Answer:
a
[tex]\^p = 0.57[/tex]
b
[tex]0.539 <p< 0.601[/tex]
c
The correct option is C
Step-by-step explanation:
The percentage of women who would like to stay at home and take care of their family due to the fact that they have a child younger than 18 is [tex]p_1 = 57\%[/tex]
The percentage of women who would rather work outside their home due to the fact that they don't have children is [tex]p_2 = 58\%[/tex]
The margin of error is [tex]E = 0.031[/tex]
Gnerally the point estimate of all US women with a child under 18 that would like to stay at home is mathematically represented as
[tex]\^ p = \frac{57}{100}[/tex]
[tex]\^ p = 0.57[/tex]
Gnerally the interval estimate for the proportion of all US women with a child under 18 that would like to stay at home is mathematically as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.57 -0.031 <p< 0.57 + 0.031[/tex]
=> [tex]0.539 <p< 0.601[/tex]
Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400.
Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region.
c. What is the optimal solution?
Answer:
Let X1 be the number of decorative wood frame doors and X2 be the number of windows.
The profit earned from selling each door is $500 and the profit earned from selling of each window is $400.
The Sanderson Manufacturer wants to maximize their profit. So for this model, the objective function is
Max: 500X1 + 400X2
Now the total time available for cutting of door and window are 2400 minutes.
so the time taken in cutting should be less than or equal to 2400.
60X1 + 30X2 ≤ 2400
The total available time for sanding of door and window are 2400 minutes. Therefore, the time taken in sanding will be less than or equal to 2400. 30X1 + 45X2 ≤ 2400
The total time available for finishing of door and window is 3600 hours. Therefore, the time taken in finishing will be less than or equal to 3600. 30X1 + 60X2 ≤ 3600
As the number of decorative wood frame door and the number of windows cannot be negative.
Therefore, X1, X2 ≥ 0
so the question s
a)
The LP mode for this model is;
Max: 500X1 + 400X2
Subject to:
60X1 + 30X2 ≤ 2400
]30X1 +45X2 ≤ 2400
30X1 + 60X2 ≤ 3600
X1, X2 ≥ 0
b) Plot the graph of the LP
Max: 500X1+ 400X2
Subject to:
60X1 + 30X2 ≤ 2400
30X1 + 45X2 ≤ 2400
30X1 + 60X2 ≤ 3600
X1,X2
≥ 0
In the uploaded image of the graph, the shaded region in the graph is the feasible region.
c) Consider the following corner point's (0,0), (0, 53.33), (20, 40) and (40, 0) of the feasible region from the graph
At point (0, 0), the objective function,
500X1 + 400X2 = 500 × 0 + 400 × 0
= 0
At point (0, 53.33), the value of objective function,
500X1 + 400X2 = 500 × 0 + 400 × 53.33 = 21332
At point (40, 0), the value of objective function,
500X1 + 400X2 = 500 × 40 + 400 × 0 = 20000
At point (20, 40), the value of objective function
500X1 + 400X2 = 500 × 20 + 400 × 40 = 26000
The maximum value of the objective function is
26000 at corner point ( 20, 40 )
Hence, the optimal solution of this problem is
X1 = 20, X2 = 40 and the objective is 26000
Send help please help :D
Answer:
A) Slope =
[tex]m = \frac{1}{4} x[/tex]
explanation:
Take 2 random points off the line, I used (4,1) & (8,2)
The formula to find the slope when given 2 points is
[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
so in this case x1 & y1 are assigned to (4,1)
4 = x11 = y1and x2 & y2 are assigned to (8,2)
8 = x22 = y2so substitute the numbers into the formula and solve !
[tex] m= \frac{y2 - y1}{x2 - x1} = \frac{2 - 1}{8 - 4} = \frac{1}{4} [/tex]
this will result in the answer I got above!!
B) yes it does show a constant rate of change cause it's increasing in 1/4x intervals
C) just because you move the placement of a line on the graph doesn't mean it's going to effect the slope as long as the numbers on the axis don't change!!
Rewrite as y−k=a(x−h)2 or x−h=a(y−k)2. Find the vertex, focus, and directrix.
y−3=(2−x)^2
Given:
The given equation is
[tex]y-3=(2-x)^2[/tex]
To find:
The vertex, focus, and directrix.
Solution:
The equation of a parabola is
[tex]y-k=a(x-h)^2[/tex] ...(i)
where, (h,k) is vertex, [tex]\left(h,k+\dfrac{1}{4a}\right)[/tex] and directrix is [tex]y=k-\dfrac{1}{4a}[/tex]
We have,
[tex]y-3=(2-x)^2[/tex]
It can be written as
[tex]y-3=(-(x-2))^2[/tex]
[tex]y-3=(x-2)^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=2,k=3,a=1[/tex]
Vertex of the parabola is (2,3).
[tex]Focus=\left(2,3+\dfrac{1}{4(1)}\right)[/tex]
[tex]Focus=\left(2,3+\dfrac{1}{4}\right)[/tex]
[tex]Focus=\left(2,\dfrac{13}{4}\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(2,\dfrac{13}{4}\right)[/tex].
Directrix of the parabola is
[tex]y=3-\dfrac{1}{4(1)}[/tex]
[tex]y=3-\dfrac{1}{4}[/tex]
[tex]y=\dfrac{11}{4}[/tex]
Therefore, the directrix of the parabola is [tex]y=\dfrac{11}{4}[/tex].
Suppose tan(b) = -2, and the terminal side of b is located in quadrant II. What is cot(b)?
Suppose tan(b) = -2, and the terminal side of b is located in quadrant II, then cot(b) = -1/2
Note that:
tan(b) = Opposite/Adjacent
Comparing the above relationship with tan(b) = -2/1:
Opposite = -2
Adjacent = 1
Also note that:
cot(b) = 1/tan(b)
cot(b) = Adjacent/Opposite
Substitute opposite = -2 and adjacent = 1 into the expression for cot(b)
cot(b) = -1/2
Learn more here: https://brainly.com/question/18164113
1.
The distribution of the number of transactions per day at a certain automated teller machine (ATM) is
approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of
the following represents the parameters of the distribution?
ī=80; s = 10
B
I = 80; 92 = 10
I = 80; o = 10
D x = 80; o = 10
Ei=80; 8 = 10
Answer:
ī=80; s = 10
Step-by-step explanation:
When the standard deviation is from a finite group it is denoted by s. The number of transactions from an atm are countable in a day. So the standard deviation will be represented by s.
and ī represents the mean.
The other choices are incorrect because mean is usually represented by a bar over the alphabet such as x.
a simple alphabet does not denote the mean of the sample or population.
Parameters are the characteristics used to define a dataset.
The representation of the parameters are: [tex]\bar x = 80[/tex] and [tex]s = 10[/tex]
From the question, we have:
[tex]Mean = 80[/tex]
[tex]Standard\ Deviation = 10[/tex]
Mean is represented as: [tex]\bar x[/tex]
So, we have:
[tex]\bar x = 80[/tex]
Standard deviation is represented as [tex]\sigma[/tex] of s.
So, we have:
[tex]s = 10[/tex]
Hence, the representation of the parameters are:
[tex]\bar x = 80[/tex] and [tex]s = 10[/tex]
Read more about parameters at:
https://brainly.com/question/8222250
Does 2x +3 = 5 +2x have infinitely many solutions
Answer:
The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. Let's see what happens when we solve it. We first combine our like terms.
Step-by-step explanation:
pply the Distributive Property. 2. Combine like terms. 3. Add/subtract on both sides. 4. Multiply/divide on both sides. Note: You might not need to do all of these steps! Special Cases – 1. Infinitely many solutions - when solving your equation, you get results like. 0=0, 7=7 ... 3) 5(2x - 7) = 7x + 3x + 7. 4) 4x +2x - 2 = 6x -- 3 + 1
The illinoian stage began about 300,000 years ago. The wallstonian began about 352,000 years ago. Compare 300,000 to 352,000
Answer:
300,000 is less than 352,000
Step-by-step explanation:
Cloud seeding has been studied for many decades as a weather modification procedure. The rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate are as follows, 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, and 31.6.
Assume this sample data follows a normal distribution.
A) Assume that the true standard deviation of the rainfall is σ = 4. Can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? Use ???? = 0.01.
B) Check that rainfall is normally distributed.
C) Compute the power of the test if the true mean rainfall is 27 acre-feet.
D) What sample size would be required to detect a true mean rainfall of 27.5 acre-feet if we wanted the power of the test to be at least 0.9?
E) Explain how the question in part (a) could be answered by constructing a one-sided confidence bound on the mean diameter.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
X : 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7,31.6
True standard deviation (σ) = 4
α = 0.01
Mean (m) of the data:
Σ(X) /n = 520.7/20
m = 26.035 = 26.04
Uaing calculator :
Sample standard deviation (s) = 4.785
Null hypothesis : μ = 25
Alternative hypothesis : μ > 25
Test statistic (t) : (m - μ) / (s/√n)
t = (26.04 - 25) / (4.785/√20)
t = 0.972
We can obtain the p value using the pvalue from t score calculator :
df = n - 1 = 20 - 1 = 19
Decision:
If p < 0.01 ; reject null
p(0.972, 19) = 0.1716
Since p > 0.1716 ; we fail to reject the Null
Solve the inequality
18 - 2a > 26
A. a<4
B. a>-4
C. a>4
D. a<-4
Answer:
D
Step-by-step explanation:
minus 18 both side, then divide it by -2. If you're going to divide by a negative you switches the sign.
Drisen has 6 groups of trains. Each group has 3 trains in it. What addition number sentence would help him solve how many trains he has in all? *
Answer:
6x3=x
x=18
Step-by-step explanation: plzz mark brainliest
easy. 25 points
help
Answer:
a- A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2.
b- a financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something.
c- income, especially when of a company or organization and of a substantial nature.
d- (of an object or action) require the payment of (a specified sum of money) before it can be acquired or done.
e- The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.
f- The substitution method is a way of solving a system of equations by expressing the equations in terms of only one variable.
g- The elimination method is where you actually eliminate one of the variables by adding the two equations.
h- Solving one particular problem without regard to related issues.
i- the point or state at which a person or company breaks even.
j- The domain of a function is the complete set of possible values of the independent variable.
k- The Range is the difference between the lowest and highest values. Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. So the range is 9 − 3 = 6.
Step-by-step explanation: Please mark brainliest
PLEASE HELP ME SOLVE!
Answer:
F(-6) = 2*(-6) + 1
5*(-6) -2
= -11
-32
= 11
32
Solve 8|x+2|−6=5|x+2|+3.
whats is the value of N in equation 72÷9=N÷2?
Answer:
N = 16
Step-by-step explanation:
[tex]72 \div 9 = N \div 2 \\ \\ \frac{72}{9} = \frac{N}{2} \\ \\ \frac{8}{1} = \frac{N}{2} \\ \\ N = 2 \times 8 \\ \\ \huge \orange{ \boxed{ N = 16}}[/tex]
Really getting the pixels in there
The graph represents the balance on Harrison’s car loan in the months since purchasing the car.
A coordinate plane showing Car Loan Payments. The x-axis shows Months since Purchase and the y-axis shows Loan Balance in dollars. There is a straight line that starts at (0, 7,000) and passes through (2, 6,500), (4, 6,000), and (26, 500).
Which statement describes the slope of the line?
The loan balance decreases $500 per month.
Harrison makes a monthly payment of $250.
The loan balance increases $250 per month.
Harrison increases his monthly payment by $500 each month.
Answer:
Step-by-step explanation:
I think it's the loan balances decreases $500 per month because every month it starts decreasing down by 500
Answer:
Answer is B
Step-by-step explanation:
An oligopoly is a market condition with which major feature
A few huge businesses control an industry Answer:
Step-by-step explanation:
Econ
PLEASE HELPP
Solve the following equation:
1/3(y-2) - 5/6(y+1) = 3/4 (y-3) - 2
1. 11/5
2. -11/ 5
3. 53/15
Answer:
1. 11/5Step-by-step explanation:
Solving in steps:
1/3(y-2) - 5/6(y+1) = 3/4 (y-3) - 21/3y - 2/3 - 5/6y - 5/6 = 3/4y - 9/4 - 21/3y -5/6y - 3/4y = 2/3 + 5/6 - 9/4 - 21/12y(4 - 10 - 9) = 1/12(8 + 10 - 27 - 24)y*(-15) = - 3315y = 33y = 33/15y = 11/5Correct option is 1.
PLZZ ANSWER THE QUESTION
Answer:
option A
I hope it helps
Sketch the graph of the tangent curve y = tan 2x in the interval from 0 to 2pi
Answer:
correct answer: a.
Step-by-step explanation:
y = tan2x graph should have right side headed up, because it's positive.
however, the graph's frequency should be changed.
Since the normal period of y = tan x graph is pi/|b|,
the period for this graph should be pi/2.
We can see that graph (a) is meeting all the needs.
If a gallon of bleach is filled to 2/3 how much bleach is it
Answer:
0.6 repeated
Step-by-step explanation:
JoAna has 3/4 of a gallon of milk
Hadley is driving to Colorado. she has been traveling for 4 hours, and she driven 260 miles. find her speed in miles per hours.
65 m/h
The formula we use for speed is Distance ÷ Time so, 260 miles ÷ 4 hours = 65 miles per hour.
In a popular casino game, you can bet one whether a ball will fall in an arc on a wheel colored red, black, or green. Say the probability of a red outcome is 18/38
, that of a black outcome is 18/38
, and that of a green outcome is 2/38
. Suppose someone makes a $ bet on . Find the expected net winnings for this single bet. Interpret the result.
Answer:
1/12
Step-by-step explanation:
help me solve each question
Answer:
32
Step-by-step explanation:
Decide whether the experiment is a binomial experiment:
A. Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of face cards obtained.
B. Survey 50 investors to see how many different stocks they own. The random variable represents the number of different stocks owned by each investor.
C. Survey 150 college students to see whether they are enrolled as new students. The random variable represents the number of students enrolled as a new student.
D. Each week, a gambler plays blackjack at the local casino. The random variable is the number of times per week the player wins.
Answer:
The correct options are A and C.
Step-by-step explanation:
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
(A)
Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of face cards obtained.
X = number of face cards .
There are n = 52 cards in a standard deck of cards.
There are 12 face cards in the standard deck of cards.
The probability of selecting a face card is, [tex]p=\frac{12}{52}=0.231[/tex].
The selection is done without replacement.
Thus, the experiment is a binomial experiment.
(C)
Survey 150 college students to see whether they are enrolled as new students. The random variable represents the number of students enrolled as a new student.
X = number of students enrolled as a new student.
The number of students selected for the survey, n = 150.
Each students response is independent of the others.
Thus, the experiment is a binomial experiment.
what are all the numbers of the square root of pie?
PLZ ANSWER QUICKLY I WILL GIVE 80 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3.1415926535897932384626433832795. But it's approximately 1.77
What is the result when the number 48 is decreased by 89%?
Answer:
42.72
Step-by-step explanation:
Answer:
5.28
Step-by-step explanation:
100%-89%=11%
48x11%=5.28
The phrase absolute magnitude refers to the
A)
perceived color of a star.
3
)
exact distance from Earth.
C)
amount of light given off by a star.
D
amount of light received on Earth from any stan
ding
Standard deviation is a useful concept in performance management. Let us say that a director in a local fire department wants to know any variation between the performance of this year and that of the last year. He draws a sample of 10 response times of this year ( in minutes):
3.0, 12.0, 7.0, 4.0, 4.0, 6.0, 3.0, 9.0, 11.0, and 15.0, comparing them with a sample of 10 response times last year ( in minutes): 8.0, 7.0, 8.0, 6.0, 6.0, 9.0, 7.0, 9.0, 8.0, and 6.0.
Required:
a. Does he see a performance variation by the mean?
b. Does he see a performance variation by the standard deviation? If he does, is it performance improvement or deterioration from the last year? Why?
Answer:
Step-by-step explanation:
Given the data :
Response time this year :
3.0, 12.0, 7.0, 4.0, 4.0, 6.0, 3.0, 9.0, 11.0, 15.0
Response time last year :
8.0, 7.0, 8.0, 6.0, 6.0, 9.0, 7.0, 9.0, 8.0, 6.0
Let's calculate the mean and standard deviation of each data sample :
Mean(m) = Σ(X) / n
n = sample size = 4
This year:
ΣX = 74 ; n = 10
Mean = 74 /10 = 7. 4
Standard deviation(s) = √(Σ(x - m)²/n - 1)
s = 4.195
Using a calculator to save computation time :Standard deviation = 4.195
LAST YEAR :
ΣX = 74 ; n = 10
Mean = 74 /10 = 7. 4
Standard deviation(s) = √(Σ(x - m)²/n - 1)
Using a calculator to save computation time :Standard deviation = 1.17
a. Does he see a performance variation by the mean?
From the mean value obtained for the two years, both are the same, hence, the value does not signify a variation in performance.
b. Does he see a performance variation by the standard deviation? If he does, is it performance improvement or deterioration from the last year? Why?
Yes, the value of standard deviation are different with the current year having a value of 4.195 and the previous year, a value of 1.17
The variation shows there is a deterioration on this year's performance from last year due to the larger value of standard deviation obtained ; 4.195 > 1.17