Answer:
281 different committees can be formed if the number of boys is more than the number of girls.
Step-by-step explanation:
The order in which the people are chosen to the committee is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Number of boys more than the number of girls:
3, 4 or 5 boys.
3 boys:
3 boys from a set of 6.
2 girls from a set of 5. So
[tex]C_{6,3}C_{5,2} = \frac{6!}{3!3!} \times \frac{5!}{2!3!} = 200[/tex]
4 boys:
4 boys from a set of 6.
1 girl from a set of 5. So
[tex]C_{6,4}C_{5,1} = \frac{6!}{4!2!} \times \frac{5!}{1!4!} = 75[/tex]
5 boys:
5 boys from a set of 6. So
[tex]C_{6,5} = \frac{6!}{5!1!} = 6[/tex]
Total:
200 + 75 + 6 = 281
281 different committees can be formed if the number of boys is more than the number of girls.
Which algebic expression is “ ten less than a number divided by twelve “
Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women
Answer:
The number of ways is 26,400 ways
Step-by-step explanation:
Given;
total number of men, M = 10
total number of women, W = 12
number of committees to be formed = 6
If there must be equal gender, then it must consist of 3 men and 3 women.
[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]
Therefore, the number of ways is 26,400 ways
find the value of x pls show work
Answer:
x = 55°
Step-by-step explanation:
120° = x° + 65° (alternate interior angles are congruent)
Subtract 65 from each side
120° - 65° = x° + 65° - 65°
55° = x
Therefore,
x = 55°
100 people study one language at a college. Some people study French, some study Spanish. The rest of the people study German. 54 of the people in Year 10 and the rest in Year 11. 20 of 29 people who study Spanish in Year 11. 31 people study German, 15 year 11 students study French. Work out the number of Year 10's who study German.
Hello,
[tex]Data:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&-&-&-&54\\Y11&15&20&-&-\\----&----&----&----&---\\&-&29&31&100\\\end{array}\\\\Calculus:\\\\\begin{array}{|c|c|c|c|c|}Year&French&Spanish&German&Total\\----&----&----&----&---\\Y10&25&9&20&54\\Y11&15&20&11&46\\----&----&----&----&---\\&40&29&31&100\\\end{array}\\\\[/tex]
20 Year10's students learn German.
========================================================
Explanation:
Make a table that has "Year 10", "Year 11", and "Total" as the three rows.
Then you'll have the columns "French", "Spanish", "German", "Total".
In the bottom right corner is the value 100. This is the grand total of everyone surveyed.
We're told that 54 people are in Year 10, which leaves 100-54 = 46 people in Year 11.
Along the "total" column on the far right side, we'll have 54, 46, and 100 in that order from top to bottom.
--------------------------
The info that "20 of the 29 people who study Spanish in Year 11" tells we have 20 people in year 11 who study Spanish, out of 29 people who study Spanish. That leaves 29-20 = 9 people in Year 10 who study Spanish. In the "Spanish" column, we have the values 9,20,29 in that exact order from top to bottom.
Next, we'll write 31 at the bottom of the "German" column to indicate 31 people study German.
The last bit of info is that "15 Year 11 students study French". So we'll write 15 in the "year 11" row and "french" column.
--------------------------
After all that info is sorted out and entered into the table, you should end up with what is shown in figure 1 (see attached image below). Ignore figure 2 for now as we'll work our way to getting there eventually.
The variables a,b,c,d are placeholders for positive whole numbers.
There are probably a few approaches to take, but possibly the quickest is to notice that in the second row, we can say
15+20+c = 46
c+35 = 46
c = 46-35
c = 11
We have 11 students who study German in Year 11.
Once you determine c, it helps us find b. Focus on the German column to see that
b+11 = 31
b = 31-11
b = 20
There are 20 students in Year 10 who study German. You could stop here if you want.
--------------------------
Just two more variables to go.
Along the top row, we see that
a+9+20 = 54
a+29 = 54
a = 54-29
a = 25
and along the bottom row we see that
d+29+31 = 100
d+60 = 100
d = 100-60
d = 40
Or you could note along this first column to say
a+15 = d
d = a+15
d = 25+15
d = 40
So there are a few alternative paths to take.
--------------------------
All of the sections mentioned so far only involve filling out the table that is shown below in figure 2.
To answer the question your teacher wants to ask, which is how many Year 10 students study German, well that's simply 20 students. Refer to the conclusion of the previous two sections earlier.
By this point, we just simply copy the value from the completed table. This value being of course in the "Year 10" row and "German" column.
What is the solution of 5/2x-7=3/4x+14
Answer:
D. x = 12
Step-by-step explanation:
if you plug 12 in
the solutoon says 23 = 23 which is correct
Answer:D 12
Step-by-step explanation:
I took the test
SOMEONE HELP ASAP PLEASEEEEE!!!!!
