Solution :
Let the three places be 1, 2, 3, 4, 5, 6, 7, 8
a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2
= 14
[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]
Therefore the required probability is
[tex]$=\frac{14}{8!}$[/tex]
= [tex]$\frac{14}{40320} = 0.000347$[/tex]
b). The probability that the marketing director to be placed in the leftmost position is
[tex]$=\frac{7!}{8!}$[/tex]
[tex]$=\frac{1}{8} = 0.125$[/tex]
c). The two events are not independent because
[tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]
[tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]
where A is the case a and B is the case b.
(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].
(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].
(c) So, the two events are dependent on each other.
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.
Total people in company A and company B is [tex]=8[/tex]
Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]
[tex]=40320[/tex]
(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]
Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].
by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]
[tex]=5040[/tex]
Again, combine the general manager and vice president in one line[tex]=2![/tex]
[tex]=2[/tex]
Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]
[tex]=\frac{10080}{40320}[/tex]
[tex]P(A)=\frac{1}{4}[/tex]
(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]
Now, fixing the position of marketing director in the leftmost.
arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]
Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]
[tex]=\frac{1}{8}[/tex]
[tex]P(B)=\frac{1}{8}[/tex]
(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.
Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.
So, the two events are dependent on each other.
Learn more about the topic of Probability: https://brainly.com/question/26959834
Dawn has two bank accounts she has been using to save money for a car. The difference between account A and account B is $100. If she uses StartFraction 3 Over 8 EndFraction of account A and StartFraction 7 Over 8 EndFraction of account B, Dawn will have a down payment of $2000. Choose the statements that are true when solving for the amount Dawn has in each account. Check all that apply.
One of the equations that represents this scenario is A – B = 100.
One of the equations that represents this scenario is StartFraction 3 Over 8 EndFractionA + StartFraction 7 Over 8 EndFractionB = 2000.
To eliminate the A variable, multiply the first equation by 3 and the second by 8.
To eliminate the B variable, multiply the first equation by 7 and the second by 8.
To eliminate the B variable, multiply the first equation by 7 and the second by –8.
Answer:
1) One of the equations that represents this scenario is A – B = 100.
2)One of the equations that represents this scenario is StartFraction 3 Over 8 EndFractionA + StartFraction 7 Over 8 EndFractionB = 2000.
4) To eliminate the B variable, multiply the first equation by 7 and the second by 8.
Step-by-step explanation:
Answer:
a b and d
Step-by-step explanation:
Simplify this expression.
6x + 3 – 4x + 2y + 7
Answer:
2x + 10 + 2y
Step-by-step explanation:
6x + 3 – 4x + 2y + 7
(6x - 4x) = 2x
2x + 3 +2y + 7
(3 + 7) = 10
Answer: 2x + 10 + 2y
Compare 0.55 ____ 0.525 using , or =
Answer:
0.55 > 0.525
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.55=0.550
0.550>0.525
so 0.55>0.525
2 divided by negative 1/5
Answer: 10
you have to find a common denominator between two and five which is 10. therefore making the number 2 into the fraction 20/10 and finding the common denominator of 1/5 makes it now 2/10. now divide 20 by 2 which gets you 10. and dividing 10 by 10 gets you. therefore making the new fraction 10/1 which is equal to 10. :)
please brainlist who ever answers
Answer:
190 square inches
Step-by-step explanation:
Answer:
190
Step-by-step explanation:
29) Which equation describes this graph?
graph that contains the points (-2,0) and (8,-10)
A. y=−2x−2
B. y=2+x
C. y=−x
D. y=−2−x
The students at Job's high school
were surveyed to determine their
favorite foods. The results are shown
in the table below. Suppose students
were randomly selected and asked
what their favorite food is. Find the
probability of each event. Write as a
fraction in simplest form.
Favorite Food Responses
Pizza 19
Steak 8
Chow-mein 5
Seafood 4
Spaghetti 3
Cereal 1
16. P(steak)
17. P(Spaghetti)
18. P(cereal or seafood)
19. P(not chow-mein)
19. P(pizza)
20. P(cereal or steak)
21. P(not steak) 22. P(not cereal or seafood)
23. P(chicken) 24. P(chow mein or spaghetti)
Can someone help? I don't understand the equasion
Answer:
a = 1/6
Step-by-step explanation:
To solve, divide both sides by 5 1/4
a = 7/8 / (5 1/4)
a = (7/8) / (21/4)
a= 7/8 * 4/21
a= 28/168
a= 1/6
Sally goes to the store and buys a camera for $65. The store is
running a discount of 10%. What is the price of the camera after the
discount?
Answer:
58.50
Step-by-step explanation:
I will give brainiest to whoever answers correctly !!
I bought a pizza Alexis ate 3/4 of the pizza how much pizza do I have left???
Answer:
8/7 left, Hope i helped :)
Step-by-step explanation:
Answer:
yyyyyyyyyyyyyyyyyyyyyyyyyyyuujuuju
Step-by-step explanation:
HI dude was good
Write 45% as a decimal.
Answer:
0.45
Step-by-step explanation:
Because you have to write 45% has money so 45.00 divide by 100 = 0.45 hope this is right and helpful. Can you mark me brainliest
so I really need help. you have to set fractions equal to each other and try and find out how many prefer sweaters and whatnot. Also, the answer isn't supposed to be a fraction, it's supposed to be a whole number, you find the answer by using fractions with the information provided in the word problem above ^
I hope that makes sense. lol, thank you :)
Answer:
84
Step-by-step explanation:
52%of math problem are pointless
52%of math problem = pointless
52% of 175
(52/100)×175
91 =pointless
math problem - pointless =not pointless
175 - 91 = 84
ANSWER FAST PLS HAVE 5 MIN FOR THIS
Employees of a painting service paint the interior walls of homes and office buidings.
The following table shows the number of cons of point the employees use, and the
number of square feet they cover.
Cans of paint
3
Area painted (square feet) 375
1125 1500
Which equation describes the relationship between the number of cons of paint
used, and the number of square feet that are covered?
1
2
750
A
y = 375x + 375
B
y=+*
375
y = 50x + 325
D
y = 375x
Answer:
Y=375x
Step-by-step explanation:
thats the answer
what is the equation
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y_1 = y - coordinate \: \: point \\ x_1 = x - coordinate \: \: point[/tex]
From the given equation.[tex]y + 8 = 4(x - 5)[/tex]
[tex]y - ( - 8) = 4(x - ( + 5))[/tex]
Answer[tex] \large \boxed{( - 8,5)}[/tex]
Which one is a better deal? Deal 1: $7.65 for 9 iTunes songs Deal 2: $6.93 for 7 iTunes songs
Answer:
yeah I would say deal #1 is better
Pls help extra points and mark brainlist easy reading
Answer: Its they second or last one but the second one sound more clear
Step-by-step explanation:
Which statement is false?
1) All points with an x-value of 3 are located in Quadrant I.
2) There is only one point on the coordinate plane that is on both the x- and y-axes.
3) All points with an x-value of 0 are located on the y-axis.
4) There is only one point on the coordinate plane with an x-value of 2 and a y-value of 2.
Answer:Choice A) All points with an x-value of 3 are located in Quadrant I.
We can show it is false through the use of a counter example. For instance, the point (3, -5) is not in quadrant 1, but rather in quadrant 4.
We would need to say "all points with x value 3 and positive y value" to ensure the point is in quadrant 1.
The school show choir is holding a car wash to raise $350 for
new costumes. After spending $30 on supplies, the students will
wash cars for donations of $6 each.
This situation can be modelled by the inequality 6C + 30 > 350,
which has the solution c> 53.33. What is the best way to
interpret this solution?
A. Show choir needs $53.33 to meet their goal.
B. Show choir should have spent another $53.33 on supplies.
C. At least 54 show choir students must participate in the car
wash.
D. Show choir needs to wash at least 54 cars.
Answer:
D.
Step-by-step explanation:
It’s the only option that makes sense. Option A. Is invalid because they need to make $350. Option B. Is just purely invalid and has no context to support the theory. C. Is possible, but we can have students wash more than one car, so we don’t need fifty four kids.
D. Is your answer.
Hope this helped!!
LunarRose3
HURRY PLEASE....... Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios. Which table shows the same data?
Answer:b
Step-by-step explanation:
two beads for every 3
the target temperature for a laboratory is 71° f. it can vary by up to 3°. if t is the temperature in the laboratory, which of the following inequalities represents this situation?
Answer:
|t-71| < 3
Step-by-step explanation:
The inequalities represents this situation is | t - 71 | < 3 .
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
According to the question
The target temperature for a laboratory = 71° f.
it can vary by up to 3°. (highest limit)
the temperature in the laboratory represented by t
Now,
inequalities represents this situation is
| t - 71 | < 3
Hence, the inequalities represents this situation is | t - 71 | < 3
To know more about inequalities here:
https://brainly.com/question/20383699
#SPJ2
The distance in feet that Karina swims in a race is represented by 5d -5, where d is the distance for eac
What is an expression equivalent to 5d -5?
