Using the permutation formula, it is found that the people can be chosen for the roles in 6840 ways.
The order in which the people are chosen is important, as there are different roles, hence the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 people will be chosen from a set of 20 people, hence the number of ways is given by:
[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]
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what is the solution to this equation ?
4(4x+1) = 3x - 4(6 - x) + 8
A. x = - 12/9
B. x = - 20/23
C. x = - 20/9
D. x = - 12/23
Answer:
x = -20/9
Step-by-step explanation:
First we need to distribute this equation 4(4x+1) = 3x-4(6-x)+8. After distributing we get 16x+4 = 3x-24+4x+8. Next we add like terms to get 16x+4 = 7x-16. Now subtract 7x on both sides to get 9x+4 = -16. Now subtract -4 on both sides to get 9x = -20. Now divide by 9 on both sides to get x= -20/9.
Hope that helps! :)
Given that 1 ton is equal to 2,000 pounds, how many pounds does 5.9 tons equal?
59,000 pounds
11,800 pounds
1,180 pounds
5,900 pounds
Answer:
11,800 lb
Step-by-step explanation:
dnt worry i got my wayz :)
Answer:
11,800 lbs
Step-by-step explanation:
5.9x2,000=11,800
Question 1
What is the length of the diagonal from A to C of this rectangle? Round your answer to
the nearest tenth to a metre
Will mark Brainest!!
Answer: 17.2
Step-by-step explanation:
By the Pythagorean theorem,
[tex]10^{2}+14^{2}=(AC)^{2}\\\\(AC)^{2}=296\\\\AC=\sqrt{296} \approx \boxed{17.2}[/tex]
catergorize the graph as linear decreasing, linear increasing, exponential growth or exponetnial decay
i cant help you with that bc there is no graph so...
Timmy has forty-five cents in his pocket. How many different ways can he have forty-five cents in change using only quarters, dimes, and nickels?
Answer:
Hi,
number of ways: 8
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|}Quater&dime&nickel\\------&---&---\\0&0&9\\0&1&7\\0&2&5\\0&3&3\\0&4&1\\1&0&4\\1&1&2\\1&2&0\\------&---&---\\\end{array}[/tex]
5x+5y=0
-8x+y=36
I need help with this.
Answer:
x= -4, y = 4.
Step-by-step explanation:
first, divide the first equation by its G.C.D (5), to obtain its simplest form.
5x/5 + 5y/5 = 0/5 to obtain x + y = 0.
Then, find the value of y by rearranging the second equation.
y = 36 + 8x. (Rem; when 8x moves to the other side of the equation, it changes the sign)
Now substitute the value of y (36 + 8x) in the first equation which is x + y = 0.
x + 36+8x = 0
Put like terms together.
36 + 9x = 0
move 9x to the other side and change its sign.
36 = -9x
divide both sides by 9,
x = -4.
Lastly, find the value of y by replacing the value of x in either equation.
-8(-4) + y = 36
32 + y = 36
rearrange to obtain
y = 36 - 32
y = 4.
A mother and daughter decided to add their ages together. The sum of their ages is 76. Six years ago, the mother was 3 times the age of her daughter. How old is the daughter now?
Answer: The answer will be 19
Answer: 23 years old
Step-by-step explanation:
the applicants for a soccer coaching position were asked how many years of coaching experience they had. here are the resuts 1,2,2,2,2,4,4,5,5,6,8,8,8,10
Answer:
Mean: 4.7
Mode: 2
Median: 4.5
Step-by-step explanation:
1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
1712 is a odd or even number
10 POINTS, please explain your answer ik so confused about how to get surface areas ty lol
Step-by-step explanation:
since there is triangle , you use the formula
1/2 × b × h
as you can see the base is 6 and the height is 4, so
1/2 × b × h
= 1/2 × 6 × 4
=12
12 × 2 = 24 , you times by 2 because there is 2 triangle
There is also rectangle in the diagram, so you use the formula , length × breadth , the length is 8 and the breadth is 5, so
length x breath
= 5 × 8
=35
35 × 2 = 70 , times by 2 because you can see 2 rectangles with the same length and breadth
length x breath
= 8 × 6
= 48
this one is different because the length is 8 and the breadth is 6.