Answer:
the answer is 35% probability
your welcome
Find the x and y intercept for the equation: − = 4
Answer:
x = (4,0)
y = (0,-4)
Step-by-step explanation:
x - y = 4
(0) - y = 4
-(-y) = -(4)
y = -4
x - (0) = 4
x = 4
x = (4,0)
y = (0,-4)
Answer:
x = 4 . 0
y = 0 . -4)
Step-by-step explanation:
A stereo was originally priced at 75.50. it was marked down 24%. a store had a big sale of 60% off the lowest marked price. what was the final price of the stereo
Answer:
We can calculate the price with both sales by multiplying the 75.5 units of money by both percentages (to multiply them, we divide them by 100 first):
75.5 * 0.24 * 0.6 [tex]\approx.[/tex] 10.8
if you roll a single die and get 4 fives in a row what is the probability that you would get a 5 on the next roll
Answer
(1/6)⁴ = 1/1296
Step-by-step explanation:
robabilty of getting a 5 in a throw of dice is 1/6 . So, the required probability of getting 4 5’s in rolling a dice 4 times is (1/6)4
find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20
Answer:
The sum of the first 20 terms is -1440.
Step-by-step explanation:
We want to find the sum of the first 20 terms of the arithmetic sequence:
4, -4, -12, -20...
The sum of an arithmetic sequence is given by:
[tex]\displaystyle S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term.
Since we want to find the sum of the first 20 terms, k = 20.
Our initial term a is 4.
Our last term is also the 20th term as we want the sum of the first 20 terms.
To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:
[tex]x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n is the nth term.
Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:
[tex]x_n=4-8(n-1)[/tex]
Then the last or 20th term is:
[tex]x_{20}=4-8(20-1)=4-8(19)=-148[/tex]
Therefore, the sum of the first 20 terms are:
[tex]\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}[/tex]
Answer:
- 1440
Step-by-step explanation:
First-term is 4 and we subtract 8 to get the next term so the general term is
a(n) = 4 - 8(n -1)
The sum of the sequence is the average of the first and last terms multiplied by the number of terms: (a1 + an)/2 * n
We need the 20th term: a20 = 4 - 8(20–1) = 12 - 160 = - 148
The sum is (4 - 148)/2 * 20 = 10*(-144) = - 1440
PLZZ HELPPPPPP I NEED TO FINISH THIS IN 8 MINS
Answer:
$29.69
Step-by-step explanation:
23.52 * 1.1 = $25.872 so this is the marked up price. ----- (1.1 = 110%)
25.872 * 0.1475 = $3.81612 is the sales tax.
Total is 25.872 + 3.81612 ~ $29.69
PLEASE HELP ITS EASY BUT LIKE yh
Answer:
40 I told u
Step-by-step explanation:
right angles are 90 degrees
Answer :
x +25 +25 =90 degrees
x +50 =90 degrees
x = 90 -50
x = 40 degrees
is Catholic Schools bad?
Answer:
Not really。。
Step-by-step explanation:
this school had remained excellent。students grduating from these school have higher ACT scores
can someone please help me with my math assignment??? really need the answer today. And also please don't answer this if you didn't know or for just points
Answer:
it cost 80 dollars
Step-by-step explanation:
cost per bag for X brand =25 $
cost per bag for y brand = 20$
minimize Z=(25X +20 y)
further formulate the problem
the given constraints are
2x + y equal 12
2x + 9y equal 36
2x + 3y equal 24
well on the graph given plot of the constraints
the corner points are
(0;0)
(6;0)
(0;4)
(9;2.5)
minimum z occurs at (0:4)
value of Z(minimum cost)=80$
Which of the four graphs has the greatest standard deviation? please help me
Answer:
Standard deviation is how far away the values are from the mean.All of your graphs have normal distribution, meaning the mean is in the center.The more spread out your graph is, the greater the standard deviation.
So the option with the most spread out graph, which I think is A, can't see very clear.
Which of the following is an even function?
The one you put is actually correct
what is the quotient of 3/4 ÷ 5/12
Answer:
1 4/5
Step-by-step explanation:
3/4 ÷ 5 /12
Copy dot flip
3/4 * 12/5
Rewriting
3/5 * 12/4
3/5 * 3
9/5
1 4/5
Which correlation is most likely a causation?
the positive correlation between the sales of apples and sales of oranges at a farmer’s market
the positive correlation between the number of crimes in a city and the number of cars in the city
the positive correlation between the height of a person and the number of times a person bumps their head on a low ceiling
the positive correlation between the number of socks and number of shoes in a home
Answer:
The positive correlation between the number of socks and the number of shoes in home
Step-by-step explanation:
Nah i just get an example so that i can get clue,if my answer is wrong sorry in advanced
3 + 5 . (-3)=
5 . ( - 6 + 2 ) - 4=
- 5 + 8 . 2 + 1=
4/6 + 13/6 - 5/6=
2 . 8 - 5 . (3 - 4)=
7/3 . 5/2=
Step-by-step explanation:
PEMDAS rule
3 -15 = -12
-20 - 4 = -24
-5 + 16 + 1 = 12
= 12/6 which = 2
15 + 5 = 20
35/6 = 5 5/6
PLEASE HELP!10 POINTS
find the maximum value of c=x+3y subject to the following constraints:
9x+2y≥35
x+3y≥14
x≥0
y≥0
Hello,
14
just see my picture
What is the slope of the line represented by the equation y=
iy=-x+ .
0
를
○ 4
0를
O
0를
Answer:
-1/2
Step-by-step explanation:
Equation is put in slope intercept form:
y = mx + b
Where m = slope
-1/2 takes the place of m meaning that the slope is -1/2
Using linear function concepts, it is found that the slope of the line is of:
[tex]-\frac{1}{2}[/tex]
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the equation is:
[tex]y = -\frac{1}{2}x + \frac{1}[4}[/tex]
Thus the slope is of [tex]m = -\frac{1}{2}[/tex].
More can be learned about linear function concepts at https://brainly.com/question/24808124
The owner of a new pet store wishes to display tropical fish in display tanks. The above table shows the species that cannot live together. What is the minimum number of different tanks needed to safely house all the fish?
Answer:
The minimum number of different tanks needed to safely house all the fish is:
3 tanks.Step-by-step explanation:
To identify the minimum number of different tanks, we're gonna concentrate in a fish species, in this case can be the A: as you see in the table, the A species can live with all the fish excepting the F and G, by their side, the F and G can't live together , by this reason, this three species must live in a different tank, in the next form:
Tank 1: A Tank 2: F Tank 3: GNow the B species, it can live with A, F and G, but for this example we can put in the tank 1 (the tank of the A species). The C especies can live with A, F and G, but how we have A and B together, we're gonna put the C especies in the tank 3 (the tank of the G especies). The D species can live with A and G, we're gonna put in the tank 1 because can live with B species too. The E species can live with A and F, we're gonna put in the tank 2 (the tank of the F species) because the E species can't live with D that is in the in the tank 1. Al last, the H species just can live with A, E, F, and H species, by this reason, the only tank that can be put is the tank 2. In this form, the order is the next:
Tank 1: A, B, D. Tank 2: F, E, H. Tank 3: G, C.And the owner of the pet store must buy three different tanks to display these tropical fish.
At a certain store, a CD costs $12. If the cost of CDs were graphed as the output, compared to the number of
CDs purchased as input, which of the following would not be true of the graph?
A. The set of points would all lie on the same line.
B. The set of points would include the origin.
C. The set of points would rise from left to right.
D. The set of points would not graph a function.
Please select the best answer from the choices provided
A
B
C
D
Round your answer to one decimal places where necessary. Please give steps.
4/3 x 3.14 x 2.25 = ?
Answer:
4/3 x 3.14 x 2.25=9.42
Hope This Helps!!!
Answer:
9.4
Step-by-step explanation:
[tex] \sf \frac{ \bold{4 }}{ 3 } × 3.14 × \underline{2.25}[/tex]
Step 1 :- Multiply decimal by the number. So, that the results equals whole number.
[tex] \sf \frac{ \underline{ 4 }}{ 3 } \\ [/tex] × 2.25 × 3.14 .
[tex] \sf \frac{9}{ 3 } \\ [/tex] × 3.14
Step 2 :- Divide the fraction.
= 3 × 3.14.Step 3 :- Multiply both .
= 9.42.Round to one decimal place :- 9.4
Consider the equation: x^2 - 4x + 4 = 2x
Rewrite the equation by completing the square:
Your equation should look like (x+a)^2 = b or (x-c)^2 = d
______
What are the solutions to the equation? (1 right answer!)
Answer:
(x+3)^2=5
Step-by-step explanation:
x^2-4x+4=2x
x^2-6x+4=0
x^2-6x+9-5=0
(x-3)^2-5=0
(x-3)^2=5
what is the slope of the graph?
Answer:
The slope is 1.5
Step-by-step explanation:
To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula
The two selected points are as follows;
(x1,y1) = (-4,0)
(x2,y2) = (-2,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(-2-(-4)
m = 3/2 = 1.5
Can someone help me with this math homework please!
Answer:i dont know
Step-by-step explanation:
If a flexible air-filled container has a volume of 40 cu ft on the surface, what would the volume be at 99 feet in sea water
Answer:
50 cu ft
Step-by-step explanation:
The volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.
What is Boyle's law?Boyle's Law states that If the temperature is constant, the volume of a gas is inversely proportional to the absolute pressure.
V 1/V2 =P2/P1
V2 = P1 x V1 /P2
Substitute 60 psi for P2, 14.7 psi for P1 and 40cu.ft for V1, we get the volume V2
V2 = 40 x 14.7 / 60
V2 = 9.8 cu.ft
Volume is approximately 10 cu.ft.
Thus, the volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.
Learn more about Boyles law.
https://brainly.com/question/1437490
#SPJ2
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
Answer:
1866.10604
Step-by-step explanation:
V=3.14(r sqaured)1/3h
Identify the parent function.
Answer:
Reciprocal
Step-by-step explanation: