In the questions below nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if a) Ben is to be in the picture? b) Both Ed and Gail are in the picture? 4200 c) Neither Ed nor Fran are in the picture? 5040 d) Dot is on the left end and Ed is on the right end? 210 e) Hal or Ida (but not both) are in the picture? 4200 f) Ed and Gail are in the picture, standing next to each other? 960 g) Ann and Ben are in the picture, but not standing next to each other?
Answers
Answer:
Step-by-step explanation:
Ben is present in all pictures so rest of 4 persons to be selected from 8 persons , no of ways to do it is
⁸C₄ = 8 x 7 x 6 x 5 / 4 x 3 x 2 x 1
= 70 .
In one of these combination , we can get 5 ! ( five factorial )
Total no of permutations
= 70 x 5 !
= 8400 .
b ) Both Ed and Gail are present
The above derivation changes to the following .
Total no of permutations
= ⁷C₃ x 5 !
= 35 x 120
= 4200
c )
exclude 2 person from 9 to be selected
permutation
= ⁷C₅ x 5 !
= 21 x 120
= 2520
d )
rest of 3 person from 7 persons , no of permutations
⁷P₃ = 7 x 6 x 5 = 210
e )
Hal or Ida can occupy any of the 5 position which can be done in 5 ways .
when one position is occupied , the rest of 4 position can be occupied by 7 persons which can be done in
⁷P₄ ways
Total ways = 5 x ⁷P₄
= 5 x 840
= 4200
f )
They can occupy position like 1,2 or 2,3 or 3,4 or 4,5
Rest of the position can be occupied in ⁷P₃ ways
Total ways = 4 x ⁷P₃
= 4 x 210
= 840
They can also be exchanged mutually so no of ways
= 840 x 2 = 1680 .
g ) No of pictures in which Ann and Ben are present
two position to be selected out of 5 = ⁵P₂
Rest of position that can be shuffled = ⁷P₃
Total no of pictures in which both are present
= ⁵P₂ x ⁷P₃
= 20 x 210
= 4200
out of which they will be standing next to each other = 1680
no of pictures in which they will not be standing next to each other
= 4200 - 1680 = 2520. .
Related Questions
Si seis conejos necesitan 10 sacos de comida a la semana, ¿cuántos sacos necesitarán nueve conejos para comer durante una semana?
Answers
Therefore, nine rabbits will need 7.5 sacks of food for one week.
What is unitary method?The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.
Here,
To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.
Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:
6/10 = 9/x
Cross-multiplying, we get:
6x = 90
Dividing both sides by 6, we get:
x = 15/2 or 7.5
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Complete question:
If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?
A bag of color tiles contains 2 red, 1 blue, 1 green, and 4 yellow. Sean reaches in and draws one
tile without replacing it. He then draws a second tile and a third tile without replacing them. Which
of the following combinations is a possible draw?
F:red,blue,blue G:red,green,green H:yellow,blue,green J:blue,blue,green
Answers
Answer:
H
Step-by-step explanation:
Since there is 4 yellows, 1 green, and 1 blue, there is no way you could draw 2 blues or 2 greens. Therefore, F, G, and J are immediately eliminated. The only answer left is H, and it makes sense. H is the answer.
Answer:
H: yellow, blue, green
Step-by-step explanation:
F: red, blue, blue = cannot be true as there is 1 blue tile in bag and it cannot be drawn twice without replacing first draw.
G: red, green, green = cannot be true because 1 original green tile in bag cannot be drawn twice
J: blue,blue, green = cannot be true for same reason; 1 original blue tile cannot be drawn twice without replacement.
top question says: Triangle ABC can be taken to triangle A'B'C' using rigid motions and a dilation. help me pls
Answers
If triangle ABC can be taken to triangle A'B'C', it means that they are similar triangles. If tow triangles are similar, it means that the ratio of their corresponding sides are equal. Thus, we have
A'B'/AB = B'C'/BC = A'C'/AC
Thus, looking at the options, the true equations are
A) A'C'/B'A' = AC/BA
D) CA/C'A' = CB/C'B'
E) A'B'/AB = C'B'/CB
If we look at these options the ratios are always the same
Jeffrey is n years old. His sister is 5 years older than Jeffrey’s age. Write an expression that represents the relationship of his sister’s age in terms of Jeffrey’s age, where n represents Jeffrey’s age. I need help ASAP PLEASE!!
Answers
Answer:
jeffreys sister is 5+n
Step-by-step explanation:
so practically jefferys sister is N or jefferys age plus 5
hope this helped
write even number between 10 and 20
Answers
solve for the missing term or number in each of the following
Answers
The value of the missing terms are;
1. N = 24
2. 144
3. 6
4. 1000
5. 12.75
How to determine the valueTo determine the value, we have that the proportion is determined by;
1. 4/25 = N/150
cross multiply the values, we have;
25N = 150(4)
multiply the values
25N = 600
N = 24
2. 48/75 = N/225
cross multiply the values
75N = 10800
Divide the values
N = 144
3. N/16 = 30/80
cross multiply the values
80N = 480
N = 6
4. 125/N = 2/16
cross multiply the values
2N = 2000
N = 1000
5. 2.75/11 = N/51
cross multiply the values
11N = 140.25
N = 12.75
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Which ordered pair makes both inequalities true?
y> -3x +3
y22x-2
O (1,0)
O (-1,1)
O (2,2)
O (0,3)
Answers
None of the ordered pairs (1, 0), (-1, 1), (2, 2), and (0, 3) make both inequalities true.
To determine which ordered pair makes both inequalities true, we can substitute the given values into the inequalities and check for validity:
1. (1, 0):
For y > -3x + 3: 0 > -3(1) + 3 -> 0 > 0, which is not true.
For y < 2x - 2: 0 < 2(1) - 2 -> 0 < 0, which is not true.
Therefore, (1, 0) does not satisfy both inequalities.
2. (-1, 1):
For y > -3x + 3: 1 > -3(-1) + 3 -> 1 > 6, which is not true.
For y < 2x - 2: 1 < 2(-1) - 2 -> 1 < -4, which is not true.
Therefore, (-1, 1) does not satisfy both inequalities.
3. (2, 2):
For y > -3x + 3: 2 > -3(2) + 3 -> 2 > -3, which is true.
For y < 2x - 2: 2 < 2(2) - 2 -> 2 < 2, which is not true.
Therefore, (2, 2) does not satisfy both inequalities.
4. (0, 3):
For y > -3x + 3: 3 > -3(0) + 3 -> 3 > 3, which is not true.
For y < 2x - 2: 3 < 2(0) - 2 -> 3 < -2, which is not true.
Therefore, (0, 3) does not satisfy both inequalities.
None of the given ordered pairs satisfy both inequalities simultaneously.
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2. The sides of a triangle are in the ratio 3:7:10 and the perimeter is 80 inches.
What are the lengths of the sides of the triangle?
Can anyone help please ?
Answers
Step-by-step explanation:
3+7+10=20
80/20=4
1 ratio =4
3(4) : 7(4) : 10(4)
= 12 : 28 : 40
How to determine open interval on which the function is increasing?
Answers
Answer:
To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.
K + 5 - 4v + 12 k = 12 and v=6
_
v
Answers
Answer: 4.8
Step-by-step explanation:
because it isn’t sorry I’m just here for points don’t put that
John wants to build a
rectangular deck with a
width of 2x and a length
of (3x + 1). What is the
perimeter of the deck?
Plzzz help thank you
Answers
Step-by-step explanation:
length of a rectangular deck= 3x+1
breadth of a rectangular deck= 2x
perimeter of a rectangular deck =?
we know that,
perimeter of a rectangular deck = 2 ( length + breadth )
2 (3x + 1)+2x
6x+2+2x
8x+2
x=8-2=6
x=6#
Write an
integer for this situation: I deposited 25 dollars into my bank account.
dollars
Answers
Given:
I deposited 25 dollars into my bank account.
To find:
The integer for the given situation.
Solution:
If any amount deposited into a bank account, then the amount in the bank increased by that amount.
We know that, positive integers represent increase and negative integers represent decrease.
If I deposited 25 dollars into my bank account, then my account balance increased by $25. Here, this situation is represents by the integer positive 25.
Therefore, the required integer for this situation is 25.
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
Answers
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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Please help me. I'm honestly really confused. I need the answers as soon as possible!
Answers
Answer:
which class can you say then I can tell answer
If a rectangle has a perimeter of 56 inches and a width of 8 inches,what is the perimeter
Answers
Answer:
192 inches ²Step-by-step explanation:
P= (l+w)
56 = 2(l+8)
56=2l+8
56-8= 2l
48=2l
Length=24
Area = ?
A = l×w
A=24×8
Area= 192inches²
rewrite the equation 10=1,000 with an exponet that makes it true .
Answers
hope this helps :)
Answer:
\(10^3=1,000\)
Step-by-step explanation:
The expression 10=1,000 is obviously false, but we can make it true by rewriting it with an exponent.
Note that 1,000=10*10*10
Or, equivalently:
\(1,000=10^3\)
Thus, if we modify the original false expression and add an exponent 3 to the base 10, then it would be true:
Original:
10=1,000 => false
Rewritten true:
\(\boxed{10^3=1,000}\)
Three vertices of a parallelogram are given. Find the coordinates of the
fourth vertex.
15. (1,5), (3, 3), (8, 3),
16. (-5, 0), (-2,-4), (3, 0)
Answers
The fourth vertex of the parallelogram is (6,5) and (0,4) respectively.
What is a vertex?
A vertex is a point on a polygon where the sides or edges of an object meet, or where two rays or line segments meet. The plural form of race is race.
vertex - side or edge
Points A, B, C, D, and E are vertices. Let A(1,5), B(3, 3), C(8,3), D(x, y) be the vertices of the parallelogram ABCD. Because the diagonals of a parallelogram bisect each other.
∴Center coordinate of AC=Center coordinate of BD
[(1+8)/2,(5+3)/2]=[(x+3)/2,(y+3)/2]
same coordinates on both sides
9/2=(x+3)/2
x+3=9
x=6
8/2=(y+3)/2
y+3=8
y=5
So the 4th corner of the parallelogram (6,5)
Points A, B, C, D, and E are vertices. Let A(-5,0), B(-2,-4), C(3,0), D(x, y) be the vertices of the parallelogram ABCD. Because the diagonals of a parallelogram bisect each other.
∴Center coordinate of AC=Center coordinate of BD
[(-5+3)/2,(0+0)/2]=[(x-2)/2,(y-4)/2]
(-1,0)=[(x-2)/2,(y-4)/2]
same coordinates on both sides
(x-2)/2=-1
x-2=-2
x=0
y-4=0
y=4
So the 4th corner of the parallelogram (0,4)
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4. The sum of three consecutive odd integers
is 189. What are the
integers?
Answers
Answer:
61,63,and 65
Step-by-step explanation:
61+63+65=189
The consecutive integers are x,x+1,x+2
X+(X+1)+(x+2)=189
3x+3=189
3x=189-3
3x=186
Divide both side by 3
X=62
X+1=62+1=63
X+2=62+2=64
Therefore , the three consecutive numbers are 62,63&64
EXTREMELY URGENT Which function, g or h, is the inverse function for function ƒ?
the function h because the graphs of ƒ and h are symmetrical about the line y = x
the function g because the graphs of ƒ and g are symmetrical about the line y = x
the function h because the graphs of ƒ and h are symmetrical about the x-axis
the function g because the graphs of ƒ and g are symmetrical about the x-axis
Answers
Answer:
The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x
Step-by-step explanation:
A function and its inverse function become symmetrical across the line y = x.
Please help me in confused
Answers
Answer:
20\(c^{6}\)
Step-by-step explanation:
using the rule of exponents
\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)
given
(- 4c³)(- 5c³) ← remove parenthesis
= - 4 × c³ × - 5 × c³
= - 4 × - 5 × c³ × c³
= 20 × \(c^{(3+3)}\)
= 20\(c^{6}\)
3. Define a variable, write an equation, and solve the problem. Carla began a
running program to prepare for track team try-outs. On her first day she ran
3 miles, and on her second day she ran 5 miles. Since then, Carla has run 7 miles
each day. If her log book shows that Carla has run a total of 99 miles, for how
many days has Carla been running 7 miles?
Answers
Answer:
Carla has been running 7 miles each day for 13 days.
Step-by-step explanation:
Carla ran 3 miles on her first day, 5 miles on her second day and then 7 miles each day onward.
Let the number of days she ran 7 miles each day = x
Total distance run by Carla = 3 + 5 + 7(x)
= 8 + 7x
If her log book shows that she has run total distance = 99 miles
Equation representing her total run will be,
8 + 7x = 99
7x = 99 - 8
7x = 91
x = \(\frac{91}{7}\)
x = 13 days
Therefore, Carla has been running 7 miles each day for 13 days.
Solve n=m+9 for m
what does m equal
Answers
Answer:
m=-9+n
Step-by-step explanation:
you want to get m by itself so you subtract 9 on both sides. 9-9 crosses out and you get m by itself. Which leads you to m= -9+n
Hhenhwrghghghrwghrwhrghshgrh
Answers
Answer:
it is proportional cause it follows a pattern
Step-by-step explanation:
can i have brainliest?
how is your day going my luv
Solve the system.
2x + y + 3z = 20
X + 2y - z = -11
3x - 2z = -3
Enter your answer as an ordered triple.
Answers
The solution to the system, as an ordered triple is: (3, -4, 6).
How to Solve a System of Equations?To solve the following given system of equations:
2x + y + 3z = 20 --> eqn. 1
x + 2y - z = -11 --> eqn. 2
3x - 2z = -3 --> eqn. 3
Multiply equation 1 by 2 to get eqn. 4:
4x + 2y + 6z = 40 --> eqn. 4
Subtract eqn. 4 from eqn. 2:
x + 2y - z = -11 --> eqn. 2
4x + 2y + 6z = 40 --> eqn. 4
-3x - 7z = -51 --> eqn. 5
Add equations 3 and 5 together:
3x - 2z = -3 --> eqn. 3
-3x - 7z = -51 --> eqn. 5
-9z = -54
z = -54/-9
z = 6
Substitute the value of z into equation 5:
-3x - 7(6) = -51 --> eqn. 5
-3x - 42 = -51
-3x = -51 + 42
-3x = -9
-3x/-3 = -9/-3
x = 3
Find the value of y by substituting the values of x and z into equation 1:
2(3) + y + 3(6) = 20 --> eqn. 1
6 + y + 18 = 20
24 + y = 20
y = 20 - 24
y = -4
The solution as an ordered triple is: (3, -4, 6).
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What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answers
Answer:
\(y-2=3(x-4)\)
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in \(y-y_1=m(x-x_1)\).
\(y-y_1=3(x-x_1)\)
Now, substitute 4 as \(x_1\) and 2 as \(y_1\).
\(y-2=3(x-4)\)
Topic: parallel and perpendicular lines
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An empty 35 gallon tank begins filling with water.
i. Which of the following statements defines a variable to represent the amount of water added to the tank?
a. Let x represent the volume of water added to the tank.
b. Let x represent the number of gallons of water added to the tank.
c. Let x represent the number of gallons.
ii. Write an expression (in terms of x) to represent the number of gallons of water needed to fill the tank.
Answers
Let x represent the number of gallons of water added to the tank. The expression to represent the number of gallons of water needed to fill the tank is 34-x.
Let x represent the number of gallons of water added to the tank.
Total number of gallons that can filled in tank is total capacity of tank which is 34.
Now, x gallons of water is already filled in the tank.
Hence the tank needs to filled with the amount of water which is the difference of total capacity of tank and the gallons with which the tank is already filled.
Number of gallons of water needed to fill the tank = Total capacity of tank - number of gallons of water added to the tank
Number of gallons of water needed to fill the tank = 34 - x.
The expression to represent the number of gallons of water needed to fill the tank is 34-x.
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What is the area of the triangle?
Answers
Answer:
16
Step-by-step explanation
Rotate the triangle so 8 is the base
1/2bh
1/2*8*4
16
Answer:
the answer is 16
may it help you
can some one help me its all the points i have :(
Answers
Answer:
-2
Step-by-step explanation:
what is the closest estimate of x where f(x) = g(x)?
Answers
x≈1.6
What are the new coordinates of point A when
it is rotated about the origin by
a) 90° clockwise?
-4
b) 180°?
c) 270° clockwise?
-3 -2 -1
Y
4-
3-
ΤΑ
2.⁰⁰
1
0
-1-
-2-
--3-
-4-
1
N.
2
3 4
X
Answers
The different coordinates after respective rotation are:
1) A'(2, 0)
2) A'(0, -2)
3) A'(-2, 0)
What are the coordinates after rotation?There are different methods of transformation such as:
Translation
Rotation
Dilation
Reflection
Now, the coordinate of the given point A is: A(0, 2)
1) The rule for rotation of 90 degrees clockwise is:
(x, y) →(y,-x)
Thus, we have:
A'(2, 0)
2) The rule for rotation of 180 degrees is:
(x, y) → (-x,-y)
Thus, we have:
A'(0, -2)
3) The rule for rotation of 180 degrees is:
(x, y) → (-y,x)
Thus, we have:
A'(-2, 0)
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