A sample of employees of Worldwide Enterprises is to be surveyed about a new health
care plan. The employees are classified as follows:
Classification Event Number of Employees
Supervisors A 120
Maintenance B 50
Production C 1,460
Management D 302
Secretarial E 68
(a) What is the probability that the first person selected is:
(i) either in maintenance or a secretary?
(ii) not in management?
(c) Are the events in part (a)(i) complementary or mutually exclusive or both
Answers
Using the probability concept, it is found that:
a) i) There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.
ii) There is a 0.849 = 84.9% probability that the first person selected is not in management.
b) The events are neither complementary nor mutually exclusive.
A probability is the number of desired outcomes divided by the number of total outcomes.
Item a:
In this problem, there is a total of 120 + 50 + 1460 + 302 + 68 = 2000 people.
Of those, 50 + 68 = 118 are either in maintenance or a secretary, hence:[tex]p = \frac{118}{2000} = 0.059[/tex]
There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.
Item ii:
2000 - 302 = 1698 people are not in management, hence:
[tex]p = \frac{1698}{2000} = 0.849[/tex]
There is a 0.849 = 84.9% probability that the first person selected is not in management.
Item b:
If a person is either in maintenance or a secretary, they are also not in management, hence the events are neither complementary nor mutually exclusive.
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Following are the solution to the given points:
For point a:
i)
[tex]\to P(B \cup E) = P(B) + P(E) - P( B\cap E)[/tex]
Where [tex]P(B \cap E) = 0[/tex] because they are both separate occasions It is impossible to be a member of both departments.
[tex]\to P(B\cup E) =\frac{50}{120 + 50 + 1460 + 302 + 68} +\frac{68}{120 + 50 + 1460+ 302 +68}\\\\[/tex]
[tex]=\frac{50}{2000} +\frac{68}{2000}\\\\=\frac{50+68}{2000} \\\\=\frac{118}{2000} \\\\=\frac{ 59}{1000} \\\\=0.059\\[/tex]
ii)
[tex]\to P(D^c) = 1 - P(D)[/tex]
[tex]=1- (\frac{302}{120+50+1460+302+68})\\\\=1- (\frac{302}{2000})\\\\=1- (\frac{ 151}{1000})\\\\= 1- 0.151 \\\\= 0.849\\\\[/tex]
For point b:
Please find the attached file.
For point c:
Events in a. I are mutually incompatible since [tex]P(B \cap E) = 0[/tex]. One would be a part of the both departments.
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Related Questions
Why can you use fraction multiplication to check the
answer to a fraction division problem? How do you use
multiplication to check a division problem?
Answers
Answer:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
have a great day :)
Because multiplication is the converse of division,
If x/y=z then x=?x/y=z
x=yz
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
Just like addition is the converse of subtraction.
If x/y=z,
then x=yz.
If x divided by y is equal to z, then x equals y times z. These are the rules of arithmetic. If they weren't true the universe would fall apart! The rule can be used as a check that you have the right answer.
Therefore converse of division is the answer.
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When are `x+2` and `3x` equal?
ARE THEY EQUAL?
Answers
Answer:
but tbh this equation cannot be equal
Step-by-step explanation:
Answer:
No, they are not equal, because you can not add x to 2, because it does not have an x after the 2, so they are not the same
Step-by-step explanation:
is the number 749 rational?
Answers
GEOMETRY Write and solve an equation to find the value of x so that it figures have the same area.
Answers
Answer:
C. x=7 and the expression is (5+x)9=x*(15 3/7)
Step-by-step explanation:
The width of the first shape is 5+x and the length is 9
The width of the second shape is x and the length is 15 3/7
You want the same area of the figures, so they are equal. And the formula for the area of a rectangle is l*w. So...
(5+x)9=x*(15 3/7)
45+9x=(108/7)x
315+63x=108x
63x-108x=-315
-45x=-315
x=7
So, your answer is C.
In an isosceles triangle the length of the legs is 8 cm and the angle between them is 150°. Find the altitude to the legs and the area of the triangle.
Find AH and Aᴬᴮᶜ
Answers
Answer:
AH = 4 units
Area of ΔABC = 16 square units
Step-by-step explanation:
Since ΔABC is an isosceles triangle,
AC = BC
∠CAB ≅ ∠ABC [Opposite angles of the equal sides in a triangle are equal]
In ΔABC,
m∠CAB + m∠ABC + m∠ACB = 180°
m∠ABC + m∠ABC + 150° = 180°
2m∠ABC = 30°
m∠ABC = 15°
Now we apply cosine rule in ΔABC,
AB² = AC² + BC² - 2(AB)(BC)cos(m∠ACB)
AB² = 8² + 8² - 2(8)(8)cos(150°)
AB² = 128 + 110.85
AB = [tex]\sqrt{238.85}[/tex]
AB = 15.45
In ΔABH,
sin(m∠ABH) = [tex]\frac{AH}{AB}[/tex]
sin(15°) = [tex]\frac{AH}{15.45}[/tex]
AH = 15.45sin(15°)
AH = 3.998
AH ≈ 4.0 units
HC = [tex]\sqrt{8^{2}-4^2}[/tex]
= [tex]\sqrt{48}[/tex]
= 6.93
Area of the triangle ABC = [tex]\frac{1}{2}(BC)(AH)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 square units
Andrew and Connie are both teachers at their local school. There are 15 female teachers at the school and 35 male teachers. What is the ratio of male to female teachers?
Answers
Answer:
7:3
Step-by-step explanation:
Determine the type and number of solutions for the follow equation.
x² – 8x=-7
Answers
x = 7 OR x = 1
Have a nice day
please help!!!!!!!!!!!
Answers
Answer:
pumpkin: 5
witch: 10
leaf: 50
bat: 20
ghost: 60
Answer:
Bat: 20
Pumpkin: 5
Ghost: 60
Leaf: 50
Witch: 10
Round the numbers to the nearest thousands.
4 252-
8 683-
50 000-
59 490-
96 156-
Answers
Answer:
1. 4,000
2. 9,000
3. 50,000
4. 59,000
5. 100,000
Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-60x+32=-60x+60−60x+32=−60x+60minus, 60, x, plus, 32, equals, minus, 60, x, plus, 60
(Choice B)
B
-60x+32=32x-60−60x+32=32x−60minus, 60, x, plus, 32, equals, 32, x, minus, 60
(Choice C)
C
-60x+32=-60x-32−60x+32=−60x−32minus, 60, x, plus, 32, equals, minus, 60, x, minus, 32
(Choice D)
D
-60x+32=32x+60−60x+32=32x+60
Answers
Answer:
B & D
Step-by-step explanation:
Options B and D have a solution from the given set of equations.
We need to find from the given which equation does not have solutions.
How to determine whether the equation has no solution?Solve the given equation for x. If you get any value then the equation has a solution.
From option (A):
-60x+32=-60x+60
⇒-60x+60x=60-32
By simplifying the above equation we get no x value. So, there are no solutions.
From option (B):
-60x+32=32x-60
⇒-60x-32x=-60-32
⇒-92x=-92
⇒x=1
From option (C):
-60x+32=-60x-32
By simplifying the above equation we get no x value. So, there are no solutions.
From option (D):
-60x+32=32x+60
⇒-92x=28
⇒x=0.304
Therefore, options B and D have a solution.
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8 Determine if the product of 32 and 8V 18 is
rational or irrational. Explain your answer.
Answers
Answer: It is irrational.
Step-by-step explanation:
√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.
What is the slope of the line?
Answers
Answer:
y = 2x-3.
Step-by-step explanation:
Slope is y =mx+b. If we look at the graph, the line passes by (0,-3) and (1,-1). Taking rise over run, (y/x), we can find out that y goes up 2 and x goes right 1. This means that it is a positive slope and that slope would be 2/1, simplified to just 2.
Irina ran 0.25 mile in 2 minutes. At this rate, how many minutes will it take her to run 2 miles?
Enter the correct answer in the box.
Answers
Answer:
16
Step-by-step explanation:
2/0.25 = 8
2 x 8 = 16
........
Terry is an up and coming florist who specializes in weddings. He uses 5 roses, 3 daises, and 4 bundles of green filler to make one bouquet. If r is the cost of a rose and d is the cost of a daisy, and f is the cost of a bundle of green filler, which expression represents the cost for making 75 bouquets
Answers
Answer:
75 (5r + 3d + 4f)
Step-by-step explanation:
Cost of 5 roses: 5rCost of 3 daises: 3dCost of 4 green fillers: 4fAmount of bouquets: 75Put them together: 75 (5r + 3d + 4f)I hope this helps!
explanation:
5r is the cost of the roses
3d is the cost of the daisies
4f is the cost of the green filler
times all of those by 75, which is how many bouquets Terry is trying to make
hope this helps :)
A waterfall is n times the height of its picture on a postcard.
Which equation represents the height, y, of the waterfall if
the picture is 6 cm tall?
A y = 6+n
y = 6+n
y = 6n
y=n-6
Answers
Answer: y=6n
Step-by-step explanation:
Which fraction is equivalent to 20
Answers
Answer:
4/16
Step-by-step explanation:
7b-2/5=6b-7/5 nudfghnkdfbvugyteugdyvbbbvybhjedfs
Answers
Answer:
b=−1
Step-by-step explanation:
Solve: -19x- 1 = -12x + 34
Answers
19−1=−12+34
19x-1=-12x+34
19x−1=−12x+34
19−1+1=−12+34+1
help me pls I don't get this question
Answers
Answer:
To multiply mixed numbers:
Step-by-step explanation:
1. convert to improper fractions
2. top * top
3. bottom * bottom
4. convert back into a mixed number
Answer:
Hi!
In these questions you're being asked to multiply mixed numbers. The easiest way to do this is to convert the mixed numbers to improper fractions, and then multiply them in that form.
For the first question:
[tex]1\frac{3}{5} = \frac{8}{5} ; 1\frac{2}{5} =\frac{7}{5} \\[/tex] To convert the mixed numbers to improper fractions, you just multiply the denominator by the whole number, and then add it to the current numerator, forming the new numerator. The denominator stays the same.
[tex]\frac{8}{5} *\frac{7}{5} = \frac{56}{25}[/tex] Next, multiply together the numerators, and then multiply together the denominators.
[tex]\frac{56}{25} = 2\frac{6}{25}[/tex]
The ratio of cows to chickens on Jack's farm is 3:5. Choose ALL correct statements that describe this relationship.
Answers
Finding the Equation of a Line
You have discovered another alien.
Move the sliders to change the slope and y-intercept.
Create an equation to produce the correct line of travel.
slope: 0
6
What is the equation of the line that provides the
correct path to rescue this alien?
A. Y=5
B. Y=x+5
C. Y=-x+5
D. Y=5x
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line is Y=-x+5. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The position of Allien in the coordinate plane is (0,5), the coordinate of the rocket is (5,0). The slope between the two is,
Slope, m = (0 - 5)/(5 - 0) = -5/5 = -1
The equation of the line can be written as,
y = -1x + C
substitute any one of the point in the equation,
0 = -1(5) + C
0 = -5 + C
C = 5
Hence, the equation of the line is Y=-x+5. Thus, the correct option is C.
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3x + 6 = y
solve for x
Answers
Answer:
x=1/3y - 2
Step-by-step explanation:
Give the 10th term of the following sequence:
1, 4, 7. 10
Answers
Answer:
28
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
The value of the x-intercept for the graph of 4x - 5y = 40 is
Answers
Answer: The x intercept is 10 or (10,0)
Step-by-step explanation:
4x - 5y = 40 The x-intercept of a line is when its y coordinate is equal to zero. Input zero into the equation for y and solve for x to find the x intercept.
4x-5(0) = 40
4x + 0 = 40
4x = 40
x= 10
The x intercept is 10 or (10,0)
Podemos calcular la profundidad d
de la nieve, en centímetros, que se acumula en el jardín de Harper durante las primeras h horas de una tormenta usando la ecuación
d=5h
Cuántas horas tarda en acumularse 1
centímetro de nieve en el jardín de Harper?
Cuántos centímetros de nieve se acumulan por hora?
Answers
Answer:
a) Cuántas horas tarda en acumularse 1
centímetro de nieve en el jardín de Harper?
0.508 horas o 30.48 minutos
b) Cuántos centímetros de nieve se acumulan por hora?
5 cm
Step-by-step explanation:
a) ¿Cuántas horas se necesitan para acumular 1 pulgada de nieve en el jardín de Harper?
1 pulgada de nieve = 2.54 cm de nieve
d = 5 × h
2.54 = 5 h
h = 2.54 / 5
h = 0.508 hora
Convertir a minutos = 0.508 horas × 60 minutos
= 30.48 minutos.
Por lo tanto, se necesitarían 0.508 horas o 30.48 minutos para acumular 1 pulgada de nieve en el jardín de Harper.
b) ¿Cuántos centímetros de nieve se acumulan por hora?
d = 5 h
Por hora = 1 hora
d = 5 × 1
d = 5 cm
Por tanto, se acumulan 5 cm de nieve por hora.
16) 56 is what percent of 40?
%
Answers
140
Step-by-step explanation:
56:40*100 =
(56*100):40 =
5600:40 = 140
PLS HELP ASAP
Write a word problem that can be represented by the expression 5/6 divided by 1/3.
Answers
Answer:
I have 5/6 of a candy bad and I want to give each of my 3 friends some. How much would each friend get?
Step-by-step explanation:
The word problem that can be represented by the expression 5/6 divided by 1/3 is "There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that".
Given :
The expression 5/6 is divided by 1/3.
The following steps can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3:
Step 1 - The knowledge of arithmetic operations can be used in order to determine the word problem that can be represented by the expression 5/6 divided by 1/3.
Step 2 - There are a total of 5/6 chocolates. Divide these chocolates such that each person will get 1/3 part of that.
Step 3 - Solve the above problem by dividing 5/6 by 1/3.
[tex]= \dfrac{5\times 3}{6\times 1}[/tex]
= 2.5
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how do you solve
16 < b + 8, if b =22
Answers
Answer:
16 < 30
Step-by-step explanation:
Substitute 22 for b, add 22 to 8 (30)
The inequality is correct, 30 is greater than 16
Help! Whoever answers correctly and is first to answer I will make brainly! In dire need of help!
Answers
Answer:
B
Step-by-step explanation:
Isoceles triangle
Answer:
B. 65 degrees
John has $100 in his bank account, and is spending $3 a day on lunch. How long until he has $55 in his account?
Answers
Answer:
15 days
Step-by-step explanation:
We know that John has $100 in his bank account and he is spending $3 a day.
We want to find how many days until he has $55 left.
d=days
55=100-3d
55+3d=100
100-55=3d
3d=45
Solving for d, we divide by 3.
Your answer is 15.