The number of ways can the committee be organized will be 2220075. Then the correct option is 3.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
The prom committee is made up of 8 boys and girls.
If there are 12 boys and 15 girls in the group to pick the committee from.
Then the number of ways can the committee be organized will be
Then the number of ways is given by the combination formula. Then we have
Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀
Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495
Number of ways = 2220075
Thus, the correct option is 3.
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Find the derivative of 1/√s+2
Using the quotient rule, it is found that the derivative of the function is given as follows:
[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]
What is the derivative of a quotient?Suppose a quotient function defined as follows:
[tex]f(x) = \frac{g(x)}{h(x)}[/tex]
Then, the derivative is given by:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]
In this problem, we have that:
g(x) = 1.g'(x) = 0.[tex]h(x) = \sqrt{s} + 2[/tex].[tex]h^{\prime}(x) = \frac{1}{2\sqrt{s}}[/tex]Then, since g'(x) = 0, the derivative is given by:
[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]
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Find the values of x and y.
x=____
(b) y=_____
[tex]sin60 = \frac{opp}{hyp} \\ sin60 = \frac{y}{12 } \\ \frac{ \sqrt{3} }{2} = \frac{y}{12} \\ 2y= 12 \sqrt{3} \\ y = 6 \sqrt{3} [/tex]
[tex]cos60 = \frac{adj}{hyp} \\ cos60 = \frac{x}{12} \\ \frac{1}{2} = \frac{x}{12 } \\ 2x = 12 \\ x = 6[/tex]
Hope it helps
Please give brainliest
there are 6 members of a board of supervisors for a park district they need to form a subcommittee of 3 people to study expanding a park how many different committees could be formed from the members
The coach recorded the scores of nine different basketball players in their last game. ● The median number of points scored by these nine players was 13. ● The mean number of points scored by these nine players was 12. Part A: List 9 values that could represent this data set. Part B: A 10th basketball player on this team scored 12 points in the last game. If her score is added to this data set, how will the median and mean change? Explain your reasoning.
The values that could represent this data set include 5, 6, 9, 10, 12, 10, 4, 6, and 19.
How to calculate the mean?It should be noted that a mean simply means the average of a set of numbers.
In this case, the values that could represent this data set include 5, 6, 9, 10, 12, 10, 4, 6, and 19. Therefore, the mean will be:
= (5 + 6 + 9 + 10 + 12 + 4 + 6 + 19)/9
= 81/9
= 9
When a 10th basketball player on this team scored 12 points in the last game, the new mean will be:
= (81 + 12)/10
= 93/10
= 9.3
Therefore, there's an increase in mean.
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HELPPPPPPPPPPPPPPPPPP
Answer:
B
Step-by-step explanation:
if we consider the coordinates of the points
(2, 3 )
(5, 6 )
(7, 8 )
we can see that the y - coordinate in each case is 1 more than the x- coordinate, then
y = x + 1 is the required rule
which graph below shows the solutions for the linear inequality y<1/3x-4
Step-by-step explanation:
the answer is C since y is less than. meaning that the line should be dashed and below the graph.
comment if you have any doubts.
Determine the type of quadrilateral created by the points of intersection of the lines x-y+3=0, y=x-2, y = -1/2x + 5, and x+2y+12=0.
The set of parallel lines in a quadrilateral leads to the parallelogram.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
Line M
x - y + 3 = 0,
y = x + 3
m = 1
Line L
y = x - 2,
m = 1
Line N
y = -1/2x + 5,
m = -0.5
Line P
x+2y+12=0
y = -x/2 - 6
m = -0.5
Here we can see that the slope of line M and L are equal and slope of line N and P are equal.
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Hence, the set of parallel lines in a quadrilateral leads to the parallelogram.
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which method is best for solving the system of equations,
3x+2y=4
-3x+y=2
The method which is best for solving the system of equations when you remove one variable by adding them is B Elimination
To answer the question, we need to know what system of equations are
What are system of equations?System of equations are pairs of equations that contain two unknowns
Ways of solving system of equationsWe have different ways of solving systems of equations which include
Guess and CheckEliminationGraphing and SubstitutionSince we have the system of equations
3x + 2y = 4
-3x + y = 2
The method which we can use to remove one variable by adding them is the elimination method.
Adding them, we have
3x + 2y = 4
+
-3x + y = 2
3y = 6
y = 6/3
y = 2
So, the method which we can use to remove one variable by adding them is B Elimination
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The perimeter of the rectangle is 146 units. what is the length of the longer side? 14 units 28 units 33 units 45 units
Answer:
45
Step-by-step explanation:
perimeter is the sum of all sides
for rectangle, it's (length + width) x 2
so do the reverse: 146/ 2 = l + w
73-45 = 30 this means the longer side is 45
=> length is 45
Answer:c
Step-by-step explanation:just took the test
Пожалуйста помогите с решением
Answer:
( x, y) =
[tex]65 \ \frac{15}{11} [/tex]
this is your answer
geometry please help (pentagons)
Answer:
144
Step-by-step explanation:
540 degrees is the sum of angles in a pentagon
Divide 540 by 5(number of sides) =108(interior angle)
Since there are two pentagons you do 108 X 2 = 216 degrees
Do 360 - 216 = 144
so your answer is right
The Transamerica Pyramid Building in San Francisco is 853 ft tall with a square base that is 149 ft on each side.
To the nearest thousand cubic feet, what is the volume of the Transamerica Pyramid?
At a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. the officer randomly selects 100 of them and asks if they intend to major in liberal arts. of the 100 first-year students, 62 state they intend on majoring in liberal arts. assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts? 0.38 plus-or-minus 1.96 startroot startfraction 0.38 (1 minus 0.38) over 100 endfraction endroot 0.62 plus-or-minus 1.96 startroot startfraction 0.62 (1 minus 0.62) over 100 endfraction endroot 0.38 plus-or-minus 1.65 startroot startfraction 0.38 (1 minus 0.38) over 1000 endfraction endroot 0.62 plus-or-minus 1.65 startroot startfraction 0.62 (1 minus 0.62) over 1000 endfraction endroot
The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is option B. 0.62 plus-or-minus 1.96 start root start fraction 0.62 (1 minus 0.62) over 100 end fraction end root .
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
Confidence interval for the population proportion can be calculated as,
p ± z × [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Here, p is the sample proportion and n is the sample size.
z value for 95% confidence interval is 1.96.
Here, n = 100,
p = [tex]\frac{62}{100}[/tex] = 0.62
Substituting the values, confidence interval of true proportion is,
0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex]
Hence the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is 0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex].
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Which of the following is an exponential function?
a. f(x)=x³ + 2x²² -6
b. f(x) = 5/x
c. f(x) = 5x + 2
d. f(x) = 4x²
e. f(x) = 4x*2*
f(x) = 4²ˣ, this is an exponential function. Then the correct option is E.
What is an exponent?Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as
y = aˣ + b
The exonentuial functions are given below.
a. f(x)=x³ + 2x²² -6, this is not an exponential function.
b. f(x) = 5/x, this is not an exponential function.
c. f(x) = 5x + 2, this is not an exponential function.
d. f(x) = 4x², this is not an exponential function.
e. f(x) = 4²ˣ, this is an exponential function.
Then the correct option is E.
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may someone help me with this question? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:3(3x + 5)[/tex]
now plug in the value of x as 5
[tex]\qquad \sf \dashrightarrow \:3(3(5) + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \:3(15 + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \:3(20)[/tex]
[tex]\qquad \sf \dashrightarrow \:60 \: [/tex]
So, the equivalent value is 60
Derrick grows vegetables on a circular patch of land. The radius of the patch is 16 meters. What is the approximate area of the patch of land?
Answer:
A≈804.25m²
Step-by-step explanation:
A=πr2=π·162≈804.24772m²
Jed places the letters A, B, C, D, E, F, G, H and I into a bag and picks 2 at random. What is the probability he chooses at least 1 vowel?
Answer:
0.583333333333Step-by-step explanation:
we have 9 letters
3 vowels: A , E , I
6 consonant: B, C, D, F, G , H
Consider the event V : «choosing at least 1 vowel»
[tex]\Longrightarrow \overline{V} \ \colon \ \text{choosing 2 consonant}[/tex]
[tex]p(V) =1-p\left( \overline{V} \right) =1-\frac{C^{2}_{6}}{C^{2}_{9}}=0.583333333333[/tex]
Can someone help me with this
Solve for x, if 4x - 24 = 1 000.
Solve for x, if 7x = 343.
Solve for x, if x4 = 4 096.
Answer with step-by-step explanation:
1) 4x - 24 = 1000
Add 24 to both sides.
4x = 1024
Divide both sides by 4.
x = 256
2) 7x = 343
Divide both sides by 7.
x = 49
3) x⁴ = 4096
Find 4th root of both sides.
x = 8
What is the domain of the given function?
{(3,-2), (6, 1), (-1, 4), (5, 9), (-4, 0)}
{x|x = -4,-1, 3, 5, 6}
Oyly=-2, 0, 1, 4, 9}
O {x|x = -4, -2, -1, 0, 1, 3, 4, 5, 6, 9)
Oyly=-4, -2, -1, 0, 1, 3, 4, 5, 6, 9)
h
Answer:
A
Step-by-step explanation:
the domain are the value on the x coordinate
i.e 3, 6, -1, 5, -4 = {-4,-1,3,5,6}
Which two shapes make up the first split of quadrilaterals on the quadrilateral hierarchy?
1. kite and square
2. square and rectangle
3. trapezoid and square
4. trapezoid and kite
Trapezoid and kite make up the first split of quadrilaterals on the quadrilateral hierarchy
What is a quadrilateral?A quadrilateral is a polygon that has four sides and four angles. Types of quadrilateral are square, kite, trapezoid, rectangle, rhombus and so on.
A quadrilateral hierarchy is a graphical way of representing the different types of quadrilaterals.
Trapezoid and kite make up the first split of quadrilaterals on the quadrilateral hierarchy
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A sugar solution currently measures 250 degrees fahrenheit. the temperature of the solution increases 5 degrees per minute. the sugar solution will caramelize at temperatures greater than 310 and less than 338 degrees fahrenheit. which inequality can be used to find x, the number of minutes it will take for the solution to begin caramelizing?
The inequality which is used to find the number of minutes taken by the solution to begin caramelising is 310 < 250 + 5x <338. The correct answer is option A.
The complete question is given below:-
A sugar solution currently measures 250 degrees Fahrenheit. The temperature of the solution increases 5 degrees per minute. The sugar solution will caramelize at temperatures greater than 310 and less than 338 degrees Fahrenheit. Which inequality can be used to find x, the number of minutes it will take for the solution to begin caramelizing? 310 < 250 + 5x < 338 310 < 250 + 5x < 338 310 < 5(x + 250) < 338 310 < 5(x + 250) < 338
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is called an inequality.
According to the given question.
The current temperature of a sugar solution is 250 degrees Fahrenheit. Per minute the temperature of the solution increases by 5 degrees. Also, x is the number of minutes taken by the sugar to caramelize.
⇒ The total increase in the temperature in x minutes = 25 + 5x
Since the sugar solution caramelizes at a temperature greater than 310 and less than 338.
Inequality will be given as:-
310 < 250 + 5x < 338
Therefore, the inequality which is used to find the number of minutes taken by the solution to begin to caramelize is given by 310 < 250 + 5x < 338.
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Help please with problem 2 I will mark brainliest
Answer:
During the rapid diagnostic test of coronavirus among 250 people 96% were found negative .how many people were found negative
what is the solution to the inequality below 14-2(x+1)< -4
Answer:
x > 8
Step-by-step explanation:
14 - 2(x + 1) < - 4 ← distribute parenthesis and simplify left side
14 - 2x - 2 < - 4
12 - 2x < - 4 ( subtract 12 from both sides )
- 2x < - 16
divide both sides by - 2 , reversing the symbol as a result of dividing by a negative quantity.
x > 8
What would the answer be?
Answer:
C
Step-by-step explanation:
since ∠ m ≅ ∠ p , then
9x - 2 = 4x + 18 ( subtract 4x from both sides )
5x - 2 = 18 ( add 2 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
then
∠ p = 4x + 8 = 4(4) + 18 = 16 + 18 = 34°
What is the area, in square feet, of the isosceles trapezoid below?
Answer:
A≈78.54
Step-by-step explanation:
A¹=7.7×6.6=50.82(area of rectangle inside)
16.1-7.7=8.4/2=4.2
A²=6.6×4.2=27.72(area of triangles)
A=50.82+27.72=78.54
What is the value of x?
2
3
6
7
Answer: 2
Step-by-step explanation:
DE * CE = AE * BE (Two Secants Segment Theorem)
▪︎ DE = 1 + x + 4
▪︎ CE = x + 4
▪︎ AE = 11 + x + 1
▪︎ BE = x + 1
=> (1 + x + 4)(x + 4) = (11 + x + 1)(x + 1)
=> (x + 5)(x+4) = (x + 12)(x + 1)
=> x^2 + 9x + 20 = x^2 + 13x + 12
=> 9x + 20 = 13x + 12
20 - 12 = 13x - 9x
8 = 4x
x = 2
Jewel spins the pointer of a spinner. the spinner has 7 equal-sized sections labeled 1 to 7. what is the probability that jewel will spin a 7?
The answer is one in seven or (1/7)!!!!!!!!!!!!!!!!!!!!!!!!!!!!
need help with this......
Based on the definition of sequence and the characteristics of the given sequence, the complete sequence is: 4, 543, 65432, 7654321, 876543210.
How to complete a sequence
Sequences are sets whose elements observes at least a condition. In this question we have a sequence formed by numbers formed by decimal digits ordered in descent way. Where the consecutive element has more digits than the previous one.
Then, we conclude that the complete sequence is: 4, 543, 65432, 7654321, 876543210.
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find the volume of the pyramid
Volume is a three-dimensional scalar quantity. The volume of the right-triangular pyramid is 1.008 m³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a right-triangle pyramid is one-third of the product of its base area and its height. Therefore, the volume is,
Volume = (1/3) × 0.5 × 1.4 × 1.8 × 2.4
= 1.008 m³
Hence, the volume of the right-triangular pyramid is 1.008 m³.
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