a) The probability of both balls drawn from the bag be red is 6/55
b) The probability of one ball red and other ball black is 4/11
Given,
Number of white balls in the bag = 2
Number of red balls in the bag = 4
Number of black balls in the bag = 5
Two balls are drawn from the bag.
Here,
a) Find the probability of both balls be red.
(²C₀ x ⁴C₂ x ⁵C₀) / ¹¹C₂
= (1 x 6 x 1)/ 55
= 6/55
That is,
The probability of both balls be red is 6/55
b) Find the probability of one ball red and other ball black
(²C₀ x ⁴C₁ x ⁵C₁) / ¹¹C₂
= (1 x 4 x 5) / 55
= 20/55
= 4/11
That is,
The probability of one ball red and other ball black is 4/11
Learn more about probability here;
https://brainly.com/question/23986809
#SPJ4
in some situations it might not be possible to carry out a randomized controlled experiment, even when the aim is to investigate causality in the collected data. in these type of situations, the researcher should be worried about potential g
it might not be possible to carry out a randomized controlled experiment, even when the aim is to investigate causality in the collected data the researcher should be worried about potential g idiographic
Type of causal reasoning is an idiographic explanation
we know that there are 2 types of approach for understanding the social life
Idiographic
nomothetic
and here idiographic approach use for understanding single or individual type case or event but a nomothetic approach that is used for understanding large scale social pattern
so here also cause of the single situation is exhaustively examined
so correct answer is an idiographic explanation
learn more about of experiment here
https://brainly.com/question/14454574
#SPJ4
A circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle. What is the area of the shaded region? Round your final answer to the nearest hundredth.
how many (non-congruent) isosceles triangles exist which have a perimeter of $10$ and integer side lengths?
As per the Pythagoras theorem, there are totally 4 triangles possible.
Pythagoras theorem:
In geometry, Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.
Given,
Here we need to find how many (non-congruent) isosceles triangles exist which have a perimeter of 10 and integer side lengths.
As per the Pythagoras theorem, we know that the sum of two sides should be greater than the third.
And here we have the isosceles triangles, then the value of two side of the triangle is equal.
Here the perimeter of the triangle is 10.
Then the values must be the sum of 10,
=> 2, 6, 2
=> 1, 1, 8
=> 3, 3, 4
=> 4, 4, 2
These are the possible combinations.
To know more about Pythagoras theorem here.
https://brainly.com/question/343682
#SPJ4
if you have string of length 50 cm, what are the dimension
of the rectangle of maximum area that you can enclose with your string?
expline your reasoning. what about string of length K cm?
The dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5
n let x = the length of one side of the rectangle and y = the length of the other side of the rectangle.
The area is:
A = xy
and the perimetere is the string of length 50 cm
50 = 2(x + y) Solve this in terms of y. Divide both sides by 2.
25 = x + y By Subtract x from both sides.
25-x = y Now substitute this into the equation for the area.
A = x (25 - x) Simplify.
A = 25x - x²
the general form of quadratic equation: ax² + bx + c
x is given by -b/2a
Here the equation is A = -x² + 25x
, a = -1, b = 25, and c = 0
so we can find the x-coordinate of the vertex by -25/2(-1) = 12.5
So the length (x) of the rectangle must be 12.5 cm to get the maximum area.
But what about the width (y)?
Since the perimeter is 50 cm and this is twice the (length + width), the (length + width) is 25 cm, so the width is 25 cm - the length.
x + y = 25
12.5 + y = 25
y = 12.5
So, we end up with x (the length) = 12.5 cm and y (the width) = 12.5 cm.
And this, of course, is a square whose sides are 12.5 cm
If the perimeter were k cm,
2(x + y) = k
x + y = k/2
x + x = k/2 (as x = y)
x = k/4
x = k/4, y = k/4
Therefore, the dimension of the rectangle of maximum area that you can enclose with the string is 12.5 x 12.5
To learn more about perimeter refer here
https://brainly.com/question/24571594
#SPJ4
B is the midpoint of AC. D is the midpoint of CE. DE=5 and AE=18. What is the length of BD?
please help
Using the concept of midpoint of a line segment, the length of BD is 9 units
Midpoint of a Line SegmentA midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C. Therefore, to calculate the midpoint, we can simply measure the length of the line segment and divide by 2.
In the question given;
AE = 18, DE = 5
But D is the midpoint of CE
CE = 2DE
CE = 2 * 5 = 10
The line CE IS 10
But AE is the total length of the line segment and it equals 18
AE = AC + CE
AC = AE - CE
AC = 18 - 10
AC = 8
If AC = 8, BC = 1/2(AC)
BC = 1/2 (8)
BC = 4
The line BD = BC + CD
BE = 4 + 5 = 9
Learn more on midpoint of line segment here;
https://brainly.com/question/24778489
#SPJ1
can you help me find the points for this question? And how to solve it?
The line segment has a length of 13 units. (Correct choice: D)
How to determine the length of a line segment
According to Euclidean geometry, any line can be constructed by the locations of two distinct points on Cartesian plane. In this question we must determine the length of the line segment by means of Pythagorean theorem, whose formula is shown below:
l = √(x² + y²)
Where:
l - Length of the line segment.x - Horizontal length of the line segment.y - Vertical length of the line segment.First, determine the horizontal and vertical lengths of the line segment:
x = 12, y = 5
Second, determine the length of the line segment:
l = √(12² + 5²)
l = √169
l = 13
To learn more on Pythagorean theorem: https://brainly.com/question/14930619
#SPJ1
approximately what percentage training hours are delivered online? group of answer choices 40% 30% 10% 20%
The approximate percentage training hours are delivered online is 30%
What is percentage ?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.
10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula used to calculate percentages.
The amount of hours remitted online are 25.6% in 2018 reports
It has reduced from last year , it has been reported 28.6% in 2017 and 30.4% in 2016
To learn more about percentage from the given link
https://brainly.com/question/24304697
#SPJ4
roll a fair die 10 times. (a) compute the probability that at least one number occurs exactly 6 times. (b) compute the probability that at least one number occurs exactly once.
The probability that at least one number occurs exactly 6 times is 0.01303 and the probability that at least one number occurs exactly once is 0.323.
In the given question, roll a fair die 10 times.
(a) We have to compute the probability that at least one number occurs exactly 6 times.
At least one number occurring exactly 6 times.
From Binomial distribution
[tex]P(X=x) = ^nC_x(p)^{x}(q)^{n-x}[/tex]
As we roll a dice 10 times. So n=6
As we know that a dice have six faces. Each faces are mark from the number 1 to 6.
That means if we rolled a dice then there is possibility of coming six numbers.
So the probability of coming number in one time is
p=1/6
The probability of not coming the same number is
q=1-p
q=1-1/6 = 5/6
x=6
Now putting the value
[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{10-6}[/tex]
[tex]P(X=6) = 6\times^{10}C_{6}(\frac{1}{6})^{6}(\frac{5}{6})^{4}[/tex]
After solving, at least one number occur exactly 6 times
Probability = 0.01303
(b) We have to compute the probability that at least one number occurs exactly once.
[tex]P(X=1)= ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{10-1}[/tex]
[tex]P(X=1) = ^{10}C_{1}(\frac{1}{6})^{1}(\frac{5}{6})^{9}[/tex]
After solving, the probability that at least one number occurs exactly once is
Probability = 0.323
To learn more about probability link is here
brainly.com/question/29657446
#SPJ4
A.) 5/4
B.) 1/2
C.) -5
D.) 3
Answer: A
Step-by-step explanation:
4y=5x-16
divide each side by 4
y=5/4x-4
Answer:
Step-by-step explanation:
5/4 is the answer
cause you add =4y to other side and -16 to left side
divide by 4 on both sides to get
5/4x -4 = y
Your team has 17 kickballs to store in baskets.
Each basket can hold 5 kickballs.
How many baskets do you need to store all the kickballs?
Answer:
85baskets
Step-by-step explanation:
17*5=85 baskets,if each basket hold 5kickballs 17*5.
suppose a random variable has population mean 141 and population standard deviation 8.85. what is the standard error of the sample mean of a sample of 43 observations? (round to 2 decimal places.)
The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).
As given in the question,
Population mean of the random variable 'μ' = 141
Standard deviation 'σ' = 8.85
Sample size 'N' = 43 observations
Standard error of the sample mean
= σ / √N
= 8.85 / √43
= 8.85 / 6.56
= 1.349
= 1.35 (round to 2 decimal places )
Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.
Learn more about standard deviation here
brainly.com/question/16555520
#SPJ4
find the area (in cm2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.
The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2
As we know that for a rectangle of width W and length L the area is given as;
A = L × W
Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.
When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.
Therefore that new triangle will have legs equal to the;
8cm - L and W.
Then we have that:
8cm - L / W = 8 cm / 3 cm
L = 8 cm - 8/3 × W
Now we can write L in terms of W so that we can replace that in the area equation to get
A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2
This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.
As we know the vertex of the general quadratic polynomial;
a × x^2 + b × x + c
is at:
x = -b / 2a
Then, in this scenario, the vertex is at;
W = (-8 cm) / (2 × 8/3) = 1.5 cm
Then the length is given by:
L = 8cm - (8/3) × 1.5cm = 4 cm
Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;
A = 1.5 cm × 4 cm = 6 cm^2
To learn more about the area; click here:
https://brainly.com/question/15199201
#SPJ4
true or false: when two variables are highly correlated, a change in the value of one will cause a change in the value of another.
It is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.
What is the variable of an equation?
An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown. In this case, x + 5 = 10. "X" in this case is a variable.
The fact that two variables are correlated does not mean that one causes the other.
False
If there is a causal relationship between two variables, then variables are correlated but it is not always true that if variables are correlated then there is a causal relationship.
Hence, it is false that when two variables are highly correlated, a change in the value of one will cause a change in the value of another.
To learn more about the variable of an equation visit,
https://brainly.com/question/28648865
#SPJ4
Select all the prime numbers.
3
9
13
23
33
Answer:
Prime Numbers: 3,13,23,33
Composite Number: 9
Step-by-step explanation:
If a number has only 2 factors 1 and itself, then the number is prime
when a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discolouration, and other defects. the whole truckload will be rejected if more than 5% of the sample is unsatisfactory. suppose that 8% of the apples on the truck do not meet the desired standard. what is the probability that the shipment will be accepted anyway? remember to check if the sample size is large enough!
The probability that the shipment will be accepted anyway is 0.0885.
Given,
In the question:
A random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that 8% of the apples on the truck do not meet the desired standard.
To find the probability that the shipment will be accepted anyway.
Now, According to the question:
The sample size, n = 150.
The population proportion, p = 0.08.
The shipment is accepted of the sample proportion is less than 5%.
Now, to find the required probability the listed conditions to verified.
Randomization: It was stated that a random sample is chosen.
Independence: It can be supposed that the fact that a sample is satisfactory is independent of the other apple's condition.
10% condition: It can be supposed that the population size is larger than 150 (sample size).
Normality: This condition requires that np and n (1 − p) must be at least 10, so it can be verified as,
np = (150 x 0.08)
np = 12 [tex]\geq[/tex] 10
The mean of the sample proportion can be estimated as:
μ[tex]_p[/tex] = p
= 0.08
Similarly, The standard deviation of the sample proportion can be estimated as:
σ[tex]_p[/tex] = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.08(1-0.08)}{150} }[/tex]
= 0.02215
Thus, the sampling distribution of sample proportion can be approximated as,
p ~ N(0.08 ~ 0.0222)
The required probability is given as:
P(p < 0.05) = P (p - μ[tex]_p[/tex] /σ[tex]_p[/tex] < 0.05 - 0.08/ 0.0222)
= P(Z < -1.35)
= 1 - P (Z < 1.35)
= 0.0885
Note: The probability value corresponding to the Z score is obtained from the unit normal table.
Thus, the probability that the shipment will be accepted anyway is 0.0885.
Learn more about Probability at:
https://brainly.com/question/16869188
#SPJ4
Please help!!
(A) Prove that the opposite sides of the rectangle are congruent.
(B) Prove the diagonals of your rectangle are congruent.
(C) Using the slopes for each side, prove there are 4 right angles on the rectangle.
**Please Show All Work**
Use Distance Formula: v(x2 - x1)^2 + (y2 - y1)^2
The parameters of the rectangle in the question can be presented as follows;
(A) The lengths of the opposite sides found using Pythagorean Theorem are the same, therefore, the opposite sides of the rectangle are congruent
(B) The lengths of the diagonals of the rectangle are both 5·√2, therefore, the diagonals are congruent
(C) The slopes of the sides of the rectangle are 1/3 and -3, therefore, the sides are perpendicular, and the and the re are 4 right angles on the rectangle.
What is a rectangle?A rectangle is a quadrilateral that has congruent opposite sides and each of the 4 interior angles of the rectangle are right angles.
(A) The lengths of the sides of the rectangle are;
Top side; √(6² + 2²)
Opposite to the top √(6² + 2²)
Left side; √(3² + 1²)
Right side; √(3² + 1²)
The lengths of the opposite side are the same
Therefore;
The opposite sides are congruent
(B) The lengths of the diagonals are as follows;
Length of first diagonal= √((2 - 1)² + (1 - 8)²) = √(1² + 7²) = √(50) = 5·√2
Length of the second diagonal = √((4 - (-1)² + (7 - 2)²) = √(50) = 5·√2
The length of the first and second diagonal are the same, therefore, the diagonals of the rectangle are congruent.
(C), Slope of the top side = (4 - 2)/(7 - 1) = 2/6 = 1/3
Slope of the opposite to the top side = (1 - (-1))/(8 - 2) = 1/3
Slope of the left side = (2 - (-1))/(1 - 2) = -3
Slope of the right side = (4 - 1)/(7 - 8) = -3
The slope of the top side are the negative inverse of the slope of the left and right sides of rectangle
Therefore, the sides of the rectangle are perpendicular, and the rectangle consists of 4 right angles
Learn more about rectangles here:
https://brainly.com/question/25292087
#SPJ1
due today can someone help
Answer:
v = 15
Step-by-step explanation:
By exterior angle theorem:
9v° = 31° + (4v + 44)°
9v° = (4v + 44 + 31)°
9v = 4v + 75
9v - 4v = 75
5v = 75
v = 75/5
v = 15
What is the value of x in the triangle?
Answer:
a I dont have a explanation but its a
How do I turn 2.1 into a decimal? Please help!!
Answer:
2/10
Step-by-step explanation:
add the numbers and minus
An earthquake near the Fiji Islands measured 4.6 on the Richter scale. Use the formula R = log() to determine
approximately how many times stronger the wave amplitude A of the earthquake was than Ao.
OA 39, 811 Ao
O A≈ 99.5A0
O A 183, 129 Ao
O A≈ 0.66A0
The correct option regarding how many times stronger the wave amplitude A of the earthquake was than the standard wave Ao is given by:
A = 39,811 Ao.
How to obtain the ratio of A and Ao?To find the ratio of A and Ao, which states how many times a earthquake measuring R in the Richter scale was stronger than the standard intensity Ao, we have to solve the following logarithmic function:
R = log(A/Ao)
The Richter scale of the earthquake in this problem is given as follows:
R = 4.6.
Hence the ratio of the measures is obtained as follows:
4.6 = log(A/Ao)
The power of 10 is the inverse function of the logarithm, hence if it is applied to both sides of the equation, then we can isolate the ratio A/Ao as follows:
A/Ao = 10^4.6
A/Ao = 39,811.
Applying cross multiplication, the ratio is given as follows:
A = 39,811 Ao.
Learn more about logarithmic functions at brainly.com/question/14379331
#SPJ1
Please answer quickly :) If wrong i will report
Answer:
(0,2)
Step-by-step explanation:
plug in 0 for x
Factorise the following: a) x² + 6x + 8 b) x²-9x + 18 c) x² - 8x-9 d) x² + 6x-27
a) To factorize this expression, we need to find two numbers that multiply to give 8 and add to give 6. The two numbers that fit this description are 4 and 2, so we can write the expression as x² + 6x + 8 = (x + 4)(x + 2).
b) To factorize this expression, we need to find two numbers that multiply to give 18 and add to give -9. The two numbers that fit this description are -6 and -3, so we can write the expression as x²-9x + 18 = (x - 6)(x - 3).
c) To factorize this expression, we need to find two numbers that multiply to give -9 and add to give -8. The two numbers that fit this description are -3 and 3, so we can write the expression as x² - 8x-9 = (x - 3)(x + 3).
d) To factorize this expression, we need to find two numbers that multiply to give -27 and add to give 6. The two numbers that fit this description are -9 and 3, so we can write the expression as x² + 6x-27 = (x + 9)(x - 3).
for a period of time, an island's population growth exponential. if the population doubles every 17 years and the current population is 1,725, what will the population be 10 years from now?
Using the exponential growth formulas, we get the population at 10 years would be 2593.
What is exponential growth?
A process called exponential growth sees a rise in quantity over time. It happens when the derivative of a quantity's instantaneous rate of change with respect to time is equal to the original quantity.
Given Initial population is Pt= 1725.
The doubling time of the population is D=17
Now we need to find the population at time t=10
Using the formula,
[tex]P_{t}=P_{0} (2)^{\frac{t}{D} } \\P_{t}=1725 (2)^{\frac{10}{17} } \\P_{t}=1725 (2)^{0.588}\\P_{t}=1725 \space\ . \space\ 1.503\\P_{t}=2593[/tex]
Hence the population of the island in 10 years would be 2593.
To learn more about exponential growth, visit the link below:
https://brainly.com/question/12490064
#SPJ4
an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha =\frac{1-0.96}{2} =0.02[/tex]
Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex].
So it is z with a p value of [tex]1-0.02=0.98[/tex], so z= 2.055
Now, find the margin M as such
M = z*σ/√n
In which σ is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
σ = 40, M = 10,
M = z*σ/√n
[tex]10=2.055*\frac{40}{\sqrt{n} } \\10\sqrt{n}=82.2\\ \sqrt{n}=8.22\\ n=67.6[/tex]
Therefore, a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
To learn more about sampling, visit:
brainly.com/question/15969003
#SPJ4
Sadio tart with aving of £15. Thoma tart with no aving. Each week from now,
Sadio will ave £3. 50 and Thoma will ave £3
in how many week will Sadio and Thoma have aving in the ratio 2:1?
In total 6 weeks, the saved money by both Sadio and Thoma will be in the ratio of 2:1.
Define the term ratios?When two or so more numbers are compared, the ratio shows how big one is in relation to the other. The dividend and number being divided is referred to as the antecedent, and the divisor for number that also is dividing is referred to as the consequent. A ratio compares two numbers by division.For the given question.
Initial money owned by each is-
Sadio = $15
Thoma = $0.
Let the number of weeks passed be 'x'.
Then, present money after x weeks.
Sadio = $3.50x + 15
Thoma = $3x
The number of weeks , when ratio becomes 2:1
(3.50x + 15)/3x = 2/1
3.50x + 15 = 6x
6x - 3.5x = 15
x = 15/2.5
x = 6
Thus, in total 6 weeks, the money held by both Sadio and Thoma will be in the ratio of 2:1.
To know more about the ratios, here
https://brainly.com/question/12024093
#SPJ4
I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
9
Step-by-step explanation: 8 - 4m = - 10 - 2m
collect the like terms, calculate
-2m = -18 divide both sides,
m = 9
Answer:
wwwwwwwwwwww upper guy
Step-by-step explanation:
A stack of Magic cards consists of 4 land cards and 6 creature cards. You draw 4 cards from the shuffled stack of 10 cards. Find the probability that you pull 4 creature cards. (give answer as a fraction or a decimal to 3 decimal places)
Find the probability that you pull 3 land cards and 1 creature card.
(give answer as a fraction or a decimal to 3 decimal places)
Answer:
1/14 ; 1/35
Step-by-step explanation:
A
6/10 x 5/9 x 4/8 x 3/7
3/5 x 5/9 x 1/2 x 3/7
1 x 1/3 x 3/14
1/14
B
4/10 x 3/9 x 2/8 x 6/7
2/5 x 1/3 x 1/4 x 6/7
2/15 x 3/14
1/5 x 1/7
1/35
The probability that 4 creature cards is pulled is 1/14 and the probability that 3 land cards and 1 creature card is pulled is 4/35
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here there are 4 land cards and 6 creature cards
thus selecting four cards at random from 10 cards is ¹⁰C₄=210
and the event of selecting 4 creature cards from a total of 6 cards is ⁶C₄ =15
Therefore probability of pulling 4 creature cards is = 15/210
= 1/14
The probability of pulling 3 land cards and 1 creature cards is
= ⁴C₃ × ⁶C₁ / ¹⁰C₄
= 4/35
Hence 1/14 and 4/35 are the respective probabilities.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ2
from a group of 7 men and 6 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?
There are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.
What is the formula of combination?
Following is the fomula of combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n is the total objects available and r is the number of object need to choose from n objects.
Consider no man refuses to serve together. Now, number of ways in which 4 men and 3 women committee can be formed from a group of 7 men and 6 woman.
[tex]^7C_4\times\ ^6C_3[/tex]
Now, consider a goup in which the two persons who do not want to serve togather are togather. Consider these person as a single person. Now, we need to choose 3 men (two individual men and one group of 2 men will make 4 men in the group) from 6 men (7 converts into 6 because group of two person is considerd as 1.).
[tex]\ ^6C_3\times\ ^6C_3[/tex]
Now, subtract [tex]\ ^6C_3\times\ ^6C_3[/tex] from [tex]^7C_4\times\ ^6C_3[/tex] to get the actual answer.
[tex]^7C_4\times\ ^6C_3-\ ^6C_3\times\ ^6C_3\\=\frac{7!}{4!3!}\times \frac{6!}{3!3!}-\frac{6!}{3!3!}\times\frac{6!}{3!3!}\\=35\times20-20\times20\\=20\times15\\=300[/tex]
Hence, there are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.
Learn more about combination from the following link:
https://brainly.com/question/4658834
#SPJ4
peter pan is studying the migration patterns of pixies. as part of this research, he counts the number of pixies over mermaid lagoon on 16 randomly selected days. what is the sample of this study?
For given study the sample would be - The number of pixies over Mermaid Lagoon on the 16 days observed.
Here, peter pan is studying the migration patterns of pixies. as part of this research, he counts the number of pixies over mermaid lagoon on 16 randomly selected days.
We need to find the sample of this study.
We know that, a sample is nothing but a group of elements chosen from the population. It is a small data set that you obtain from a larger set of data to represent the population.
In this case ths sample would be - The number of pixies over Mermaid Lagoon on the 16 days observed.
Therefore, sample for this situation - The number of pixies over Mermaid Lagoon on the 16 days observed.
Learn more about sample here:
https://brainly.com/question/14893265
#SPJ4
The options for given question:
1) The number of pixies over Mermaid Lagoon on the 16 days observed.
2) Peter Pan
3) The number of pixies in Neverland
4) The number of pixies over Mermaid Lagoon on any day.
You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 13 percent and Stock Y with an expected return of 8 percent. Your goal is to create a portfolio with an expected return of 12.4 percent. All money must be invested. How much will you invest in stock X? A. $800B. $1,200C. $4,600D. $8,800E. $9,200
The money invested in stock X is $8,800.
Given,
Total investment in stock portfolio=$10000
Expected return from stock X=13%=0.13
Expected return from stock Y=8%=0.08
Expected return from portfolio=12.4%=0.124
The portfolio return is calculated by taking the weighted average of individual stock returns.
Let x represent the portfolio weightage of stock X.
1-x is the portfolio weightage of stock Y.
money invested in stock X be
0.124=0.13x+0.08(1-x)
0.124=0.13x+0.08-0.08x
0.124-0.08=0.05x
0.044=0.05x
x=0.88
money invested in stock X=0.88*10000=$8800
Thus, the money invested in stock X is $8,800.
To learn more about percentages refer here
https://brainly.com/question/26718419
#SPJ4