A family of six consisting of a mother, father, and four children line up (shoulder-to-shoulder) for a family portrait in a random order. Find the probability mass function of the random variable X, the number of children located between the father and mother in the photograph.
Answers
The probability mass function for this is given by the table that is attached below.
Probability is defined as the proper fraction which signifies the likelihood of an event to occur.
Total number of possible arrangements of 6 people are 6! = 720
Here X can take value 0, 1, 2, 3, or4.
For the probability function : When X= 0 , it means there is no child between mother and father. Taking mother and father as one , number of possible arrangements of 5 people are 5!.
And mother and father can arranged themselves is 2! ways. So for X=0, possible ways are 5! *2 = 240.
Therefore the require probability at X=0 is given by:
P(X=0) = 240 /720 = 0.3333
For the probability function : When X = 1 , then there is one child between mother and father. Number of ways of selecting one child is C(4,1) = 4.
Mother and father can be arrange themselves in 2 ways so possible number of arrangements are 4 * 2 * 4! = 192
Therefore the require probability at X=1 is given by:
P(X=1) = 192 /720 = 0.2667
For the probability function :When X=2 , then there are two children between mother and father. Number of ways of selecting two children is C(4,2) = 6.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 2 ways so possible number of arrangements are 6 * 2 * 2* 3! = 144
Therefore the require probability at X=2 is given by:
P(X=2) = 144 /720 = 0.2
For the probability function : When X=3 , then there are three children between mother and father. Number of ways of selecting three children is C(4,3) = 4.
Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 3! ways so possible number of arrangements are 4 * 2 * 3!* 2! = 96
Therefore the require probability at X=3 is given by:
P(X=3) = 96 /720 = 0.1333
For the probability function: When X=4 , then there are 4 children between mother and father. Number of ways of selecting 4 children is C(4,4) = 1.
Mother and father can arranged themselves in 2 ways, children between mother and father can arranged themselves in 4! ways so possible number of arrangements are 1 * 2 * 4! = 48
Therefore the require probability at X=0 is given by:
P(X=4) = 48 /720 = 0.0667
Hence the probability mass function can be represented by a table below.
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Related Questions
L is a point of a tangency . Segment PL have a common point at P . Find the length of KN
Answers
a student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have
Answers
Answer:
360 naira hope it will be helpful
Step-by-step explanation:
12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?
Answers
The value of x is 4.
The perimeter of any shape is the sum of lengths of all its sides.
We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.
So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)
The perimeter of a triangle = 12.2x + 8 equation 1
Also, we are provided with the side of square i.e., 6.5x -11.8.
The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)
The perimeter of a square = 26x - 47.2 equation 2
As per question,
Perimeter of a triangle = Perimeter of a square
12.2x + 8 = 26x - 47.2
13.8x = 55.2
x = 4
So we can write, the value of x is 4.
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Please help me I was sick today and missed out on class and I don’t understand this question
Answers
Answer: 72 i think
Step-by-step explanation:
The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2
Answers
Using the graph, we can deduce the following:
• x-intercept: x = -2
,• y-intercept: y = -3
Let's determine the zero of the function.
The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.
The zero of a function is the point the line crosses the x-axis.
From the graph the x-intercept is at x = -2.
Therefore, the zero of the function is:
x = -2
ANSWER:
D. -2
A candy company has fixed costs (costs that it must pay regardless of how much candy they
make) of $500 per day, and it costs them an additional $3 to manufacture each box of candy.
They can sell their candy for $3 a box. If we jet x represent the boxes of candy sold, the number of
boxes they need to sell to break even can be found by solving the equation 3x + 500 = 3x. How
many boxes of candy to they need to sell to break even?
Answers
You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.
What is Break even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."
Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
Fixed cost (in manufacturing) = $500
Manufacturing cost of each candy = $3
and selling price of candy = $3
let x be a box of candy sold,
hence for no of box to be sold for a break even,
3x + 500 = 3x
but if you see above equation, that has no solution
Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.
hence there is no solution, and you will never be able to achieve break even.
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Solve the linear programming problems: (find the constraints, objective function, feasible region, and the minimumand maximum values)12. A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week.Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week formaterials. Each oak chair sells for $400 and each walnut chair sells for $500. What are the number of oak and walnutchairs that the small business should produce in order to maximize / minimize sales?
Answers
The firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
What are linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So,
Production of oak chairs: xProduction of walnut chairs: y(Refer to the graph attached below)
Then,
x + y ≤ 20100x + 150y ≤ 2400x ≥ 0y ≥ 0I = 400x + 500ySo, oak chair produced:
(0, 16) ⇒ $8000(20, 0) ⇒ $8000(12, 8) ⇒ $8800Therefore, the firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
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The correct question is given below:
Solve the linear programming problem: A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week. Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week for materials. Each oak chair sells for $400 and each walnut chair sells for $500. How many each types of chairs should the business make each week to maximize income?
