A committee of 6 people is chosen from 6 women and 6 men. How many different committees are possible that consist of 3 women and 3 men?
Answers
there are 400 different committees possible that consist of 3 women and 3 men.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components.
To form a committee of 3 women and 3 men from a group of 6 women and 6 men, we need to choose 3 women from 6 women and 3 men from 6 men. We can use the combination formula to calculate this:
Number of ways to choose 3 women from 6 women = 6C3 = (6!)/(3!3!) = 20
Number of ways to choose 3 men from 6 men = 6C3 = (6!)/(3!3!) = 20
To find the total number of possible committees, we need to multiply these two numbers:
Total number of possible committees = 20 x 20 = 400
Therefore, there are 400 different committees possible that consist of 3 women and 3 men.
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Related Questions
The area of this rectangle is 72 what is the length,x, if the width is 4
Answers
Answer:
18
Step-by-step explanation:
you have to divide 72 by 4. when you get 18 you can multiply that by 4 and you would get 72.
6) 1,1,3,8,19, 41
a) 60
b) 81
c) 90
d) 101
Analogias
Answers
The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.
To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:
1 1 3 8 19 41
0 2 5 11 22
Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.
Let's check if the differences between consecutive terms are square numbers:
2 = 1²
5 = 2² + 1²
11 = 3² + 2²
22 = 4² + 3²
Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:
41 + 57 = 98
Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.
Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.
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Points A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a square ABCD. The square ABCD is reflected about the line through (0, 0) and (-2, 2). Find the vertices of the image of the square ABCD and present both the figures on the same graph.
Answers
The vertices of the reflected square.
Let's calculate them:
A' = (-0.914, 3.914)
B' = (-2.828, 5.828)
C' = (-0.086, 7.086)
D' = (1.828, 5.172)
The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:
Find the equation of the reflection line:
The reflection line passes through (0, 0) and (-2, 2).
We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):
m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.
Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:
y - 0 = -1(x - 0)
y = -x.
Find the midpoint of each side of the square:
The midpoints of the sides of a square are also the midpoints of its diagonals.
The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).
The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).
The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).
The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).
Reflect the midpoints about the line:
To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.
The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:
d = (y + x) / √(2).
The coordinates of the reflected points can be found using the formula for reflection across a line:
x' = x - 2d / √(2)
y' = y - 2d / √(2).
Calculate the reflected vertices:
The coordinates of the reflected vertices are as follows:
A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))
B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))
C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))
D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))
Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.
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* Required 32 * 32. We assume that SAT score is linearly associated with GPA and determine the correlation coefficient to be 0.8. What does this value suggest? A. SAT score decreases as GPA increases B. There is no relation between SAT score and GPA C. GPA increases as SAT decreases D. SAT score increases as GPA increases ОА
Answers
The correlation coefficient gives us a precise measurement of the relationship between two variables, in this case the variables are the SAT score and the GPA score, the values of a correlation coefficient goes from -1.0 and 1.0, the question is telling us that the correlation coefficient is 0.8, this means that the correlation is positive and the relationship between the variables is strong because the vaue is closer to 1.
The image is an example of a correlation and shows us a strong positive correlation.
Then we can determine that the answer is:
D. SAT score increases as GPA increases.
STATEMENTREASON1. AWXY 21 an exterior 21.Given22.exterior = sum ofremoteinterior 2's3. 1 > 223. Ifa=b+c and c>0,then a > bWhich of the following statements would complete the proof in line 2?O 21 = 22 + 23O Z1 = 22 + 24Z1 = 23 + 24
Answers
The reason given is:
\(\text{exterior }\angle=\text{ sum of remote interior }\angle^{\prime}s\)This means that an exterior angle is equal to the sum of the non adjacent interior angles.
In this case the non adjacent angles are 2 and 3, then the statement will be:
\(\angle1=\angle2+\angle3\)hence the answer is the first option.
Is 4(7-1) and 28-1 equal?
Answers
Answer:
fasdfjahlskfhkajshf
Step-by-step explanation:
jfdlhgkdfhgldfhg lsdfjhgsdhflhg klsfdhgjdsfhgkdfhgh
∑⊥⇆Ф↑↓∩¬║⊅α∨∧
(testing answer, sorry for that)
Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere
x^2+y^2+z^2=125
Answers
The parametrization shown below,
\(x(t),y(t),z(t)=10cost,5,10sint\)
Given equation of sphere,
\(x^{2} +y^{2} +z^{2} =125\)
Substitute y = 5 in above relation.
\(x^{2} +z^{2}=125-25=100\\ \\x^{2} +z^{2}=10^{2}\)
For parametrization,
Substitute \(x=rcos(t),z=rsin(t)\) and \(r=10\)
So that, \(x(t),y(t),z(t)=10cost,5,10sint\)
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Can someone help me with this please?
Answers
Answer:
The triangles are similar.
Explanation:
Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.
Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses
Answers
Answer:
37
Step-by-step explanation:
x=-4
=2(5-(-4)2+1
=2(5+4)2+1
=2(9)2+1
=18(2)+1
=36+1
=37
Pat and Kamal had $575 altogether. Pat spent of her money and Kamal
spent $150. Pat then had three times as much money as Kamal. How much
did Kamal have at first?
Answers
Answer:
$200Step-by-step explanation:
This question has some missing information, here is a complete one
Pat and Kamal had $575 altogether. Pat spent 3/5 of her money and Kamal spent $150. Pat then had three times as much money as Kamal. How much did Kamal have at first.
you can find attached a detailed solution of the question for your reference
University Bank pays 5% interest compounded quarterly on regular savings accounts and Rosemont
Savings Bank
pays 5.5% compounded semiannually. Vasily and Oxana Cherchenko had $4,000 to invest
for 4 years. Based on the interest to be earned, which bank offers the better investment?
Answers
well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years
\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)
\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)
\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)
\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)
Write a function g in terms of f so that the statement is true
Answers
Horizontal changes are often the opposite of what you'd expect to see in the formula.
12:
To shrink/compress horizontally by a factor of 2/3, you need \(g(x) = f(\frac{3}{2}x)\).
Notice we have the reciprocal inside of the function notation.
13:
To translate left 5 units, you have \(g(x) = f( x+5 )\).
Notice we have the opposite sign inside of the function notation.
All of the following are irrational except _____.
Answers
The number that is not irrational is \(1.\overline{45}\). The correct option is the second option \(1.\overline{45}\)
Irrational numbersFrom the question, we are to determine which of the given options is not irrational
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.
\(1.\overline{45}\) is a repeating decimal and it can be expressed as a fraction
\(1.\overline{45} = \frac{144}{99}\)
∴ \(1.\overline{45}\) is not an irrational number. It is a rational number
The other options cannot the expressed as a fraction.
Hence, the number that is not irrational is \(1.\overline{45}\). The correct option is the second option \(1.\overline{45}\)
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Find the sum of 16.99+8.305
Answers
Answer:
25.295
Step-by-step explanation: Just add them up
A point in the table for the transformed function is
Answers
Answer:
linear function
Step-by-step explanation:
straight line then add up
Picture below/above.........
Answers
Answer:
a= -12
hope it helps.
and also sorry, if I'm wrong.
Answer:
a=-24
Step-by-step explanation:
a-8×6=12×-6
a-48=-72
a=-72+48
a=-24
NEED HELP ASAP (30Points!!) Which answers are examples of the Law of Syllogism? Select each correct answer. A) If there is a children’s movie playing at the cinema, Maria’s mother will take her to see it. When Maria’s mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria. B) If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram. C) If a quadrilateral is a rectangle with 4 equal sides, then it is a square. Quadrilateral ABCD is a rectangle with 4 equal sides. Therefore, quadriateral ABCD is a square. D) Sally goes to the mall every Saturday. Today is Saturday. Therefore, Sally will go to the mall today.
Answers
Answer:
The correct answer is: (just took the test)
if a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram
if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria
Step-by-step explanation:
For the given answers the answers that follow the law of syllogism is options A and B.
Given that,
4 statement is given, and we have to pick the statement that follows the low of syllogism.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here
There are only two statements that are following the law of syllogism. ie.
A. If there is a children's movie playing at the cinema, Maria's mother will take her to see it. When Maria's mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children's movie playing at the cinema, Maria's mother will buy popcorn for Maria.
B. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.
C. and D. are invalid statement because it does not follow the Law of Syllogism.
Thus, for the given answers the answers that follow the law of syllogism is options A and B.
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Can someone help me
Answers
Answer:
Y = -½x + 3/2
Y = -3x + 5
Y = 1/4x - 3¼
Step-by-step explanation:
Parallel implies they have the same gradient
Perpendicular implies the gradient is a negative reciprocal of the other.
Since she bought it. Nissa's favorite baseball card increased in value from $1.20 to $6.
What is the percent change in the card's value?
Enter your answer in the box
Answers
Answer:
500%
Step-by-step explanation:
\( \frac{6 \times 100}{1.2} = 500\%\)
The amount you pay for a car is not usually the "sticker price," which may be the starting price. The price of a car was reduced by $300 from the sticker price, increased by $900 for additional features, and then reduced by $600 by the dealer. What integer represents the total change in price with respect to the sticker price? Use a number line to represent the change from the sticker price.
Answers
There will be no change in the price of the car.
What is a number line?A number line is a representation of a graduated straight line used to abstract real numbers in elementary mathematics. Its points are considered to correspond to real numbers and vice versa.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let the sticker price = x, Price reduced by $300
Hence the new price is,
N= x-$300
The cost of additional features = $900
Hence the new price for selling will be.
=x-$300+$900
=x+$600
Dealer also provides a discount of $600
Hence Final selling price will be
=x+$600-$600
Hence there seems to be no change in the sticker price as the sticker price and the final selling price are the same.
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I really need help with this Triangle problem.
Answers
Answer:
12
Step-by-step explanation:
Here we use SOHCAHTOA
Seeing as we have the hypotenuse and we are working to find out the opposite, we use SOH
Sin(x)= Opposite/Hypotenuse
Sin(45) = x/\(12\sqrt{2} \\\)
×12 root 2
sin(45) times 12 root 2= 12
x=12
(12²-15+17)+16= what is the answer
Answers
162
Step-by-step explanation:
(12 square - 15 + 17) + 16
=(144 - 15 + 17) + 16
=146 + 16
=162
Nelda drove 315 kilometers and used 35 liters of gasoline. Her car averaged how many kilometers per liter of gas?
Answers
Going 315 km uses up 35 liters of gasoline
On average, 1 liter of gasoline can travel the number of kilometers:
315 : 35 = 9 liters of gasoline
A theater sells 2 types of fixed-price tickets - orchestra and balcony. Peter pays $50 for 1 orchestra and 4 balcony tickets. Justine pays $150 for 3 orchestra and 12 balcony tickets. А B The cost of 1 balcony ticket. The cost of 1 orchestra ticket. The quantity under A is greater than the quantity under B. The quantity under B is greater than the quantity under A. The quantities under A and B are equal. The information given is insufficient to make the comparison.
Answers
Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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The stock price of Alps Co. is $53.50. Investors require a return of 13 percent on similar stocks. If the company plans to pay a dividend of $3.40 next year. what groeth rate is expected for the company's stock price?
Answers
Answer:
The expected growth rate for the company's stock price is 9.7%. This is calculated by subtracting the dividend yield (3.40/53.50 = 0.0635) from the required return (13%).
CAN SOMEONE PLS HELP I NEED ANSWERS TO PASS THIS CLASS
Answers
Which fraction is closest to 1/2
?
Answers
The fraction which is closest to 1/2 is, 3/8. So option B is correct
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
A fraction number 1/2
In decimal form = 0.5
Closest fraction number = ?
Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,
Lets take, A fraction 1/6
In decimal form it can written as, 0.167
Difference 1 = 0.5 - 0.167
= 0.333
Similarly, For numbers 3/8, 3/4, -1/2
Difference 2 = 0.5 - 0.375 = 0.125
Difference 3 = 0.5 - 0.75 = -0.25
Difference 4 = 0.5 - (-0.5) = 1.0
It can be seen that,
Magnitude of difference in case of 3/8 is very less
Hence, the closest number is 3/8
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how many apples are in 4 dozen
Answers
There are 48 apples in 4 dozen
Explanations:1 dozen = 12
This means that:
1 dozen of apples = 12 apples
4 dozen = 12 x 4
4 dozen = 48 apples
What is the value of x in the following equation:
((x + 5) / 3) + ((x - 7) / 4) = ((2x + 1) / 2)
Answers
Answer: To solve this, you'll need to find a common denominator and simplify the equation before solving for x.
The answer is: x = 23/5 or 4.6
oliver walks 5/8 of a mile in 1/6 of an hour. What is his unit rate in miles per hour?
Answers
Answer:
3.75 miles per hour
Step-by-step explanation:
(5/8)/(1/6)=3.75 mph, or you could do 5/8 x 6, since 1/6 x 6 equals one hour
Answer:
3 3/4 miles per hour
Step-by-step explanation:
Take the miles and divide by the hours
5/8 ÷ 1/6
Copy dot flip
5/8 * 6/1
Rewriting
5/1 * 6/8
5/1 * 3/4
15/4
3 3/4