To solve the question, calculate the total possible ways to form a committee and the ways for each specific case. The probability can be determined by dividing the specific event by the total outcomes. This involves the mathematical principles of combinatorics and probability.
Explanation:
The question is dealing with the concept of combinatorics and probability. In such cases, we look at the total possible outcomes and the outcomes of our specific event of interest.
For the first case, we need to select 2 students and 2 faculty members from respective pools of 20 and 5. The total ways to form a committee are combinations of 4 from 25 (20 students + 5 faculty). So, we have:
Total outcomes = C(25,4)
The event of interest (2 students and 2 faculty) can be calculated as the product of combinations of selecting 2 from each pool:
Specific event outcomes = C(20,2)*C(5,2)
To get the probability, we divide the outcomes of our event of interest by the total outcomes.
The second scenario works similarly. You want one faculty and three students:
Specific event outcomes = C(20,3)*C(5,1)
You'd again divide this result by the total possible outcomes (determined the same as the first scenario) to obtain the desired probability.
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The probability of forming a committee with two students and two faculty members is 15%, while the probability of forming a committee with one faculty member and three students is 45%.
Explanation:a. Two students and two faculty members:
To find the probability of selecting two students and two faculty members, we need to calculate the number of ways this combination can occur and then divide it by the total number of possible combinations.
The number of ways to select two students from 20 is C(20, 2) = 190.
The number of ways to select two faculty members from 5 is C(5, 2) = 10.
The total number of ways to form a committee of 4 from 25 volunteers is C(25, 4) = 12,650.
So the probability is (190 * 10) / 12,650 = 1900 / 12,650 = 0.15, or 15%
b. One faculty member and three students:
Similarly, the number of ways to select one faculty member from 5 is C(5, 1) = 5, and the number of ways to select three students from 20 is C(20, 3) = 1,140.
The total number of ways to form a committee of 4 from 25 volunteers is still C(25, 4) = 12,650.
So the probability is (5 * 1,140) / 12,650 = 5,700 / 12,650 = 0.45, or 45%
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PLEASE HELP ASAP!!!!!!!!!!
Use the table below to answer this question:
x y
0
2
1
−1
2
−6
Find the average rate of change for the given function from x = 0 to x = 2.
2
4
−4
1
Did hamiltons plans favored the northern states? true or false
Answer:
true
Step-by-step explanation:
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what is 7x10^-5 in decimals
7x10^-5 as a decimal is 0.00007, achieved by multiplying 7 by 0.00001, which represents 10^-5.
To convert 7x10^-5 into decimal form, you can use the concept that a negative exponent indicates the inverse. This means that 10^-5 is the same as 1/10^5 or 1 divided by 100,000. Thus, to find 7x10^-5 in decimal form, you multiply 7 by 0.00001.
Here's the calculation:
7 x 0.00001 = 0.00007
Therefore, 7x10^-5 in decimal form is 0.00007.
If you were to place $5,000 in a savings account that pays 6% interest compounded continuously, how much money will you have after 4 years? Assume you make no other deposits or withdrawals.
A. $6,356.25
B. $11,821.07
C. $5,024
D. $6,312.38
...?
Answer:
Option D - $6312.38
Step-by-step explanation:
Given : If you were to place $5,000 in a savings account that pays 6% interest compounded continuously.
To find : How much money will you have after 4 years?
Solution :
Using compound interest formula,
[tex]A=P(1+r)^t[/tex]
Where A is the amount,
P is the principle P=$5000
r is the rate r=6%=0.06
t is the time t= 4 years
Substitute the value,
[tex]A=P(1+r)^t[/tex]
[tex]A=(5000)(1+0.06)^4[/tex]
[tex]A=(5000)(1.06)^4[/tex]
[tex]A=5000\times 1.262[/tex]
[tex]A=6312.38[/tex]
The money he have after 4 years is $6312.38
Therefore, Option D is correct.
Answer:
A. $6,356.25
Step-by-step explanation:
To calculate the amount of money you will have after 4 years in a savings account with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the amount of money accumulated after t years
P = the initial principal amount (in this case, $5,000)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (in decimal form, so 6% becomes 0.06)
t = the number of years (in this case, 4)
Plugging in the values, we get:
A = 5000 * e^(0.06 * 4)
Using a calculator, we can evaluate this expression:
A ≈ 5000 * 2.71828^(0.24)
A ≈ 5000 * 1.276281
A ≈ 6381.405
Rounding to the nearest cent, the amount of money you will have after 4 years is approximately $6,381.41.
Therefore, the closest answer option is A. $6,356.25.
How many points are used to define a plane?
A. zero
B. one
C. two
D. three
Answer:
it will be D
Step-by-step explanation:
Solve for the indicated variable
A= bh/2, solve for b
Answer:
b = 2A/have a nice day :)
The required simplified solution for b for the given expression is b=2A/h.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
A = bh/2
Isolate the variable B, and multiply both sides by 2/h,
2A/h = b
So
b = 2A/h
Thus, the required simplified solution for b for the given expression is b=2A/h.
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Two numbers are in a ratio of 3:6 their sum is 63 find the bigger number
To find the bigger number in the given ratio of 3:6 with a sum of 63, simplify the ratio to 1:2, assign a variable to the smaller number, and solve for the larger one. The bigger number is found to be 42.
Explanation:To find the bigger number when two numbers are in a ratio of 3:6 and their sum is 63, first simplify the ratio to its lowest terms. The ratio 3:6 simplifies to 1:2, since both terms can be divided by 3. Let's assign the variable x to the smaller number, which corresponds to the '1' part of the ratio. Therefore, the bigger number is twice the smaller one, so it can be represented as 2x.
The sum of the two numbers is given by the equation x + 2x = 63. Combine like terms to get 3x = 63. Dividing both sides by 3 gives x = 21. Since 2x represents the bigger number, we have 2x = 2 imes 21 = 42.
Hence, the bigger number in this ratio is 42.
24 plus something =120÷3
Find the perimeter of △ABC with vertices A(−4, 3), B(1, −5), and C(−4, −5). Round your answer to the nearest hundredth.
Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. the side pockets are halfway down the rails (longside)
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| |12
| |
| |
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6
Find the distance, to the nearest tenth of an inch, diagonally across from the corner pocket to side pocket ...?
Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.
Answer: [tex]\dfrac{8}{9}[/tex]
Step-by-step explanation:
Given : Marty has saved $72. He spent $8 on a video rental.
i.e. The amount of money he saved = $72
The amount of money he spent on video rental = $8
Now, the amount of money he had left = [tex]\$72-\$8=\$64[/tex]
Thus , the ratio that represent what portion of his savings he has left :-
[tex]\dfrac{64}{72}=\dfrac{8}{9}[/tex]
Hence, the ratio that represent what portion of his savings he has left :-
[tex]=\dfrac{8}{9}[/tex]
Oscar needs to ship 14 rock cds, 12 classical cds, and 8 pop cds. he can only pack only one type of cd in each box and he must pack the same number of cds in each box. what is the greatest number of cds oscar can pack in each box?
Answer:
2
Step-by-step explanation:
Oscar needs to pack only one type of cd in each box and he must pack the same number of cd's in each box.
To solve this problem we would need to find the greatest common factor of the numbers given; the numbers that we have are 14, 12, 8.
First we are going to find the factors of all these three numbers:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
The common factors of these three numbers are bolded:
14 = 1 x 2 x 7
12 = 1 x 2 x 2 x 3
8 = 1 x 2 x 2 x 2
We can see that the common factors are 1 and 2. The biggest of them is 2.
Therefore, the greatest number of cd's Oscar can pack in each box is 2
Since 2 is common to them all, hence the greatest number of cds oscar can pack in each box is 2 CDs
Given the number of cars needed to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs
In order to get the greatest number of cds oscar can pack in each box, we will have to calculate the GCF of each value as shown:
The prime factors of each value is as shown
14 = 2 * 7
12 = 3 * 2 * 2
8 = 2 * 2 * 2
From the factors, we can see that only 2 is common to them all, hence the greatest number of CDs oscar can pack in each box is 2 CDs
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If ΔABC and ΔGEF are congruent by the ASA criterion, which pair of angles must be congruent?
Answer:
it should be CAB and GEF
Step-by-step explanation
Compare and contrast simplifying the numeric expression 3 – (2 + 5) to the algebraic expression 3x – (2x + 5)
how many 5/6s are in 3 and 1/3
HELP ME- 15 points
Jaycee is writing a coordinate proof to show that the diagonals of a rectangle bisect each other. She starts by assigning coordinates to a rectangle. Then she uses these coordinates to write the coordinates of the midpoint of each diagonal. She finds that the midpoints of the diagonals have the same coordinates, so the diagonals must bisect each other.
What are the coordinates of the midpoint of the diagonals of the rectangle?
Enter expressions in the box for the coordinates of the midpoint.
(__,__)
The coordinates of the midpoint of the diagonals of a rectangle are found by averaging the x-coordinates and the y-coordinates of the endpoints of the diagonals. Because of the properties of a rectangle, the midpoint will be the same for both diagonals, confirming that the diagonals bisect each other. The midpoint's coordinates are ((x1+x2)/2, (y1+y2)/2).
Explanation:To find the coordinates of the midpoint of the diagonals of a rectangle, you must first know the coordinates of the rectangle's vertices. Suppose the rectangle has vertices at (x1, y1), (x1, y2), (x2, y1), and (x2, y2). Without loss of generality, let (x1, y1) and (x2, y2) be the endpoints of one diagonal and (x1, y2) and (x2, y1) be the endpoints of the other diagonal.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by averaging each of the x-coordinates and the y-coordinates of the endpoints. Thus, the midpoint M1 has coordinates ((x1+x2)/2, (y1+y2)/2). Similarly, the midpoint M2 for the other diagonal has coordinates ((x1+x2)/2, (y2+y1)/2). Because of the properties of a rectangle, these midpoints will be the same, confirming that the diagonals bisect each other.
Therefore, the coordinates of the midpoint of the diagonals of a rectangle are ((x1+x2)/2, (y1+y2)/2).
how to find the hypotnuse
Final answer:
To find the hypotenuse of a right triangle, apply the Pythagorean theorem: a² + b² = c². After squaring the lengths of the two other sides and adding them together, take the square root of the sum to get the length of the hypotenuse, which is approximately 10.3 units in the example provided.
Explanation:
To find the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This can be written as the equation a² + b² = c². To solve for the hypotenuse, you would rearrange the equation to c = √(a² + b²).
For example, if the legs of a right triangle measure 9 and 5 units:
First, square both of the leg lengths: 9² = 81 and 5² = 25.Add these two values together: 81 + 25 = 106.Take the square root of the sum: √106 ≈ 10.3 units.Thus, the hypotenuse would measure approximately 10.3 units, where we use three significant figures for precision in measurement.
What is 75% of 60? tell me the answer?
List the first three commen multiples of 2 3 9
which is a factor of 54xy+45x+18y+15?
a) x-5
b)6y+5
c)6y+1
d)3y+5 ...?
One of the factors of 54xy + 45x + 18y + 15 is b) 6y + 5.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given,
54xy + 45x + 18y + 15.
= 54xy + 18y + 45x + 15.
= 18y(3x + 1) + 15(3x + 1).
= (3x + 1)(18y + 15).
= (3x + 1)(3)(6y + 5).
So, a factor of 54xy + 45x + 18y + 15 is (6y + 5).
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9 is 35 percent of what number
Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. What is the measure of the angle subtended by the arc?
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use?
Which of the following statements describes the absolute value of a number "a"?
A) The opposite value of a number "a" can be represented by the absolute value of a number "a."
B) Given |a|, "a" is always positive
C) The distance from the number "a" to 0 on a number line can be represented by the absolute value of a number "a."
D) The positive value of a negative number "a" can be represented by the absolute value of a number "a."
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
The maximum volume of the box is:
1000 cm³
Step-by-step explanation:Let x be the length of the square base
and h be the height(h) of the box.
As we know that the length(l) and width(w) of the box is same( since the base is in the shape of square)
As we know that the surface area of box is given by:
[tex]Surface\ Area=2(lw+wh+hl)\\\\\\i.e.\\\\\\Surface\ Area=2(x^2+xh+xh)\\\\\\Surface\ Area=2(x^2+2hx)[/tex]
We are given surface area of box=600 cm²
Hence,
[tex]2(x^2+2hx)=600\\\\i.e.\\\\x^2+2xh=300\\\\i.e.\\\\h=\dfrac{150}{x}-\dfrac{x}{2}[/tex]
The volume of box is given by:
[tex]Volume(V)=l\times w\times h\\\\\\Volume=x^2h\\\\\\Volume=x^2(\dfrac{150}{x}-\dfrac{x}{2})[/tex]
Hence,
[tex]V=150x-\dfrac{x^3}{2}[/tex]
Now, for maxima or minima we have derivative equal to zero.
[tex]i.e.\\\\\\\dfrac{dV}{dx}=0\\\\\\i.e.\\\\\dfrac{d}{dx}(150x-\dfrac{x^3}{2})=0\\\\\\i.e.\\\\\\150-\dfrac{3x^2}{2}=0\\\\\\i.e.\\\\\\150=\dfrac{3}{2}x^2\\\\\\x^2=100\\\\\\i.e.\\\\\\x=\pm 10[/tex]
Now,
[tex]\dfrac{d^2V}{dx^2}=\dfrac{-6x}{2}\\\\\\=-3x[/tex]
Now, as we know if for a given x
[tex]\dfrac{d^2V}{dx^2}<0[/tex]
then that x is a point of maxima.
Hence, when we put x=10 we get: [tex]\dfrac{d^2V}{dx^2}<0[/tex]
Hence, x=10 is a point of maxima
Also, the value of V at x=10 is:
[tex]V=150\times 10-\dfrac{(10)^3}{2}\\\\\\V=1500-\dfrac{1000}{2}\\\\\\V=1500-500\\\\V=1000\ cubic\ cm.[/tex]
Hence, the maximum volume of the box is:
1000 cm³
What is the explicit rule for this geometric sequence? 2, 6, 18, 54, …
Answer:
A term at position n can be expressed as \[2*3^{n-1}\]
Step-by-step explanation:
The given geometric sequence is 2, 6, 18, 54, …
Starting term = 2
Second term = 6
So second term is 3 times the first term.
Similarly, Third term = 18
This is 3 times the second term, that is , 3 * 6
Fourth term is is 54.
This is 3 times the third term, that is , 3 * 18
Generalizing, a term in the sequence can be expressed as \[2*3^{n-1}\]
where n represents the position of the term in the sequence.
How many x-intercepts are there in y = –3x2 + 4x + 4
What fraction is £1 of 13p?
If BC bisects the angle ACD, then B is the midpoint of AD.
A. True
B. False
Answer:
It’s true
Step-by-step explanation: just took the test