Answer:
Step-by-step explanation:
Total number of workers = 20+ 15 + 10 = 45
Suppose 6 workers are selected from 45 workers, the number of ways they can be selected is [tex](^{45}_6)[/tex] ways
If 7 workers are selected from 20 workers on a day shift;
Then, the number of ways to select 7 members from a group of 20 is [tex](^{20}_7)[/tex] ways;
∴
P( all 7 selected workers will be from the day shift) is:
[tex]= \dfrac{(^{20}_7)}{(^{45}_6)}[/tex]
[tex]=\dfrac{ \dfrac{20!}{7!(20-7)!} } { \dfrac{45!}{6!(45-6)!}}[/tex]
= 0.0095
The possible number of ways to select all day shift workers is:
[tex]=(^{20}_{7})[/tex]
The possible number of ways to select all swing shift workers is:
[tex]=(^{15}_{7})[/tex]
The possible number of ways to select all graveyard shift workers is:
[tex]= ( ^{10}_{7})[/tex]
∴
The probability that all selected workers are from the same shift is:
[tex]= \Bigg [ \dfrac{ (^{20}_7) }{(^{45}_6) } + \dfrac{ (^{15}_7) }{(^{45}_6) } + \dfrac{ (^{10}_7) }{(^{45}_6) } \Bigg][/tex]
[tex]= \begin {bmatrix} \dfrac{ \dfrac{20!} {7!(20-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } + \dfrac{ \dfrac{15!} {7!(15-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } + \dfrac{ \dfrac{10!} {7!(10-7)!}}{ \dfrac{ 45! }{6!(45-6)!} } \end {bmatrix}[/tex]
= 0.0095 + 0.00079 + 0.000015
= 0.010305
P(selected workers are from at least two different shifts)
= 1 - P(selected workers are from 1 shift from any of the 3 shifts)
= 1 - 0.010305
= 0.989695
≅ 0.9897
We can determine the probability that at least one shift is unrepresented through the following ways:
Let assume that:
[tex]X_1 =[/tex] event that day shift is unrepresented
[tex]X_2 =[/tex] event that swing shift is unrepresented
[tex]X_3 =[/tex] event that graveyard shift is unrepresented
Thus; [tex](X_1 \cap X_2)[/tex] = event that all of them are drawn from graveyard shift.
[tex](X_1 \cap X_3) =[/tex] event that all are drawn from swing shift
[tex](X_2 \cap X_3) =[/tex] event that they are all drawn from day shift.
So;
[tex]P(X_1) = \dfrac{(^{25}_{7})} { (^{45}_{6}) } = 0.0590[/tex]
[tex]P(X_2) = \dfrac{(^{30}_{7})} { (^{45}_{6}) } = 0.2499[/tex]
[tex]P(X_3) = \dfrac{(^{35}_{7})} { (^{45}_{6}) } = 0.8256[/tex]
[tex]P(X_1 \cap X_2) = \dfrac{(^{10}_{7})} { (^{45}_{6}) } = 0.000015[/tex]
[tex]P(X_1 \cap X_3) = \dfrac{(^{15}_{7})} { (^{45}_{6}) } = 0.00079[/tex]
[tex]P(X_2 \cap X_3) = \dfrac{(^{20}_{7})} { (^{45}_{6}) } = 0.0095[/tex]
[tex]P(X_1 \cap X_2 \cap X_3) =0[/tex]
Probability (that at least one shift is unrepresented) is:
[tex]= P(X_1) + P(X_2) +P(X_3) - P(X_1 \cap X_2) - P(X_1 \cap X_3) - P(X_2 \cap X_3) + P(X_1 \cap X_2 \cap X_3)[/tex]
= 0.0590 + 0.2499 + 0.8256 - 0.000015 - 0.00079 - 0.0095 + 0
≅ 1.124
I need help with these 2 questions!! please 20 points!!!
9514 1404 393
Answer:
45 cm²38 cm²Step-by-step explanation:
The conventional way to work these problems is to make use of the formulas for areas of a triangle, rectangle, and semicircle. If you've used these formulas for a while, you recognize that they give you certain relationships that may make these problems easy to do mentally.
__
1. The area of a triangle is half the product of height and width, so is equivalent to the area of a rectangle either half as high, or half as wide. We note that the width of the sail is 5 cm, so half that is 2.5 cm--exactly the same as the height of the boat's hull. That means we can add the height of the sail to the length of the boat, and the total area can be considered to be the same as that of a rectangle that is
2.5 cm high × (12 cm + 6 cm) long = (2.5)(18) cm² = 45 cm²
__
2. The usual formula for the area of a circle is ...
A = πr²
When expressed in terms of diameter, this becomes ...
A = π(d/2)² = (π/4)d²
Then the area of a semicircle is half that, or (π/8)d². This is equivalent to the area of a rectangle that is "d" wide and "π/8·d" high. That is, the approximate area of the semicircle is that of a rectangle 4 cm high by (π/8·4 cm) = π/2 cm wide. In other words, the semicircle effectively adds π/2 cm to the left end of the 6 cm central rectangle of the figure.
As discussed above, the area of a triangle is equivalent to the area of a rectangle half as high. In this figure, the triangle is 10-6 = 4 cm wide, so can be considered to contribute 4/2 = 2 cm to the right end of the 6 cm central rectangle.
If we consider π ≈ 3, then the approximate area of the figure is ...
(4 cm)(3/2 cm + 6 cm + 2 cm) = (4)(9.5) cm² = 38 cm²
__
The exact value is 4(8+π/2) = 32+2π ≈ 38.283 cm².
A map is drawn to scale such that 1 inch equals 100 miles. To mark a distance of 500 miles, the length on the map must be_____ inches.
Answer:
5 inches
Step-by-step explanation:
its simple
1in-100m
500m= 100m x 5
so multiply five to the other side
1in x 5=5 in
5in-500m
Answer:
5 inches
Step-by-step explanation:
100 miles = 1 inch
500 miles = 500/100 * 1 = 5 inches
you're welcome....
This assignment is due in a little can you guys help me, please?
Answer and Step-by-step explanation:
First, read through the phrase and then break it down.
4 less than the product (multiplying) of 7 and a number (can be noted as 'x')
7x - 4 is the answer, since 4 will be less than the product of 7 and a number, with x being the placeholder.
#teamtrees #WAP (Water and Plant)
The width of a rectangle measures (5v-10w)centimeters, and its length measures (2v+3w)centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
A) −14w+14v
B)−10+6w+14v
C)−14+14v
D)7v−7
Answer:the perimeter of the rectangle =A) (−14w+14v) centimeters
Step-by-step explanation:
Step 1
The perimeter of a Rectangle is given as 2 (l+ w)
If Length = 2v+3w centimeters.
and width =5v-10wcentimeters
Then Perimeter =2 (2v+3w + 5v-10w)
Perimeter=2(7v -7w)
Perimeter= 14v - 14w or can be written as -14w +14v
A circular swimming pool is 12 feet across and is enclosed by a fence. How long is the fence? (Round your answer to one decimal place.)
Answer:
the length of the fence is 37.7 feet
Step-by-step explanation:
The computation is given below:
Given that
Diameter = 12 feet
So, the radius is the half of the diameter = 6 feet
Now the length of the fence is
= 2 × π × r
= 2 × 3.14 × 6
= 37.68 feet
= 37.7 feet
Hence, the length of the fence is 37.7 feet
The length of the fence will be 37.7 feet.
Based on the information given, we are informed that the circular swimming pool is 12 feet across and is enclosed by a fence. We want to calculate the perimeter.
The perimeter of a circle will be:
= πd
where,
π = 3.142
d = 12 feet
Therefore, the length of the fence will be:
=πd
= 3.142 × 12
= 37.7 feet
The length of the fence is 37.7 feet.
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Find the area of the following shape:
Answer:
63 in^2
Step-by-step explanation:
Area = base x height
Base: 7
Height: 9
9 x 7 = 63
Answer:
63 inches squared or [tex]63in^{2}[/tex]
Step-by-step explanation:
The answer is 63 inches squared.
The area of a parallelogram is always base times height.
In this case, the base is seven and the height is nine.
To find the area, we must multiply nine by seven
We get 63
But, we are multiplying inches and inches together
When we multiply something by itself, it becomes squared
Since we are multiplying inches by inches, it becomes inches squared
Therefore, the area of the shape is 63 inches squared, or
[tex]63in^2[/tex]
3. Elena can make 15 pizzas in 3 hours. If the number of pizzas is represented by p and time is represented by t, Write an equation that shows the total number of pizzas made in terms of time. [2 points]
Answer:
Your answer is 3x = 15
Step-by-step explanation:
3x = 15
Since 3 is being multiplied by x, we divide both sides by 3. 3x/3 cancels out, and you're left with x.