A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Answers
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
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How many months does it take $428 to double at a simple interest rate of 12%
Answers
When $428 doubles, it means that the
hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?
Answers
The height of balloon is 1.99 miles above the ground.
What is angle of depression ?In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.
Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.
We can state the following if the angle of this milepost's depression is 24 degrees:
Tan(24)=[tex]\frac{h}{b}[/tex]
b = [tex]\frac{h}{tan(24)}[/tex]
We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.
tan(20)=[tex]\frac{h}{b+1}[/tex]
b +1 = [tex]\frac{h}{tan(20)}[/tex]
Therefore, substituting equation 1
[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]
1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]
1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )
h = 1.99 miles
Consequently, the height of balloon is 1.99 miles above the ground.
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Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).
Answers
The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.
How to derive the standard equation of the circle based on the coordinates of diameter endpoints
In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:
(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)
(h, k) = (4, 0)
And the radius of the circle is determined by Pythagorean theorem:
r = √[(4 - 5)² + (0 - 5)²]
r = √[(- 1)² + (- 5)²]
r = √26
Then, the equation of the circle in standard form is describe below:
(x - h)² + (y - k)² = r²
If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:
(x - 4)² + y² = 26
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7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.
Answers
We can use the following formula:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]So:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]Answer:
0.3%
An election ballot asks voters to select six city commissioners from a group of twenty two candidates. In how many ways can this be done?
Answers
In this case, we have 6 places to fill from a pool of 22 candidates. There is no difference in the places: they are all commissioners, so if candidate A is selected, the order does not matter, but there is only one candidate, so there is no repetition.
Then, this is a combination (as the order does not matter) with no repetition of 22 elements in 6 places.
We can calculate this as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(22,6)=\frac{22!}{6!(22-6)!}=\frac{22!}{6!\cdot14!}=\frac{22\cdot21\cdot20\cdot19\cdot18\cdot17\cdot16\cdot15}{6\cdot5\cdot4\cdot3\cdot2\cdot1}=17907120 \end{gathered}[/tex]Answer: there are 17,907,120 ways this can be done.
What is the next step in the construction?
Answers
An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. Make an arc by setting the compass's needle at A. Please indicate intersections B and C.
What is meant by arc?An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the full curve).
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle.
Therefore, the correct answer is option b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
The complete question is:
What is the next step in the construction?
a) Step 1: Select a point on line 1 and label it point A. Draw in PA.
b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
c) Step 3. Without changing the compass setting. put the compass at point P and make an identical arc. Label the intersection D
d) Step 4. Put the compass at point B and use it to measure the distance to C.
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Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=-1/6x+3
Answers
The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.
How to rewrite equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
where
A , B and C are constantx and y are the independent and dependent variables respectivelyTherefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .
y = - 1 / 6 x + 3
multiply the equation by 6 to eliminate the fraction
6y = 6(- 1 / 6 x) + 6(3)
Therefore,
6y = - x + 18
x + 6y = 18
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Solve the given equation or inequality graphically. State your answers rounded to two decimals. (a) x3 + 5x2 = −x2 + 5x + 3
Answers
The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.
Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.
Consider the equation,
x³ + 5x² = - x² + 5x + 3
Solving Equations Graphically:
The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.
Therefore,
f(x) = x³ + 5x² and g(x) = - x² + 5x + 3
By graphing the function we find the intersection of the two functions.
Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).
Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.
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Scott is a software salesman. His base salary is $2500, and he makes an additional $80 for every copy of English is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 28 copies of English is Fun.
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to get the equation
Step 1: Represent the statement using mathematical notation
Base salary is $2500 (Base salary is constant since it does not change)
P represent his total pay (in dollars)
N represent the number of copies of English is Fun he sells
price made per copy of the product is $80
The equation relating P to N will be written as:
[tex]P=2500+80N[/tex]Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun
[tex]\begin{gathered} P=2500+80N \\ N=28 \\ P=2500+80(28) \\ P=2500+2240 \\ P=\text{\$}4740 \end{gathered}[/tex]Hence, his total pay if he sells 28 copies of English is Fun is $4740
y= −2x+8
x-intercept:
Enter as a coordinate: such as
(a,b)
y
-intercept:
Enter as a coordinate: such as
(a,b)
Answers
For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
In this question, we have been given an equation y = -2x + 8
We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)
To find the x-intercept we need to substitute y = 0 in the above equation.
0 = -2x + 8
2x = 8
x = 4
So, the x-intercept is (4, 0)
To find the y-intercept we need to substitute x = 0 in the above equation.
y = -2(0) + 8
y = 0 + 8
y = 8
So, the y-intercept is (0, 8)
Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
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Can you check work please?
Answers
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]
Can you show me step by step how to get this answer please?
Answers
Answer: first six cannot go into three because three is too small so six is going to go into 31 Six can go into 31 five times because 6×5 = 30 then since you’re subtracting 31 and 30 you would be left with one you would have to bring the 1 from the 12 down and then it would be 11. 11 can go into six once so 6-11 =5 so then you have to bring the two from the 12 down so then that would equal 6-2=4 and your done! It was a little confusing so if it didn’t make sense I’m sorry
Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.
Answers
The first unit is kilograms because the bus is really heavy.
The second is kilometers because meters are too small.
The third one is milliliters because liters are too much for ice cream.
The surface area of the rectangular prism is given by formula S=2(ab+bh+ah). Find the value of h when a=6, b=5 and s=214
Answers
The value for the height of the rectangular prism is found as; h = 7.
What is defined as the rectangular prism?A rectangular prism is a three dimensional solid shape with six faces that have rectangles as their bases. Right rectangular prisms as well as non-right (oblique) rectangle prisms are the two types of rectangular prisms. The right rectangle prism does have two parallel end faces and 4 lateral faces, each of which is an rectangle; this same faces are perpendicular to the bases of the prism.The formula for the surface area of rectangular prism is;
S = 2(ab+bh+ah)
Where,
a=6, b=5 and s=214
Substitute the values in the formula.
214 = 2(6×5 + 5h + 6h)
Simplifying;
30 + 11h = 107
11h = 107 - 30
11h = 77
h = 7
Thus, the value for the height of the prism is found as; h = 7.
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i need help the problem is
solve for y
2x+y=3
Answers
Answer:
y = 3 - 2x
Step-by-step explanation:
Subtract 2x from both sides of the equation.
Answer:
y = x or 1x
Step-by-step explanation:
x as a variable can also be expressed as 1x.
so we can say that 2x + 1x
because x & y are two different type of variables. you think of y as a question mark ( ? ).
Now the new equation is
y = ?
so 1x + ? = 3
because x is the same thing as a 1x you can say that 2x + 1x = 3
What is the value of x?
-6x + 6 > 12
Answers
Subtract 6 from both sides.
−6x > 12 - 6Subtract 6 from 12 to get 6.
−6x > 6Divide both sides by −6. Since −6 is <0, the inequality direction is changed.
x < 6/-6Divide 6 by −6 to get −1.
x<−11. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points
Answers
First of all, we have to find the mean of x values.
According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.
So, the mean is
[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]The mean of x values is 3.3.
The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.
The mean would be
[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]The mean of y values is 4.4.
Now, we find the standard deviation for x values and y values.
[tex]undefined[/tex]The equation for the line that has a slope of -3/8 and passes through (0, 10) is: y = -3/8x + 10 : y = 3/8 x - 10
Answers
The standard form of expression equation of a straight line is;
[tex]y\text{ = mx+c}[/tex]where;
m is the slope
c is the intercept
Given
slope m = -3/8
Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ 10\text{ = -3/8(0)+c} \\ 10\text{ = 0+c} \\ c\text{ = 10} \end{gathered}[/tex]Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ y\text{ = -}\frac{3}{8}x+10 \end{gathered}[/tex]Hence the first option is correct
Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*
Answers
Answer:
7500$
Step-by-step explanation:
Provide the correct reason for the statement in line 1. (please help)
Answers
Answer:
d) given
Step-by-step explanation:
nothing has been done yet, the statement is given as stated above the statement
find the midpoint between. (-1,2) and (-7,-4).
Answers
The midpoint of two coordinates can be obtained using the formula:
[tex]\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}[/tex]x1 = -1
y1= 2
x2= -7
y2= -4
[tex]\begin{gathered} \frac{-7\text{ +(-1)}}{2},\frac{2+(-4)}{2} \\ \\ \frac{-7-1}{2},\frac{2-4}{2} \\ \frac{-8}{2},\frac{-2}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{midpoint} \\ (-4,-1) \end{gathered}[/tex]Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?
Answers
Ivan will catch up to Horatio in 3 hours .
In the question ,
it is given that
speed of Horatio is 1 miles per hour
speed of Ivan is 2 miles per hour .
and Ivan leaves 3 hours late than Horatio .
Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,
So, the distance covered by Ivan will be 2*t .
Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).
So, the distance covered by Horatio will be 1*(t+3) .
The distance covered for Horatio and Ivan will be equal ,
which means
2*t = 1*(t+3)
2t = t + 3
2t - t = 3
t = 3
Therefore , Ivan will catch up to Horatio in 3 hours .
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