SA = 48 + 35 + 24
= 107 cm ²
Sorry for my bad eng ,its not my first language.
can you help me please?
prolly 4.36 just use the Pythagorean theorem
2(z + 5) + 5(z + 2) = 10 (z - 1)
Answer:
z = 10
Step-by-step explanation:
simplify to
2z + 10 + 5z + 10 = 10z-10
2+5z-10z=-10-10-10
-3z = -30
z = 10
give brainiest please!
hope this helps :)
Answer:
z = 10
Step-by-step explanation:
Distribute:
(2z + 5) + 5(z + 2) = 10(z - 1)
2z + 10 + 5(z + 2) = 10(z - 1)
and distribute again:
2z + 10 + 5(z + 2) = 10(z - 1)
2z + 10 + 5z +10 = 10(z - 1)
and add the 2 tens that are in bold.
2z + 10 + 5z +10 = 10(z - 1)
2x + 20 + 5z = 10(z-1)
Theres a lot more steps but just
comebine like terms
Distribute
Stubtract 20 from both sides
simplify
subtract 10z from both sides
simplfy
divide both sides by the same factor
and simplfy.
Segment Given: BA= BC and DA= EC
Proofs
Prove: BD BE
Statements
BA BC 3 DA FC. Given
BDE BE
A
Reasons
Answer:
Step-by-step explanation:
[tex]1) \overline{BA} \cong \overline{BC}, \overline{DA} \cong \overline{EC} \text{ (given)}\\2) \overline{BD} \cong \overline{BE}[/tex] (congruent segments subtracted from congruent segments form congruent segments)
1.)which of the following is the formula to find the volume of rectangular prism?
A. V =lwh
B. V = lw
C. 1/3(Bh)
D. 1/2(Bh)
2.)the volume of a cone is _____ the volume of a cylinder with the same base area (B) and height (h).
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Answer:
First answer:
A
Second answer:
I think A
Answer:
A and B
Step-by-step explanation:
1
the volume (V) of a rectangular prism is calculated as
V = lwh ( l is length, w is width, h is the height )
= Bh ( B is the area of the base )
2
the volume of a cone is [tex]\frac{1}{3}[/tex] the volume of a cylinder with the same base area (B) and height (h)
Which is the correct answer ?
Answer: D
Step-by-step explanation:
As the measure of the 75 degree angle is less than the measure of the 80 degree angle, rule out RS.
Also, the two triangles with the 80 degree angle are congruent, so PQ=QR.
This leavesc us with SP
There are 18 students on the debate club. How many ways can the club send 4 students to the next debate
There are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have the total number of students = 18
The number of ways the club send 4 students to the next debate is:
= C(18, 4)
[tex]= \rm \dfrac{18!}{4!(18-4)!}[/tex]
= 3060
Thus, there are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
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PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS
Answer:
scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]
Find the area of the following sector. Round your answer to the nearest tenth.
The area of the sector is 188.9 km².
What is a sector?A sector is a plane figure enclosed by two radii and an arc between them.
To calculate the area of the sector, we use the formula below.
Formula:
A = ∅πr²/360................. Equation 1Where:
A = Area of a sectorr = Radius of the circle∅ = The angle sustained by the sector at the center of the circleFrom the diagram,
Given:
r = 19 km∅ = 60°π = 3.14Substitute these values into equation 1
A = 60×3.14×19²/360A = 188.9 km²Hence, the area of the sector is 188.9 km².
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Katrina lives directly east of the park. The football field is directly south of the park. The
library sits on the line formed between Katrina's home and the football field at the exact point
where an altitude to the right triangle formed by her home, the park, and the football field
could be drawn. The library is 4 miles from her home. The football field is 18 miles from the
The distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.
What is Similar Triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Here, mark the park as A, Home as B, Library as C and field as D.
