Answer: 34,560
Step-by-step explanation:
Total crayons of different color = 12
Total children = 3
Each child will get 4 crayons.
Number of combinations of selecting r things out of n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways of selecting the first 4 crayons for first child = [tex]^{12}C_4=\dfrac{12!}{4!(12-4)!}=\dfrac{12\times11\times10\times9\times8!}{(24)\times 8!}\\\\=495[/tex]
Colors left = 12-4 =8
Now, the again selecting 4 colors out of 8 for second child = [tex]^{8}C_4=\dfrac{8!}{4!(8-4)!}=\dfrac{8\times7\times6\times5\times4!}{(24)\times4!}=70[/tex]
Colors left =4
Number of ways of selecting 4 colors out of 4 for third child =1
Total number of ways = 495 x 70 x 1 = 34650 [By fundamental principle of counting]
Hence, the total number of ways = 34,560.
Please answer it now in two minutes
Answer:
47
Step-by-step explanation:
It's just aligning each number / line to each matching one.
Answer:
47 degrees
Step-by-step explanation:
The angle that matches the angle U is angle C
The measure of angle U is 47 degrees
PLZ HELP Point C(3.6, -0.4) divides in the ratio 3: 2. If the coordinates of A are (-6, 5), the coordinates of point B are? If point D divides in the ratio 4: 5, the coordinates of point D are?
Answer:
In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.
To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB.
1. Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3
A (-2,-1) and B(-6, -7)The distance between A and B would be:
x= x2-x1 = -6 - (-2)= -4
y= y2-y1 = -7 - (-1)= -6
Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.
Point C(-3.6, -3.4) divides AB in the ratio 2:3
x3= x1 + AB ratio* AB distance
x3= -2 + (2/2+3)*(-4)= -3.6
y3= y1 + AB ratio* AB distance
y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4
2. Point C(0, 1) divides AB in the ratio 4:7
A(4,-3) and B(-7,8)
The distance between A and B would be:
x= x2-x1 = -7 - (4)= -11
y= y2-y1 = 8 - (-3)= 11
Since both x and y distance is 11, let's try answer with total ratio 11
Point C(0, 1) divides AB in the ratio 4:7
x3= x1 + AB ratio* AB distance
x3= 4 + (4/4+7)*(-11)= 4- 4=0
y3= y1 + AB ratio* AB distance
y3= -3 + (4/4+7)*(11)= -3 +4= 1
3. Answer: Point C(8, 9) divides AB in the ratio 5:3
A(3,4) and B(11,12)The distance between A and B would be:
x= x2-x1 = 11 - (3)= 8
y= y2-y1 = 12 - (4)= 8
Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.
Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus
Point C(-2, 5) divides AB in the ratio 2:6 -----> total ratio 8, x minus
Point C(8, 9) divides AB in the ratio 5:3 -----> total ratio 8, both x and y plus
x3= x1 + AB ratio* AB distance
x3= 3 + (5/5+3)*(8)= 3+ 5=8
y3= y1 + AB ratio* AB distance
y3= 4 + (5/5+3)*(8)= 4 +5= 9
4. Point C(-2, 5) divides AB in the ratio 2:6
A(-5,2)and B(7, 14)
The distance between A and B would be:
x= x2-x1 = 7 - (-5)= 12
y= y2-y1 = 14 - (2)= 12
Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.
Point C(4, 1.6) divides AB in the ratio 3:2 -----> x more than y
Point C(-2, 5) divides AB in the ratio 2:6 -------> y plus, y more than xx3= x1 + AB ratio* AB distance
x3= -5 + (2/2+6)*(12)= -5+ 3=-2
y3= y1 + AB ratio* AB distance
y3= 2 + (2/2+6)*(12)= 2 +3= 5
Step-by-step explanation:
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)? (4 points)
If the plane is flying at an altitude of 21,000 feet, it is perpendicular to the observer's horizontal line of sight. Thus, I concluded that the given information be assigned to the attachment below.
Given -
( Observer at point O, plane flying at point P
( Plane at 55° angle to horizontal line of sight, altitude of 21,000 feet
The distance ( x ), is represented by the line segment OP, with which we have to determine the length of. Therefore we can conclude the following -
[tex]Sin( 55 ) = Altitude / Distance,\\Sin( 55 ) = 21,000 / x,\\----------------\\x = \frac{21,000}{Sin( 55 )},\\x = 21,000 / 0.81915204428\\\\x = ( About ) 25636 feet\\[/tex]
As you can see, the distance from the plane to the observer is about 25,636 ft!
Answer:
25,636 feet
Step-by-step explanation:
I took the test on FLVS and got 100%
Which of the following equations have exactly one solutions 19x + 18 = -19x +18
Answer:
there's only one equation listed, and it has one solution, which is 0
Step-by-step explanation:
Answer: There is only one equation here...
Anyway it's ans is 0
Step-by-step explanation:
Feel pleasure to help u
Find the area of the parallelogram. HELP ASAP PLS!! A=192cm^2 A = 273cm^2 A = 208cm^2 A = 252 cm^2
Answer:208
Step-by-step explanation:
13 x 16 = 208
<!> Brainliest is appreciated! <!>
EZ car rental charges $40 a day plus $0.25 per mile. Ace Rent-A-Car charges, $25 a day plus $0.45 per mile. What number of miles result in the same cost for one day?
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Hey there!
We have the equation: y2-y1/x2-x1.
So, we have: 8-2/8-6.
6/2, or 3.
Hope this helps!
can someone help i have less than an hour !!
Answer:
[tex]x \geqslant 4[/tex]Option D is the correct option.
Explanation:
Since, there is a solid circle(blue) at X=4 which implies the value '4' is included in the inequality solution.
Hope this helps...
Good luck on your assignment...
What is the value of x?
Answer:
x=12
Step-by-step explanation:
Intersecting Chords Formula:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
10 * x = ( 3+x) *8
10x = 24+8x
Subtract 8x
10x-8x = 24+8x-8x
2x= 24
Divide by 2
2x/2 =24/2
x = 12
Lori is making 3 mugs of hot chocolate. Each mug holds 1/2 a pint. How many cups of hot chocolate does Lori pour?
Answer:
3 CUPS pints
Step-by-step explanation:
Multiple to get it by doing this (1/2) US pint x 3 = 1.5 US pints *2= 3 cups
How many kilobytes have been downloaded so far?
Answer:
Do you have a photo or some other information to go with this?
Step-by-step explanation:
Function of a Function
Answer:
B. 8
Step-by-step explanation:
Step 1: Find g(-2)
g(-2) = (-2)² + 1
g(-2) = 4 + 1
g(-2) = 5
Step 2: Find f(5)
f(5) = 2(5) - 2
f(5) = 10 - 2
f(5) = 8
a regular pentagon-based pyramid has 5 faces which are equilateral triangles the perimeter of it's net is 70cm what is the perimeter of the base?
Answer:
35cm
Step-by-step explanation:
The net of a regular pentagon has 10 sides.
Since each of the faces are equilateral triangles, the side lengths are equal.
Therefore:
Length of each side of the net = 70/10 =7cm
Therefore, the base is a regular pentagon of side length 7cm.
The perimeter of the base of the pyramid = 5 X 7
=35cm
The perimeter of the base of the pyramid is 35cm.
Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable.
Complete question:
Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?
Answer:
Here,
Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)
We are also told only 10 participants are available.
All 10 participants are being exposed to all five levels of the color variable in the same order.
Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.
Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.
But using counterbalancing technique, Dr. Lyte can avoid such an error.
Help please urgently❤️ With atleast some Plz
Answer:
2. -3, 1.
3. -2, 0.
4. 6, 8.
5. 20.
Step-by-step explanation:
2. x - 3y + 6 = 0
-3y = -x -6
y = 1/3x + 2
y + 4 = -5/4(x - 1)
y + 4 = -5/4x + 5/4
y = -5/4x + 5/4 - 16/4
y = -5/4x - 11/4
If you sketch these two lines on paper (or draw them on a graphing calculator), you will find that they intersect at (-3, 1).
So, the values you enter on the response would be -3, 1.
3. x + 3y = -2
x = -3y - 2
-3x + 5y = 6
-3(-3y - 2) + 5y = 6
9y + 6 + 5y = 6
14y + 6 = 6
14y = 0
y = 0
x + 3 * 0 = -2
x + 0 = -2
x = -2
-3 * -2 + 5 * 0 = 6
Since everything works out, the solution to the two equations is (-2, 0).
So, the values you enter on the response would be -2, 0.
4. 3x - 4y = -14
2x + 5y = 52
2(3x - 4y = -14)
3(2x + 5y = 52)
6x - 8y = -28
6x + 15y = 156
6x + 15y = 156
-6x + 8y = 28
23y = 184
y = 8
3x - 4 * 8 = -14
3x - 32 = -14
3x = 18
x = 6
2 * 6 + 5 * 8 = 12 + 40 = 52
Everything works out, so your solution is (6, 8).
Your answer will be (6, 8).
5. For a system of equations to have no solution, the y's and the x's must have the same coefficients.
5x - Ky - 10 = 0
y = 1/4x + 6
-Ky = -5x + 10
Ky = 5x - 10
1/5Ky = x - 2
1/20Ky = 1/4x - 1/2
1/20K = 1
K = 20
y = 1/4x - 1/2
y = 1/4x + 6
1/4x - 1/2 = 1/4x + 6
1/4x - 1/4x = 6 + 1/2
0 = 6.5
There is no solution, so K = 20.
Hope this helps!!
If x = 2 and y = 14 , evaluate the following expression: x y Give your answer as a fraction in its simplest form.
Answer:
1/7
Step-by-step explanation:
x/y
Plug in the values.
(2)/(14)
Simplify.
1/7
Answer:
1/7
Step-by-step explanation:
=> x/y
Given that x = 2, y = 14
=> (2)/(14)
=> 1/7
The number of kilometers traveled by a bus is represented by x. If a train traveled 200 kilometers farther than the bus, represent the number of kilometers traveled by the train.
Answer:
The train travelled x + 200 km
Answer:
The number of kilometres traveled by the bus is x kilometres. The train travels 200 kilometres farther than the bus, meaning that the train traveled x kilometres, and an additional 200 kilometres.
So, the number of kilometres traveled by the train would be the x km traveled by bus, plus 200 km; or x + 200 km.
Hope this helps!
What does the graph of f(x)=3x^2-2x+1 look like
Answer:
Below.
Step-by-step explanation:
This is a parabola.
As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').
If we convert to vertex form we can find the line of symmetry and the coordinates of the vertex:
f(x) = 3x^2 - 2x + 1
f(x) = 3(x^2 - 2/3 x) + 1
f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1
f(x) = 3(x - 1/3)^2 - 1/3 + 1
f(x) = 3(x - 1/3)^2 + 2/3
So the line of symmetry is x = 1/3 and
the vertex ( the minimum of the curve) is at (1/3, 2/3).
PLZ HELP QUICK............
Answer:
[tex]4^m[/tex]
Step-by-step explanation:
When you exponent an exponent, you multiply the powers together.
When you divide exponents, you subtract the powers.
Step 1: Convert to same base
log₄64 = 3
Step 2: Rewrite equation
[tex]\frac{(4^3)^{0.5m}}{4^{0.5m}}[/tex]
Step 3: Simplify
[tex]\frac{4^{1.5m}}{4^{0.5m}}[/tex]
Step 4: Simplify
[tex]4^m[/tex]
The coefficient of x in the expansion of the following is (x+3)^3 a) 1 b) 3 c) 18 d) 27 e) 9
Answer:
d) 27
Step-by-step explanation:
The expanded form of (a+b)³ is ...
(a +b)³ = a³ +3a²b +3ab² +b³
When we are expanding (x +3)³, the x-term is ...
3(x)(3²) = 27x
The coefficient of x in the expansion is 27.
To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her ac To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her account when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend count when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend
i got this question too as my homework it so hard ill let you know if i find out the answer.
I need help ASAP snsnnsbsbsbs
Answer:
The value of a is 50°.
Step-by-step explanation:
In an isosceles triangle, 2 sides have the same lengths and same angles so we can assume that the other side of the triangle is 65°.
Given that the total angle of a triangle is 180°, so have to subtract it :
[tex]a = 180 - 65 - 65[/tex]
[tex]a = 180 - 130[/tex]
[tex]a = 50[/tex]
Solve for x, given a=117. Round your answer to one decimal place.
Answer:
x = 63
Step-by-step explanation:
We can find the value of x by multiplying the difference of large arc to small arc with 1/2
if a = 117° then the large arc would be 243
1/2 × (243 - 117) = 63
Small library contains 700 novels. how many ways can You check out three novels
The first book you select can be any one of 700.
. . . For each of those ...
The second book can be any one of the other 699.
. . . For each of those ...
The third book can be any one of the remining 698.
The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = 341,531,400 ways .
BUT ...
When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.
So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.
I need assistance can I get help
Answer:
5x-8
Step-by-step explanation:
Consider the function. f(x)= -2/3x-24 Which conclusions can be drawn about f–1(x)? Select two options. f–1(x) has a slope of -2/3 . f–1(x) has a restricted domain. f–1(x) has a y-intercept of (0, –36). f–1(x) has an x-intercept of (–36, 0). f–1(x) has a range of all real numbers.
Answer:
(D) [tex]f^{-1}{(x$) has an x-intercept of (-36, 0).[/tex]
(E)[tex]f^{-1}{(x)[/tex] has a range of all real numbers.
Step-by-step explanation:
Given the function: [tex]f(x)= -\dfrac23x-24[/tex]
[tex]f(x)+24= -\dfrac23x\\$Multiply both sides by $ -\dfrac32\\x=-\dfrac32(f(x)+24)\\f^{-1}(x)=-\dfrac32f(x)-36[/tex]
When y=f(x)=0
[tex]f^{-1}(x)=-\dfrac32(0)-36\\f^{-1}(x)=-36[/tex]
Therefore, [tex]f^{-1}(x)$ has a x-intercept of -36[/tex]
Also, [tex]f^{-1}(x)[/tex] has a range of all real numbers.
Therefore, Options D and E are correct.
Answer:
4 and 5
Step-by-step explanation:
EDGE
Find the area of this triangle..
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the altitude.
h^2 = 9^2 - 6.4^2
h^2 = 40.04
h = 6.328
area = base * height/2
area = (2 * 6.4) * 6.328/2
area = 40.5 square units
A rectangular octagon is shown in the ceiling of a cathedral. The radius is 10.5 feet and the perimeter is 64 feet. The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet. What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot. feet Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot. square feet
Answer:
9.7 , 310.4
Step-by-step explanation:
length of each side = 64/8=8
using theorem Pythagoras
A²=10.5² – (8/2)²
A=9.7 ft
area of triangle
1/2×8×9.7=38.8
area of octagon
38.8×8=310.4
The Length of the octagon is 9.7 and the area of octagon is 310.4.
Length and area of octagonLength of octagon
Length of each side = 64/8
Length of each side =8
Pythagoras theorems
A²=√10.5² – (8/2)²
A²=√110.25 – 16
A²=√94.25
A=9.7 ft
Area of octagon
Area of triangle=1/2×8×9.7
Area of triangle=38.8
Area of octagon=38.8×8
Area of octagon=310.4
Therefore the Length of the octagon is 9.7 and the area of octagon is 310.4.
Learn more about Length and area of octagon here:https://brainly.com/question/358118
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What is the next number in the pattern below?
3, 5, 9, 15, 23, ___
A.
31
B.
33
C.
35
D.
37
Answer:
the answer you are looking for is the letter B. 33
Eli chooses two shirts from a group of five to pack for a weekend trip. Let each shirt be represented by A, B, C, D, and E. Which statements about the situation are true?
Answer:
A, B and E statements are true
Step-by-step explanation:
Since in the question, it is mentioned that Eli selected two shirts out of pack 5 for a weekend trip
Classify each shirt as A, B, C, D, and E.
Now we have to go through the options
In the first statement it is mentioned that AB and BA are the similar. This is true as it contains in same bag.
Since Eli select two shirts so the second statement is also correct
And, the last statement is also true as he selects shirt B so there are four possible ways to second the second shirt as there are four remaining shirts are left after select one shirt
Hence, A, B and E statements are true
Answer: A, B, and E.
Step-by-step explanation:
A is correct: the combination of AB and BA are the same because they both contain the same letters, just a different order.
B is correct: each shirt can be paired with any one of the other remaining shirts because she will be choosing 2 shirts.
E is correct: If he chooses shirt B, there are 4 possible outcomes for choosing the 2nd shirt. This is true because there is only one B in a group of 5 shirts, so 5-1 = 4 possible outcomes.
Hope this helped.
Have a nice day. :)