Using the combination formula, it is found that there are 99768240 ways in which they can travel.
The passenger seat positions are not important, which means that the order is not important, which is why the combination formula is used.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
In the first car, 7 of the 20 friends are going to sit.In the second, 5 of the remaining 13 are going to sit.In the bus, the remaining 8.The, the number of ways is given by:
[tex]N = C_{20,7}C_{13,5}C_{8,8}[/tex]
[tex]N = \frac{20!}{7!13!} \times \frac{13!}{5!8!} \times \frac{8!}{0!8!} = 99768240[/tex]
There are 99768240 ways in which they can travel.
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1. :4
32+4 x (16 x 2)-2-
37:
---
Answer
Step-by-step explanation:
mulitiply the numbers
add the numbers
rearrange the numbers
find the slope of the graph
Answer:
No image please add it on your next question.
Find the area of the shape, there are 6 sides
Answer:
Step-by-step explanation:
all the three sides of a triangle are equal.
length of perpendicular from center on the side=[tex]h=\sqrt{21^2-(\frac{21}{2})^2} =\frac{21}{2}\sqrt{3} \\area ~of~shape=6 \times \frac{1}{2} \times 21 \times \frac{21}{2}\sqrt{3} \\=\frac{1321}{2}\sqrt{3} ~sq. ~ft.[/tex]
FIRST CORRECT ANSWER GETS BRANLIEST PLEASE HELP!!!! PHOTO ABOVE
Answer:
Step-by-step explanation:
The Pythagorean theorem is that (for right triangles)
a^2+b^2=c
Meaning c is the side opposite the right angle
Hope this helps!
Which of the following correctly gives the center and radius of the circle defined by the equation (x - 7)2 + (x - 2)2 = 10? A. Center: (7, 2); Radius = 100 B. Center: (7, 2); Radius = 10 C. Center: (-7, -2); Radius = 100 D. Center: (-7, -2); Radius = 10
Answer:
Center (7,2) and radius = 10
Step-by-step explanation:
Generally, we have the equation of a circle as follows;
(x-a)^2 + (y-b)^2 = r^2
where (a,b) represents the circle center and r represents the radius of the circle
Looking at the given equation of a circle, we have it that the center is (7,2) while the radius of the circle is 10
Help.me please!!!!!!
Answer:
5 seconds
Step-by-step explanation:
need help will give brainliest
Answer:
40.56
Step-by-step explanation:
2pir
8÷2=r=4
2pi4=25.13
25.13÷2=12.565
10+10+8+12.56=40.565
Equivalent expression of 5g +7g
Answer:
12g
Step-by-step explanation:
[tex]5g+7g=12g[/tex]
Answer:
12g
Step-by-step explanation:
5g+7g = 12g
have a great day
My grandmother’s cookie recipe uses 4 cups of sugar to make 35 cookies. My Uncle’s cookie recipe uses 3 cups of sugar to make 28 cookies. Whose cookies are sweeter?
Grandma's
Uncle's
Answer:
uncle's cookies
Step-by-step explanation:
Answer:
I think ur answer would be uncle cookies
Step-by-step explanation:
srry if wrong
hope this helps!
Choose the right one
Answer:
g(x) = 8x
Step-by-step explanation:
cause of IXL
Of the players on a bowling team7/10 or 7 won trophies. Explain how you can find the number of players on the team.?
Answer:
10players
Step-by-step explanation:
Using the concept of probability
probability = expected outcome/total outcome
Total outcome s the numbers of players on the team
Given
Total number of trophy won = 7 (expected)
Fraction of those that won = 7/10 (probability)
Substitute
7/10 = 7/total outcome
1/10 = 1/total outcome
Reciprocate both sides
10/1 = total outcome
Swap
Total outcome = 10
Hence the number of players on the team is 10players
which equation represents that relationship ??
Answer:
A
Step-by-step explanation:
A proportional relationship either increases or decreases its points at the same rate. In the first set of ordered pairs, the x values all increase by 3 while the y values all increase by 6, which is twice the value of the x values' increasing. The second set of ordered pairs is not proportional because all pairs' x values increase by 2 while the y values increase by 8 until ordered pair (5, 20), so this set therefore is non-proportional. y = x + 3 is the correct equation because it represents that the y value is always 3 greater than the x value. All the shown ordered pairs for set 1 supports this (3 - 0 = 3, 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3).
How many solutions can be found for the equation 3z + 2[z - 3) = 7z+12
3z + 2(z - 3) = 7z + 12
Solution :-3z + 2(z - 3) = 7z + 12
3z + 2z - 6 = 7z + 12
3z + 2z - 7z = 12 + 6
5z - 7z = 18
-2z = 18
z = 18/2
z = 9
[tex] \\ [/tex]
Answered by - ItzAdmire
3z + 2(z - 3) = 7z + 12
Solution :-3z + 2(z - 3) = 7z + 12
3z + 2z - 6 = 7z + 12
3z + 2z - 7z = 12 + 6
5z - 7z = 18
-2z = 18
z = 18/2
z = 9
[tex] \\ [/tex]
Answered by - ItzMaster
Find f-1(x) if f(x) = 2x/3-4
Given:
The function is:
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
To find:
The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{2x}{3}-4[/tex]
Step 1: Substitute [tex]f(x)=y[/tex].
[tex]y=\dfrac{2x}{3}-4[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{2y}{3}-4[/tex]
Step 3: Isolate y.
[tex]x+4=\dfrac{2y}{3}[/tex]
[tex]3(x+4)=2y[/tex]
[tex]\dfrac{3x+12}{2}=y[/tex]
[tex]\dfrac{3}{2}x+6=y[/tex]
Step 4: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]
Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].
y is directly proportional to x^3
y = 17
when
x = 4
Work out an equation connecting y and x.
Answer:
[tex] 64y = 17 {x}^{3} [/tex]
Step-by-step explanation:
[tex]y \: \alpha \: {x}^{3} ....(given) \\ \therefore \: y = k {x}^{3} .. (1)\\ (k =arbitrary \:constant) \\when \: x = 4, \: \: y = 17, \:k =? \\ 17 = k {(4)}^{3} \\ 17 = 64k \\ k = \frac{17}{64} \\ plug \: k =\frac{17}{64} \: in \: equation \: (1) \\ y = \frac{17}{64} {x}^{3} \\ 64y = 17 {x}^{3} [/tex]
The correct equation connecting y and x is,
⇒ y = 17/64x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
⇒ y is directly proportional to x³
Hence, We get;
⇒ y = kx³
Here, y 17 at x = 4;
Hence,
⇒ 17 = k × 4³
⇒ k = 17 / 64
Thus, The correct equation connecting y and x is,
⇒ y = 17/64x
Learn more about the mathematical expression visit:
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I need helppppppppppppp please
Answer:
I want to say A)
Step-by-step explanation:
GODD SOMEONE HELP ME RIGHT NOW PLEASE THIS IS DUE TODAY AND I AM DUM I GIVE POINTS AND BRAINLIEST JUST HELP MEEE
Answer:
-5 and -6
Step-by-step explanation:
For trinomial factoring, you need two numbers that add up to get the -11x and two numbers that multiply to get 30.
-5 + (-6) = -11
-5 × -6 = 30
Help me please and if you do, I will add you and give you brainliest
Answer: B
Step-by-step explanation:
Please help quick! I’ll give brainluilyst just please help me
How do you break apart the factor 627 using place value?
Answer:
6 hundreds
2 tens
7 ones
Step-by-step explanation:
Un albañil construye una casa en 5 días si debe construir 3 casas cuántos días se demorará
AABChas coordinates A (-4,-2), B(0,4), and C(4,-2). Find the midpoint of AC.
Answer:
( 0, - 2 )
Step-by-step explanation:
Mid point formula : -
( x1 + x2 ) / 2, ( y1 + y2 ) / 2
Here,
Let ( x1, y1 ) = ( - 4, - 2 )
Therefore,
x1 = - 4
y1 = - 2
Let ( x2, y2 ) = ( 4, -2 )
Therefore,
x2 = 4
y2 = - 2
Midpoint of AC
= ( - 4 + 4 ) / 2, ( - 2 - 2 ) / 2
= ( 0 / 2, - 4 / 2 )
= ( 0, - 2 )
The midpoint of AC is ( 0, - 2 ) when coordinates of A (-4,-2), B(0,4), and C(4,-2) is given.
What is the Midpoint of a Line?
The midpoint of a line is a point that is equidistant from the endpoints of the line and in the middle of the line. If the endpoints of the line are (x)1, (y)1, and (x)2, (y)2, then the formula for the midpoint of the line is {[(x)1 + (x)2]/2, [(y)1 + (y)2]/2}.
Mid point formula is given as : -
( x1 + x2 ) / 2, ( y1 + y2 ) / 2
Here,
Let ( x1, y1 ) = ( - 4, - 2 )
x1 = - 4
y1 = - 2
Let ( x2, y2 ) = ( 4, -2 )
x2 = 4
y2 = - 2
now using Midpoint formula to find the coordinates of AC
= ( - 4 + 4 ) / 2, ( - 2 - 2 ) / 2
= ( 0 / 2, - 4 / 2 )
= ( 0, - 2 )
Therefore, the midpoint of AC is ( 0, - 2 )
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The hot tub is shaped like a rectangular prism. It is 7 feet long, 3 1/4 feet deep, and has a volume of 159 1/4 cubic feet. What is the width of the hot tub?
Answer:
w = 7 feet
Step-by-step explanation:
Volume of a rectangle prism = length × width × height
Length = 7 feet
Width = ?
Height = 3 1/4 feet
Volume = 159 1/4 cubic feet
Volume of a rectangle prism = length × width × height
159 1/4 = 7 × w × 3 1/4
637/4 = 7 × w × 13/4
637/4 = 7 × 13/4 × w
637/4 = 91/4w
w = 637/4 ÷ 91/4
= 637/4 × 4/91
= 637*4 / 4*91
= 2548 / 364
w = 7 feet
if tan27° =k express the following in terms of k
1. sin 27°
Answer:
) ''You need to consider 200^o = 180^o + 20^o , hence you need to use the next formula to evaluate sin 200^o in terms of k:
sin (alpha + beta) = sin alpha*cos beta + sin beta*cos alpha
Plugging alpha = 180^o , beta = 20^o in the formula yields:
sin 200^o = sin (180^o + 20^o) = sin 180^o*cos20^o + sin 20^o*cos 180^o
Plugging sin 180^o = 0 and cos180^o = -1 in the formula yields:
sin 200^o = - sin 20^o = -k''
Step-by-step explanation:
''Given sin 20°=k express the following in terms of k a) sin 200° b) cos 20° c) tan(-20°) d) sin 70° Related to trigonometry.'' https://www.enotes.com/homework-help/given-sin-20-k-express-following-terms-k-sin-200-b-307263 hope this helps
Find the length of side x in simplest radical form with a rational denominator.
45
X
45
V8
Answer:
relationship between perpendicular and hypotenuse is given by sin angle
sin45=p/h
sin45=√8/x
1/√2=√8/x
x=2√2×√2=2×2=4
x=4
Can someone help me with this problem?
Answer:
a) 2
b) 3
c) 1
hope this helps :)
3 times a number is 4 less than the square of that number. Find the negative solution.
While mike was visiting his sister in arlington,he bought an aquarium that was marked down 60% from an original price of $100 .if the sales tax in Arlington is 5% ,what was the total cost of the arquarium?
Answer:
The cost of the aquarium was $38
Step-by-step explanation:
I got 60% of 100 and it was 60 so it was $40 but then the sales tax was $2 so I subtracted and got 38
The total cost of the aquarium is the sum of the marked down price and
the sales tax.
The total cost of the aquarium is $42
Reasons:
The known information are;
Original price of the aquarium = $100
The marked down percentage of the aquarium = 60%
The sales tax = 5%
[tex]Mark \ down = \dfrac{Difference}{Current \ selling \ price} \times 100[/tex]
[tex]60 \% = \dfrac{Difference}{100} \times 100[/tex]
Which gives;
The difference in sale = $100 - Marked down price = $60
Marked down price = $100 - $60 = $40
The marked down price = $40
The tax is applied to the marked down price, therefore, we get;
Sales tax = 5% × $40 = $2
The total cost = Marked down price + Sales tax
The total cost of the aquarium = $40 + $2 = $42
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A bag contains 9 blue marbles and 36 green marbles. If a representative sample contains 3 blue
marbles, then how many green marbles would you expect it to contain? Explain.
Answer:
It is 12 green marblesStep-by-step explanation:
[tex] \frac{9}{3} = 3 \\ \\ \frac{36}{x} = 3 \\ x = \frac{36}{3} \\ x = 12[/tex]
I hope that is useful for you :)
GEOMETRY - triangle similarity
Answer:
ΔABC ≈ ΔDEF
∡B ≅ ∡E
x = 4.5
BC is similar to EF
Step-by-step explanation:
to find 'x':
6/16 = x/12
16x = 72
x = 4.5
Answer:
1) tri ABC ~ tri DEF
2) angle B ~ angle E
3) x= 4.5
4) ?= BC
Step-by-step explanation:
hi! a note: pls let me know if any of the answers are wrong ! i want anyone to have a wrong answer because of me thank u vm! (obviously, my explanations are not the official mathematical explanations)
1) I just matched up the letters, A to D, B to E, C to F
You can also use ratios, but if you dont need an explanation then ignore it.
2) matched up the angles: B corresponds to E
3) Ratio: 6/16 = x/12
16x = 72 cross multiply
x = 4.5
4) Again, just match up the sides
BC corresponds to EF
hope this helps :D best of luck
GIVING BRAINLIEST!!!!!
What type of triangle is shown in the image?
Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle
Answer:
A. Obtuse triangle
B,C,D. Acute
Step-by-step explanation: