the student council for a school of science and math has one representative from each of the five academic departments: biology (b), chemistry (c), mathematics (m), physics (p), and statistics (s). two of these students are to be randomly selected for a university-wide student committee. the two students will be selected by placing five slips of paper (numbered 1, 2, 3, 4, and 5) into a bowl, mixing, and drawing out two of them.
Answers
There are a total of 10 possible combinations when selecting two students for the university-wide student committee from the five academic departments.
To determine the number of possible combinations when selecting two students for the university-wide student committee from the five academic departments, we can use the combination formula.
The number of combinations, denoted as C(n, r), represents the number of ways to select r items from a set of n items without regard to the order of selection.
In this case, we have five academic departments, and we want to select two students. Therefore, we can calculate C(5, 2) as follows:
C(5, 2) = 5! / (2! * (5 - 2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2
= 10
Therefore, there are 10 possible combinations when selecting two students for the university-wide student committee from the five academic departments.
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Related Questions
Please help me with this
Answers
Answer:
1850is the correct answer
18=5a-2a+3
answer this pleaseee
Answers
Answer:
a=5
Step-by-step explanation:
18=5a-2a+3
Combine like terms
18 = 3a +3
Subtract 3 from each side
18-3 = 3a+3-3
15 = 3a
Divide by 3
15/3 =3a/3
5 =a
add and reduce to lowest terms: 1 2/3+ 2 3/7 I need help ASAP
Answers
Answer:
The answer is 4 2/21
Step-by-step explanation:
Answer: 4 4/21
Step-by-step explanation: 1 2/3=1 14/21. 2 3/7=2 9/21
the glitz jewelry kit contains round beads in 6 different colors plus 100 star-shaped beads. there are 250 beads in all. which equation can you use to find r, the number of round beads in each color?
Answers
The number of round beads in the glitz jewelry kit are 25
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Let x be the number of round beads in the glitz jewelry kit. Then the equation is written as,
6x + 100 = 250
Simplify the equation, then the value of 'x' is given as,
6x + 100 = 250
6x = 250 - 100
6x = 150
x = 150/6
x = 25
The number of round beads there in each color will be 25.
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Which one?
A. B. C. or D?
Answers
Step 1. When there is a minus in front of an expression in parentheses, change the sign of each term in the expression.
-> 2 - 7 + 7 + 6
Step 2. Since two opposites add up to zero, remove them from the expression.
-> 2 + 6 = 8
PLEASE HELP!!! NEED IN 10 MIN!!!
Answers
Answer:
8a^3x^3
Step-by-step explanation:
2. Determine the points of intersection of each pair of functions. a) y = 4x^– 15x + 20 and y = 5x – 4 = - - b) y = - 2x^ + 9x +9 and y = - 3x – 5
Answers
To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.
a)
Let's equate the functions and solve for x:
\(\begin{gathered} 4x^2-15x+20=5x-4 \\ 4x^2-15x-5x+20+4=0 \\ 4x^2-20x+24=0 \\ 4(x^2-5x+6)=0 \\ x^2-5x+6=0 \\ (x-3)(x-2)=0 \\ \text{ then} \\ x=3 \\ or \\ x=2 \end{gathered}\)Now we find the corresponding values of y for each value of x; to do this we use the second equation.
When x=3:
\(\begin{gathered} y=5(3)-4 \\ y=15-4 \\ y=11 \end{gathered}\)Hence the functions intersect at (3,11)
When x=2:
\(\begin{gathered} y=5(2)-4 \\ y=10-4 \\ y=6 \end{gathered}\)Hence the functions intersect at (2,6)
Therefore the function intersect at the points (3,11) and (2,6).
b)
Let's equate the functions and solve for x:
\(\begin{gathered} -2x^2+9x+9=-3x-5 \\ 2x^2-9x-9-3x-5=0 \\ 2x^2-12x-14=0 \\ 2(x^2-6x-7)=0 \\ x^2-6x-7=0 \\ (x-7)(x+1)=0 \\ \text{ then} \\ x=7 \\ or \\ x=-1 \end{gathered}\)Now we find the corresponding values of y for each value of x; to do this we use the second equation.
When x=7:
\(\begin{gathered} y=-3(7)-5 \\ y=-21-5 \\ y=-26 \end{gathered}\)Hence the functions intersect at (7,-26)
When x=-1:
\(\begin{gathered} y=-3(-1)-5 \\ y=3-5 \\ y=-2 \end{gathered}\)Hence the functions intersect at (-1,-2)
Therefore the function intersect at the points (7,-26) and (-1,-2).
What is the composition of the translations (T ∘ T ) (x, y) as one translation
Answers
Answer:
Step-by-step explanation:
A car is traveling at a steady speed. It travels 1(1/2) miles in 2(1/4) minutes. How far will it travel in 26 minutes? In 1 hour?
Answers
Answer:
17\(\frac{1}{3}\)miles
40miles
Step-by-step explanation:
Given parameters;
Distance traveled by the car = 1\(\frac{1}{2}\)miles = \(\frac{3}{2}\)miles
Time taken = 2\(\frac{1}{4}\)minutes = \(\frac{9}{4}\)minutes
Unknown:
Distance covered in 26minutes and in 1hr = ?
Solution:
Speed is the rate of change of distance with time.
Speed = \(\frac{distance}{time taken}\)
A. Insert the parameters and find the speed;
Speed = \(\frac{\frac{3}{2} }{\frac{9}{4} }\) = \(\frac{3}{2}\) x \(\frac{4}{9}\) = \(\frac{2}{3}\)miles/minutes
Distance covered in 26minutes;
Distance = speed x time
Distance = \(\frac{2}{3}\) x 26 = \(\frac{52}{3}\) miles = 17\(\frac{1}{3}\)miles
B. Distance covered in 1hr or 60minutes;
Distance = \(\frac{2}{3}\) x 60 = 40miles
(7−2)3×(24−11)? cause im in 6th grade lol
Answers
Answer:
(7−2)(3)(24−11)
=(5)(3)(24−11)
=15(24−11)
=(15)(13)
=195
Step-by-step explanation:
HURRY I NEED BY 6:15 The recipe calls for 1/4 cup of rice for every 1 cup of veggies. Now, use the double number line to find the number of cups of rice the restaurant would need for 20 cups of veggies. Solve on paper, then enter your answer on Zearn.
Answers
The number of cups of rice the restaurant would need for 20 cups of veggies is 5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
The recipe calls for 1/4 cup of rice for every 1 cup of veggies.
Now,
1cup veggie = 1/4 cup rice
20cup veggies= 1/4 * 20 cup rice
=5
Therefore, by algebra the count of cups of rice will be 5.
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A(1,5), B(-4,-3), C(3,-3), and find the area of the triangle it forms.
Answers
Answer:
first calculate the lenght of a triangle with the distance formula
A lorry weighs 3.2 tonnes when empty. It weighed 7.7 tonnes when loaded with 90 kg bags of maize. How many bags of maize were loaded?
Answers
The number of bags of maize loaded is A = 50 bags
Given data ,
A lorry weighs 3.2 tonnes when empty. It weighed 7.7 tonnes when loaded with 90 kg bags of maize.
To find the number of bags of maize loaded onto the lorry, we need to calculate the difference in weight between the loaded and empty states, and then convert that difference into the weight of the bags.
The weight of the lorry when loaded with bags of maize is 7.7 tonnes, and when empty, it weighs 3.2 tonnes. Therefore, the weight of the bags of maize is:
7.7 tonnes - 3.2 tonnes = 4.5 tonnes
On simplifying the equation , we get
Number of bags = (Weight of maize) / (Weight per bag)
= 4.5 tonnes / 0.09 tonnes
= 50 bags
Hence , there were 50 bags of maize loaded onto the lorry
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An assembly line has 16 hours to make 1.000 units. What is the required cycle time? (slide 23) 72sec 216sec 57.65sec 14,4sec
Answers
The required cycle-time is approximately 57.6 seconds.
To find the required cycle time, we need to divide the total available time by the number of units to be produced.
Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds
Number of units to be produced: 1,000 units
Required cycle time: Total available time / Number of units
Cycle time = 57,600 seconds / 1,000 units
Cycle time ≈ 57.6 seconds
Therefore, the required cycle time is approximately 57.6 seconds.
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Page 1 For each question below, mark whether or not the statement is correct. Yes No Choose one option for each line 3n4 +2n} = O(nº) O 4n + 45 log n = (n) = O 5 n = 2(m+) O 2n+2 = (2") о (3n5 + n+n
Answers
For each question below, mark whether or not the statement is correct. 1. 3n^4 + 2n = O(n^0) - No, 2. 4n + 45 log n = O(n) - Yes, 3. 5n = 2^(m+) - No, 4. 2n + 2 = 2^n - Yes, 5. 3n^5 + n + n = O(n^5) - Yes,
The correct answers are as follows:
1. 3n^4 + 2n = O(n^0) is incorrect. The correct answer is No because the polynomial expression has a higher degree than n^0, indicating a higher time complexity.
2. 4n + 45 log n = O(n) is correct. The expression represents linear time complexity as it grows linearly with the input size n.
3. 5n = 2^(m+) is incorrect. The correct answer is No because the expression represents an exponential relationship between 5n and 2^m, indicating a higher time complexity.
4. 2n + 2 = 2^n is correct. The expression represents an exponential relationship where 2^n grows significantly faster than 2n.
5. 3n^5 + n + n = O(n^5) is correct. The expression represents a polynomial relationship with the highest term being n^5, indicating a time complexity of O(n^5).
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(0,7) (1,5) (1.5,3) (2,5) (2.3,3.2) ( 3,2) (3.5,4) the regression line is y= the correlation coefficient is r=
Answers
1) In this question, we can start setting our table:
2) Now let's find the regression line by finding the slope and the linear coefficient, according to these formulas below:
So
\(\begin{gathered} m=\frac{41.86-12.3\times24.2}{6\times32.79-(32.79)^2} \\ m=0.2911\approx0.29 \\ b=\frac{24.2-0.29\times12.3}{6} \\ b=3.4388\approx b=3.44\text{ } \end{gathered}\)Therefore we can write the regression line as:
\(y=0.29x\text{ +3.44 }\)3) Now let's find the correlation coefficient through another formula:
\(\begin{gathered} r=\frac{n\Sigma xy\text{ - (}\Sigma x)(\Sigma y)}{\sqrt[]{\lbrack n(\Sigma x)^2-(\Sigma x)^2\lbrack}n\Sigmay^2-\Sigmay^2)\text{ }} \\ r=\frac{6\times41.86-12.3\times24.2}{\sqrt[]{(6\times(12.3)^2)(6\times(24.2)^2-24.2)}} \\ r=-0.0261 \end{gathered}\)
A university claims that the mean number of hours worked per week by the professors is more than 50 hours. A random sample of 9 professor has a mean hours worked per week of 60 hours and a standard deviation of 15 hours. Assume α = 0. 5
Answers
From hypothesis testing, the university claim that mean number of hours worked per week by the professors is more than 50 hours has no evidence to support, i.e., p-value > 0.5.
The university claim is that mean number of hours worked per week by the professors is more than 50 hours.
Sample size of professors, n = 9
Sample mean of hours, \(\bar x = 60\) hours
Standard deviations= 15 hours
Level of significance, α = 0. 5
To verify the claim we have to consider a hypothesis testing, let the null and alternative hypothesis be defined as
\(H_0 : \mu = 50 \\ H_a : \mu > 50 \)
To test the hypothesis performing a test statistic, Using the t-test, \(t = \frac{ \bar x - \mu }{\frac{ \sigma}{\sqrt{n}}}\)
Substitute all known values in above formula, \(t = \frac{ 60 - 50}{\frac{ 15}{\sqrt{9}}}\)
\( = \frac{ 10}{\frac{ 15}{3} } = 2 \)
Also, degree of freedom, df = n - 1 = 8
Using the critical value calculator or t-distribution table value critical value for t = 2 and Degree of freedom 8 is equals to 0.7064. As P-value = 0.7064 > 0.5, so
we fail to reject the null hypothesis.
Hence, the claim is not true.
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Someone please help me with these.
Answers
The equations in the slope-intercept form are
p = 3b + 2 and p = (5/2)b + 15/2.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
From the table and scatter plot;
(a). The line for 'Build it' passes through (1, 10) and (3, 15),
then the equation of the line is,
p = (5/2)b + 15/2
Similarly, the equation of the line-'All things home' is,
p = 3b + 2.
(b) the graphs of the lines are given in the attached image.
(c) The equation in the slope-intercept form;
p = 3b + 2 and p = (5/2)b + 15/2.
(d) When b = 65,
then p = 3(65) + 2 and p = (5/2)(65) + 15/2.
So, p = 197 and p = 170
Therefore, all the required values are given above.
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when a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. by what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?
Answers
The driving time along this stretch was reduced by 36% for a person who always drives at the speed limit.
To calculate the percent reduction in driving time along the stretch, we need to consider the effects of both the distance decrease and the speed increase.
First, let's assume the original distance of the stretch was D. After the reconstruction, the distance is now 0.8D (since it was decreased by 20%).
Next, let's assume the original speed limit was S. After the reconstruction, the speed limit is now 1.25S (since it was increased by 25%).
To calculate the original driving time along the stretch, we would use the formula: time = distance / speed. So the original driving time would be D/S.
After the reconstruction, the driving time would be (0.8D) / (1.25S) = 0.64D/S.
To calculate the percent reduction in driving time, we can use the formula: (original time - new time) / original time * 100%.
Plugging in the values we calculated, we get:
(original time - new time) / original time * 100% = (D/S - 0.64D/S) / (D/S) * 100% = 36%.
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You are taking hang-gliding lessons. The cost of the first lesson is one and a half times the cost of each additional lesson. You spend $260 for six lessons.
Answers
First thing to do is to figure out how many additional lessons are in that, which are 5.
Then you can make a 1 variable equation with the information you have. I’m using x as my variable.
260= 3/2x + 5x
Combine like terms.
260 = 13/2x
Divide both sides by 13/2 (treat it as a fraction, and if your calculator cannot make fractions, then decimal might help for this. 13/2=6.5)
X=40
Simplify.
-2(-3y+v) + 2(-4x+y)
Answers
Answer:
answer is this =8y-2v-8x
Step-by-step explanation:
Answer:
8y - 2v - 8x
Step-by-step explanation:
-2(-3y + v) + 2(-4x + y)
~Distribute
6y - 2v - 8x + 2y
~Combine like terms
8y - 2v - 8x
Best of Luck!
If z = 2x2 - 3y with u = x2 siny and v= 2y cosx, determine expressions for dz/du and dz/dv
Answers
The expressions for dz/du and dz/dv are as follows:
dz/du = 4x siny
dz/dv = -6y cosx
To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.
1. dz/du:
Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:
z = 2u - 3y
Now, we differentiate z with respect to u while treating y as a constant:
dz/du = d/dx (2u - 3y)
= 2(d/dx (x^2 siny)) - 0 (since y is constant)
= 2(2x siny)
= 4x siny
Therefore, dz/du = 4x siny.
2. dz/dv:
Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:
z = 2x^2 - 3v
Now, we differentiate z with respect to v while treating x as a constant:
dz/dv = d/dy (2x^2 - 3v)
= 0 (since x^2 is constant) - 3(d/dy (2y cosx))
= -6y cosx
Therefore, dz/dv = -6y cosx.
In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.
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MATH HELP. ( please answer both questions ) thank you !
Answers
Answer:
A. 3500
B. The wall is unidentified, therefore we have to multiply 6 and 50 to recieve a, the height.
Step-by-step explanation:
The profit p gained from selling an item can be modeled by a quadratic function in terms of its cost c. If the cost of the item is at $100 or $400, there will be no profit or loss. But if the cost is $250, the item generates the maximum profit of $30.
Answers
Answer:
Uh I'm not really sure how to screenshot on my laptop, but the answer should be B.
Step-by-step explanation:
Lets say I made a graph, P being profit C being cost.
P
50|___|___|___|___|___|
40|___|___|___|___|___|
30|___|___|___|___|___|
20|___|___|___|___|___|
10 |___|___|___|___|___|C
0___100|200|300|400|500
It goes from 100 (LOW) to 400 (HIGH). 250 being the the cost of the item, and the maximum profit being 30. Cost 250,0__Profit 0,30. In all 250,30.
Therefore whatever the letter answer is they might be shuffled, do the one that most compares to this formula.
Please mark me Brainliest, the graph was really annoying to make.
Quadrilateral ABCD is similar to quadrilateral FGHJ with a ratio of similitude of 7:11. If FJ=11, AB=2x, BC=3x, CD=4x, and AD=x, what are FG, GH, and HJ?
Answers
To find the lengths of FG, GH, and HJ in quadrilateral FGHJ, given that quadrilateral ABCD is similar to FGHJ with a ratio of similitude of 7:11 and FJ=11, AB=2x, BC=3x, CD=4x, and AD=x, follow these steps:
1. Set up the ratio of similitude: (ABCD side)/(FGHJ side) = 7/11.
2. Use the given side lengths of FGHJ (FJ) and ABCD (AB, BC, CD, AD) to find the corresponding side lengths in FGHJ.
a. For FG (corresponding to AB), the ratio is (2x)/FG = 7/11. Solve for FG:
11 * (2x) = 7 * FG
22x = 7 * FG
FG = 22x / 7
b. For GH (corresponding to BC), the ratio is (3x)/GH = 7/11. Solve for GH:
11 * (3x) = 7 * GH
33x = 7 * GH
GH = 33x / 7
c. For HJ (corresponding to CD), the ratio is (4x)/HJ = 7/11. Solve for HJ:
11 * (4x) = 7 * HJ
44x = 7 * HJ
HJ = 44x / 7
So, FG = 22x / 7, GH = 33x / 7, and HJ = 44x / 7.
Tom buys a condominium for $42,600. he makes a down payment of 15%, and pays these closing costs: survey $225; inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286. what is the amount of the down payment? what are the total closing costs? how much will he need to bring to the closing (down payment + closing costs)?
Answers
Tom will need to bring to the closing $54,341.27 He would need 12 and it would cost 50k.
What is the meaning of down payment?The meaning down payment is a part of the full price paid at the time of purchase or delivery with the balance to be paid later.
We have given that,
Tom buys a condominium for $42,600.
Inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286
He makes a down payment of 15% and pays these closing costs to survey $225.
9% payments: $563.24
7% payments: $494.75.
Monthly savings: $69.49
9% total repaid: $2022,764.90
7% total repaid: $148,423.63
Savings: $54,341.27
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EEEEeee Can someone help?
Answers
Answer:
5.61 billion dollars.
Step-by-step explanation:
4.61+1.03=5.61
Answer:
0.223
Step-by-step explanation:
Change the divisor 4.61 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
103 ÷ 461 = 0.223
and therefore:
1.03 ÷ 4.61 = 0.223
Both calculated to 3 decimal places.
twenty-five percent of the employees of a large company are minorities. a random sample of 7 employees is selected. what is the probability that the sample contains exactly 4 minorities?
Answers
The probability that the sample contains exactly 4 minorities is 0.0577
How to find the probability?We know that 25% of the employees of a large company are minorities. So, from any set of N employees that we ranodmly select from that large company, we can estimate that the number of minorities there is:
0.25*N
Now, we want to find the probability that the sample contains exactly 4 minorities.
Then we need to compute:
\(P = 0.25^4*0.75^3\)
We also need to count the permutations for that probability, then we need to add the factor:
\(P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )\)
Solving that we will get:
\(P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )\\\\P = 0.25^4*0.75^3*(\frac{7*6*5}{3*2} )\\\\P = 0.0577\)
That is the probability.
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C.
Minh and Mikayla are selling wrapping paper for a school fund-raiser. Customers can
buy either packages of folded paper or rolls of paper. Minh sold 6 rolls of paper and 2
packages of folded paper for a total of $44. Mikayla sold 3 rolls of paper and 9 packages
of folded paper for a total of $54. How much does each roll cost? How much does each
package of folded paper cost?
Answers
Answer:
Rolls $6, Folded $4
Step-by-step explanation:
Minh: 6r + 2f = 44
Mikayla: 3r + 9f = 54
Multiply Mikayla's x 2: 6r + 18f = 108
Subtract Minh: 6r + 2f = 44
16f = 64
f = 4, Folded paper is $4.
Substitute 4 for f into one of the equations.
6r + 2(4) = 44
6r + 8 = 44
6r = 36
r = 6 Rolled paper is $6
Marissa bought 60 horns for her new year's eve party for $83. 40. She needs to purchase an additional 18 horns for the party at the same unit price. What is the unit price for each horn?
Answers
The unit price for each horn is $4.63.
To find the unit price for each horn, we can divide the total cost of the horns by the number of horns purchased. Marissa bought 60 horns for $83.40, so the unit price can be calculated as $83.40 divided by 60.
$83.40 / 60 = $1.39
This means that the unit price for each horn is $1.39. Now, Marissa needs to purchase an additional 18 horns at the same unit price. To find the cost of the additional horns, we can multiply the unit price by the number of horns.
$1.39 * 18 = $25.02
Therefore, the additional 18 horns will cost $25.02. Adding this amount to the previous total cost, we get:
$83.40 + $25.02 = $108.42
In conclusion, the unit price for each horn is $1.39, and Marissa needs to spend a total of $108.42 to purchase the additional 18 horns for her New Year's Eve party.
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