Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0, -1). The directrix is the line y=0. What is the equation of the parabola in vertex form?
Answers
Check the picture below, so the parabola looks more or less like so, with the vertex half-way from the focus point and the directrix.
Now, the distance from the directrix to the focus point is only 1 unit, so half that, or namely the "p" distance is 1/2 unit, and since the parabola is opening downwards, "p" is negative, so
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=-\frac{1}{2}\\[1em] p=-\frac{1}{2} \end{cases}\implies 4\left( -\frac{1}{2} \right)\left( ~~y-\left( -\frac{1}{2} \right) ~~ \right)~~ = ~~(x-0)^2 \\\\\\ -2\left( y+\frac{1}{2} \right)=x^2\implies y+\cfrac{1}{2} =\cfrac{x^2}{-2}\implies y = -\cfrac{1}{2}x^2-\cfrac{1}{2}[/tex]
now, we could also write that as either
[tex]y = -\cfrac{1}{2}(x^2+1)\qquad or\qquad y = \cfrac{1}{2}(-x^2-1)[/tex]
Related Questions
A package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45. How many pounds did the package weight
Answers
The total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.
In the question, we are given that a package weighs P pounds, P being a whole number. To ship this package by express costs $1.65 for the first five pounds and 12c for each additional pound. The total shipping cost was $3.45.
We are asked for the package weight in pounds.
First, we design a general cost function.
The cost is given to be $1.65 for the first 5 pounds, and 12c for each additional pound.
The weight of the package is given to be P pounds.
We assume the total cost function to be C(P), a function of the weight of the package, P pounds.
Thus, the total cost function can be shown as the sum of $1.65 and 12c or $0.12 multiplied with (P - 5), as it is the cost for additional pounds after 5 pounds.
Thus, the total cost function, C(P) = 1.65 + 0.12(P - 5).
Now, we are given that the total shipping cost was $3.45.
Thus, to find the weight of the package, we equate the total cost function, C(P) to 3.45, to get:
1.65 + 0.12(P - 5) = 3.45,
or, 1.65 + 0.12P - 0.6 = 3.45,
or, 0.12P + 1.05 = 3.45,
or, 0.12P = 3.45 - 1.05,
or, 0.12P = 2.40,
or, P = 2.40/0.12 = 20.
Thus, the total weight of the package was 20 pounds, given the total shipping cost was $3.45, using the total cost function, C(P) = 1.65 + 0.12(P - 5), where P is the weight of the package in pounds.
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Dad is 4 times as old as his son Jim is now. In 10 years, Dad's age will be 20 years more than twice Jim's age. If D = dad's age now and J = Jim's age now, how old is Jim?
Answers
Answer:
Jim is 5
Step-by-step explanation:
word problems can be sort of like translation questions
'times' means multiply
'as old as' means equal or =
'will be' means equal or =
'more than' means plus or +
when I saw
"Dad is 4 times as old as his son Jim is now"
I knew needed to make
Jim = x &
Dad = 4x
when I saw
"In 10 years, Dad's age will be 20 years more than twice Jim's age"
I knew
'Dad's age' means 4x
'In 10 years' means 10 +
'will be' means equal sign or =
'20 years more than' means 20 +
'twice Jim's age' means 2x
sentence can be re written
4x+10=20+2x
'if D = dad's age now' means 4x=D (Dad)
'J = Jim's age now' means x = J (Jim)
I solved for x
4x+10=20+2x
2x=10
x=5
then I checked the math
today
x = Jim = J = 5
4x = Dad = D = 20
'in 10 years'
Dad is 20 + 10 = 30
means
does 30 = 20 years more than twice Jim's age?
does 30 = 20 + 2x ?
does 30 = 20 + 2(5)?
does 30 = 20 + 10?
does 30 = 30?
yes!
it checks out!
The total mass of 4 identical pencil boxes and a notebook is 700 g. each pencil box has a mass of 140 g. what is mass of the notebook?
Answers
Answer:
140g
Step-by-step explanation:
One pencil box has a mass of 140g, to find out the weight of 4 pencil boxes we multiply 140 by 4: 140*4 = 560g
Let the mass of the notebook be x: 560+x = 700
560+x = 700
x = 140g
Gaby mi mejor amiga <3
Answers
Answer:
que necesitas? acaso necesitas algo fan de Sparta o no
Step-by-step explanation:
ok
What total length of ribbon is needed to line the two long sides of the hat? 10 in. 11 in. 20 in. 22 in.
Answers
A kite is a quadrilateral with four sides that may be divided into two adjacent pairs of equal-length sides. The total length of ribbon that is needed to line the two long sides of the hat is 22 inches.
According to the question,
A kite is a quadrilateral with four sides that may be divided into two adjacent pairs of equal-length sides. A parallelogram, on the other hand, has two sets of equal-length sides that are opposite each other rather than adjacent.
Since the two adjacent small and two adjacent long sides of a kite are always equal. Therefore, the length of the smaller sides can be written as,
(2x + 1) inches = 5 inches
2x + 1 = 5
2x = 4
x = 2
Now, the length of the longer side of the kite can be written as,
(3x + 5) inches
= 3(2) + 5
= 11 inches
As both the long sides are needed to be covered with the ribbon, therefore, the length of the ribbon needed is,
Ribbon needed = 11 inches × 2
= 22 inches
Hence, a kite is a quadrilateral with four sides that may be divided into two adjacent pairs of equal-length sides. the total length of ribbon that is needed to line the two long sides of the hat is 22 inches.
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If the probability that a chef likes carrots is 0.13, the probability of those who like broccoli is 0.72, and the probability of those who like neither is 0.22, what is the probability of those who like both
Answers
Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.
Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
C: The event that a chef likes carrots.B: The event that a a chef likes broccoli.Then you know:
P(C)= 0.13P(B)= 0.72In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:
P(C∪B)= P(C) + P(B) -P(C∩B)
Then, the probability that a chef likes carrots and broccoli is calculated as:
P(C∩B)= P(C) + P(B) -P(C∪B)
In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:
P [(C∪B)']= 1- P(C∪B)
In this case, the probability of those who like neither is 0.22
0.22= 1 - P(C∪B)
Solving
0.22 - 1= - P(C∪B)
-0.78= - P(C∪B)
- (-0.78)= P(C∪B)
0.78= P(C∪B)
Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:
P(C∩B)= 0.13 + 0.72 -0.78
Solving:
P(C∩B)= 0.07= 7%
Finally, the probability of those who like both is 0.07 or 7%.
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The number 21 is the sum of two consecutive integers 10 and 11. What is the largest number of positive, consecutive integers whose sum is 21
Answers
Answer:
11
Step-by-step explanation:
For which pair of functions is the vertex of g(x) 2 units to the right of the vertex of f(x)?
Answers
For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),
f(x) = x² and g(x) = (x - 2)²
What are functions?
Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
Determining the Correct Pair of Functions
For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.
If a > 0, then it indicates a right translation of a units.
If a < 0, then it indicates a left translation of a units.
The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).
Thus, if f(x) = x², then g(x) = (x - 2)²
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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. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answers
The equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
Writing equationsFrom the question, we are to determine the equations that have the same solution as the given equation
The given equation is
2.3p – 10.1 = 6.5p – 4 – 0.01p
Simplifying,
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Thus, 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation
Also,
If we multiply both sides of the given equation by 100
That is,
100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
230p – 1010 = 650p – 400 – p
∴ 230p – 1010 = 650p – 400 – p is equivalent to the given equation
Hence, the equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
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State the conditions required for a random variable x to follow a poisson process.
Answers
The conditions required for a random variable X to follow a Poisson process. The probability of success is the sme for aany two intervals of equal length. The probability of two or more successes in any sufficiently small subinterval is 0.
Is the time required to upload a file to the Internet discrete or continuous?Is the length of time it takes to download a file from the Internet a random variable, a continuous random variable, or not at all? A continuous random variable, that is.Is the a discrete random variable a continuous random variable or not a random variable?A variable whose value is determined by counting is referred to as a discrete variable. A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event. There are a countable number of potential values for the discrete random variable X.How do you determine whether the random variable is discrete or continuous?A discrete variable is one that is random. if the number of possible values is either countable or finite. Continuous refers to a variable that is random. if the range of possible values includes all conceivable numbers.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answers
[tex]Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
Step-by-step explanation:
[tex]D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
then he started to prepare the games for this 4 friends. if each game takes 5 minutes to prepare and he prepared a total of 5 games. how many minutes did it take for andrew to prepare all the games
Answers
Answer:
25 minutes
Step-by-step explanation:
If it takes 5 minutes to prepare one game we need to multiply 5 games by 5 minutes: 5*5 = 25 minutes
On a coordinate plane, a line goes through (0, 1) and (5, 0). what is the equation of the line that is perpendicular to and has the same y-intercept as the given line? y = one-fifthx 1 y = one-fifthx 5 y = 5x 1 y = 5x 5
Answers
Answer: [tex]y=5x+1[/tex]
Step-by-step explanation:
The slope of the given line is
[tex]\frac{1-0}{0-5}=-\frac{1}{5}[/tex]
Since perpendicular lines have slopes that are negative reciprocals, the slope of the line we want to find is 5.
Since the y-intercept is (0,1), the equation is [tex]y=5x+1[/tex].
Answer: the answer is c
20 points, help me, please !!!!!
Answers
(a) |-9| + 6 = 9 + 6 = 15
(b) |-9 + 6| = |-3| = 3
Warm-Up
Consider the graph of function f.
Determine which equation matches each described transformation of function f.
Drag the tiles to the correct boxes to complete the pairs.
Answers
If this is the one you are talking about then:
horizontal translation of 3 units is: y= f(x-3)
vertical stretch by a scale factor of 3 is: y= 3f(x)
reflection over the x-axis is: y= -f(x)
vertical translation of 3 units is: y= f(x)+3
Step-by-step explanation:
Adding a value to f(x) translates the graph of f vertically. So, the equation that shows a vertical translation of 3 units is y = f(x) + 3.
Adding a value to the input, x, of f(x) translates the graph of f horizontally. So, the equation that shows a horizontal translation of 3 units is y = f(x − 3).
Multiplying f(x) by a negative value reflects the graph of f over the x-axis. So, the equation that shows a reflection over the x-axis is y = -f(x).
Multiplying f(x) by a constant, k, vertically stretches the graph of f by a scale factor of k. So, the equation that shows a vertical stretch by a scale factor of 3 is y = 3f(x).
A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
Answers
The net Change in latitude and longitude of the helicopter are; 28.47° and 7.35° respectively.
What is the net Change in latitude and longitude of the helicopter?The net change in latitude of the helicopter can be evaluated as follows;
x = |-6.20° - 22.27°| = |-28.47°|
x = 28.47°
The net change in longitude of the helicopter can be evaluated similarly as follows;
y = |106.80° - 114.15°| = |-7.35°|
x= 7.35°
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this is a question on a review assignment that i’m stuck on , my summer school teacher said i could get help if i needed. any help would be greatly appreciated
Answers
Answer:
may be 3549 cube inch while rounded up.
Volume of cylinder = 1570
Volume of area in box not filled with cylinder
=3550
I’m not sure which one you need, cylinder or shaded area in box, so…
First find volume of cylinder
V= pi r^2 height
V = (3.14) (5^2) (20)
V= (3.14) (25) (20)
V= 1570
Next find TOTAL volume of box
V= Length x width x height
V= 20 x 16 x 16
V= 5120
Now take box (5120) subtract cylinder (1570)
Volume of box not filled with Cyl (shaded area) = 3550
In a class of 48 students, one fourth of them regularly watch a particular tv programme. how many of the students do not regularly watch the programme?
Answers
36 students does not watch regularly the programme.
Lets simplify the problem,
Total students = 48
Regular students 1//4*48
=> 12 students
Through Simple Subtraction method,
Irregular students = Total students - regular students
Irregular students = 48-12
=36
Hence 36 students does not watch regularly the programme.
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1. Convert the following vector into coordinate
notation rule: (-3,1).
Answers
The coordinate notation is (x-3, y+1).
How can be vector converted into coordinate notation?
Let <a, b> be the vector then the coordinate notation will be
(x + a, y + b)
And if <-a, -b> be the vector then the coordinate notation will be
(x - a, y - b)
We can convert vector into coordinate notation as shown below:
For converting given vector into coordinate, we will use above formula
that is <a, b> = (x + a, y + b>
here a = -3, and b = 1
So, <-3, 1> = (x-3, y+1)
Hence, the coordinate notation is (x-3, y+1).
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5/8 of the students in siena's class have brown eyes. 2/3 of the students with brown eyes are girl. what fraction of the students in siena's class are girls with brown eyes? *
Answers
The fraction of the students in Siena's class are girls with brown eyes is 5/12.
Let the fraction of students in Siena's class with brown eyes be a=5/8.
And the fraction of students in Siena's class with brown eyes are girls be b=2/3.
Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b
Therefore, by substituting the fraction values, we get
z=(5/8)×(2/3)
z=5/12.
Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.
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Someone help pls, its urgent! ASAP!! (Geometry)
“Complete the proofs”
Answers
Question 8
1) [tex]\triangle ACE[/tex] with [tex]\overline{AC} \cong \overline{EC}[/tex], [tex]\overline{BC} \cong \overline{DC}[/tex] (given)
2) [tex]\angle C \cong \angle C[/tex] (reflexive property)
3) [tex]\triangle ACD \cong \triangle ECB[/tex] (SAS)
Question 9
1) [tex]\overline{PQ}[/tex] and [tex]\overline{PR}[/tex] are the legs of isosceles [tex]\triangle PQR[/tex], [tex]\overline{PS} \cong \overline{QR}[/tex] (given)
2) [tex]\angle PSQ[/tex] and [tex]\angle PSR[/tex] are right angles (definition of perpendicular lines)
3) [tex]\angle Q \cong \angle R[/tex] (angles opposite the legs of an isosceles triangle are congruent)
4) [tex]\overline{PS} \cong \overline{PS}[/tex] (reflexive property)
5) [tex]\angle PSQ \cong \angle PSR[/tex] (all right angles are congruent)
6) [tex]\triangle PSQ \cong \triangle PSR[/tex] (AAS)
Question 10
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AB} \perp \overline{BC}[/tex], [tex]\overline{CD} \perp \overline{AD}[/tex] (given)
2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
3) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle ABC[/tex] and [tex]\triangle ADC[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle ABC \cong \triangle CDA[/tex] (HL)
6) [tex]\overline{AD} \cong \overline{CB}[/tex] (CPCTC)
Solving equations with fractions- how do i solve this
Answers
Answer:
[tex]x=\frac{83}{36}[/tex]
Step-by-step explanation:
1) Convert [tex]2\frac{1}{4}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]x-\frac{2\times4+1}{4} = \frac{1}{18}[/tex]
2) Simplify [tex]2\times4[/tex] to 8.
[tex]x-\frac{8+1}{4} =\frac{1}{18}[/tex]
3) Simplify [tex]8+1[/tex] to 9.
[tex]x-\frac{9}{4} =\frac{1}{18}[/tex]
4) Add [tex]\frac{9}{4}[/tex] to both sides.
[tex]x=\frac{1}{18} +\frac{9}{4}[/tex]
5) Simplify [tex]\frac{1}{18} +\frac{9}{4}[/tex] to [tex]\frac{83}{36}[/tex].
[tex]x=\frac{83}{36}[/tex]
Decimal Form: 2.305556
Answer:
83/36
Step-by-step explanation:
x - 2 1/4 = 1/18
x = 1/18 + 9/4
L.C.M= 36,
x = 1x2/18x2 + 9x9/4x9
x = 2/36 + 81/36
x = 83/36
Decimal form = 2.305556
PLEASE HELP IM SERIOUSLY STUCK
Answers
Answer: -1
Step-by-step explanation:
Remember to use the slope formula.
[tex]\frac{y2-y1}{x2-x1}[/tex]
Then plug in your points:
[tex]m=\frac{-1-(4)}{2-(3)}[/tex]
Simplify
[tex]m=\frac{-5}{5}[/tex]
Divide -5 by 5 and your Answer is:
[tex]m=-1[/tex]
Hopes this helps!
Answer:
-1
Step-by-step explanation:
As given in the picture you provided, the slope is defined as: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and the reason for this, is because in subtracting y_1 from y_2, you're finding how much the y-value changed, or in other words, the rise. When subtracting x_1 from x_2 you're finding how much the x-value changed, or in other words the run. Another way of expressing the slope that you may have seen is: [tex]\frac{rise}{run}[/tex] which is essentially what this slope formula is doing.
One thing to note is that what I assign to (x_1, y_1) and (x_2, y_1) doesn't matter, as long as they're two different points on the linear line.
So let's just say that: [tex](x_1, y_1) = (-3, 4)[/tex] and that: [tex](x_2, y_2) = (2, -1)[/tex]
Now plugging these values into the equation we get: [tex]\frac{-1-4}{2-(-3)} = \frac{-5}{5} = -1[/tex]
So the slope is -1
What is the simplified form of startroot 100 x superscript 36 baseline endroot ?
Answers
The simplified form of the expression is [tex]10 x^{18}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The given expression is [tex]\sqrt{100x^{36} }[/tex]
Applying the rule, [tex]\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}[/tex]
Now, [tex]\sqrt{100} \sqrt{x^{36} }[/tex]
Simplifying, we get;
[tex]10\sqrt{x^{36} }[/tex]
Applying the exponent rule, [tex]a^{bc} = (a^{b} )^{c}[/tex]
We get
[tex]10 \sqrt{(x^{18} })^{2}[/tex]
[tex]10 x^{18}[/tex]
Therefore, the simplified form of the expression is [tex]10 x^{18}[/tex].
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Answer:
10 x 18
Step-by-step explanation:
In a certain card game, the probability that a player is dealt a particular hand is. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly times? why or why not?.
Answers
No, you will not be dealt this hand exactly 48 times. This can be obtained by understanding the concept of probability.
What does the probability mean?The probability means that out of 100 times nearly 48 times the player is dealt the particular hand.
No, you will not be dealt this hand exactly 48 times since 48 times is an approximate value out of 100 times.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: In a certain card game, the probability that a player is dealt a particular hand is 0.48. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 48 times? Why or why not?
Nine tiles are numbered $\color[rgb]{0.35,0.35,0.35}1, 2, 3, \ldots, 9$. Each of three players randomly selects and keeps three of the tiles, and sums those three values. Find the probability that all three players obtain an odd sum.
Answers
The probability that all three players obtain an odd sum is 3/14.
What is probability?The probability is the ratio of possible distributions to the total distributions.
I.e.,
Probability = (possible distributions)/(total distributions)
Calculation:Given that,
There are nine tiles - 1, 2, 3,...9, respectively.
A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.
In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.
The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.
So,
One player can be selected in [tex]^3C_1[/tex] ways.
The 3 odd tiles out of 5 can be selected in [tex]^5C_3[/tex] ways.
The remaining 2 odd tiles can be selected and distributed in [tex]^2C_1[/tex] ways.
The remaining 4 even tiles can be equally distributed in [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex] ways.
So, the possible distributions = [tex]^3C_1[/tex] × [tex]^5C_3[/tex] × [tex]^2C_1[/tex] × [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex]
⇒ 3 × 10 × 2 × 6 = 360
To find the total distributions,
The first player needs 3 tiles from the 9 tiles in [tex]^9C3=84[/tex] ways
The second player needs 3 tiles from the remaining 6 tiles in [tex]^6C_3=20[/tex] ways
The third player takes the remaining tiles in 1 way.
So, the total distributions = 84 × 20 × 1 = 1680
Therefore, the required probability = (possible distributions)/(total distributions)
⇒ Probability = 360/1680 = 3/14.
So, the required probability for the three players to obtain an odd sum is 3/14.
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CORRECT ANSWER GETS BRAINLIST
Answers
Answer:
y = -1x + 1
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = -1x + 1
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What is the area of the trapezoid?
33 in2
52.5 in2
82.5 in2
91 in2
Answers
Answer:
91 in2
Step-by-step explanation:
11+15 over 2 , times by 7 equals 91 ??
Select the correct answer.
Darren is going to the state fair. Each ride costs $6 to ride, and each exhibit costs $3 to view. Darren can spend at most $84 at the fair.
The inequality and graph that represent this situation are shown, with x representing the number of rides Darren can ride and y representing
the number of exhibits he can view
6x+3y< 84
-10
A (9,10)
B (85.11)
C (11.2)
D. (-3,15)
Answers
The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of rides Darren can ride and y represent the number of exhibits he can view. Hence:
6x + 3y ≤ 84
The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.
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It was A! I got it right on the Edmentum/Plato test!! YW!!!
the population of happy land is 15.8 happys per acre exactly 553 happys live in happy land. how many acres is happyland
Answers
Answer:
35 acres.
Step-by-step explanation:
Proportions:
15. 8 ⇒ 1 acre
553 ⇒ P acres
P = 553*1/15.8
P = 35 acres