Pine Lane Middle School's student council has 10 seventh graders and 8 eighth graders serving as representatives. A subcommittee containing 3 seventh graders and 3 eighth graders is formed to organize a student dance. How many different subcommittees can be formed
Hey there! I'm happy to help!
When dealing with picking things and finding the number of possibilities, we can be dealing with two different types of things: permutations or combinations. We use permutations when order is important to the groups and we use combinations if order is not important.
It appears here that order is not important here as the subcommittee doesn't have to be in a specific order, so we will be using combinations.
So, we have ten seventh graders to choose from. Then we will have 9, and then 8. So, we multiply these numbers of choices.
10×9×8=720
Now, we need to divide by 6. This is to show that order doesn't matter. Why? Because there are 6 possible ways to organize 3 seats on the committee (3×2×1), and we want to divide out all of the different orders so it is just the specific group of people and not their different organizations that are counted.
720/6=120
Now, we need to find this with the eighth graders.
8×7×6=336
And we divide by the number of seats factorial (3 seats for the eighth graders, so 3×2×1=6 again)
336/6=56
Now, we multiply our numbers for seventh and eighth graders to find all off the possibilities.
120×56=6720
So, there are 6720 subcommittees possible.
Have a wonderful day and keep on learning! :D
A student was conducting a study to determine how many pagos he would need for the book he is writing. So, he found that the following number of words fit on each type of the following papers using an 11 point font:
The student looks up the word count on his favorite book, if the book has pages that are 5.5 in. x 6.5 in. and 67,062 words how many pages is the book?
Answer:
224 pages
Step-by-step explanation:
The book has pages that are 5.5in x 6.5 in (which holds 300 words)
There are a total of 67,062 words
Equation:
67,062 / 300 = total number of pages
67,062 = 223.54
That means 224 pages, because the last page is partially filled.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
PLEASE HELP!!! Sketch the graphs: y=|x-1|+2 y=|x-1|-2
Does the answer help you?
Prove:1/sin²A-1/tan²A=1
Step-by-step explanation:
1/sin^2A -cos^2A/sin^2 A. ~tan = sin/cos
(1-cos^2)/sin^2A. ~ take lcm
sin^2A/sin^ A. ~ 1-cos^2A = sin^2A
1
for more free ans check bio
Answer:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]
Step-by-step explanation:
Prove that:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]
Recall that by definition:
[tex]\displaystyle \tan x=\frac{\sin x}{\cos x}[/tex]
Therefore,
[tex]\displaystyle \tan^2x=\left (\frac{\sin^2x}{\cos^2x}\right)^2=\frac{\sin^2x}{\cos^2x}[/tex]
Substitute [tex]\displaystyle \tan^2x=\frac{\sin^2x}{\cos^2x}[/tex] into [tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\tan^2x}=1[/tex]:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{1}{\frac{\sin^2x}{\cos^2x}}=1[/tex]
Simplify:
[tex]\displaystyle \frac{1}{\sin^2x}-\frac{\cos^2x}{\sin^2x}=1[/tex]
Combine like terms:
[tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]
Recall the following Pythagorean Identity:
[tex]\sin^2x+\cos^2x=1[/tex] (derived from the Pythagorean Theorem)
Subtract [tex]\cos^2x[/tex] from both sides:
[tex]\sin^2=1-\cos^2x[/tex]
Finish by substituting [tex]\sin^2=1-\cos^2x[/tex] into [tex]\displaystyle \frac{1-\cos^2x}{\sin^2x}=1[/tex]:
[tex]\displaystyle \frac{\sin^2x}{\sin^2x}=1,\\\\1=1\:\boxed{\checkmark\text{ True}}[/tex]
Decrease 4,500 by 18%.
Answer:
5,310.
Step-by-step explanation:
Answer:
3690
Step-by-step explanation:
Simplify 18% to 0.18
4500-(4500×0.18)
4500-810
=3690
Which models show 60%? Check all that apply.
Answer:
OPTION A AND B.
AS OPTION A IS 3/5=6/10=60%
Option C=60/100=60%
Answer:
the first and the last option
Step-by-step explanation:
In the first option 3/5 of the rectangle are filled in. if you divide 3 by 5, you will get 0.6, which when converted in to percent is equal to 60%
3/5 = 0.6
0.6 = 60%
*to convert decimals into percent, you just have to move the decimal point 2 places to the right and add the present sign*
in the second option 5 out of the 10 rectangles inside the square are filled in. that means that 5/10 of the square are filled in, the model shows 50%
5/10 = 1/2 = 0.5 = 50%
in the third model 6 out of the 10 rows in the square are filled in. that means that 6/10 of the square are filled in which is equal to 60%
6/10 = 0.6 = 60%
hope this helps! if you have any questions, let me know!
Help with this question please!
Answer:
Step-by-step explanation:
6cos^2(x) + 7cos(x) +2 = 0
Call cos(x) = y to change this to something a little bit more familiar.
6y^2 + 7y + 2 =0
This equation is a quadratic. Solve it first. Then we'll go back to solving for cos(x)
This equation factors into 2 possible answers
(3y + 2)(2y + 1) = 0
3y + 2 = 0
3y = - 2
y = - 2/3
2y + 1 = 0
2y = - 1
y = - 1/2
Now let's start with
cos(x) = - 1/2
That means that x is in quadrant two or three.
cos-1(1/2) = 60 degrees.
Quad 2: x = 180 - 60 = 120
Quad 3: x = 180 + 60 = 240
Now cos(x) = - 2/3
cos-1(2/3) = 48.19
Quad 2: x = 180 - 48.19 = 131.81
Quad 3: x = 180 + 48.19 = 228.19
Find the area of the triangle
Answer:
Step-by-step explanation:11/2x(8-4)=22
The ratio of the corresponding dimensions of two similar parallelograms is 3.1. The
ratio of the base to height for each parallelogram is 5:4. If the height of the smaller
parallelogram is 100, what is the base of the larger parallelogram?
A А
125
В.
240
C.
300
D.
375
If ram have 30 apple& each apple rs is 26 . 14 are rotten .he had eat 9 apple. 6 apple he sold each price 35 . Now say me ram have got profit or loss.
Answer:
Profit
Step-by-step explanation:
30*26
14*26
9*14
6*26*30
2. If you move 50 meters in 10 seconds, what is your speed?
Answer:
5 meters per second
Step-by-step explanation:
Find your speed by dividing the number of meters traveled by the number of seconds it took:
50/10
= 5
Your speed is 5 meters per second.
Answer:
5 m/sec
Step-by-step explanation:
The speed would be calculated as follows, as a unit rate:
50 m
----------- = 5 m/sec
10 sec
Which of the following values are in the range of the function graphed below? Check all that apply
Answer:
B
-10-10=20
10+10=20
20/20=0
Write 128 as a product of its prime factors
Answer:
The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
I need help ASAP!! Please explain how to solve the problem
Answer:
B=.5*8*6=.5*48=24
h = 8
P=10+6+8=24
Surface area =2*24+24*8=48+192=240
Step-by-step explanation:
The base is a triangle, and the area of a triangle is 1/2 base (or width) times height (or length). In this case, base is 8 and height is 6, so the area can be found either by multiplying .5*8*6 or by dividing 8*6 by 2, either of which will give you the same answer of B=24.
Height is given, h=8.
Perimeter is simply the sum of the sides, which are given, so the perimeter is 8+6+10=24.
The formula for surface area is given, so all you need to do is plug in your previous answers and you've got it!
How do you solve part c
the unit are ???
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Solve d−85=p for d .
Answer:
d = p + 85
Step-by-step explanation:
We don't have a lot to go on for this problem. We have two undefined variables.
In order to solve for d, we need to isolate it:
d - 85 = p
Add 85 to both sides
d = p + 85
HELP PLEASE ITS URGENT PLEASE
Answer: 17
Step-by-step explanation:
Using Pemdas, simplify the exponents, and then solve the multiplication and division inside the parentheses before subtracting. 10-9 = 1 so 1*7 =7
10 +7 is 17.
also i hope this helps and i hope this is not a test...
the sides of this right triangle are 18 inches and 24 inches in length.
how long would the hypotenuse of this triangle be?
Answer:
30
Step-by-step explanation:
[tex]c^{2} = b^{2} + a^{2} \\[/tex] = formula
a = 24
b = 18
576+324 = 900
do [tex]\sqrt{900} \\[/tex]
= 30
What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
Negative StartFraction 15 Over 2 EndFraction
Negative one-half
StartFraction 22 Over 9 EndFraction
StartFraction 24 Over 7 EndFraction
Answer:
[tex]\displaystyle m = \frac{22}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (1, 3)
Point (10, 25)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{25 - 3}{10 - 1}[/tex]Subtract: [tex]\displaystyle m = \frac{22}{9}[/tex]Answer:
c
Step-by-step explanation:
Which is the equation of the line with y-intercept -2 and slope 6.
Answer:
The equation would be y=m-2+6
Step-by-step explanation:
Have a great day :)
-8n+34=6(5+4n) help please
Answer:
n=1/8
Step-by-step explanation:
-8n+34=6(5+4n)
We move all terms to the left:
-8n+34-(6(5+4n))=0
We add all the numbers together, and all the variables
-8n-(6(4n+5))+34=0
We calculate terms in parentheses: -(6(4n+5)), so:
6(4n+5)
We multiply parentheses
24n+30
Back to the equation:
-(24n+30)
We get rid of parentheses
-8n-24n-30+34=0
We add all the numbers together, and all the variables
-32n+4=0
We move all terms containing n to the left, all other terms to the right
-32n=-4
n=-4/-32
n=1/8
Answer:
n= 0.125 or 1/8
Step-by-step explanation:
Distrubute 6 into (5+4n). It should give you 30+24n.
The equation should now look like this: -8n+34=30+24n.
Swap -8n with 30, giving -30+34=8n+24n. Add the numbers and the pronumerals together.
Now it will look like 4=32n. Divide the numbers, but unfortunately the number is small so the answer will have to be a decimal or a fraction. So it's 0.125 or 1/8.
If I didn't explain everything or something is wrong, please comment. I just signed up, so it's my first time using this.
Four thousand runners began the marathon. Eighty-nine percent of them completed the run. What percentage of the runner finished the marathon?
Answer:
3560 people.
Step-by-step explanation:
You have to do 89% × 4000.
Or 0.89×4000=3560.
So 3560 is the answer.
Dr. Perry conducts a study in which she evaluates the effectiveness of an adult literacy program. The study is both quantitative and qualitative in nature, and the 30 participants are treated as equal researchers in the study. What research method is Dr. Perry MOST likely to use
The method is Dr. Perry most likely to use is Participatory action research.
Participatory action research is a type of research characterized by :
Qualitative and quantitative method Active participation of the community involved in the researchAdditionally, in this type of research, the community involved is treated as researchers and their contributions are taken into account in the result of the same.
According to the above, the type of research suitable for Dr Perry's study is participatory action research, since it includes all the factors that Dr Perry takes into account for her research such as quantitavie/qualitative method and active participation from the community involved.
On the other hand, case study, naturalistic observation, and focus group are not the correct options because they use other methods in which the studied community does not actively participate.
Learn more in: https://brainly.com/question/15930435
Note:
This question is incomplete because the options are missing. Here are the options.
A. Case study
B. Naturalistic observation
C. Participatory action research
D. Focus group
PLEASE HELP!!! very confused
Answer:
Step-by-step explanation:
The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] and so far we have that h = 0 and k = 0.
By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.
The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:
If h+c = 13 and h = 0, then
0 + c = 13 and c = 13.
We need that c value to help us find b:
[tex]c^2=a^2+b^2[/tex] and
[tex]13^2=5^2+b^2[/tex] and
[tex]169=25+b^2[/tex] and
[tex]144=b^2[/tex] so
b = 12. Now we're ready to fill in the equation:
[tex]\frac{x^2}{25}-\frac{y^2}{144}=1[/tex] and there you go!
100÷50000 it's has to be step by step aka show work
100÷50000 can be written as 100/50000, then cancel out 2 of the zeroes, and you will get 1/500 or 0.002 as your final answer.
Your neighbor pays $40 to have her lawn mowed and always adds a 15% tip. You and your friend decide to mow the lawn together and split the earnings evenly.
How much will each of you make?
Answer:
$23
Step-by-step explanation:
A 15% tip on $40 is $6. The total you and your friend will receive is $46. When you split that evenly, you will each receive $23.
Cost of Mowing = $40
Tip = 15%
= 15/100×40
= $6
So you get $40 + $6
= $46
When you divide it in 2 people
= 46/2
= $23
Therefore each of you will make $23
Must click thanks and mark brainliest
everything I do is not right help please
49 - 2/3 x = 32 - 1/6 x
Move the constant terms to one side and the terms containing x to the other:
49 - 32 = 2/3 x - 1/6 x
Simplify the left side, and pull out the common factor of x on the right side:
17 = (2/3 - 1/6) x
Write the fractions in terms of a common denominator. In this case, you would take
2/3 = 4/6
so that
(2/3 - 1/6) x = (4/6 - 1/6) x = 3/6 x = 1/2 x
Then the equation is
17 = 1/2 x
Multiply both sides by 2:
2 × 17 = 2 × 1/2 x
34 = x
The area of a square is given as (s³)6.
What is its perimeter?
Answer:
hi friends good evening
169.2 is what percent of 208
Answer:
The percentage is 81.35% (2.d.p)
Step-by-step explanation:
[tex]\frac{169.2}{208}[/tex] x 100 = 81.34615285
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
PLSSS SHOW WORK <3
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
Answer:
Step-by-step explanation:
[tex]\frac{20x+108}{20x+381}[/tex] = [tex]\frac{372}{589}[/tex]
589( 20x + 108 ) = 372( 20x + 381 )
11780x + 63612 = 7440x + 141732
4340x = 78120
x = 18