Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is allowed to return with a limited number of consumer items not generally available in Cuba. The items, which are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the items at highly inflated prices. The three most popular items in Cuba are denim jeans, CD players, and CDs of U.S. rock groups. The weight and profit (in U.S. dollars) of each item are as follows:
Item Weight (lb.) Profit
Denim jeans 2.1 $40
CD players 3.2 48
Compact discs 0.8 16
uan wants to determine the combination of items he should pack in his duffel bag to maximize his profit. This problem is an example of a type of integer programming problem known as a "knapsack" problem. Formulate and solve the problem.
Answer:
z (max) = 96
x₁ = 2
x₂ = 0
x₃ = 1
Step-by-step explanation:
Fromproblem statement:
weight (lb) . Profit $
Denim jeans 2.1 40
CD players 3.2 48
Compact Discs 0.8 16
Objective Function z is:
z = 40*x₁ + 48*x₂ + 16*x₃ to maximize
Subject to:
Weight constrain: 5 lb
2.1*x₁ + 3.2*x₂ + 0.8*x₃
x₁≥ 0 x₂ ≥ 0 x₃ ≥ 0 All integers
Using AtomZmath on-line solver and after 2 iterations
Solution:
z (max) = 96
x₁ = 2
x₂ = 0
x₃ = 1
The maximized profit is the highest profit Juan can get by selling his items.
The maximized profit is $96
Let x represents the Denim jeans, y represents the CD players and z represent the compact discs.
So, we have the following parameters
Weights
[tex]x = 2.1[/tex]
[tex]y = 3.2[/tex]
[tex]z = 0.8[/tex]
The weight cannot exceed 5 pounds.
So, the constraint is
[tex]2.1x + 3.2y + 0.8z \le 5[/tex]
The profit is given as:
[tex]x = 40[/tex]
[tex]y = 48[/tex]
[tex]z = 16[/tex]
So, the objective function to maximize is
[tex]Max\ Z = 40x + 48y + 16z[/tex]
The integer programming model is then represented as:
[tex]Max\ Z = 40x + 48y + 16z[/tex]
Subject to:
[tex]2.1x + 3.2y + 0.8z \le 5[/tex]
[tex]x,y,z \ge 0[/tex]
Using a graphing calculator, the values that maximize the objective function are:
[tex]x = 2[/tex]
[tex]y = 0[/tex]
[tex]z = 1[/tex]
Substitute these values in the objective function
[tex]Max\ Z = 40x + 48y + 16z[/tex]
[tex]Z = 40 \times 2 + 48 \times 0 + 16 \times 1[/tex]
[tex]Z = 80 + 0 + 16[/tex]
[tex]Z = 96[/tex]
Hence, the maximized profit is $96
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help me it’s more but i can’t post it
Answer:
( 2 x + 1 ) ( 3 x + 2)
Step-by-step explanation:
srry, i could only do the first one-
HELP!!! WILL GIVE BRAINLIEST +LIKE AND 5 STARS ANSWER THE QUESTION IN THE PICTURE
Answer:
b, c , a
Step-by-step explanation:
I am guessing
Answer:
B, C, D
Step-by-step explanation:
Which BEST describes the system of equations graphed on a coordinate plane?
A) Consistent
B) Inconsistent
C) Consistent and Dependent
D) Consistent and Independent
Answer:
D) Consistent and Independent
Answer:
D.consistent and independent
Please help me please is it 2 or 4
Answer:
its 4
Step-by-step explanation:
What is the volume of a cone with a radius of 8.7 inches and height of 14 inches? (Use 3.14
for N)
Answer:
1109.1cm³
Step-by-step explanation:
V
=
π
r
2
h
3
3.14 ×8.7² × 14/3
What is −y+9z−16y−25z+4 written in simplest form?
Answer:
[tex] - 17y−16z+4[/tex]
Step-by-step explanation:
[tex] - y+9z−16y−25z+4[/tex]
[tex] - 17y+9z−25z+4[/tex]
[tex] - 17y−16z+4[/tex]
Hope it is helpful....What is 4× +20= factor form
What is the equation of a circle with center (-2,3) and radius 4?
A. (x + 2)^2 +(y-3)^2 = 4
B. (x-2)^2 +(y +3)^2= 16
C. (x + 2)^2 + (y - 3)^2 = 16
D. (x+2)^2- (y - 3)^2 - 16
What is the area help fast
Answer:
142.5 cm2
Step-by-step explanation:
The small markings create a new height, so that would be 9.5 cm.
Multiply:
9.5x15=142.5
Therefore, the area is 142.5 cm2
Miguel makes bags. He can make 8 bags with 2 yards of fabric. Write an equation to represent the yards of
fabric, x, needed to make a certain numbers of bags, y.
2yrds/8= 9 inches
9 inches are needed to make 1 bag
:)
The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
2 yards of fabric for 8 bags,
y/x = 8/2 = 4
y = 4x
Hence "The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x".
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1
32. A friend plans to purchase a mattress that sells for $1200 at a particular store. The store
is offering 15% off any one mattress. He also has an internet coupon for an additional
10% off any discounted price. How much will your friend save (a) in dollar amount and
(b) in percent
Answer:
(A) Your friend will save $282.
(B) Your friend will get 23.5% off the original price of the mattress.
Step-by-step explanation:
We first need to find out the price of the mattress after the 15% discount. Our first step is to find what 15% of 1,200 is. We can do this by multiplying the two numbers.
1,200 x 15% -----> 1,200 x 0.15= 180.
15% of $1,200 is $180.
Next subtract $180 from $1,200, which equals $1,020. We can now apply the 10% off internet coupon.
1,020 x 10% ------> 1,020 x 0.10= 102.
10% of $1,020 is $102.
Next we subtract $102 from $1,020 and we get $918, the final price of the discounted mattress.
We subtract to see how much money the friend saved.
$1,200 - $918= $282.
We can get the percentage by dividing $282 by $1,200.
282 / 1200= 0.235 decimal form ----> 23.5%
Most college-bound students take either the SAT(Scholastic Assessment Test) or the ACT (which originally stood for American college testing). Scores on both the ACT and the SAT are approximately normally distributed. ACT scores have a mean of about 21 with a standard deviation of about 5.SAT scores have a mean of about 508 with a standard deviation of about 110. Nicole takes the ACT and gets a score of 24. Luis takes the SAT. what score would Luis have to have on the SAT to have the same standardized score(z-score) as Nicole's standardized score on the ACT?
Answer:
Luis would need to have a SAT score of 574.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Nicole's z-score:
ACT scores have a mean of about 21 with a standard deviation of about 5, which means that [tex]\mu = 21, \sigma = 5[/tex]
Nicole gets a score of 24, which means that [tex]X = 24[/tex]. Her z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 21}{5}[/tex]
[tex]Z = 0.6[/tex]
What score would Luis have to have on the SAT to have the same standardized score(z-score) as Nicole's standardized score on the ACT?
Luis would have to get a score with a z-score of 0.6, that is, X when Z = 0.6.
SAT scores have a mean of about 508 with a standard deviation of about 110, which means that [tex]\mu = 508, \sigma = 110[/tex].
The score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.6 = \frac{X - 508}{110}[/tex]
[tex]X - 508 = 0.6*110[/tex]
[tex]X = 574[/tex]
Luis would need to have a SAT score of 574.
Two window washers, Tori and Nathan, lean a ladder against the side of a building so that Tori can wash a window while Nathan holds the ladder. The top of the ladder reaches the window, which is 12 feet off the ground. The base of the ladder is 5 feet away from the building. How long is the ladder?
Answer:
13 feet
Step-by-step explanation:
This is a right triangle problem
Use the Pythagorean Theorem
c² = a² + b²
c² = 12² + 5²
c² = 144 + 25
c² = 169
Take the square root of both sides
c = 13
Mrs. Simpson is frosting circular sugar cookies. Each cookie is 6 cm in diameter. About how many square centimeters will she need to frost each cookie?
Answer:
9 pi
Step-by-step explanation:
Answer:
28.274 cm^2 (remember units are important)
Step-by-step explanation:
The answer is the area of the cookie. The area of the cookie (neglecting its thickness) is:
A = pi(r^2)
here the radius is 1/2 the diameter of 6 cm:
A = 3.14159 * 3^2 or A = 3.14159* 9 = 28.274 cm^2
Select the correct answer. Simplify the following expression. 3^2/5 * 3^-7/5
Answer:
1/6075
Step-by-step explanation:
Rayann has 4 bracelets, Jennifer has 8 bracelets, June has 3 bracelets, and Tammy has 5 bracelets. They want to redistribute the bracelets so that each girl has the same number of bracelets. If the bracelets are redistributed, how many should each girl get?
A balance diagram going from 1 to 9. 1 circle is above 3, 4, 5, and 8.
4
5
6
7
Answer:
they will each get 45 bracelets
Step-by-step explanation:
add all the bracelets then divide by the number of girls
Answer:
B= 5
Step-by-step explanation:
took the test
in a class of students, the following data table summarizes how many students play an instrument or squirt. What is the probability that a student who plays this for also plays an instrument?
Answer:
Step-by-step explanation:
What's a squirt? Did you mean sport for the word for?
So there are 15 separate students in all who play a sport and an instrument. There are 4 more that play an instrument, but not a sport.
There are 8 that that do not play an instrument including 2 that don't do either.
So the total is 15 + 4 + 8 = 27
My best guess is that 15 out of 27
P(sport and instrument) = 15 /27 = 5/9 or 0.556
Consider the function.
f(x)=2 1/2 - 3 1/3
What is the x-intercept of f-1(x)?
o (-3 1/3,0)
o (-3/10,0)
o (3/4,0)
o (2 1/2,0)
Answer:
Option 4
Step-by-step explanation:
Given function is,
[tex]f(x)=2\frac{1}{2}-3\frac{1}{3}x[/tex]
Steps to get the inverse of the given function,
Step 1,
Convert the function into equation,
[tex]y=2\frac{1}{2}-3\frac{1}{3}x[/tex]
Step 2,
Interchange the variables 'x' and 'y',
[tex]x=2\frac{1}{2}-3\frac{1}{3}y[/tex]
Step 3,
Solve the equation for the value of y,
[tex]x-2\frac{1}{2}=-3\frac{1}{3}y[/tex]
[tex]x-\frac{5}{2}=-\frac{10}{3}y[/tex]
[tex]-x+\frac{5}{2}=\frac{10}{3}y[/tex]
[tex]-3x+\frac{15}{2}=10y[/tex]
[tex]-\frac{3}{10}x+\frac{15}{20}=y[/tex]
[tex]y=-\frac{3}{10}x+\frac{3}{4}[/tex]
Step 4,
Convert the equation into inverse function,
[tex]f^{-1}x=-\frac{3}{10}x+\frac{3}{4}[/tex]
For x-intercepts,
Substitute y = 0,
[tex]0=-\frac{3}{10}x+\frac{3}{4}[/tex]
[tex]\frac{3}{10}x=\frac{3}{4}[/tex]
[tex]x=\frac{10}{4}[/tex]
[tex]x=\frac{5}{2}[/tex]
[tex]x=2\frac{1}{2}[/tex]
Therefore, x-intercept of the inverse function is [tex](2\frac{1}{2},0)[/tex].
Option 4 will be the answer.
Pls help it’s for a grade in math pls help
Answer:
25,200
Step-by-step explanation:
First, find what 1% equals. Divide the total amount of people by 100. 105,000 divided by 100 = 1050. Multiply this by 24, because:
If 1% = 1050
To get 24% you need to multiply 1% by 24. Whatever you do to o ne side you have to do to the other.
1050 * 24 = 25,200
Therefore, the answer is 25,200 people
Tessellations
Determine whether the given figure tessellates the plane.
a. yes
b. no
Please select the best answer from the choices provided
Answer:
B. No
Step-by-step explanation:
I calculated it logically
Find the surface area of a triangular pyramid.
Answer:
91in^2
Step-by-step explanation:
SA of base = 7x7 = 49in^2
SA of each triangle = 1/2 x 7 x 3 = 10.5in^2
SA of all 4 triangles = 10.5 x 4 = 42in^2
SA Total = 49 + 42.= 91inch^2
Please help ill give u brainliest!!!
.........................................
Answer:
221mile per day
Step-by-step explanation:
Mean=total distance her car traveled/days
11477-10150=1327
1327/6=221.167≈221mi
Does a compromised account on Instamean your banned for a few days????? Yes or no?
Answer ASAP
Answer:
Not necessarily
Step-by-step explanation:
Not necessarily. Compromised accounts tend to happen for one of two reasons. The first is that the system detects and overdose of activity on your account meaning your are spamming likes, shares, etc on the account. The second is due to unauthorized access or suspicious activity. Both of these can either cause a temporary ban on your account that lasts for a 24 hours or a deactivation of the account. To reactivate your account you will need to login, and reactivate it in the settings, which may ask you to reset your login information.
Plz help I've been crying about this question about number 8 plz help with number 8 I'll give brainiest.
Answer: I got ~17% (It's 17% as the problem asked for the answer to be rounded)
Step-by-step explanation:
I added the 12 possible chances from the spinner with the 6 sided die chances. This gets me 18. Since the problem is asking the probability of rolling an 8 or 10 alongside a 3, I did 3/18 and got 16.66% (repeating). I'm not entirely sure if I did this right, but I hope this helped somehow. Let me know if it's not the correct answer.
Please answer the question correctly with factual information for brainliest.
Evaluate each limit given that lim f(x) =1/3 and lim g(x)=2/3
Answer: 2,1 & 2
Step-by-step explanation:
[tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)] = \frac{-1}{3}[/tex], [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
What is Limit?"A limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value."
We have Limit functions
[tex]\lim_{x \to c} f(x)[/tex] [tex]= \frac{1}{3}[/tex]
[tex]\lim_{x \to c} g(x)[/tex] = [tex]\frac{2}{3}[/tex]
(i) [tex]\lim_{x \to c} [3g(x)] = 3 \lim_{x \to c} [g(x)][/tex]
= [tex]3[/tex] × [tex]\frac{2}{3}[/tex]
= 2
(ii) [tex]\lim_{x \to c}[f(x)+g(x)][/tex]
= [tex]\lim_{x \to c} f(x)+ \lim_{x \to c} g(x)[/tex]
= [tex]\frac{1}{3}-\frac{2}{3}[/tex]
= [tex]\frac{1-2}{3}[/tex]
= [tex]\frac{-1}{3}[/tex]
(iii) [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ][/tex]
= [tex]\frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}[/tex]
= [tex]\frac{\frac{1}{3} }{\frac{2}{3} }[/tex]
= [tex]\frac{1}{2}[/tex]
∴ [tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)][/tex] = [tex]\frac{-1}{3}[/tex] , [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
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[3 x 2⁵ + 13 × (-2)] +7[8-(4-9)]
Chris drops an egg with a parachute from the top of a building. The height, h, in feet, of the egg above the ground after t seconds is given
by h (t) = 100 - 16t2
After how many seconds does the egg hit the ground?
I
Answer:
The egg hits the ground after 2.5 seconds.
Step-by-step explanation:
Height of the egg:
The height of the egg after t seconds is given by:
[tex]h(t) = 100 - 16t^2[/tex]
After how many seconds does the egg hit the ground?
This is t for which [tex]h(t) = 0[/tex]. So
[tex]h(t) = 100 - 16t^2[/tex]
[tex]16t^2 - 100 = 0[/tex]
[tex]16t^2 = 100[/tex]
[tex]t^2 = \frac{100}{16}[/tex]
[tex]t = \sqrt{\frac{100}{16}}[/tex]
[tex]t = \frac{10}{4}[/tex]
[tex]t = 2.5[/tex]
The egg hits the ground after 2.5 seconds.
A building has 7 office suites generating annual potential rent of $9,000 each. Vacancy = 8% and annual expenses are $25,000. Vending machines yield $3,000. What is the NOI?
Answer: use the link
Step-by-step explanation: sdghs/dt/776n.tvbusaa.;