a classroom of children has 11 boys and 18 girls in which five students are chosen to do presentations. what is the probability that at least four boys are chosen?
Answers
The total Number of ways to select five students out of 11 boys and 18 girls will be=104642
We have, total number of boys = 11, while the total number of girls = 18
Let us assume that,
X = total number of boys chosen
As it is given,
P(X>=4)=1
-P(X<=3)
Where, P(at most 3 boys are chosen) needs to be found out
As we know,
Here, the total number of ways to get at most 3 boys= Number of ways to get three boys and two girls + number of ways to get one boy and four girls + Number of ways to get two boys and three girls + Number of ways to get zero boys and five girls
Making the combination as per above arrangements:
We will get it as:
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
As we know,
The formula of combination is:
\($${ }_n C_r=\frac{n !}{r !(n-r) !}$$\)
\(${ }_n C_r=$\) number of combinations
n= total number of objects in the set
r= number of choosing objects from the set
So, applying the concept of combination in the above,
=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5
\(= \frac{11!}{8! \times 3!} \times \frac{18!}{16! \times 2!}+\frac{11!}{9! \times 2!} \times \frac{18!}{15! \times 3!}+\frac{11!}{10! \times 1!} \times \frac{18!}{14! \times 4!}+\frac{11!}{11! \times 0!} \times \frac{18!}{13! \times 5!}\)
\([\frac{11 \times 10\times9\times8! }{8!\times 6} \times \frac{18\times17\times16!}{16!\times2}]+[\frac{11\times10\times9!}{9!\times2} \times \frac{18\times17\times16\times15!}{15!\times6}]+[\frac{11\times10!}{10!} \times \frac{18\times17\times16\times15\times14!}{14!\times24}]+[\frac{1}{1} \times \frac{18\times17\times16\times15\times14\times13!}{13!\times120}]\)
\(=(165 \times153)+(55\times816)+(11\times3060)+(1\times856.8)\)
=25245+44880+33660+856.8
=104641.8 = 104642 (approx)
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Related Questions
Let x (t) = 5 cos(2π(400)t +0.5π) + 10 cos(2π(500)t – 0.5π). Find the Nyquist rate of x(t).
Answers
Explain how to write 5 thirds as a product of awhole number and a unit fraction
Answers
Answer:
To write 5 thirds as a product of a whole number and a unit fraction, you can multiply 5 by the unit fraction 1/3. So, 5 thirds can be written as 5 x (1/3).
Matt is using 2 mixtures of saltwater solution to make a 6% saltwater solution for his aquarium. One mixture is a 2% saltwater solution, and the other is an 8% saltwater solution. Matt made a chart to calculate the correct amount of each solution to use. Using the information in the table, which equation can Matt use to find x, the amount of 2% mixture he needs to use for his aquarium?
Answers
Answer:
matt needs to use more than 2% mixture for his aquarium
Step-by-step explanation:
urn i contains two red chips and four white chips: urn ii, three red and one white. a chip is drawn at random from urn i and transferred to urn ii. then a chip is drawn from urn ii. what is the probability that the chip drawn from urn ii is red?
Answers
The probability that the chip drawn from urn II is red is 4/15. Let's call the event that the chip drawn from urn I and transferred to urn II is red "R1", and the event that the chip drawn from urn II is red "R2".
The probability of event R1 is 2/6 = 1/3.
Given that event R1 has occurred, the number of red chips in urn II becomes 4, and the number of total chips becomes 4+1=5. The probability of event R2 is 4/5 = 4/5.
The probability of both events occurring is (1/3) * (4/5) = 4/15.
So, the probability that the chip drawn from urn II is red is 4/15.
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What is the probability of randomly selecting a number between 5 and 11 from the numbers 1 - 15
Answers
The probability of randomly selecting a number between 5 and 11 from the numbers 1-15 would be 1/3 or approximately 0.46.
What will be the probability for numbers 5 to 11?The possible outcomes are calculated first. There are 15 possible outcomes in this situation because the numbers 1 through 15 can be chosen.
Count the number of favourable outcomes. There are seven favourable outcomes in this situation because the numbers 5 to 11 are selectable.
By dividing the number of favourable outcomes by the total number of possible possibilities, you may calculate the probability.
The probability in this situation is 7/15, or roughly 0.333 (1/3).Therefore, 7/15, or 0.333, represents the probability of choosing at random number between 5 and 11 from the range of 1 to 15.
Number of events = 7
Total events = 15
Probability = 7/15
Probability = 0.46
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Select the correct answer.
Consider functions f and g.
Which expression is equal to ?
A.
B.
C.
D.
Answers
Answer:
C
Step-by-step explanation:
f(x) • g(x)
= \(\sqrt{x^2+12x+36}\) × (x³ - 12)
= \(\sqrt{(x+6)^2}\) × (x³ - 12)
= (x + 6)(x³ - 12)
= x(x³ - 12) + 6(x³ - 12) ← distribute parenthesis
= \(x^{4}\) - 12x + 6x³ - 72
= \(x^{4}\) + 6x³ - 12x - 72
Answer:
See photo
Step-by-step explanation:
Plato/Edmentum
the perimeter of square s is 40. square t is inscribed in square s. what is the least possible area of square t ?
Answers
The area of the square t inscribed in square s of perimeter 40 cm is 50 sq cm.
If a square is inscribed in a square then the square is formed by joining the midpoints of the square of edges. This is the only square thus the square with the minimum possible area that can be inscribed in a square. Thus we can calculate the side of the inscribed square t as we following:
In right-angled triangle APS, right-angled at A,
By Pythagoras' theorem,
\(a^2=b^2+c^2\)
where a is the hypotenuse
b is the base
c is the height
\(PS^2=AP^2+AS^2\)
Since P is the midpoint, the length of AP and AS is 5 cm.
\(PS^2\) = 25 + 25
PS = \(5\sqrt{2}\) cm
Thus, the side of the square t is \(5\sqrt{2}\) cm
The area of square t is \(side^2\)
= \((5\sqrt{2})^2\)
= 50 sq cm.
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PLSSSSSSSSS I WILI WILL GIVE BRAINLIEST PLSSSSSSSSSSS
The area of a rectangle is 3/4 square yards. If the width of the rectangle is 3/5, what is the length?
EXPRESSION :
ANSWER:
Answers
Answer:
3/8 or 0.375
Step-by-step explanation:
............
Answer:
5/4
Step-by-step explanation:
Area of a rectangle = length * width
A = 3/4, W = 3/5, L = ?
3/4 = L * 3/5
\(\frac{3}{4}= L\frac{3}{5}\)
L * 3 * 4 = 3 * 5
12L = 15
L = 15/12 = 5/4
What are the solution(s) of x2-4-0?
X=-4 or X-4
X=-2 or X= 2
X=2
X=4
Answers
Answer:
X = - 2 or X = 2
Step-by-step explanation:
*completing the square*
X^2 - 4 = 0
X^2 = 4
X = +-√4
x = +-2
x= -2, 2
*factoring*
X^2 - 4 = 0
(x-2)(x+2) = 0
|. |
x = 2, x = -2
________________________________
(x-2)(x+2) = x(x+2) - 2(x+2) = x^2 + 2x - 2x - 4 = x^2-4
In an experiment, the probability that even A occurs is 0.2 and the probability that event B occurs is 0.5. If A and B are independent events, which statement is true?
A.
P(A and B) = 0.1
Answers
Answer:
oop
Step-by-step explanation:
The probability of event A and event B will be 0.10. Then the correct option is A.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
In an experiment, the probability that event A occurs is 0.2 and the probability that event B occurs is 0.5.
If A and B are independent events. Then the probability is given as,
P(A and B) = P(A) x P(B)
P(A and B) = 0.2 x 0.5
P(A and B) = 0.10
The probability of event A and event B will be 0.10. Then the correct option is A.
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The missing options are given below.
A. P(A and B) = 0.1
B. P(A or B) = 0.1
C. P(A and B) = 0.7
D. P(A or B) = 0.7
factor y^3-1 completely
Answers
Answer:
The answer is (y - 1)^3 = (y - 1) (y^2 + y + 1)
Step-by-step explanation:
\((y - 1)^{3} = (y - 1)( {y}^{2} + y \: \: 1 + {1}^{2} ) \\ \\(y - {1)}^{3} = (y - 1)( {y}^{2} + y + 1)\)
Two planes are parallel and each plane contains a line. Are the two lines skew? Explain your reasoning.
Answers
If Two planes are parallel and each plane contains a line, the two lines are not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.
Do two parallel lines on a plane have a skew?Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.
The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.
Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.
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44 - (3c + 4) = 2(c + 5) + c
Answers
Answer:
19/3
Step-by-step explanation:
44 - 3c + 4 = 2c + 10 + c
-2c - 3c -c = - 44 - 4 + 10
-6c = -38
c = 6/1/3 or 19/3
Answer : 5
Process : up up
. Statement I : If the annual simple interest rate equals the annual compound interest rate, then the accumulated value at any time t of an initial deposit of $X using the compound interest rate is always greater. Statement II : If i is unknown, then the value of d plus v cannot be determined. Statement III: 1 is greater than i for all values 0 < i < 1.
A. Only statement I is true
B. Only statement II is true
C. Only statement III is true
D. All 3 statements are false
E. None of the above answers are correct
Answers
The correct option is A) Only statement I is true. Statement I is true: If the annual simple interest rate equals the annual compound interest rate, then the accumulated value at any time t of an initial deposit of $X using the compound interest rate is always greater.
Statement II is false:
If i is unknown, then the value of d plus v cannot be determined.
Statement III is false:1 is greater than i for all values 0 < i < 1.
For instance, if i = 0.5, then 1 is not greater than i.
Let's learn about each statement:
Statement I:If the annual simple interest rate equals the annual compound interest rate, then the accumulated value at any time t of an initial deposit of $X using the compound interest rate is always greater.
This statement is true.
Suppose you deposit $100 at 10 percent for one year. If it is compounded annually, the balance is $110. However, if it is simple interest, the balance is only $100.
Statement II:
If i is unknown, then the value of d plus v cannot be determined.
This statement is false. The sum of d plus v is completely separate from the value of i.
Thus, even if we do not know the value of i, we can find out the sum of d and v.
Statement III:1 is greater than i for all values 0 < i < 1.
This statement is false. For instance, if i = 0.5, then 1 is not greater than i.
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Find 3 rational number between: 1) -5 and -6 2)
Answers
Answer:
3 rational numbers between -5 and -6 include -5.6, -5.7, and -5.1.
Step-by-step explanation:
Answer:
-5.2, -5.6, and -5.8.
Step-by-step explanation:
3 rational numbers between -5 and -6.
-5 > x > -6
Where x is a rational number, that can be expressed in p/q form.
The numbers can be -5.2, -5.6, and -5.8.
-5.2 = -26/5
-5.6 = -28/5
-5.8 = -29/5
The numbers can be expressed in p/q form, so they are rational.
u - 4u + 4 = 7 what is U
Answers
u - 4u = 7 - 4
combine like terms
-3u = 3
divide by -3
u = -1
Answer:
U = -1
Step-by-step explanation:
Combine U with -4U and you get -3.
-3u + 4 = 7
Subtract 4 from 7, you get 3.
Divide 3 by -3, you get -1.
U = -1
Which equation can be used to determine the time for each leg? 600t = 480t 600t = 18 – t 600t = 480 – t 600t = 480(18 – t).
Answers
The equation takes into account the initial 480 units of distance covered in the first leg and the remaining distance (480 - t) covered in the second leg. By solving this equation, one can find the value of t, which represents the time taken for each leg of the journey.
To understand the equation 600t = 480(18 – t), let's break it down. The left-hand side of the equation, 600t, represents the total distance traveled in both legs combined, with 't' representing the time taken for each leg. The right-hand side of the equation, 480(18 – t), calculates the distance covered in the first leg (480) plus the distance covered in the second leg (480 - t).
The equation is derived from the concept of distance-speed-time relationship, where distance is equal to speed multiplied by time. In this case, the distance covered in each leg is represented by 480, and the time taken for each leg is represented by 't'. The remaining distance for the second leg is (480 - t), as the time taken for the second leg is subtracted from the total time of 18 (the total journey time).
By equating the two expressions, 600t and 480(18 – t), we are essentially saying that the total distance covered in both legs is equal to the sum of the distances covered in each individual leg. Solving this equation will yield the value of 't', providing the time taken for each leg of the journey.
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What is the measurement of angle 2?
what’s the measurement of angle 3?
what’s the measurement of angle 4?
what’s the measurement of angle 6?
what’s the measurement of angle 8?
PLEASE QUICK RESPONSE !!! HELPP !
Answers
Then you find out what angles are the same and you have your answer.
a.
Area of a square: 81 in?
Answers
Answer:
Area of square=81 cm^2. ✳But area=side^2. ✳81=s^2
Answer:
Assuming the question is wanting to know the area of a square with sides of 81 inches each, the answer would be
6561 inches squared
Step-by-step explanation:
if each side of the square is 81 inches, you multiply
81 x 81 = 6561
2.01 as a mixed number
Answers
Answer:
2 1/100
Step-by-step explanation:
First you put the 2 in Then you get the 1/100 and put it next to the 2
5. How many ways are there to distribute 10 indistinguishable candies among 4 different
children? Children may end up with no candies.
PLSSSSS HELP IT IS EXTREMELY URGENT PLSSSS
Answers
By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.
What is combination?Combination is the arrangement of objects in which order is not taken into account.
The applicable formula is:
n combination r = n!/[(n - r)!r!]
where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).
Hence;
10 combination 4 = 10!/[(10 - 4)!4!] ways
10 combination 4 = 10!/(6! × 4!) ways
10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways
10 combination 4 = 10 × 3 × 7 ways
10 combination 4 = 210 ways
Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.