Now, CD = 18 miles
BC = 4 miles
we have to find AC (distance between library and park)
BD = BC + CD = 18 + 4 = 22 miles
Using property of similar triangles,
AD² = BD X CD
AD² = 22 X 18
AD = √22 X √18
AD = 6√11 miles
By Pythagoras theorem,
AD² = AC² + CD²
396 = AC² + 324
AC² = 396 - 324
AC² = 72
AC = √72
AC = 6√2 miles
Thus, the distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.
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PLEASE HELP!!! EOC REVIEW!
From his eye, which stands 1.52 meters above the ground, Wyatt measures the angle of elevation to the top of a prominent skyscraper to be 28 degrees. If he is standing at a horizontal distance of 331 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
The height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper.
What is Trigonometric Ratio?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, h₀ = 1.52 m, angle of elevation = 28⁰
d = 331 m
Now, tan 28⁰ = h/d
h = d. tan 28⁰
h = 331 X 0.5317
h = 175.99 m
Total height = h + h₀
= 175.99 + 1.52
= 177.51 m
Thus, the height of the skyscraper is 177.51 m which is 331 m from the base of skyscraper..
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Answer:
Step-by-step explanation:
The answer is 177.5 dont add the .1
Find the number of terms in the sequence.
-3, -3, -9, -15, ...,-9
Answer:
6
Step-by-step explanation:
I use the information I from my Nathan teacher
quadrilateral PQRS is transformed to create quadrilateral P’Q’R’S
Answer:
D
Step-by-step explanation:
Reflection over the X-axis
All point passes, (x,-y)
Answer:
D.
Step-by-step explanation:
Reflection over the x-axis because the quadrilateral reflected.
PLEASE HELP! 50 POINTS! IF YOURE NOT GOING TO ACTUALLY ANSWER, PLEASE DON'T SAY ANYTHING.
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
Could someone explain how to do this question?
Answer:
[tex]p\left( A|B\right) =0[/tex]
Step-by-step explanation:
Formula:
[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]
The only prime outcome is 3
Then
The set A = {3}
1 and 2 are the divisors of 2
Then
The set B = {1 , 2}
Therefore , p(A∩B) = 0
Also p(B) = 0.4+0.1 = 0.5
[tex]\Longrightarrow p\left( A|B\right) =\frac{0 }{0.5 }=0[/tex]
Brett draws the shape shown below.
He says the shape can be classified as a quadrilateral, parallelogram, rhombus, and square.
Is Brett correct? Explain.
The given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
What is a square?A square is a quadrilateral with all the sides equal and all the four sides are perpendicular to each other.
We know that it is a quadrilateral as a quadrilateral is having four sides and the sum of the angles is 180 degrees.
The given figure is a parallelogram as opposite sides of the figure are parallel and equal.
The given figure is a rhombus as all the sides are parallel and equal.
The given figure can not be a square as in the square all the four sides are perpendicular to each other.
Therefore given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
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What is 4:3 in the form of 1:n
Answer: 1:0.75
Step-by-step explanation:
Ratio 4 to 3 = 4:3
Simplified Ratio 4.00:3.00
Ratio in Form 1:n 1:0.75
Ratio in Form n:1 1.33:1
Joey wants to buy a gym membership. He visits two gyms with two different fees. Gym A has a $40
sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month. How
many months will he have to belong to each before the costs are the same?
Answer:
2 months
Explanation:
50 - 40 = 10
25-20 = 5
10/5 = 2
The months for which Joey have to belong to each before the costs are the same are 2 months.
What is equation modelling?
Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.
Given is different fees structure of two gyms → Gym A has a $40 sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month.
Assume that the months for which Joey have to belong to each before the costs are the same be x.
Then -
For Gym A -
Total cost for x months = C[A] = 25x + 40
For Gym B -
Total cost for x months = C[B] = 20x + 50
For same cost -
C[A] = C[B]
25x + 40 = 20x + 50
25x - 20x = 50 - 40
5x = 10
x = 2
Therefore, the months for which Joey have to belong to each before the costs are the same are 2 months.
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Classify the following triangle. Check all that apply.
Answer:
The answer to the question is F
Step-by-step explanation:
Why it is an Scalene Triangle ,it because all the sides and angle are not equal