15/3 = 5
x = 5
This is my take using algebraic methods.
PLEASE HELP!! I HAVE TO TURN IT IN BY THE END OFF THE DAY (PLEASE DONT GUESS)
Answer:
Step-by-step explanation:
There are two 35° angles, so the triangle is isosceles.
The ratio of girls to boys in Lizas classroom is 5 to 4 how manny girls are in her classroom if there is a total of 27 students.
Add the ratios: 5 + 4 = 9
Divide total students by 9:
27/9 =3
Girls are listed first so the 5 part of the ratio is girls.
Multiply 5 by the 3 from above:
5 x 3 = 15
There are 15 girls.
Answer:
There are 12 girls in the classroom because if you take 4+4+4=12 and you do the same with 5 so 5+5+5=15 then add them together you get 27. So, therefore, your answer would be 12
Step-by-step explanation:
Solve this inequality for x. -46-8x>22
Answer:
x < -8.5
Step-by-step explanation:
[tex]-46-8x>22[/tex]
add 46 to both sides
[tex]-8x >68[/tex]
divide both sides by -8
[tex]x < -8.5[/tex]
Three times the smaller of two consecutive even integers increased by the larger integer i’d at least 26
Is 4 a solution to the inequality?
Is 6 a solution to the inequality?
Answer:
a is your correct answer
Answer:
6
Step-by-step explanation:
Which value is equivalent to 8?
Answer:
I cant see the answers to help you.
Step-by-step explanation:
Your test in math class has problems worth 2 points and problems worth 4 points. Altogether the test has 100 points. Write an equation that represents the total points on the test formed by the number of 2-point problems and the number of 4-point problems.
Answer:
100 = 2x + 4y
Step-by-step explanation:
solutions to 2-variable equations y=-2x-5
Answer:(1, -3).
Step-by-step explanation:
If y=2x-5 is equation (1) and 4x-y=7 is equation (2), then substitute equation (1) in equation (2):
4x - (2x - 5) = 7
4x - 2x + 5 = 7
2x = 7-5
2x = 2
x = 1
Now substitute the value of x in equation (1) to find the value of y:
y = 2 (1) - 5
y = 2 - 5
y = -3
Find the nonzero whole number in the definition of "less than" 22<34
Answer:
The inequality is always true.
True
(づ￣ ³￣)づ
is that algebra?
A rectangular prism has a volume of 60 cubic centimeters. The height of the prism is 3 centimeters. What is the area of the base? (Answer numerically only. Units have been provided) (PICTURE DOWN BELOW).
_____ square centimeters
Answer:
Area = 20 square centimeters
Step-by-step explanation:
V = lwh
V = lw3
V = 4x5x3
V = 60
A = lw
A = 4x5
A = 20
Find the zero of the linear function F(x)=-4x+5
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
we can find the zero of the linear function
F(x)= -4x+5 ,by solving the equation -4x+5 = 0
Solving the equation:
-4x+5 = 0
⇔ -4x = -5
[tex]\Longleftrightarrow x=\frac{-5}{-4} =\frac{5}{4}[/tex]
⇔ x = 1.25
PLEASE ANSWER THIS QUESTION RIGHT.A ball thrown in the air has a height of h (t)
- 16t2 + 50t + 3 feet after t seconds.
Part A: What is the average rate of change for h(t) between t= 0 and t = 2?
A.36 Seconds per second
seconds per second
B.-36 feet per second
C.-18 seconds per second
D.18 feet per second
Find the area, in square units, of the shaded region without counting every square. (please help)
Marcus has opened a savings account where the yearly interest rate is 10%. He deposits $1,000 to start the account. After t years, the amount of money in the account is modeled by the function An=1,0001+0.10t. Which functions below would be an approximate equivalent function?
Select all that apply.
A. An=1,000(1.10)t
B. An=1,000(1+0.008)^12t
C. An=1,000(1+0.46)^4t
D. An=1,000(1.008)^t/12
E. An=1,000(1.46)^t/4
Answer:
Option A and option B applies
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Marcus has opened a savings account where the yearly interest rate is 10%. He deposits $1,000 to start the account.
This means, respectively, that: [tex]r = 0.1, P = 1000[/tex]. So
[tex]A(t) = 1000(1 + \frac{0.1}{n})^{nt}[/tex]
Option A:
[tex]n = 1[/tex]. So
[tex]A(t) = 1000(1 + \frac{0.1}{1})^{t}[/tex]
[tex]A(t) = 1000(1.1)^{t}[/tex]
So option A applies
Option B:
[tex]n = 12[/tex]. So
[tex]A(t) = 1000(1 + \frac{0.1}{12})^{12t}[/tex]
0.1/12 = 0.008. So
[tex]A(t) = 1000(1 + 0.008)^{12t}[/tex]
[tex]A(t) = 1000(1.008)^{12t}[/tex]
So option B also applies.
The other options will not apply.
Answer:
A and B
Step-by-step explanation:
A Cub with 40members elects a finance committee having 3members. How many committees
are possible?
Answer:
9880
Step-by-step explanation:
[tex]C^3_{40}=\frac{40!}{3!(40-3)!} =\frac{40!}{3!*37!}=13*19*40=9880.[/tex]
Parker drank 36 fluid ounces of a sports drink at her basketball game. How many pints did she drink
Answer:
2 1/4 pints
Step-by-step explanation:
create a ratio with the fact there are 16 ounces in 1 cup
let 'p' = number of pints
16 = 36
1 p
cross-multiply: 16p = 36
p = 36/ 16, which is 9/ 4, or 2 1/4
X+X+(60% of X)=180
Ez points plus brainliest
Answer:
x = 900/ 10 + 3fo
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
At a restaurant, the bill comes to $30. If you decide to leave a 10% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer:
$3
Step-by-step explanation:
you multiply 30 by 0.10 giving you 3
A shop has this offer.
£5 reduction if you spend more than £80
or
£10 reduction if you spend more than £130
At the shop, dresses cost
£37 each.
Sue buys 3 dresses
Ann buys 5 dresses
or
£20 reduction if you spend more than £180
How much more than Sue does Ann pay?
Your final line should say, Ann pays £... more
Answer:
£59
Step-by-step explanation:
3×37=111 111-5=106
5×36=185 185-20=165
165-106=59
Can someone help me Write an equation for this graph?
Solve the problem
There were 36,000 people at a ball game in Los Angeles. The day's receipts were $304,000. How many people paid $14 for reserved seats and how many paid $6 for general
admission?
Answer:
paid $14 for reserved seats and
paid $6 for general admission
Answer:
11,000 paid $14 for reserved seats.
25,000 paid $6 for general admission.
Step-by-step explanation:
First, we need to establish the system of equations:
x= number of people that pay $14
y= number of people that pay $6
14*x + 6*y= $304,000
x + y= 36,000
Now, we isolate x in one equation and substitute it in the other one:
x= 36,000 - y
14*(36,000 - y) + 6y = 304,000
504,000 - 8y = 304,000
200,000 = 8y
25,000 = y
x= 36,000 - 25,000
x= 11,000
11,000 paid $14 for reserved seats.
25,000 paid $6 for general admission.
Please help I will mark brainlist
True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant
Answer:
I believe that it is false
of the last 60 people who went to the cash register at the department store, 16 had blomd hair, 20 had black hair, and 3 had red hair. determine the empirical probability the next person will have brown hair
Answer: 20
Step-by-step explanation:
Answer: Plz don't come for me if its wrong but I think the answer is 21
Step-by-step explanation: Because there are 60 people in all and 16 had blond hair, 20 had black hair and 3 had red hair and 60-16-20-3=39 then you have to take 60-39 and you get 21
In a class of 26 students, 11 are female and 10 have an A in the class. There are 2 students who are female and have an A in the class. What is the probability that a student is a female given that they have an A?
The probability that a student is a female given that they have an A is 0.2
How to determine the probability?The given parameters are:
Female = 11
A= 10
Female and A = 2
The probability is calculated using:
P(Female given A) = P(female and A)/P(A)
This gives
P(Female given A) = 2/10
Simplify
P(Female given A) = 0.2
Hence, the probability that a student is a female given that they have an A is 0.2
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