The solution is Option C.
The number of ways 3 positions can be filled by the 12 students is given by combinations where ¹²C₃ = ( 12 x 11 x 10 ) / 3 x 2 x 1
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students n = 12 students
The number of positions in the council x = 3 positions
So , the number of ways the 3 positions can be filled by 12 students is calculated by combinations
where n = 12 and x = 3
ⁿCₓ = n! / ( ( n - x )! x! )
Substituting the values in the equation , we get
¹²C₃ = ( 12! / ( 12 - 3 )! 3! )
On simplifying the equation , we get
¹²C₃ = ( 12! / 9! 3! )
And ,
¹²C₃ = ( 12 x 11 x 10 x 9! / 9! 3! )
¹²C₃ = ( 12 x 11 x 10 ) / 3!
¹²C₃ = ( 12 x 11 x 10 / 3 x 2 x 1 )
¹²C₃ = 220 ways
Hence , the number of ways the 3 positions can be filled by the 12 students is 220 ways
To learn more about combinations click :
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which is cube number
Answer:
??????
Step-by-step explanation:
Answer:
2³ = 2 × 2 × 2 = 8.
3³ = 3 × 3 × 3 = 27.
4³ = 4 × 4 × 4 = 64.
5³ = 5 × 5 × 5 =125.
Step-by-step explanation:
A polynomial function has a root of 6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2
and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which
statement about the graph is true?
The graph of the function is positive on (-6, -2).
The graph of the function is negative on (-00, 0).
The graph of the function is positive on (-2, 4).
The graph of the function is negative on (4,00).
Answer:
Step-by-step explanation:
This graph is a monster. No one should solve it by hand. Desmos drew the one below. The way the graph looks, I would say it is negative at (4,0)
The first choice isn't a point on the graph.
(0,0) goes both ways.
(-2,4) is positive.
A tree casts a shadow 72 feet long. At the same time, a man who is 6 feet tall casts a shadow 8 feet long. What is the height of the tree? *
QUICK PLS
Answer: 54 feet.
Step-by-step explanation:
Ratio between a tree's height and its shadow's length = x : 72ft
Ratio between man's height and his shadow's length = 6ft : 8ft = 3 : 4
In order to solve this problem, we have to cross multiply the two ratios (image)
So, 4x = 216.
By solving this equation we learn that x = 54ft
So, the tree is 54 feet tall.
I am not a professional, simply using prior knowledge.
Note- It would mean the world to me if you could mark me brainliest!
Can ya’ll help mee?? Thnksss❤️
The san andreas fault began to form approximately 25 million years ago. during that 25 million year period the fault has grown to be 2,600 km in length. On average, how much has the fault grown per year over 25 million years?
Plss give the solution for me to study... thnkss❤️
Answer:
.000104 km per year or .104 m per year
Step-by-step explanation:
divide 2600 by 25 million
A teacher gives her class a particular examination on mathematics at the end of each year. The results are normally distributed with a mean test score of 60 and a standard deviation of 8. The teacher has told the class that students with a test score in the top 2.5% will win a special prize. Calculate the test score above which 2.5% of all test scores lie. Give your answer to 1 decimal place. Test score
Answer:
Test score of 75.7.
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The results are normally distributed with a mean test score of 60 and a standard deviation of 8.
This means that [tex]\mu = 60, \sigma = 8[/tex]
Calculate the test score above which 2.5% of all test scores lie.
Above the 100 - 2.5 = 97.5th percentile, which is the value of X when Z has a pvalue of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 60}{8}[/tex]
[tex]X - 60 = 8*1.96[/tex]
[tex]X = 75.7[/tex]
Test score of 75.7.
so I don't know what 5*7 is because it confusing
Answer:
35/16
Explanation:
(5*7)/2^4
= 35/2^4
= 35/16
Note:
Please mark as brainliest! <3
Help me with this please 100 points if its done right
Answer:
[tex]P=24\sqrt{x}[/tex] and [tex]A=36x[/tex]
Step-by-step explanation:
To find the perimeter of the triangle, you have to add all the sides of the triangle. So, we get:
[tex]P=8\sqrt{x} +7\sqrt{x} +9\sqrt{x}[/tex]
Combine like terms, meaning the numbers with [tex]\sqrt{x}[/tex]
[tex]P=24\sqrt{x}[/tex]
To find the area of the triangle, we will use the formula [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height
The base is: [tex]9\sqrt{x}[/tex]
The height is: [tex]8\sqrt{x}[/tex]
Plug and chug:
[tex]A=\frac{1}{2} *9\sqrt{x} *8\sqrt{x}[/tex]
[tex]A=\frac{1}{2} *72x\\A=36x[/tex]
KEVIN USES EACH OF THE DIDGETS 5,7,4 AND 9, ONCE AND ONCE ONLY. TO MAKE FOUR DIDGET NUMBERS. WHATS THE LARGEST AND SMALLEST NUMBER HE CAN MAKE?
Answer:
9754 and 5794
Step-by-step explanation:
Answer:
Largest - 9,754
Smallest - 4,579
Step-by-step explanation:
Mike spent 11/12 hour talking on his cell phone. Brent spent 7/12 hour talking on his cell phone. How much more time did mike spend on his cell phone than Brent?
Write in the simplest form. Be sure to put your answer as well as the unit (hour).
Answer:
1/3
Step-by-step explanation:
If a guy named josh got 45 bucks for his b-day and already had 237 bucks. How much money does josh have all together.
Will give brainly!!!!!!
Answer:
That’s easy it is 282
Step-by-step explanation:
He will now have 282 bucks altogether.
Step-by-step explanation:
We already know that he has 237 bucks before his birthday, but now he has an additional 45 bucks that he got from his birthday. With this, you can create an equation that looks like this: 237+45. You then solve the equation by adding 45 to 237, which gets you 282 bucks altogether.
remi and vishal start at the same point and begin jogging in different directions. remi is jogging east at a speed of 4 miles per hour. vishal is jogging South at a speed of 2 miles per hour. after how many hours will they be exactly 12 miles apart
Answer:
2.68 hours
Step-by-step explanation:
piete)
Decide whether the following statement makes sense or does not make sense. Explain your reasoning.
I drove at a speed of 35 miles for the entire trip.
Answer:
It doesn't make sense
Step-by-step explanation:
Given
Statement: .... at a speed of 35 miles .....
Required
Does it make sense?
In motion, speed is measured in km/h, m/s, miles per hour (depending on context) while distance is measured in km, m or miles.
However, the given statement mention the unit of speed to be miles which is incorrect.
Hence, we can conclude that the statement does not make sense.
A correct statement would be: I drove at a speed of 35 miles per hour .......
Given that R = 6x + 9y
Find y when X = 1 and R= 39
Give your answer as an improper fraction in its simplest form.
y=
Answer:
11/3
Step-by-step explanation:
x=1, R=39, y=?
R=6x + 9y
(substitute the parameters into the equation)
39=6(1) + 9y
39= 6 + 9y
(collect like terms)
39 - 6 =9y
33=9y
(divide both sides by 9)
33/9=9y/9
11/3=y
therefore, y= 11/3
WILL MARK BRAINLIEST AND EXTRA POINTS ONLY HAVE 5 MINS
Answer:
1/3?
Step-by-step explanation:
A line has a slope of 2. It passes through the points, (1,2) and (3,y) . what is the value of y?
Answer:
y=6
Step-by-step explanation:
y=mx+b
y=2x+0
the y-intercept is at the origin so going off that when you go to put your line on a graph you come off with the points (0,0) (1,2) (2,4) and finally your answer (3,6)
Find x so that a is parallel to b. state the converse used
Answer:
x = 7
If a is parallel to b, then 9(7) + 11 = 74.
Step-by-step explanation:
We don't know if the lines are parallel, so we need to see what x is in 9x + 11 = 74, then substitute that value for x in the equation. If both sides are true, the two lines are parallel.
9x + 11 = 74
Step 1: Subtract 11 from both sides.
9x = 63
Step 2: Divide both sides by 9.
x = 7
To make sure, let's substitute 7 for x in the earlier equation.
9(7) + 11 = 74
Step 3: Multiply 9 by 7 to get 63.
63 + 11 = 74
Step 4: Add 11 to 63 to get 74.
74 = 74
The two sides are equal, so a and b are parallel. The definition of a converse is the reverse of a conditional statement. As a result, the converse here is "If a is parallel to b, then 9(7) + 11 = 74."
What is the equation of the function that is graphed as line b?
Answer:
I feel like this is a trick question
----
Find angle picture below
Answer:
T = 67.5
V = 22.5
Step-by-step explanation:
The Sum of triangle angles = 180
180 = W + T + V
180 = 90 + 3X + X
X = 22.5
What is the slope OF THE GRAPH.
Answer:
The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x.
I hope it's helpful!
2x + 3 – 4 = 5x - 7
2
-2
- 9
9
2x + 3 - 4 = 5x - 7
=> 2x + 3 - 4 + 7 = 5x
=> 3 - 4 + 7 = 5x - 2x
=> 3 - 4 + 7 = 3x
=> -1 + 7 = 3x
=> 6 = 3x
=> 6/3 = x
=> 2 = x
Step-by-step explanation:
2x + 3 - 4 = 5x - 7 2x - 1 = 5x - 7 (-1 + 7 )= 5x - 2x6 = 3x 6 ÷ 3 = x2 = xMARK ME AS BRAINLISTpls helppppppppppppppppppppp
Answer:
10 2/3
Step-by-step explanation:
Multiply 4 and 2 and then multiply 2 and 4. If you do that then you get 8 8/3. You then just take the numerator and turn it into whole numbers to get 10 2/3.
find the measures of the interior angles 49 degrees
Answer:
x+49+90=180sum of interior angle of triangle
x=180-139=41 is your answer
Make x the subject of the formula a = b x + c
Answer:
[tex] x = \frac{a - c}{b}[/tex]
Step-by-step explanation:
[tex]a = bx + c \\ \\ a - c = bx \\ \\ \orange{ \bold{x = \frac{a - c}{b}}} [/tex]
I need help. This is due tonight at 11:59 pm
Answer:
Answer: $118.50 per day
Step-by-step explanation:
1,000-348.25= 651.75
651.75÷5.5= 118.50
Please help ASAP. Thanks so much
Answer:
A. -3,-8
Step-by-step explanation:
That's the answer positive
A map has a scale of 1/2 inches=16 miles the distance between two parks on the map is 2 3/4 inches how many miles apart are the parks
Answer:
88
Step-by-step explanation:
Find the value of x
PLEASE HELP!!
Answer:
x =45
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
3x+45 = 180
Subtract 45 from each side
3x+45-45 =180-45
3x= 135
Divide by 3
3x/3 = 145/3
x =45
Which of the following is a solution to the inequality below?
10b≤ 59
A.) b=2
B.) b=7
C.) b=11
D.) b=9
Answer:
A.) b=2
Step-by-step explanation:
10b ≤ 59
Divide both sides by 10.
b ≤ 5.9
Any number that is 5.9 or less than 5.9 is a solution.
The only such number in the choices is 2.
Answer: A.) b=2
For f(x) = 2x+1 and g(x) = x2 – 7, find (f/g)(x)
Step-by-step explanation:
Since f(x) is "2x + 1" and g(x) is "x2 - 7" then f(x) + g(x) [which is the same as (f + g)(x)] is "2x + 1" + "x2 - 7" which is 2x + 1 + x2 - 7 or x2 + 2x - 6
So (f + g)(x) = x2 + 2x - 6
is it right? i hope it is
b is 30 more than a. b is 6 times as many as a. Find the values of a and b.
Answer:
a = 6 and b = 36
Step-by-step explanation:
Set up equations:
b = 30 + a
b = 6a
Subtract the two equations:
b = 6a
- (b = 30 + a)
5a - 30 = 0
5a = 30
divide both sides by 5
a = 6
Plug a = 6 into the original equation:
b = 30 + 6
b = 36
you could also do:
b = 6 * 6
b = 36
Answer:
Step-by-step explanation:
