangle to the right, and one triangle on top.
The area of these areas we can calculate very easily. and then we ad all 3 of them and we have the answer.
What is the area of a rectangle?The area of a rectangle is,
[tex]A=length\times width.[/tex]
What is the area of triangle?The area of triangle is
[tex]A^*= \frac{1}{2} \times base\times height[/tex]
Where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.
The area of rectangle
[tex]R =l\times w \\R=10\times 6 \\R= 60[/tex]
The triangle to the right
[tex]T_1 = (14-10)\times 6/2 = 12[/tex]
The triangle on the top
[tex]T_2 = 10\times (10-6)/2 = 20[/tex]
Therefore, the total area is,
60+12+20 = 92
Therefore the area of the given figure is 92.
To learn more about the area visit:
https://brainly.com/question/3948796
HELP ME PLEASEEE
[WILL GIVE BRAINLIEST TO TOP ANSWER]
Answers
Answer:
C) 157 [tex]cm^3[/tex]
Step-by-step explanation:
[tex](3.14)5^2*6/3= 157[/tex][tex]cm^3[/tex]
Hope this helped! :)
How many degrees are in the angle formed by the hands of the clock?
A, 9
B, 90
C, 180
D, 270
Answers
Answer:
90°
Step-by-step explanation:
15 mins = 1/4 of full circle
1/4 of 360 = 90
90°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
B, 90
Step-by-step explanation:
a right angle is exactly 90 degrees
Which equation gives the sum of infinity sigma 6( 1/3) HURRY PLEASE
Answers
Answer:
3rd option
Step-by-step explanation:
The sum to infinity of a geometric sequence is
S = [tex]\frac{a}{1-r}[/tex]
where a is the first term and r the common ratio
The expression inside the summation is
6 [tex](\frac{1}{3}) ^{n-1}[/tex]
which is in the form of the nth term of a geometric sequence
with a = 6 and r = [tex]\frac{1}{3}[/tex] , then
S = [tex]\frac{6}{1-\frac{1}{3} }[/tex] ← expression required
= [tex]\frac{6}{\frac{2}{3} }[/tex]
= 9
Answer:
C I took the quiz
Step-by-step explanation:
I NEED AN ANSWER ASAP!!!
Answers
whats the sqaure root of 987
Answers
Answer:
31.4
Step-by-step explanation:
Please help I am so confused lol. I’ll mark you the brainiest
Answers
Answer:
Since the pentagon is regular, the line connecting the centre of the circle to the verticles (A,B,C,D,E) should inscribe an equal angle in them
You can see what I mean in the attachment
So to mark other points we follow the following steps
Connect OAWith OA as base, make angle of 72°. Say th new line is OB. Similarly, do for the rest of themThis is a cyclic pentagonStep-by-step explanation:
Hope this helps... Pls vote as brainliest
what is 2-78 please help me
Answers
Answer:
2-78=-76
hope it is helpful to you ☺️
Answer:
[tex]76[/tex]
Step-by-step explanation:
[tex]2 - 78[/tex]
[tex]-76[/tex]
Hope it is helpful....The length of a rectangle is 16 units more than it's with. The area of the rectangle can be expressed as x^4 - 64.
Answers
Answer:
[tex]Width = x^2 - 8[/tex]
Step-by-step explanation:
Given
[tex]L = 16 + W[/tex]
[tex]Area = x^4 - 64[/tex]
Required
An expression for the width
We have:
[tex]Area = x^4 - 64[/tex]
Express as difference of two squares:
[tex]Area = (x^2 + 8)(x^2 - 8)[/tex]
For all acceptable values of x,
[tex]x^2 + 8>x^2 - 8[/tex]
So:
[tex]Length = x^2 + 8[/tex]
[tex]Width = x^2 - 8[/tex]
The height, h metres, of a springboard diver above the surface of the water t seconds after she leaves the board is given by h=-5t-12+7. Find the maximum height reached by the diver? How long does it take for the diver to reach maximum height? Find the height of the diving board?
Answers
Answer:
[tex]h_{max} = 14.2m[/tex]
[tex]t = 1.2[/tex]
The height of the diver is 7m
Step-by-step explanation:
Given
[tex]h(t) =-5t^2 + 12t + 7[/tex]
Solving (a): The maximum height reached
First, we calculate the time to reach the maximum height using:
[tex]t = - \frac{b}{2a}[/tex] --- maximum of a function
Where
[tex]a = -5; b = 12; c = 7[/tex]
So, we have:
[tex]t = -\frac{12}{-2 * 5}[/tex]
[tex]t = \frac{12}{10}[/tex]
[tex]t = 1.2[/tex]
So, the maximum height is:
[tex]h(t) =-5t^2 + 12t + 7[/tex]
[tex]h(1.2)=-5 * 1.2^2 + 12 * 1.2 + 7[/tex]
[tex]h(1.2)=14.2[/tex]
Hence:
[tex]h_{max} = 14.2m[/tex]
Solving (b): Time to reach maximum height
This has been calculated in (a)
[tex]t = 1.2[/tex]
Solving (c): Height of the board.
This can be calculated by setting [tex]t =0[/tex] --- i.e. the height of the diver before diving
So, we have:
[tex]h(t) =-5t^2 + 12t + 7[/tex]
[tex]h(0) = -5 * 0^2 + 12 * 0 + 7[/tex]
[tex]h(0) = 7[/tex]
3. Which number represents 5.33 written
Answers
533/100 then simplify
5 and 33/100
But that isn't an option and none of those options convert into 5.33, and I haven't been able to solve 3.75 repeating yet nor think it would convert into 5.33 anyhow. Please correct me if I'm solving this wrong.
Helppppppppppppppppppp I’ll mark you brainlist don’t respond if you’re going to put something random I will report you :)
Answers
Answer:
y would be 3
Step-by-step explanation:
x would be 0 since the line goes up, meaning it's positive, not negative btw
IMA In a certain Algebra 2 class of 23 students, 7 of them play basketball and 12 of them play baseball. There are 9 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball
Answers
Answer:
19/28 or about 68%
Step-by-step explanation:
7 + 12 + 9 = 28
7 + 12/28
19/28
Solve for x: 1.5x - 8 = 7
PLS ANSWER
Answers
Answer:
x = 10Step-by-step explanation:
1.5x - 8 = 7
=> 1.5x = 7 + 8
=> 1.5x = 15
[tex] = > \frac{15x}{10} = 15[/tex]
[tex] = > x = 15 \times \frac{10}{15} [/tex]
=> x = 10 (Ans)
Answer:
x=10
Step-by-step explanation:
Simplifying
1.5x + -8 = 7
Reorder the terms:
-8 + 1.5x = 7
Solving
-8 + 1.5x = 7
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '8' to each side of the equation.
-8 + 8 + 1.5x = 7 + 8
Combine like terms: -8 + 8 = 0
0 + 1.5x = 7 + 8
1.5x = 7 + 8
Combine like terms: 7 + 8 = 15
1.5x = 15
Divide each side by '1.5'.
x = 10
Simplifying
x = 10
Help
Will give
Brainlist
:))).
Answers
thanks me later, pa brainliest po ako
Can someone help me please
Answers
Answer:
Here you go
Step-by-step explanation:
BTW what is meant by point in the last blank?
Answer:
equation y = 3x-1
slope = 3
about the point blank I'm not sure what it is asking for
Which of the following ordered pair are equal. a) (6,2) and (2,6)
Answers
Does anyone know this ?
Answers
116 / 2 = 58 :)
Check: 58 + 58 + 64 = 180
Conrad borrowed $5 400 for a second-hand ATV
If his loan was over the course of 3 years at 17.6% compounded quarterly, how much money will he have to repay to cover his loan?
Select one:
a. $9 129.76
O b. $8793.85
O C. $9 226,64
O d. $9053.15
e. $8 903.41
Answers
Answer:
The answer is D
Sketch a graph of
y=3(x − 2)(x + 1) (x – 4)
ASAPP!
Answers
Answer:
Use the distributive property to multiply 3 by x−2.
y=(3x−6)(x+1)(x−4)
Use the distributive property to multiply 3x−6 by x+1 and combine like terms. y=(3x 2 −3x−6)(x−4)
Use the distributive property to multiply 3x 2 −3x−6 by x−4 and combine like terms. y =3x 3 −15x 2 +6x+24
Step-by-step explanation:
I also up a link there of a graph. Please tell me if you can open it. Hope this helps! :P
Find the midpoint of the segment with endpoints:
(9,8) and (3,5).
pls pls pls pls help!!!! for geometry final
Answers
Answer:
Step-by-step explanation:
here x1=9 y1=8 x2=3 y2=5
midpoint=(x2+x1/2 , y2+y1/2)
=(3+9/2 , 5+8/2)
=(12/2 , 13/2)
=(6 , 13/2)
I need help ill give you 15 points. no links or I will like report you.
Answers
all real numbers are greater than or equal to 2
( 2+ 3y)(2-3Y) pls help meeeeeeeeee
Answers
Answer:
4-9y^2
Step-by-step explanation:
(2+3y)(2-3y)
2*2
2*-3y
3y*2
3y*-3y
4-6y+6y-9y^2
4-9y^2
Answer:
[tex]4−9 {y}^{2} [/tex]
Step-by-step explanation:
[tex](2+3y)(2−3y)[/tex]
[tex]2(2−3y)+3y(2−3y)[/tex]
[tex]2 \times 2+2(−3y)+3y(2−3y)[/tex]
[tex]2 \times 2+2(−3y)+3y \times 2+3y(−3y)[/tex]
[tex]4−6y+6y−9 {y}^{2} [/tex]
[tex]4+0−9 {y}^{2} [/tex]
[tex]4−9 {y}^{2} [/tex]
Hope it is helpful...can someone please identify one solution please?
Answers
y ≥ 2x - 3
Jacob travelled 708 km on a bus in 8 hours. Alissa travelled 496 km on a
train in 5 hours. What was the speed per hour of the faster vehicle?*
99.2 km/h
62.0 km/h
141.6 km/h
88.5 km/h
Answers
Answer:99.2
Step-by-step explanation:
Speed = distance÷time
496÷5=99.2
What is it called in cubic inch of a cylinder with a height of 4in and a base radius of 5in to the nearest tenths place?
Answers
Answer:
1,256.8in
Step-by-step explanation:
Given data
Height h =4in
Radius r= 5in
The expression for the volume of cylinder is
V=πr²h
Substitute
V=3.142*4²*5
V=3.142 *16*25
V=1,256.8in³