This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.
Given that,
A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.
A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata
Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.
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Q8.
Solve the simultaneous equations
2x + 3y = 5p
y = 2x + p
where p is a constant.
Give your answers in terms of p in their simplest form.
Answer:
x = 1/4p
y = 3/2p
Step-by-step explanation:
2x + 3y =5p__________________equ 1
y = 2x + p____________________equ 2
sub equ 2 for y in equ 1
2x + 3(2x + p) = 5p_______________open brackets
8x = 2p______________________divide both sides by 8
x = 1/4p
sub 1/4p for x in equ 2
y = 2(1/4p) + p___________________open brackets
y = 3/2p
how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
Given that;
We need to get 3 letter passwords using a through z by two case;
(a) If repetition is allowed
(b) If repetition is not allowed
Case (a): If repetition is allowed.
The total number of letters from a through z are 26
⇒ The total number of 3 letter passwords made are;
= 26³
= 26 * 26 * 26
= 17576
If repetition is allowed then the required passwords generated are 17576.
Case (b): If repetition is not allowed.
⇒ The total number of 3 letter passwords made are;
= 26 * 25 * 24
= 15600
If repetition is not allowed then the required passwords generated are 15600.
Therefore,
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
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What is the equation of the line that passes through the point (−2,−7) and has a slope of 6?
The equation of the line in slope intercept form is y = 6x + 5
How to determine the equation of the line?The given parameters are
Slope, m = 6
Points, (x₁, y₁) = (-2, -7)
A linear equation can be represented as
y = slope * x + y-intercept
i.e.
y = m(x - x₁) + y₁
Substitute the known values in the above equation
So, we have the following equation
y = 6(x + 2) - 7
Expand
y = 6x + 12 - 7
Evaluate the like terms
y = 6x + 5
Hence. the linear equation is y = 6x + 5
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given that the probability of a family owning a dog is 0.91, and the probability of a family owning a cat and a dog is 0.15, what is the probability of a family owning a cat given that the family owns a dog?
The probability of a family owning a cat given that the family owns a dog is 0.164
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
Here
probability of a family owning a dog is 0.91,
P(dog) = 0.91
probability of a family owning a cat and a dog is 0.15,
P(dog ∩ cat) = 0.15
according to conditional probability
the probability of occurring of B after event A takes place is
P(A|B)=P(A∩B)/P(A)
so, the probability of a family owning a cat given that the family owns a dog is
P(dog | cat) =P(dog∩cat)/P(dog)
= 0.15/0.91
=0.164
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What are the roots of the equation x 2 + 16 x + 80 = 0 x 2 +16x+80=0 in simplest a + b i a+bi form?
The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).
How to determine the roots of a quadratic equation
In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:
b² - 4 · a · c > 0: Two different real roots. b² - 4 · a · c = 0: Two equal real roots. b² - 4 · a · c < 0: Two conjugate complex roots.If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:
x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)
x = - 1 / 10 ± (1 / 10) · √(- 64)
x = - 1 / 10 ± i (4 / 5)
The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).
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A midwife delivers 10 babies considering a % chance of delivering a boy and 50% chance of delivering a girl, answer the following questions what is the probability that 6 of the babies will be boys?
A midwife delivers 10 babies, with 50% chance of delivering a boy and 50% of delivering a girl. The probability that 6 out of 10 babies will be boys is 20.5%
The problem can be solved using binomial distribution, that is the probability of 2 possible outcomes in a number of trials.
The formula is given by:
P(x) = ⁿCx . P^x . (1 - P)^(n-x)
x = total number of event A
n = number of trials
P = probability of A in a single trial
Parameters given in the problem:
n = 10
x = 6
P = 50% = 0.5
Plug these parameters into the formula:
P(6 boys) = ¹⁰C₆ . (0.5)⁶ . (0.5)⁴
= 0.205 = 20.5%
Hence, the probability that 6 out of 10 babies will be boys is 20.5%
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PLEASE HELP ME QUICK!!!
The model shows that 3 1/5 divided by 4/5 = 4.
What happens if you divide by 8/5 instead of 4/5
The solution after divide by 8/5 instead of 4/5 will be 2.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The model shows that 3 1/5 divided by 4/5 = 4.
Now,
Substitute 8/5 instead of 4/5, we get;
⇒ 3 1/5 ÷ 8/5
⇒ 16/5 ÷ 8/5
⇒ 16/5 × 5/8
⇒ 2
Thus, The solution after divide by 8/5 instead of 4/5 will be 2.
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Answer:
Step-by-step explanation:
In the diagram below, \overline{TU} TU is parallel to \overline{QR} QR . If TUTU is 55 less than TSTS, QS=45QS=45, and QR=36QR=36, find the length of \overline{TS} TS . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The length of TS, using similar triangles, is given as follows:
TS = x = 25.
What are similar triangles?Similar triangles are two triangles that share these two features:
Same angle measures.Proportional side lengths.In the context of this problem, the similar triangles are given as follows:
STU and SQR.
The proportional side lengths from these two similar triangles are given as follows:
TS = x and QS = 45.TU = x - 5 and QR = 36.Hence the proportional relationship that relates these lengths on the similar triangles is given as follows:
x/45 = x - 5/36
Applying cross multiplication, the length of TS, equals to x, is obtained as follows:
45(x - 5) = 36x
45x - 225 = 36x
9x = 225
x = 225/9
x = 25.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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Lena made $60 babysitting for 3 hours on Sunday. He made $140 for 7 hours
on Tuesday. What is the rate of change?
Answer:20 dollars per hour
Step-by-step explanation:60/3 = 20
20 dollars per hour
7 x 20 = 140
7(x+4)-2[x-3(5+x)]=2/3(x-6)
Hope this helps! Bye, have a nice day!
How do I find the measure of the triangles? Help.
Answer:
Step-by-step explanation: I am guessing that it is 180
Bryan paid $144.00 for an item at the store that was 20% off the original price. What was the original price?
Answer:
$180
Step-by-step explanation:
[tex]P\times{(1-0.20)}=144[/tex]
[tex]P\times{0.80}=144[/tex]
[tex]P=\frac{144}{0.80}[/tex]
[tex]P=180[/tex]
Which equations are true? Select all that apply.
Answer:
The equation that is true is equation two
find y when x=17 if y varies directly as x, and y=43 when x=11
The value of y when x = 17 is 66.5
How to determine the value of y?From the question, we understand that:
The variation is a direct variation
The equation of a direct proportion can be represented as
y = kx
Where:
y = independent variablek = constant of proportionalityx = independent variableFrom the question, we have
When x = 11, we have = 43
So, we have
11k = 43
Make k the subject
k = 43/11
Substitute k = 43/11 in y = kx
y = 43/11x
When x = 17, we have
y = 43/11 x 17
This gives
y = 66.5
Hence, the value of y is 66.5
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the motel in the preceding example uses approximately600 bars of soap each day, and this tends to be fairly constant. lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. a service level of 90 percent is desired. the re-order point (rop) is:
The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
Define the term reorder point (ROP)?An exact level where the your stock has to be restocked is characterized as a reorder point (ROP). To put it another way, it advises you when to order so that you won't run out of supply.You'll need to be aware of the following factors in order to figure out the ROP for every item:Lead period: Days needed (in days) for the vendor to complete your orderSafeguard stock: The quantity of excess stock, if any, you maintain on hand to assist prevent stockoutsDaily usage: Average number of sales that particular item typically sees per day.ROP = (Daily usage x Lead period) + Safeguard stock
For the given question;
Lead time = 6 days
Safety stock = 2 days x 600 bars = 1200 bars
ROP = (600 x 6) + 1200 = 4800 bars.
Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
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it was 5 degrees above zero in the morning. By afternoon the temperature rose 27 degrees. How warm was it?
It was 33 degrees warm in the afternoon
How to determine how warm it was?From the question, we have the following parameters that can be used in our computation:
In the morning = 5 degrees above zero
Afternoon = Rise of 27 degrees
The degree of warmth in the afternoon is then calculated as
Degree of warmth = Temperature In the morning + Rise of the temperature
Substitute the known values in the above equation, so, we have the following representation
Degree of warmth = 5 + 27
Evaluate the sum
Degree of warmth = 33
Hence, the temperature is 33 degrees
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This shows a figure.
What is the measure of angle n?
65\degree65°
70\degree70°
110\degree110°
115\degree115°
To find the value of n we first have to find the value of angle m. because we know the sum of angle m and angle n would be equal to 180 degrees as they both lie on a straight line. to find angle m we have to use the angle sum property of a triangle which says the sum of all the internal angles of a triangle is equal to 180 degrees.
so using the angle sum property,
65+45+m = 180
m= 180-65-45
m=70
now we know m is 70 degrees
for n,
m+n = 180 -(i)
putting m=70 in equation (i)
70 + n = 180
n = 180-70 = 110 degree
i need help like immediately
1/4 (8x+4)=2x-4
Answer: the statement is false
Step-by-step explanation:
the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. what is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes?
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
What is probability?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.
A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx = ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
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factorise 2x^[2]-9x-5
Answer:
(2x + 1) and (x - 5)
Step-by-step explanation:
(2x + 1)(x - 5) = 2x^2 - 9x - 5
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Answer: What??
Step-by-step explanation:
The length of a rectangle is 5 more than twice the width . If the length is 60 inches ,what is the width?
Answer:27.5 inches
Step-by-step explanation:
Find the solution for −0.5x − 3.69 = x − 1.9 − 2.39. x = 0.4 x = −0.4 x = 2.5 x = −2.5
The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34
The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.
since the given expression is :
-0.5x-3.69=x-1.9-2.3
=>-0.5x-x=-1.9-2.3+3.69
=>-1.5x=-0.51
=>x=0.34
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a determined gardener has 100 ft of deer-resistant fence. she wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 600 ft2. what range of values (in ft) is possible for the length of her garden? (enter your answer using interval notation.)
The range of values for the rectangle length is 20 ≤ y ≤ 30 .
What is a rectangle made of?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Rectangles are two-dimensional shapes, and as such, they have length and width as their defining characteristics.The garden is to be rectangular shape.
Let x = width
Let y = length
Set the equations for perimeter and area.
2(x + y) = 100 -----> perimeter
x + y = 50 ------> perimeter
xy = 600 ----> area
We have two equations to work with.
x + y = 50 eq1
xy = 600 eq2
Substitute eq1 into eq2. We can get eq2 in terms of x.
x(50 - x) = 600
-x2 + 50x = 600
-x2 + 50x - 600 = 0
Divide both sides of the equation by -1, so that we have a positive x2. The goal is to try to use FOIL to factor.
x2 - 50x + 600 = 0
(x - 30)(x - 20) = 0
x = 30 and x = 20
Next, we plug in these values of x into eq1 to solve for y.
y = 50 - x and y = 50 - x
y = 50 - 30 y = 50 - 20
y = 20 y = 30
Based on this, the range of values for the length is
20 ≤ y ≤ 30
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Identify all of the roots of f(x) = x² + 2x + 2.
Answer: -1-1i and -1+1i
Step-by-step explanation:
Guys, what is the answer to 5-x=12?
Answer:
x= -7
Step-by-step explanation:
here you go.....
please mark brainliest
Given the function below, find value (a) of x if f(x)=7
The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7
How to determine the value of the function?From the possible question, the definition of the function is given as
f(x) = 2x + 1
Also, from the question, we have:
f(x) = 7
Substitute 7 for x in the equation f(x) = 2x + 1
So, we have the following representation
2x + 1 = 7
Subtract 1 from both sides of the equation
This gives
2x = 6
Divide both sides by 2
x = 3
So, we can conclude that the value of x is 3
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Possible question
Given the function below, find the value of x if f(x)=7
f(x) = 2x + 1
four people (john, paul, george, and ringo) are seated in a row on a bench. the number of ways to order the four people so that john is next to paul is 12. how many ways are there to order the four people on the bench so that john is not next to paul?
The Number of ways that four people can be seated on the bench so that john is not next to paul is 12
Permutations :
In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.
The arrangement of n items in r ways is given by
ⁿPr = n! /(n-r)!Here we have
4 people (John, Paul, George, and Ringo) are seated in a row on a bench
Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24
The number of ways of seating the four people so that john is next to paul is 12
Then the number of ways the four people on the bench so that john is not next to paul can find as given below
= Total No of ways, 4 can be seated - No of ways that john next to paul
= 24 - 12 = 12
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Please help I will give the brainiest for the fastest answer.
Answer: Campbell to Hillsboro to Richmond to Winchester
(Note: Not taking the Washington route)
Step-by-step explanation:
Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi
12.2+5.2=17.4 mi while the other choice is only 15.7 mi
So taking the 15.7 mi option is faster