Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?

Answer:

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Step-by-step explanation:

Let the price  of popcorn be x

Let the price  of drink be y.

price  of  12 bags of popcorn will be 12x

price  of  2 drinks  will be 2y

it is given that "Kennedy spends a total of $77.50 on 12 bags of popcorn and 2 drinks."

thus

12x + 2y = 77.50

dividing LHS and RHS by 2 we have

12x/2 + 2y/2 = 77.50/2

=> 6x + y = 38.75 _________(1)

__________________________________________________

price  of  3 bags of popcorn will be 3x

price  of  6 drinks  will be 6y

it is given that "Olivia spends a total of $51.00 on 3 bags of popcorn and 6 drinks."

thus

3x + 6y = 51.00

dividing LHS and RHS by 3 we have

3x/3 + 6y/3 = 51/3

=> x + 2y = 17   _____________(2)

__________________________________________________

Thus we have two equation

6x + y = 38.75 _________(1)

x + 2y = 17

=> x = 17 - 2y

putting this value of x in equation 1 we have

6( 17 - 2y) + y = 38.75

=> 102 - 12y + y = 38.75

=> 102 - 11y = 38.75

=> -11y = 38.75 -102

=> -11y = -63.25

=> y = -63.25/-11 = 5.75

as we have x = 17 - 2y

using 5.75 in place of y

x = 17 - 2(5.75 )

=> x = 17 - 11.5

=> x = 5.5

Thus, system of equations are

6x + y = 38.75

x + 2y = 17

price of drink is $5.75

Answer:

436

Step-by-step explanation:

A rectangular prism is made up of 3 pairs of rectangles. In this case, one pair has dimensions of 4 by 9, another pair has dimensions of 4 by 14, and the last pair has dimensions of 9 by 14. The surface area of this rectangular prism is therefore:

2(4*9)+2(4*14)+2(9*14)=72+112+252=436 square inches

Hope this helps!

Answer:

436 in²

Step-by-step explanation:

A= 2*(4*14+4*9+9*14) in²= 436 in²

Answer:

No

Step-by-step explanation:Because there is not degree higher than one in the equation. Therefore it is linear.

Answer:

I couldn't find the link you wanted me to click.

Anyway the Pyramid Volume Formula is

Volume= (Area of the Base * Height) ÷ 3

It's hard to determine the volume because I can't tell the dimensions from the graphic.

I'd guess the answer to question 4 is "A" means area of the base

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Since mAB = mCD

So

3x+9 = 11x-71

9+71 = 11x-3x

80 = 8x

So

x = 10

Now

Arc AB = 3x+9

= 3(10)+9

= 39°

Answer:

Option A. Base of the triangle is 3unita

Option B. Height of the triangle is 5units

Option B. Area of the triangle is 7.5units

Step-by-step explanation:

The question is incomplete and lacking appropriate diagram. Here is the complete question.

The base (b) of the triangle is _ units.

A) 3 B) 5 C) 8 D) 13

The height (h) of the triangle is units.

A) 3 B) 5 C) 8 D) 13

The area of the triangle is square units.

A) 5 B) 7.5 C) 15 D) 30

Also find the attachment below.

From the graph, each square box in the graph will be taken as 1unit.

Since the base of the triangle is sitting on 3-square boxes, the total units of its base will be 3units. The base of the triangle is therefore 3units.

Similarly, the height of the triangle covers 5 square boxes, therefore the height of the triangle will be 5units.

Area of the triangle = 1/2 × base × height

Area of the triangle = 1/2 × 3 × 5

Area of he triangle = 15/2 = 7.5units

Answer:

3,5,7.5

Step-by-step explanation:

just got the answer right.

Answer:

2) Option D is correct.

f = (15m + 35)

3) Check Explanation

Step-by-step explanation:

The diagram of the question is presented in the attached image to this question

English Translation

Efraín has a rectangular land whose area is (120m² + 280m) as shown in the figure. According to these data, how much does side f measure?

a) 12 m² + 35

b) 15 m + 35 cm

c) 12 m + 35

d) 15 m + 35

3.- A child made four plasticine figures: two quadrangular prisms and two cylinders. In which figure did you occupy the most amount of modeling clay? JUSTIFY YOUR ANSWER

Solution

2) The area of a rectangle is given as

Area = Length × Breadth

Area = (120m² + 280m)

Length = f

Breadth = 8m

(120m² + 280m) = f × 8m

f = (120m² + 280m)/(8m)

f = (15m + 35)

Option D is correct.

f = (15m + 35)

3) For the second question, the images for the question and the dimensions of the figures aren't provided, hence, a very accurate answer can be provided. But without This, we can only speculate.

The figure that would use the most clay is the figure whose volume is the highest if the volumes of each of the figures are calculated.

Volume of a quadrangular prism = (Area of base) × (perpendicular height)

Volume of a cylinder = (Area of base) × (Height) = (πR² × H) = πR²H

So, it is in the evaluation of these volumes that the solution of this question is obtained.

Hope this Helps!!

Answer:

$21

Step-by-step explanation:

Take 40 percent of 35:

35(0.4) = 14

$14 has been taken off the original price:

35 - 14 = 21

And we have our final answer.

Answer:

21

Step-by-step explanation:

$35x40%= $14

$35-$14= $21

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If I get this worng I'm sorry

Brainleist will be appreciated, if not that's ok

Sorry that my spelling is relly bad

Anyway, hope this helps :D

Answer:

the nominal interest rate is the periodic interest rate.

it  is the periodic interest rate times the number of periods per year.

Answer: 120 members

Step-by-step explanation: So, we know 12 of the members signed up, and 90% of the member did not sign up.

Therefore, 12 members is equal to 10%...

All we have to do now is...

12 * 10 = 120

The club has 120 members in total, I hope this helps!

Answer:

The area of the remaining board is [(L × B) - (l × b)].

Step-by-step explanation:

Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.

Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.

The area of any rectangle is:

Area = Length × Breadth

The area of the bigger rectangle is:

Area of ABCD = L × B

The area of the smaller rectangle is:

Area of PQRS = l × b

Then the area of the remaining board will be:

Area of remaining board = Area of ABCD - Area of PQRS

                                         = (L × B) - (l × b)

Thus, the area of the remaining board is [(L × B) - (l × b)].

Answer:

112

Step-by-step explanation:

The centroid is 1/3 of the vertical distance between QV

QV = 3 x VT = 3 x 5 = 15

QT = 15-5 = 10

Answer:

1) [tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]  

We can calculate the p value with the following formula:

[tex]p_v =2*P(z>0.729)=0.466[/tex]  

The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.

2) [tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]  

And rounded up we have that n=2167

Step-by-step explanation:

Information given

n=300 represent the random sample taken

X=21 represent the number of peanuts empty  

[tex]\hat p=\frac{21}{300}=0.07[/tex] estimated proportion of peanust empty

[tex]p_o=0.06[/tex] is the value to test

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Part 1

We want to test if the true proportion is 6% or no the system of hypothesis are:  

Null hypothesis:[tex]p=0.06[/tex]  

Alternative hypothesis:[tex]p \neq 0.06[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.07 -0.06}{\sqrt{\frac{0.06(1-0.06)}{300}}}=0.729[/tex]  

We can calculate the p value with the following formula:

[tex]p_v =2*P(z>0.729)=0.466[/tex]  

The p value for this case is very high and using the significance level of 0.01 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the statment makes sense.

Part 2

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.06(1-0.06)}{(\frac{0.01}{1.96})^2}=2166.66[/tex]  

And rounded up we have that n=2167

Answer:

y=2/3x +7/3

2/3(4)+7/3=5

Answer:

all even numbers

Step-by-step explanation:

Answer:

Any and all of the Even numbers are scale factors of two!

Answer:

A) neither Normal, not Binomial

The sampling distribution is the product of the sample size and the population proportion, hence the number ld samples in the distribution which will answer yes is 2.6

The proportion of the population who believe freedom of speech is of highest priority = 13% = 0.13

The sample distribution can be defined as :

Therefore, the average Number of persons in the sample who will answer yes will be 2.6

Learn more : https://brainly.com/question/18153040

Answer:

5

Step-by-step explanation:

She received $75

1 CD cost $14.95

Therefore the number of CDs that can be bought are $75/$14.95 is

5.016

Answer:  B

Step-by-step explanation:

Times $74.95 by each number, and the one closet will be your answer:

$14.95 x 5 = $74.95 rounded to the nearest whole dollar is $75

Answer:a true

Step-by-step explanation:

Hope this help

Answer:

[tex]\dfrac{3}{2}[/tex]

Step-by-step explanation:

We are given 2 fractions.

1st fraction is Negative StartFraction 3 over 8

i.e.

[tex]-\dfrac{3}{8}[/tex]

2nd fraction is negative one-fourth

i.e.

[tex]-\dfrac{1}{4}[/tex]

We have to find the quotient when 1st fraction is divided by 2nd fraction.

Definition of quotient is given as:

Quotient is the result obtained when one number is divided by other number.

[tex]-\dfrac{3}{8} \div -\dfrac{1}{4} \text{ is to be calculated.}[/tex]

[tex]\div[/tex] is converted to [tex]\times[/tex] and the 2nd fraction is reversed i.e.

if the fraction is [tex]\frac{p}{q}[/tex] it becomes [tex]\frac{q}{p}[/tex] and the sign [tex]\div[/tex] is changed to [tex]\times[/tex].

Solving above:

[tex]-\dfrac{3}{8} \times -\dfrac{4}{1}\\ \text {Multiplication/Division of 2 negative number gives a positive number}\\\Rightarrow \dfrac{3}{2}[/tex]

So, the quotient is [tex]\frac{3}{2}[/tex].

Answer:

no solution

Step-by-step explanation:

Modular equation:

The modular of a function f(x)(|f(x)|) is the distance of f(x) to the origin.

In the case of a point, the modulus of the point is the distance to the origin.

If we have:

|f(x)| = a, it means that:

f(x) = a or f(x) = -a.

However

It is only true for non-negative values of a, since the modulus is a distance, which is a positive measure.

|–x| = –10

The modular is never a negative number, so it cannot be -10.

This means that there is no solution.

Answer:

I believe its "D"

Step-by-step explanation:

Answer:

20 grams

Step-by-step explanation:

10 grams is 50%. 50% x 2= 100%. so you do 50/100=10/20, and you will get 2. Apply that to the 10, 10 x 2=20.

Step-by-step explanation:

In the given question, the study was performed to analyse the effect of eating dark chocolate on the person with hypertension or increased blood pressure.

a) The biasness in the experiment could be that the funding for the study has been provided with a Private Company which mainly aims at selling their product.

b) The research is reasonable as it has been proved that eating a small amount of Dark chocolate can help cardiovascular disease like hypertension or increased blood pressure.

5 yrs+ 6 yrs =11 yrs

6 months+9 months=15 months

so,the answer is 11  yrs 15 months.

Answer:

Answer to problem number 1: 576cm cubed

Step-by-step explanation:

The height times the length time the width in this shape is the formula for the volume.

Answer:

question 1. i believe is 576

Step-by-step explanation:

Answer:

2/3, 5/6, 1/2, 1/6, 1/2

Step-by-step explanation:

One afternoon, they each had 2 large  chocolate bars.

Amy 8/6  of her chocolate bar = (2 - 8/6) = 2/3

Bill 1 1/6 of his chocolate bars = (2 - 11/6 = 2 - 7/6 = 5/6)

Katie 9/6 of her chocolate bars  = (2-9/6) = 1/2

Gretchen 1 5/6 of her chocolate bars  = (2- 1 5/6) = 2 - 11/6 = 1/6

Dylan 1 3/6 of his chocolate bars = 2 - 1 3/6 = 2-9/6 = 1/2

Answer:

como pongo en español

Answer:

2 small boxes

Step-by-step explanation:

The chocolatier makes 1313 chocolate covered strawberries.

The large boxes contains 9 strawberries and the small box contains 4 strawberries.

The large boxes are filled first.

We need to divide 1313 by 9 and find the remainder.

1313 / 9 = 145 remainder 8

This means that 145 large boxes will be needed and 8 strawberries will be left.

The number of small boxes needed is therefore:

8 / 4 = 2 boxes

Answer:

Step-by-step explanation:

Joseph : y = 25x + 15

Molly: y = 25x + 25

Joseph: y = 25(4)+ 15= 100+ 15= 115

Molly: y = 25(4)+ 25= 100+25= 125

Answer:

I hope this helps! <:

Step-by-step explanation:

The start is 15 and 25 so you keep on adding 25 to each of them, let's start with 15, 15+25=40 and 40 plus 25 is 65 and 65+25 is 90 the last one is 90+25= 115, now let's move on to 25. 25+25= 50 and the next one is 50+25=75 and then 75+25=100 and 100+25= 125.

Answer:

k=4

Step-by-step explanation:

y=3(1)-1

y=2

2=-2x+k

2=-2(1)+k

2=-2+k

4=k

Answer:

k = 4

Step-by-step explanation:

y = 3x -1

y = -2x+k

Set the two equations equal

3x -1 = -2x+k

Combine like terms

Add 2x to each side

3x+2x -1 =-2x+2x +k

5x - 1 = k

We know they are equal when x= 1

Let x=1

5*1 -1= k

5 -1= k

4 = k