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Find the volume of the figure above. Round to the nearest tenth.
Answers
Answer:
1796.6 m³
Step-by-step explanation:
area of base = 1/2(11 + 16) x 9.5 = 128.33 m²
128.33(14) = 1796.6 m³
Which equation represents the line that passes through the point (9,4) and is perpendicular to the graph of 5x+y=30?
Answers
Answer:
x-5y=-11
Step-by-step explanation:
PLEASE I WILL GIVE U 50
Answers
Answer: Number of kids who attended the party = 12 / 0.60
Step-by-step explanation:
60% = 12
x 0.60 = 12
Number of kids attending = x = 12 / 0.60
Answer:
12 is 60
Step-by-step explanation:
Answer: 12 is 60 percent of 20. (60% of 20 = 12) Percentages are fractions with 100 as the denominator.
find the area of the red shaded region round to the nearest tenth.
Answers
Answer:
28.5 in²
Step-by-step explanation:
find the area of the quarter circle:
(pi x r²)/4
100pi/4 =
25pi
To get the shaded region minus the triangle from the quarter circle:
Formula for triangle is bh/2
25 pi - Area of triangle
25 pi - (10x10)/2
25pi - 50
Which is approximately 28.5 square inches.
A country's population in 1990 was 154 million.
In 2001 it was 159 million. Estimate
the population in 2005 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Answers
Using the exponential growth formula, the population in 2005 was 161 million.
The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.
Growth factor = (159/154) for the eleven-year period between 1990 and 2001.
The population growth might thus be described by the exponential equation
p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.
The model forecasts a population of... p(15) = 154(159/154)^(15/11)
= 160.86 = 161 million
In 2005, there were about 161 million people living there.
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Correct Question:
A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.
What happens to (-9,3) when it is translated 3 units right and 4 units down?
Answers
It creates a translation which is (-6,-1).
Find an equation of the sphere with center (-3, 2, 6) and radius 5. What is the intersection of this sphere with the yz-plane? x = 0
Answers
The intersection of the sphere with the yz-plane is a circle centered at (2, 6) with a radius of 5.
The equation of a sphere with center (h, k, l) and radius r is given by (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2. In this case, the center is (-3, 2, 6) and the radius is 5, so the equation of the sphere is (x + 3)^2 + (y - 2)^2 + (z - 6)^2 = 25.
To find the intersection of the sphere with the yz-plane (x = 0), we substitute x = 0 into the equation of the sphere. This gives (0 + 3)^2 + (y - 2)^2 + (z - 6)^2 = 25, which simplifies to 6^2 + (y - 2)^2 + (z - 6)^2 = 25. This equation represents a circle in the yz-plane centered at (2, 6) with a radius of 5.
Therefore, the intersection of the sphere with the yz-plane is a circle centered at (2, 6) with a radius of 5.
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Callie uses leather cord to make necklace she has a piece of leather cord that gas a lengh of 4 yards each necklace will have a lengh of 28 inches how many necklace can callie make
Answers
Since Callie cannot make a fraction of a necklace, she can make a maximum of 5 necklaces from the given length of leather cord.
To determine the number of necklaces Callie can make from the given length of leather cord, we need to convert the measurements to a consistent unit.
Given:
Length of leather cord = 4 yards
Length of each necklace = 28 inches
First, let's convert the length of the leather cord from yards to inches:
1 yard = 36 inches (since there are 3 feet in a yard and 1 foot = 12 inches)
4 yards = 4 * 36 = 144 inches
Now we can calculate the number of necklaces:
Number of necklaces = Length of leather cord / Length of each necklace
Number of necklaces = 144 inches / 28 inches ≈ 5.143
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Molly is making a quilt for her mother. The quilt will have several designs. One of the designs is shown below. What is the total perimeter of the design below?
Answers
Answer: (A) \(12+12\sqrt{12}\) .
Step-by-step explanation:
Perimter is the sum of the all sides of a figure.
As the given design has three exactly same or identical triangles with side-lengths \(2\sqrt{2}\ in, 2\sqrt{2}\ in, 4\ in\) joined by ending vertices.
Then, the combined operimetr of thge design would be :
3 x (Perimeter of the one triangle)
For this , Perimeter of one triangle = \(2\sqrt{2}+2\sqrt{2}+4\ in =(4\sqrt{2}+4) = 4(\sqrt{2}+1) \ in\)
Now , the combined operimetr of thge design would be :
\(3\times4(\sqrt{2}+1)=12(\sqrt{2}+1)\ in\) or \(12+12\sqrt{12}\ in\)
Hence, the correct option is (A) \(12+12\sqrt{12}\) .
Answer:
it is a
Step-by-step explanation: