Given:
Total number of people = 10
To find:
The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.
Solution:
We know that the number of ways to select r items form n times is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].
The number of remaining people is [tex]10-2=8[/tex].
The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].
The number of remaining people is [tex]8-3=5[/tex].
The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].
Now, the total number of ways is:
[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]
[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]
[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]
[tex]Total=45\cdot 56\cdot 1[/tex]
[tex]Total=2520[/tex]
Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.
Diana and Dulce were selling tickets for their upcoming
softball game. Dulce sold 20% more than Diana. If they
sold 55 tickets total, how many tickets did each of them
sell?
Answer:
Diana sold 25 tickets and Dulce sold 30 tickets
Step-by-step explanation:
Let us assume that Diana sold x number of tickets, dulce sold 20% more x or 1.2x. ATQ, x+1.2x=55. x=25. So Diana sold 25 tickets and Dulce sold 30 tickets
CX is an altitude in triangle ABC.
Which statements are true? Select two options. .
Answer:
Does the answer help you?
Lydia runs an experiment to determine if a coin
I do not understand this question can someone help me with good explanation will give Brainliest
Answer:
60 (E)
Step-by-step explanation:
He plants seeds -> plants grow to 12 times the original weight of the seeds -> he sells 50 tonnes from the harvest -> remainder is used as the next batch of seeds
He harvested 120 tonnes this year which means the original weight of the seeds planted was 120÷12 = 10 tonnes. This means that last years harvest would be the 10 tonnes used as seeds plus the 50 tonnes that would have been sold immediately, 10+50 = 60 tonnes
A baby can crawl ¾ foot in ¼ minute. How far does the baby get per minute?
Answer:
3 ft per minute
Step-by-step explanation:
Take the distance and divide by the time
3/4 ft ÷ 1/4 minute
Copy dot flip
3/4 * 4/1
Rewriting
3/1 * 4/4
3/1 *1
3 ft per minute
5. Which expression is a simplified form of (3x2 + 2x - 4) + (-7x2 + 6x - 2)?
a 10x2 + 8x - 6
b. -4x2 + 8x - 2
C.-4x2 + 8x + 2
d. -4x2 + 8x - 6
Answer:
d. -4x² + 8x - 6
Step-by-step explanation:
(3x² + 2x - 4) + (-7x² + 6x - 2)
3x² + 2x - 4 - 7x² + 6x - 2
3x² - 7x² + 2x + 6x - 4 - 2
-4x² + 8x - 6
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
O A. Form an equation:
B. Draw a diagram.
C. List potential formulas.
D. Guess at the solution and see if you are close.
E. Organize into a table.
F. Write down the facts.
Answer:
Organize into a table for good gatherings.
Kristian and Stephanie share money in the ratio 3 :2 Kristian receives $72 How much will Stephanie receive
Answer:
48
Step-by-step explanation:
Kristian : Stephanie
3 2
Kristian receives 72
72/3 = 24
Multiply each side by 24
Kristian : Stephanie
3*24 2*24
72 48
I really need help anyone know which option is correct.?
Answer:
B, [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
This problem is essentially asking one to envision a line passing through the set of points on the coordinate plane, then to find the constant of proportionality of that line. The constant of proportionally, also known as the rate of change, or the slope, is a number that can be used to describe the range that happens between points on a line. The following formula can be used to find the slope of a line passing through a set of points.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the points ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line.
As one can see, on the given coordinate plane, the points ([tex]2,-1[/tex]), and ([tex]4,-2[/tex]) are on the coordinate plane. Substitute these points into the formula to find the slope of the line, then simplify to evaluate the equation and find the slope,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
([tex]2,-1[/tex]), ([tex]4,-2[/tex])
[tex]=\frac{-2-(-1)}{(4)-(2)}[/tex]
[tex]=\frac{-2+1}{4-2}\\\\=\frac{-1}{2}\\\\=-\frac{1}{2}[/tex]
Suppose that a sales person observes that if an item is priced at $9 per item then 6 items are sold. If 4 items are sold for $11 per item then find a linear equation to model the number y of items sold for x dollars per item. Find the slope-intercept form of the equation of the line.
Answer:
y = -x + 15
Step-by-step explanation:
if an item is priced at $9 per item then 6 items are sold.
Thus, the input is 9 while the output is 6.
Thus, we can say; x, y = (9, 6)
4 items are sold for $11 per item. Thus, the coordinate is; (11, 4)
Now,slope is;
m = (y2 - y1)/(x2 - x1)
m = (4 - 6)/(11 - 9)
m = -2/2
m = -1
We know that slope intercept form is;
y = mx + c
Let's try the first point.
Thus;
6 = -1(9) + c
6 + 9 = c
c = 15
Thus, equation of line is;
y = -x + 15
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 2 with
these dice. Be sure to reduce.
[?]
Answer:
1/36
Step-by-step explanation:
it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}
you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...
The probability of rolling a sum of 2 with these dice is 1/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Pair of dice have= {1,2,2,3,3,4}
Now,
The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.
However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.
This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.
Therefore, the probability will be 1/36.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
find the missing side
Answer:
[tex]\boxed{x=13.89\:km}[/tex]
Step-by-step explanation:
Pythagorean theorem
[tex]x^2=(12^2)+(7^2)[/tex]
[tex]x^2=144+49[/tex]
[tex]x^2=193[/tex]
[tex]x=\sqrt{193}[/tex]
[tex]\boxed{x=13.89\:km}[/tex]
f(x) = 5x + 2x^2-7x+4
g(x) =3x-7
find (f+g)(x)
Answer:
(f+g)(x)=5x+2x²-7x+4+3x-7 = 2x²+x-3
Step-by-step explanation:
Answer:
=6x^3-20x^2+26x-28
Step-by-step explanation:
whats the volume the triangular prism?
Answer:
the volume is 1000 cm^3
Step-by-step explanation:
first we need to find where is the base, and height, for this case, the trian is the base, not the rectangle, so it maybe eas if you draw a upright angle os the shape, with the triangle facing down.
As show you need to have bare and height for the volume of the prism, which we already know the height is 25 (h=25) so now we need to find the base.
for the base, since it’s a triangle, which has the area formal of 1/2(bh), so now just plot the number in, 1/2x10x8= 40 cm^2
now using the volume of prism formal; V = bh = 40 x 25 = 1000 cm^3
solve this question :
-10k2+7
Answer:
-10k×2+7
= -20k+7
Step-by-step explanation:
is the answer
A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x + 2) square inches. If the area of thi
photograph is 48 square inches, what is the width of the photograph?
The width of the photograph is
inches.
How do I find the Derivative of a Function where the x is a number?
If I was to find d/dx g(1) for example, would I first find the value of the function g(x) at x=1 and then find the derivative of that which becomes 0 because the result would probably be a constant. Or do I first find the derivative of g(x) and then plug in x=1 to calculate it?
Thanks
Given a function g(x), its derivative, if it exists, is equal to the limit
[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]
The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).
Alternatively, you can directly find the derivative at a point by computing the limit
[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]
But this is essentially the same as the first method, we're just replacing x with 1.
Yet another way is to compute the limit
[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]
but this is really the same limit with h = x - 1.
You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.
Can someone help me out
Answer:
82.8
Step-by-step explanation:
area of the parallelogram = base × height
= 13.8×6
= 82.8 in²
Answered by GAUTHMATH
What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠D B C is a straight angle Prove: ∠ABC ≅ ∠A B D A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle. definition of angle bisector segment addition property definition of congruent angles transitive property
Answer:
Definition of Congruent angles.
Step-by-step explanation:
Given
See attachment
Required
Complete the proof at step 8
At step 8, we have:
[tex]\angle ABC \cong \angle ABD[/tex]
When the sign [tex]\cong[/tex] is used, it means congruence
In other words;
ABC and ABD are congruent
Hence, the missing statement at step 8 is: Definition of Congruent angles.
Answer:
ABC and ABD are congruent
Step-by-step explanation:
Can anyone help me with this
Answer:
x=0, - 9
Step-by-step explanation:
x^2+9x=0
x(x+9)=0
x=0 or x=-9
Answer:
x =0 x= -9
Step-by-step explanation:
x^2 + 9x = 0
Factor out x
x(x+9) =0
Using the zero product property
x =0 x+9 =0
x =0 x= -9
Can sone One help me please, Thanks a lot
Answer:m
Step-by-step explanation:m
What is the range of function represented by the graph below?
Answer:
y ≥ 0
Step-by-step explanation:
The range of the function is the output values.
The y value goes from 0 to infinity
y ≥ 0
Which models best illustrates the inequality and its graph?
t< 55
a.) t is at least 55
b.) t is less than 55
c.) t is 55 or more
d.) t is at most 55
Answer:
B
Step-by-step explanation:
Open circle means the number is not included.
Hope this helps <3
The radius of a circle is 3 cm. Find its area in terms of pi
Answer:
A = 9 pi cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
r=3
A = pi (3)^2
A = 9 pi cm^2
Area of circle = πr²
Area = π3²
Area = 9π
There area in terms of pie is 9πcm²
Must click thanks and mark brainliest
URGENT
really need help
Answer:
Step-by-step explanation:
.007 = 7 x [tex]10^{-3}[/tex]
.07 = 7 x [tex]10^{-2}[/tex]
7 = 7 x [tex]10^{0}[/tex]
700 = 7 x [tex]10^{2}[/tex]
3x – (7x + 2) > 5x + 4
Answer:
x < -2/3Step-by-step explanation:
3x – (7x + 2) > 5x + 4= 3x -7x - 2 > 5x + 4= -4x - 2 > 5x + 4= -4x -5x > 4 + 2 = -9x > 6= x < -2/3[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Write the area A of an equilateral triangle as a function of the length s of its sides.
STEP 1: Find the base of the equilateral triangle in terms of s.
STEP 2: The height of an equilateral triangle can be found via the Pythagorean theorem. Use this information to find h in terms of s.
Write the area A of an equilateral triangle as a function of the length s of its sides. Draw the triangle; label each side "2s". Draw the altitute; it will bisect the base into s and s. ... Therefore, the area is equal to the measure of the bisected side times the measure of the altitude, quantity divided by 2.
HOPE SO IT HELPS YOU
Answer:
Step-by-step explanation:
Part A
Each side including the base is s.
Part B
Use 1/2 the base to find the height. The height meets the base at 90 degrees which gives you the right to use c^2 = b^2 + a^2
The hypotenuse is s
The base is 1/2s
h^2 = s^2 - (1/2s)^2
h^2 = s^2 - 1/4 s^2
h^2 = 3s^2/4
h = sqrt(3)/2 *s
Area = 1/2 * s * sqrt(3)/2 s
Area = 1/4 * s^2 * sqrt(3)
the cost of a ford is 2/13 of the cost of a rolls Royce. If the current price of a rolls Royce is $211 250, what is the cost of a ford ?
PLEASE HELPP!!!!
Find the area.
A.530in²
B. 779in²
C.390in²
D.1060in²
Answer:
530in²
Step-by-step explanation:
Area of triangle(a)=1/2bh=1/2*40*26.5=530
Let ε = {5,6,7,8,9}, A = {x | x >7} and B = {5,6} Find
1. P(A’)
2. P(A) U P(B)
3. P(A) ∩ P(B)
4. P(A ∩ B)
Answer:
A={x| x>7} = 8,9
B= {5,6}
1,
2,{5,6,8,9}
3,{}
4{}
