Answer:
$722444.49386776
Step-by-step explanation:
Use Compound Intrest Formula
[tex]a = p(1 + \frac{r}{n} ) {}^{nt} [/tex]
where p is the original amount.R is the amount of percentage compoundedN is amount of times compounded per year.T is how long the interest last.P is 400,00p
T is 12% or 0.12
N is 4 since it is compounded quarterly
T is 5.
Plug the values in
[tex]400000(1 + \frac{0.12}{4} ) {}^{20} [/tex]
Ypu get
$722444.49386776
Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and Hers models. Each chair requires four legs and two rockers but differing numbers of wooden dowels. Each His chair requires four short dowels and eight long dowels while each Hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each Hers chair contributes $12. The company has 900 legs, 400 rockers, 1200 short dowels, and 1056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many His chairs as Hers chairs.
Required:
a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Find the optimal solution.
Answer:
x = 76 y = 112 z (max) = 2104 $
Step-by-step explanation:
legs rockers short dowels long dowels Profit $
Model His (x) 4 2 4 8 10
Model Her (y) 4 2 8 4 12
Availability 900 400 1200 1056
From the table above we find z
Objective Function z :
z = 10*x + 12*y to maximize
Subject to
Constraint 1 quantity of legs available: 900
4*x +4*y ≤ 900
Constraint 2 quantity of rockers available: 400
2*x + 2*y ≤ 400
Constraint 3 quantity of short dowels available: 1200
4*x 8*y ≤ 1200
Constraint 4 quantity of long dowels available: 1056
8*x + 4*y ≤ 1056
Constraint 5 condition between x and y
x ≥ 0.5*y
The model:
z = 10*x + 12*y to maximize
Subject to:
4*x +4*y ≤ 900
2*x + 2*y ≤ 400
4*x 8*y ≤ 1200
8*x + 4*y ≤ 1056
x ≥ 0.5*y or x - 0.5*y ≥ 0
General constraints:
x ≥ 0 y ≥ 0 both integers
After 6 iterations with AtomZmath on-line solver optimal solution is:
x = 76 y = 112 z (max) = 2104 $
Determine the derivatives of g(x)=-3x at any point by using first principle
Answer:
[tex]{ \tt{g(x) = - 3x}} \\ { \tt{g(x + h) = - 3(x + h)}} \\ \\ { \bf{ \binom{ \frac{ \delta \: y}{ \delta \: x} }{lim \: h→0} = \frac{g(x + h) - g(x)}{h} }} \\ \\ { \tt{ = \frac{ - 3(x + h) - ( - 3x)}{h} }} \\ \\ { \tt{ = \frac{ - 3x - 3h + 3x}{h} }} \\ \\ { \tt{ = \frac{ - 3h}{h} }} \\ \\ { \tt{ = - 3}} \\ { \bf{h→0, \: \frac{ \delta \: y}{ \delta \: x} = \frac{dy}{dx} }} \\ \\ { \tt{ \frac{dy}{dx} = - 3 }}[/tex]
A woman's age is thirteen more than half of 60.How old is she?
Answer:
half of 60 is 30
13 more than that is
13+30=43
so the answer is 43
Step-by-step explanation:
hope it helps you
MATH PROBLEM 20 POINTS
Divide using a common factor of 2 to find an equivalent fraction for
Answer:
2/10ths?
Step-by-step explanation:
then it would be 1/5th
Find the area of the isosceles trapezoid shown below.
9 cm
6 cm
4.5 cm
Answer:
area = 40.5 cm^2
Step-by-step explanation:
A quick calculation tells me it is none of them
Area = 6*(9 + 4.5) / 2
Area = 3*13.5
Area = 40.5
can someone pls help me quickkk
Answer:
(-4) ^6
Step-by-step explanation:
(-4)*(-4)*(-4)*(-4)*(-4)*(-4)
There are six (-4)'s multiplied together
(-4) is the base and 6 is the exponent
(-4) ^6
Answer:
A.(-4)^6
Step-by-step explanation:
-4 is being multiplied by itself 6 times
So you would get rid of all but one negative for and add ^-6
. Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
B làm k cho mình KQ với
Which of the folloing pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answer:
18/48 and 15/40
Step-by-step explanation:
18/48 = 3/8
15/40 = 3/8
•°• 18/48 is equivalent to 15/40
During each summer, many families spend part of their vacation time at a beach along the East or West Coast. Due to the popularity of movies like Jaws and The Shallows, and publicity about recent shark attacks on surfers, swimmers, snorkelers, and spearfishermen, Americans have become increasingly concerned about water activities. Research suggests that 58% of all shark attacks involve surfers. One thousand records of shark attacks are selected, and each is categorized by the victim group. Identify the population, sample, and variable for the study.
Population Sample Variable
a. all families who spend part of their vacation at a beach along the East or West coast
b. Americans who are concerned about water activities
c. the percentage of shark attacks that involve surfers
d. the set of groups to which the victims of shark attacks belong
e. all shark attacks
f. the 1000 records of shark attacks that were examined
Answer:
Population = e. all shark attacks.
Sample = f. the 1000 records of shark attacks that were examined.
Variable = d. the set of groups to which the victims of shark attacks belong.
Step-by-step explanation:
The population in a particular study refers to the entire set of people to which the research study encompasses, that is all those who are eligible to be a part of the study or those who the study relates to and the outcome of the study Cann be applied to them. In the research study described above, the population of the study is all events of shark attacks.
The sample is a subset of the larger population ; the subset selected in the scenario above is the 1000 records examined out of all the events of shark attacks.
The variable in the study may refer to a set of independent variables which is according to the scenario is the set of groups to which victims of shark attack belong.
Which is the graph of f(x) =3 sqrtx/4?
Step-by-step explanation:
f(x) = 3√x /4
x=0 => y = 0
x=1 => y = 0.75
x=4 => y = 1.5 ==> (4, 1.5)
x=16=>y= 3
the right answer is the second graph
What is the probability of spinning a yellow?
Answer:
number of total colour = 8
number of yellow colour = 1
the probability of spinning a yellow is :
p(y) = 1/8
in percentage it will be :
(1×100)/8
= 12.5 %
100 Brainly points!! Need help ASAP :)
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?
A. 1
B. 2
C. 0.5
D. -0.5
Answer:
B
Step-by-step explanation:
I'm not really shure tho
Answer:
D. -0.5
Step-by-step explanation:
AB dilated by scale factor -0.5 to produce AB'.
the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5
I got 7 to go :( help plz
Answer:
I think the second one is the answer ; 2√b
I NEEEEED HELP!!!!!!
If a book costs N10,000, at what price will the book be sold to make a profit of 15%?
Answer:
11,500
Step-by-step explanation:
cost price of a book (CP) = 10000
profit percent = 15%
selling price of a book (SP) = ?
SP = CP + profit% of CP
=10000 + 15 / 100 * 10000
=1000000 + 150000/100
=1150000/100
=11500
Therefore, the book will cost 11,500
Data with 950 observations are drawn from a bell-shaped distribution with a mean of 78 and a standard deviation of 19. Approximately how many observations are more than 116
Answer: there are 22 observations that are more than 116.
Step-by-step explanation:
Let x be the random variable.
Given: Sample size = 950
Mean = 78
Standard deviation = 19
The probability that the observations are more than 116 is given by :-
[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]
Number of observations are more than 116 = [tex]0.0228\times950[/tex]
[tex]=21.66\approx22[/tex]
Hence, there are 22 observations that are more than 116.
Somebody help please.
Answer:A
Step-by-step explanation: The formula for finding volume is LxWxH. 21x 11 is 231, and since one side is 11 so will the other side be, and then you get 2,541 m cubed.
A jug is 80% full of water. After 360 millimeters of water are poured out, the jug is 60% filled with water. What is the capacity of the jug?
15 POINTS!!
Answer:
1800ml
Step-by-step explanation:
Given data
let the capacity of the Jug be x millimeters
from 80% to 60% = 20%
Since 20% of the capacity is equivalent to 360ml
the 100% will be x ml
cross multiply we have
360*100= 20*x
x= 36000/20
x= 1800ml
Hence the capacity of the jug is 1800ml
the population of a town increases at a rate proportional to its population with an initial population of 1000. The corect initial value problem for the population p(t) as a function of time is
Answer:
This means that the correct initial value problem for the population p(t) as a function of time is is [tex]P(0) = 1000[/tex]
Step-by-step explanation:
The population of a town increases at a rate proportional to its population:
This means that this situation is modeled by the following differential equation:
[tex]\frac{dP}{dt} = kP[/tex]
In which k is the growth rate.
By separation of variables, the solution is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
In which P(0) is the initial population.
Initial population of 1000.
This means that the correct initial value problem for the population p(t) as a function of time is is [tex]P(0) = 1000[/tex]
Which of the following is NOT an example of a repeated-measures design?
a researcher tests the memory performance of students before and after their first year of high school
a researcher tests symptoms of anxiety before and after a new therapeutic treatment
a researcher measures self-perception before and after participants take a Zumba class
a researcher tests whether individuals from Generation Z use social media in ways that are different from Millenials
Answer:
its D
Step-by-step explanation:
the research is done on two groups seeing what they do on the same platform and isn't on before and after results of one subject
Which choices are correct when determining the distance between −56 and −31?
Answer:
I dont know sorry so much
Select the correct answer from the drop-down menu. Consider this system of linear equations: y − x = -13 -4x + 3y = -51 The solution of the system of equations is .
Answer:
b
Step-by-step explanation:
Answer:
its b
Step-by-step explanation:
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
You currently have a balance of $34 in your checking account. You then write a check for $76 dollars to pay for groceries. Finally, you deposit a check for $30.
What is your new balance?
Answer:
Correct me if I'm wrong but I'm sure it's -12
Step-by-step explanation:
34+30= 64
64-76= -12
As a manager of a company you are given 2 estimates for the annual firm’s profits: 1) Estimate A predicting that the mean profit would be between $1mil and $1.5 mil which is a 95% confidence interval; 2) Estimate B that the annual profits are between $1.2 mil and $1.4 mil, a 93% confidence interval. Which of the two estimates is more accurate and why?
Answer and Explanation:
A confidence interval determines the probability that a range of values(e.g-given a large data set )has the true parameter. Example, to find mean of height of 30+ men, our confidence interval will say that there is 96% confidence that the mean height of 30+ men is between 5ft and 6ft. While confidence intervals, narrow or broad with high or low significance levels may not be akin to accuracy, it will only help to determine the precision or otherwise of our estimate. For example, if confidence interval is narrow as in second option and confidence level is lower, it only narrows down our options to ascertain the true mean or parameter we are investigating and doesn't exactly affect accuracy since we are still not 100% confident our true mean lies in this interval.
Jeans are on sale for 20% off the regular price. Which function would give you the total cost for purchasing a pair of jeans that costs x dollars?
Answer:
0.8X = Final cost
Step-by-step explanation:
Given that jeans are on sale for 20% off the regular price, to determine which function would give you the total cost for purchasing a pair of jeans that costs X dollars, the following calculation must be performed:
1X = Initial cost of the jeans
20% = 0.2
1 - 0.2 = 0.8
0.8X = Final cost
There are 24 chairs in a room numbered 1 through 24. If nine girls and 15 boys sit on these chairs at random, what is the probability that the thirteenth chair is occupied by a boy?
Answer:
[tex]5/8[/tex]
Step-by-step explanation:
Since all the people sit on the chairs at random, the probability of a certain chair being occupied by a boy is equal to the probability of randomly picking a boy from the class. Since there are 24 people total and 15 of them are boys, there is a [tex]\frac{15}{24}=\boxed{\frac{5}{8}}[/tex] chance that the thirteenth chair is occupied by a boy.
Given that 9x – 6y= 19
Find y when x=-6
Give your answer as an improper fraction in its simplest form.
[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]
Given that 9x – 6y= 19
Find y when x=-6
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)}[/tex]
[tex] \tiny\pink{SO \: PUTTING \: VALUE} \: \orange{OF \: x \: FOR \: \: VALUE \: OF \: y}[/tex]
[tex] \red{Equation - > } \\ \blue{9x – 6y= 19} \\ {9( - 6) – 6y= 19} \\ - 54 - 6y = 19 \\ 6y = - 54 - 19 \\ - 73 = 6y \\ \green{ \frac{ - 73}{6} = y}[/tex]
[tex] \red{VARIFICATION - > }[/tex]
PUTTING VALUES IN EQUATION TO VARIFY THE ANSWER:-
[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ \purple{x = - 6 \: \: (given)} \\ \green{y = \frac{ - 73}{6}} [/tex]
PUTTING VALUE
[tex] \pink{Equation - > } \\ \blue{9x – 6y= 19} \\ 9( - 6) - 6( \frac{ - 73}{6} ) = 19 \\ - 54 \cancel{-}^{ \tiny{+} } \cancel{6} \frac{ \cancel{- }73}{ \cancel{6}} = 19 \\ - 54 + 73 = 19 \\ 19 = 19 \\ \orange{L.H.S} \purple{=} \green{ R.H.S}[/tex]
Answer:
y = 73 / -6
Step-by-step explanation:
Given ;
9x - 6y = 19
Where, x = - 6
Solve for y
9x - 6y = 19
plug the value of x
9 ( -6 ) - 6y = 19
- 54 - 6y = 19
Add 54 to both sides
- 54 + 54 - 6y = 19 + 54
-6y = 73
divide both side by -6
-6y / -6 = 73 / -6
y = 73 / -6
Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
a = 8; r = -5
Answer:
[tex]a_n = 8(-5)^{n-1}[/tex]
The fifth term of the sequence is 5000.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio. The nth term of a geometric sequence is:
[tex]a_n = a_1(r)^{n-1}[/tex]
a = 8; r = -5
Thus:
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_n = 8(-5)^{n-1}[/tex]
Fifth term:
This is [tex]a_5[/tex]. So
[tex]a_5 = 8(-5)^{5-1} = 5000[/tex]
The fifth term of the sequence is 5000.