The probability that one player receives all the 13 hearts is 1/2598960.
How likely something is to occur can be determined using probability. For many events, it is challenging to make an accurate prediction.
The number of ways to distribute the 13 hearts among the 4 players is 4!. The number of ways to distribute the remaining 39 cards among the 4 players is 39!/(13!13!13!13!). Hence, the total number of ways to distribute the 52 cards among the 4 players is (52!)/(13!13!13!13!).
Therefore, the probability that one player receives all the 13 hearts is (4!)/((52!)/(13!13!13!13!)) = 1/((52515049)/(13121110)) = 1/2,598,960.
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you may want to review (page) . for help with math skills, you may want to review: quadratic equations for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of time in the air for a tossed ball. part a how long is the ball in the air before it hits the ground? (the student moves her hand out of the way.)
It takes 0.7143 seconds for the ball in the air to hit the ground.
Therefore the answer is 0.7143 s.
The time it takes for the ball to hit the ground can be calculated using the formula for vertical motion with constant acceleration (g = 9.8 m/s²):
t = √(2 * h / g)
where h is the height the ball is thrown and t is the time it takes to hit the ground.
Plugging in the values to find time:
t = √(2 * 2.50 m / 9.8 m/s²)
t = √(0.51) s
t = 0.7143 s
So, the ball is in the air for approximately 0.7143 seconds before it hits the ground.
--The question is incomplete, answering to the question below--
"A student standing on the wall throws a ball straight up. The ball leaves the student's hands with a speed of 19.0 m/s when the hand is 2.50 m above the ground.
How long is the ball in the air before it hits the ground? (the student moves her hand out of the way.)"
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Will mark Brainliest!! The table shows the city bus schedule for certain bus lines. Both buses are at the bus stop right now. In how many minutes will both busses be at the bus stop again?
Table is A=25 minutes
Table is B=15 minutes
Answer:
75 minutes
Step-by-step explanation:
You want to know when both buses will be at the stop again if bus A arrives every 25 minutes, and bus B arrives every 15 minutes.
Least common multipleThe number of minutes until both buses are at the stop again is the least common multiple (LCM) of their arrival times.
Factors of the times are ...
25 = 5·5
15 = 3·5
A common multiple must have all of these factors, so will have factors ...
LCM = 3·5·5 = 75
After 75 minutes, both buses will be at the stop again.
__
Additional comment
You can see that 5 is a common factor of the two numbers. The LCM can also be found as the product of the two numbers, divided by their greatest common factor (GCF).
LCM(a, b) = a·b/GCF(a, b)
LCM(15, 25) = 15·25/5 = 75
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help I don't get this
Answer:
me neither bro
Step-by-step explanation:
solve this system of equations by using the elimination method.
2x+y=4 x+3y=2
Answer:x=1 y=5
Step-by-step explanation:
Four friends shared the cost of a pizza dinner. They ordered 1 large pizza for $17.50, 4 sodas for $1.25 each, and 4 salads. Salads normally cost $1.75 but were on sale: "Buy one, get one free." If the friends split the total cost of dinner equally, what was each person's share?
Answer:
$6.50
Step-by-step explanation:
So writing out everything
1 Pizza = $17.50
1 soda = $1.25
1 salad = $1.75
Exception; Salad is buy 1 get 1 free, so only 2 salads were paid for
Now we multiple
1 Pizza * 17.50 = 17.50
4 soda * 1.25 = 5
2 salad * 1.75 = 3.50
Now we add
17.50 + 5 = 22.50 + 3.50 = $26.00
Now lastly, we divide by 4 since there are 4 friends
26/4 = 6.5
Giving us a answer of $6.50
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The solution for the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p is p = -4.19/6.1
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
2.3p - 10.1 = 6.5p - 4 - 0.01p
Solve for p.
2.3p - 10.1 = 6.5p - 4 - 0.01p
Combining the like terms.
2.3p - 10.1 = 6.49p - 4
4 - 10.1 = 6.49p - 2.3p
-6.1 = 4.19p
p = -4.19/6.1
Thus,
The solution is p = -4.19/6.1
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In each figure for what values of x and y is the figure a parallelogram
The values of x and y that makes the figure a parallelogram are x = 17 and y = 26
How determine what values of x and y makes the figure a parallelogram?
A parallelogram is a four-sided geometric shape that has opposite sides that are parallel to each other.
The opposite sides of a parallelogram have the same length, and the opposite angles are also equal. The opposite sides of a parallelogram are also known as the bases, and the other two sides are known as the legs.
Since the opposite sides of a parallelogram are equal in length, we can say:
3x + 6 = 4 - x
3x + x = 4 - 6
4x = -2
x = -2/4
x = -1/2 = -0.5
y + 2 = 2y - 3
2 + 3 = 2y - y
5 = y
y = 5
Likewise, the opposite angles of a parallelogram are equal, so we can say:
(4x - 12)° = (3x + 5)°
4x - 12 = 3x + 5
4x - 3x = 5 + 12
x = 17
(3y + 46)° = (5y - 6)°
3y + 46 = 5y - 6
46 + 6 = 5y - 3y
52 = 2y
2y = 52
y = 52/2
y = 26
Thus, x = 17 and y = 26 makes the figure a parallelogram
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FOR WHICH INEQUALITY IS Z = 3 A SOLUTION??/
The inequality is z = 3 a solution. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (A), the inequality is given as follows:
z+5 ≥ 9
z ≥ 9 - 5
z ≥ 4
As per option (B), the inequality is given as follows:
z+5 > 9
z > 9 - 5
Apply the subtraction operation,
z > 4
As per option (C), the inequality is given as follows:
z + 5 ≤ 8
z ≤ 8 - 5
z ≤ 3
Since the solution is less than or equal to three,
Then, this inequality is z = 3 a solution.
Hence, the correct answer would be option (C).
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This question seems incomplete, the complete question would be as:
For which inequality below is z = 3 a solution?
A. z+5 ≥ 9
B. z+5 > 9
C. z+5 ≤ 8
D. z+5 <8
Find the inverse Laplace transforms of the following functions. First, perform partial-fraction expansion on G(s); then, use the Laplace transform table. (a). G(s)= 1 / s(s+2)(s+3) (b). G(s)= 10 / (s +1)^2(s+3) (c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x
(d). G(s)= 2(s+1) / s(s^2+s+2) (e). G(s)= 1 / (s+1)^3 (f). G(s)= 2(s^2+s+1) / s(s+1.5)(s^2 +5s+5)
(g). G(s)= [2+2se^(-x) + 4e^(-2x)] / [s^2 + 3s + 2] (h). G(s) = 2s+1 / (s^2 + 6s^2 +11s +6)
(i). G(s) = (3s^3 + 10s^2 + 8s + 5) / (s^4 + 5s^3 + 7s^2 + 5s +6)
The inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(a). G(s)= 1 / s(s+2)(s+3)
Using partial fraction expansion, we can write G(s) as 1/s + 2/s+2 + 3/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 1/s is 1, the inverse Laplace transform of 2/s+2 is 2e^(-2t) and the inverse Laplace transform of 3/s+3 is 3e^(-3t). Therefore, the inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(b). G(s)= 10 / (s +1)^2(s+3)
Using partial fraction expansion, we can write G(s) as 5/s+1 + 5/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 5/s+1 is 5e^(-t) and the inverse Laplace transform of 5/s+3 is 5e^(-3t). Therefore, the inverse Laplace transform of G(s) is 5e^(-t) + 5e^(-3t).
(c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x
Using partial fraction expansion, we can write G(s) as 50/s + 50/s+1 + 50/s+2 + 50/s+4. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 50/s is 50, the inverse Laplace transform of 50/s+1 is 50e^(-t), the inverse Laplace transform of 50/s+2 is 50e^(-2t) and the inverse Laplace transform of 50/s+4 is 50e^(-4t). Therefore, the inverse Laplace transform of G(s) is 50 + 50e^(-t) + 50e^(-2t) + 50e^(-4t)e^-x.
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find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
The surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
The equation for the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane is given by -
x = 3y2 + 3z2
To explain this equation, let us consider a point P(x, y, z) on the surface. The distance from this point P to the x-axis is given by |x|, and the distance from P to the yz-plane is given by √y2 + z2.
Now, the given condition states that the distance from P to the x-axis is 3 times the distance from P to the yz-plane. This can be written as |x| = 3√y2 + z2. By squaring both sides, we get x2 = 9(y2 + z2), which can be rearranged to give the equation x = 3y2 + 3z2.
This equation thus gives the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
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Evaluate this expression using order of operations when x=1.5 7.5 - 2 ÷ (4x - 2)
Evaluate 0.3 y+\dfrac yz0.3y+
z
y
0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
The value of the expression when y = 10 and z = 5 is 5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
0.3y + y/z
Also, from the question, we have the following values:
y = 10 and z = 5
substitute the known values in the above equation, so, we have the following representation
0.3y + y/z = 0.3 * 10 + 10/5
Evaluate the expression
0.3y + y/z = 5
Hence, the solution is 5
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courtney has constructed a cricket out of paper and rubber bands. according to the instructions for making the cricket, when it jumps it will land on its feet half of the time and on its back the other half of the time. in the first 50 jumps, courtney's cricket landed on its feet 35 times. in the next 10 jumps, it landed on its feet only twice. based on this experience, courtney can conclude that
A confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps. Thus, the correct answer is option D.
A confidence interval is a range of values that is likely to contain the true population parameter (in this case, the true probability of the cricket landing on its feet) with a certain level of confidence. The width of the interval depends on the sample size and the level of confidence.
In the first 50 jumps, the cricket landed on its feet 35 times out of 50, giving a proportion of 0.7. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively wide due to the small sample size.
In the final 10 jumps, the cricket landed on its feet only twice out of 10, giving a proportion of 0.2. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively narrow due to the large sample size.
When comparing the two intervals, it is clear that the interval based on the final 10 jumps is narrower than the interval based on the first 50 jumps. This means that after the final 10 jumps, Courtney has a more precise estimate of the true probability of the cricket landing on its feet than she did before the final 10 jumps.
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The complete question is -
Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the
time and on its back the other half of the time. In the first 50 jumps, Courtney's cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice.
Based on this experience, Courtney can conclude that -
A. the cricket was due to land on its feet less than half the time during the final 10 jumps since it had landed too often on its feet during the first 50 jumps
B. a confidence interval for estimating the cricket's true probability of landing on its feet is wider after the final 10 jumps than it was before the final 10 jumps
C. a confidence interval for estimating the cricket's true probability of landing on its feet after the final 10 jumps is exactly the same as it was before the final 10 jumps
D. a confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps
E. a confidence interval for estimating the cricket's true probability of landing on its feet based on the initial 50 jumps does not include 0.2, so there must be a defect in the cricket's construction account for the poor showing in the final 10 jumps
The question is in the image below
Answer:
y=4/3x-3
Step-by-step explanation:
By using rise/run, you can see the slope in the equation, as it goes 4 units up and 3 units to the right.
For the y-intercept, you can see that the line intercepts (0,-3), which makes it the y-intercept.
Answer: y=-3+4/3x
Step-by-step explanation:
You get -3 because that is the point on the y axis
You get 4/3x from rise every additional point after
-------
run
please help me with math i’ll give you brainlist
Answer:
1. Funnel cakes- 12
2. Oreos- 21
Step-by-step explanation:
1. x= 42/3.50
x=12
2. y= 42/2
y= 21
Solve the following using roots 5x^2-45=0
The solutions to the equation 5x² - 45 = 0 are -3 and 3.
What are the solutions to the equation?Given the equation in the question;
5x² - 45 = 0
To solve using square root property, add 45 to both sides.
5x² - 45 + 45 = 0 + 45
5x² = 45
Divide both sides by 5
5x²/5 = 45/5
x² = 45/5
x² = 9
Take the square root of both sides.
√(x²) = √9
x = ±√9
x = -3, 3
Therefore, the value of x are -3 and 3.
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Solve the system of linear equations by substitution.
5x+2y=9
x+y=-3
Evaluate the expression using the given value of the variable:[ z + (-1 (z - x)) ]; use [x = 4], and [z = 5] .
Answer:
[z+(-1( z-x))]
given,
z=5 X=4
[5+(-1(5-4))]
[5+(-1x(1))]
5+(-1)
5-1
4
Which of the following statements about quadrilaterals are true? Select each correct answer. Responses All squares are rhombuses, but not all rhombuses are squares. All, , squares, , are, , rhombuses,, , but, , not, , all, , rhombuses, , are, , squares., EndFragment, Opposite angles in a parallelogram are congruent. Opposite, , angles, , in, , a, , parallelogram, , are, , congruent., EndFragment, The diagonals of a rectangle are perpendicular.
All of the statements about quadrilaterals that are true include the following:
A. all squares are rhombuses, but not all rhombuses are squares.
B. opposite angles in a parallelogram are congruent.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumGenerally speaking, a typical characteristics of all squares are rhombuses is simply that all squares are classified as rhombuses, but it is not all rhombuses that are classified as squares.
Additionally, the opposite angles of any parallelogram are always congruent because they form parallel lines. However, the diagonals of a rectangle, parallelogram, and trapezium are not perpendicular.
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Vectors: Find the vector from the point (-4,8,7) to the point (6,5,5).Enter the coordinates (_, _, _)Equations of lines: Consider the vector equation of the line through the two points listed above. For each equation listed below, answer T if the equation represents the line, and F if it does not. Here is the list of questions:1. (x,y,z) = (-4,8,7) + t (-10,+3,+2)2. (x,y,z) = (6,5,5) + t (10,-3,-2)3. (x,y,z) = (-4,8,7) + t (6,5,5)4. (x,y,z) = (-4,8,7) + t (10,-3,-2)5. (x,y,z) = (6,5,5) + t (-4,8,7)
The direction vector from the point (-4,8,7) to the point (6,5,5) is (10, -3, -2). The equations which represent the line are: 1. True 2. True 3. False 4. True 5. False.
The direction vector for the line that passes through the two points A (-4,8,7) and B (6,5,5), the position vector of point A is subtracted from the position vector of point B, hence:
v = AB = (6 –(-4), 5 – 8, 5 – 7) = (10, -3, -2)
The vector equation of the line is given by:
r = r0 + tv
where r0 is position vector, t is a scalar parameter, and v is position vector.
Considering the vector equation, the equation which represents the line are:
1. (x,y,z) = (-4,8,7) + t (-10,+3,+2); True
2. (x,y,z) = (6,5,5) + t (10,-3,-2); True
3. (x,y,z) = (-4,8,7) + t (6,5,5); False
4. (x,y,z) = (-4,8,7) + t (10,-3,-2); True
5. (x,y,z) = (6,5,5) + t (-4,8,7); False
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< Question 8 of 42
Macmillan Learning
>
Arrange the given numbers from largest to smallest.
Largest
0.51
7.6
10²
5.6
105
4.9
10-3
Smallest
Answer Bank
From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
What is Descending order?
Descending order can be defined in such a way that the order is from largest to smallest.
Given numbers are ,
0.51 , 7.6 , 10^2 , 5.6 , 105 , 4.9 , 10^-3
10^2 = 10*10 = 100 .
so a^m = a multiplied by m times .
a^-m = 1/ a^m.
10^-3 = 1/1000 = 0.001
So,
We have to write from largest to smallest
we get,
105,100,7.6,5.6,4.9,0.51,0.001
Hence, From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
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Please help I don’t get how to answer this !!
The length of sides in congruent triangles are MN=30, MP=18, PN=30
How to find MN, MP, PN, PS?QR=30, RS=30, SQ=18
In the diagram two congruent triangles are given ΔPMN ≅ ΔQSR.
So by CPCTC (corresponding parts of congruent triangles are congruent)
In ΔPMN and ΔQSR
PN=QR=30 in.
PM=SQ=18 in.
MN=RS= 30 in.
PN=QR=30 then PN=30
PM=SQ =18 then PM=18
MN=RS =30 then MN=30
Congruent triangles are the triangles of which all the sides and all the angles are congruent.
If two triangles are said to be congruent then its all corresponding parts must be equal.
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A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of 8 dollars.
What proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars?
The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars are 0.0099.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the datas are arranged in a symmetrical bell shaped graph.
Given that,
Mean, μ = 87
Standard deviation, σ = 8
We have to calculate P (104.60 < x < 108.20).
For that find z score.
z = (x - μ) / σ
At x = 104.60, z = (104.60 - 87) / 8 = 2.2
At x = 108.20, z = (108.20 - 87) / 8 = 2.65
From the z table,
P(z < 2.65) = 0.9960 and P(z < 2.2) = 0.9861
P (104.60 < x < 108.20) = 0.9960 - 0.9861 = 0.0099
Hence the proportion is 0.0099.
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jahdiel is waxing a hardwood floor that has an area of 4 3/8 square yards. He takes a break aftr waxing 8/9 of the total area of the floor. What is the area, in square yards,that jahdiel waxed? write your answer as a mixed fraction in simplest form.
The amount of hardwood floor that Jahidel waxed is 3 8/9 yards²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of hardwood floor that Jahidel waxed be A
Now , the equation will be
The total area of the hardwood floor is = 4 3/8 yards²
The total area of the hardwood floor is = 35/8 yards²
The amount of floor waxed by Jahidel A = ( 8/9 ) x total area of the hardwood floor
Substituting the values in the equation , we get
The amount of floor waxed by Jahidel A = ( 8/9 ) x ( 35/8 ) yards²
On simplifying the equation , we get
The amount of floor waxed by Jahidel A = ( 35/9 ) yards²
The amount of floor waxed by Jahidel A = 3 8/9 yards²
Hence , the amount of floor waxed is 3 8/9 yards²
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the distribution of the time it takes for different people to solve a certain suduko puzzle is strongly skewed to the right, with a mean of 30 minutes and std of 15 minutes. the distribution of z-scores for those times is:
The distribution of z-scores would be a normal distribution centered at 0, with a standard deviation of 1.
The distribution of time it takes for people to solve a certain Sudoku puzzle is strongly skewed to the right. This means that most people take a shorter amount of time to solve the puzzle, but some take a longer amount of time. The mean (average) of this distribution is 30 minutes and the standard deviation is 15 minutes.
To find the distribution of z-scores, we need to convert the times into z-scores, which is done by subtracting the mean (30) from each time and then dividing by the standard deviation (15). This gives us a new distribution of z-scores, which is centered at 0 (since the mean of the times was subtracted from each time) and has a standard deviation of 1.
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a random sample of n people selected from a large population will be asked whether they have read a novel in the past year. let the random variable r represent the number of people from the sample who answer yes. the variance of random variable r is 6. assume the responses are independent of each other. if the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable r ?
If the proportion of people from the population who read a novel in the past year is 0.40, then a binomial variable with 25 independent trials is the best interpretation of random variable R. So the option 2 is correct.
If the proportion of people from the population who read a novel in the past year is 0.40, then we have define which of the following is the best interpretation of random variable R.
The variance of random variable R is 6.
The variance of binomial distribution is:
var = np(1-p)
n = number of trials
p = the probability
6 = n × 0.40 × (1-0.40)
6 = n × 0.40 × 0.60
6 = n × 0.24
Divide by 0.24 on both side, we get
n = 25
The number of binomial trails is 25.
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The complete question is:
A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ?
1. A binomial variable with 15 independent trials
2. A binomial variable with 25 independent trials
3. A variable that is not binomial with 25 independent trials
4. A binomial variable with 40 independent trials
5. A variable that is not binomial with 40 independent trials
There are 4 boys and 4 girls. In how many ways they can sit in a row
(i) there is no restriction.
(ii) not all girls sit together.
(iii) no two girls sit together.
If there are 4 boys and 4 girls , then the number of ways in which
(i) there is no restriction is 40320 ways ,
(ii) not all girls sit together is 37440 ways ,
(iii) no two girls sit together is 2880 ways .
the number of boys in the class is = 4 boys ;
the number of girls in the class is = 4 girls ;
Part(i) ,
we have to find number of ways in which they can sit in a row where there is no restriction .
there are total of 8 persons ,
So ,the number of ways in which 8 persons can be arranged without any restrictions is = 8! ways.
= 40320 ways
Part(ii) ,
we have to find number of ways in which they can sit in a row where not all girls sit together.
the cases where all gets sit together is written as :
= B₁ , B₂ , B₃ , B₄ , G ⇒ 5! ways ;
= B: G₁ , G₂ , G₃ , G₄ ⇒ 4! ways ;
the number of ways all girls are together is = 5! × 4! ;
So , the number of ways not all girls are together is = 8! - 5!×4! ;
= 37440 ways
Part(iii) ,
we have to find number of ways in which they can sit in a row where no two girls sit together.
this case can be denoted as : G , B₁ , G , B₂ , G , B₃ , G , B₄ .
So , the boys can be arranged in 4! ways ;
and there will be 5 places for 4 girls , which can be arranged in ⁵P₄ ways ;
total number of ways is = 5!×4! = 2880 ways .
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problem solving you go on a hayride to take photographs of landmarks. the map shows your path and two landmarks. each unit in the coordinate plane corresponds to 10 yards. approximate your minimum distance from the giant pumpkin. if necessary, round your answer to the nearest tenth.
The minimum distance from the giant pumpkin is 8.9 yards.
We will use the minimum distance formula between a line and a point to obtain the distance in this case.
A linear function is given according to the standard notation by:
Ax+By+C=0
A point with 'x' and 'y' coordinates are given by:
P(x*,y*)
The formula to find the shortest distance between a point and a line is denoted by the formula:
d=|Ax*+By*+C|/√(A²+B²)
In this issue, the path's line includes:
When x = 0, and y = 0, the intercept is 0.
0.5 slope means that when x rises by 4, y rises by 2.
Thus, y=1/2x
-1/2x+y=0
or, -x+2y=0
The coefficients of the line are:
A=-1 and B=2
Coordinates of the giant pumpkin is (x*,y*)=(-4,-3)
Therefore, the minimum distance is:
d=|(-1)(-4)+2(-3)|/√5
or,d=2/√5
or, d=0.89 units
We know, 1 unit=10 yards
or, 0.89 units=8.9 yards
Thus, the minimum distance between a point and a line is 8.9 yards.
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suppose that 22 inches of wire cost 66 cents. how much will 38 inches of wire cost in cents?
Answer:
114 cents
Step-by-step explanation:
1. 66÷22=3 cents per inch
2. 3×38=114
3. 114 cents ($1.14) for 38 inches
the owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. the following data with waiting times in minutes were collected over a one-month period. 9 11 3 12 11 4 3 3 4 24 13 22 5 18 6 9 12 23 15 2 (a) develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24.
Classes Frequency
0-4 7
5-9 5
10-14 2
15-19 4
20-24 1
The frequency of each class is determined by counting the number of waiting times that fall within each range. For example, the class 0-4 has a frequency of 7, meaning 7 customers waited between 0 to 4 minutes for their oil change.
The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.
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