Choose the correct answer below.
A. 5d - 5 = 5(-5)
B. 5d -5 = -5 + 5d
C. 5d - 5 = 5-5d
D. 5d - 5 = -5(d+5)
Answer:
C. 5d - 5 = 5-5d
Step-by-step explanation:
A 300 room hotel can rent every one of its rooms at $80 per room. For every $1 increase in rent, 3 fewer rooms are rented.
How much should the hotel charge for each room to maximize its daily revenue? What is the maximum daily revenue?
Answer:
The hotel charge for each room to maximize its daily revenue and the maximum daily revenue is explained below in details.
Step-by-step explanation:
So for every $1 hike in price, the number of rooms goes underneath by 1.
So the earnings can be displayed by R(x) = (300-x)(80+x)
From that, you require to subtract 22(300-x) since it takes $22 per occupied room.
AND there is a framed cost of $1000 per day.
So your profit function is P(x) = (300-x)(80+x) - 22(300-x) - 1000
Simplified, this is P(x) = -x2 +242x + 16400.
P'(x) = -2x + 242 Set it = to 0
x = 121 which displayed the number of unoccupied rooms.
P(121) = -14641 + 29282 + 16400 = $31041
You can verify by computing P(120) and P(122) which both even $31040.
Hope this helps.
Four co-workers contributed $2.58, $10.20, $19.89, and $12.89 respectively to purchase a retirement gift for their boss. What is the maximum amount they can spend on a gift?
Answer:
the answer is $45.56!
Step-by-step explanation:
you just have to add all of there amounts to find how much money they have
Find the slope and y-intercept.
Answer:
slope is four and the y-intercept is 1/5
Help due in 30 min!!!!!!!!!!!!!!!
Answer:
b. - 1/4
Step-by-step explanation:
Start at the point highest on the line(3,4). Subtract the x value of the second point, from the x value of the first point.(3-7) Then do the same with the y values.(4-3) This gives you x=-4and y= 1. Slope= y/x, so you get -1/4
3x + 1 = -2 (solve for x)
Answer:
x = -1
Step-by-step explanation:
3x + 1 = -2
Subtract 1 from both sides.
3x = -2 - 1
Simplify -2 - 1 to 3.
3x = -3
Divide both sides by 3.
x = -1
i don't really understand, please help!!
Step-by-step explanation:
the proof is given above
Step-by-step explanation:
In Triangle ICU,
Angle 2 = 180° - Angle 1 (Angles on a straight line)
CR = CU - RU
In Triangle ISR,
Angle 3 = 180° - Angle 4(Angles on a straight line)
SU = RS - RU
Angle 1 = Angle 4
Therefore, Angle 2 is equal to Angle 3
CU = RS
Therefore, CR is equal to SU
Triangle ICR and Triangle ISU
IC = IS
Angle 2 = Angle 3
CR = SU
Therefore, Triangle ICR and Triangle ISU are congruent (SAS congruency).
As the two triangles are congruent, Angle CIR = Angle SIU
5x - 10y=-20
5x + 3y = 6
Show work
Answer:
5x -10y= -20
5x + 3y = 6
-(5x + 3y=6)
5x-10y=-20
-5x-3y=-6
-10y -3y = -20 -6
-13y=-26
y= -26/-13
y=2
5x-10(2)=-20
5x-20=-20
5x=-20-20
5x=-40
x= -40/5
x= -8, and y= 2
Please help me if u know
Answers
x= -3/2
x= 3i
x= -3i
Step-by-step explanation:
f (x) = 2x3 + 3x2 + 18x + 27
Set 2x^3 + 3x^2 + 18x + 27 equal to 0.
2x^3 + 3x^2 + 18x + 27 = 0
Solve for x.
Factor the left side of the equation.
Factor out the greatest common factor from each group.
x^2 (2x + 3) + 9 (2x + 3) = 0
Factor the polynomial by factoring out the greatest common factor, 2x + 3. (2x + 3) (x^2 + 9) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2x + 3 = 0
x^2 + 9 = 0
Set 2x + 3 equal to 0 and solve for x.
Set 2x + 3 equal to 0. 2x + 3 = 0
Solve 2x + 3 = 0 for x. Tap for more steps...
3 x = − 2
Set x2 + 9 equal to 0 and solve for x.
Set x2 + 9 equal to 0. x2 + 9 = 0
Solve x2 + 9 = 0 for x.
x = 3i, −3i
The final solution is all the values that make (2x + 3) (x2 + 9) = 0 true.
x = − 3/2 , 3i, −3i