The Pitts Barbecue Company makes three kinds of barbecue sauce: Extra Hot, Hot, and Mild. Pitts’ vice president of marketing estimates that the company can sell 8,000 cases of its Extra Hot sauce plus 10 extra cases for every dollar it spends promoting this sauce; 10,000 cases of Hot sauce plus 8 extra cases for every dollar spent promoting this sauce; and 12,000 cases of its Mild sauce plus 5 extra cases for every dollar spent promoting this sauce. Although each barbecue sauce sells for $10 per case, the cost of producing the different types of sauce varies. It costs the company $6 to produce a case of Extra Hot sauce, $5.50 to produce a case of Hot sauce, and $5.25 to produce a case of Mild sauce. The president of the company wants to make sure the company manufactures at least the minimum amounts of each sauce that the marketing vice president thinks the company can sell. A budget of $25,000 total has been approved for promoting these items of which at least $5,000 must be spent advertising each item. How many cases of each type of sauce should be made, and how do you suggest that the company allocate the promotional budget to maximize profits?

a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?

9514 1404 393

Answer:

  about 0.299 kg/m³

Step-by-step explanation:

Density is the ratio of mass to volume.

  ρ = M/V

  ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³

Set up a ratio:

16/12 = 28/?

Cross multiply:

16? = 12 x 28

16? = 336

Divide both sides by 16:

? = 336/16

? = 21

9514 1404 393

Answer:

Step-by-step explanation:

The angle shown is 75°. It is less than 90°, so is an acute angle. (The diagram is misleading in that respect.)

__

The two marked angles are vertical angles, so have the same measure.

  3x° = 75°

  x = 25 . . . . . . . . divide both sides by 3°

Answer:

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Step-by-step explanation:

Answer:

a.) a = -34 and b = 2

b.) a = -91.11 b = 2.22

c.) David scored 124, nancy scored 84.27

David scored higher

Step-by-step explanation:

for those in the 3rd grade

mean u = 67

s = 10

we used the z formula

[tex]z=\frac{x-u}{s}[/tex]

[tex]z=\frac{x-67}{10}[/tex]

we have the new score

u = 100

s = 20

we use this formula [tex]z*s+u[/tex]

[tex][\frac{x-67}{10} ]20\\[/tex] + 100

multiply through by 20

[tex][\frac{20x-1340}{10} ] +100[/tex]

dividing the bracket by 10

= [tex]2x-134+100[/tex]

= [tex]2x-34[/tex]

from this solution above,

a = -34 and b = 2

b.)

we solve for those in the 6th grade

u = 86

s = 9

[tex]\frac{x-86}{9}[/tex]

for new score,

y = 100

s = 20

[tex][\frac{x-86}{9} ]20+100[/tex]

[tex]2.22x-191.11+100\\= 2.22x - 91.11[/tex]

from this solution

a = -91.11

b = 2.22

c.) if David scored 79

[tex]= 2(x)-34[/tex]

= 2(79) - 34

= 158 - 34

= 124

if nancy scored 79

= 2.22(79) - 91.11

= 175.38 - 91.11

= 84.27

from these scores we can see that David scored higher in his grade

Answer:

Area of front and back = 2 * 2 * 5 = 20 cm^2

Area of sides = 2 * 3 * 4 = 24 cm^2

Area of top and bottom = 2 * 4 * 5 = 40 cm^2

TOTAL area = 84 cm^2

Step-by-step explanation:

Answer:

x<7

Step-by-step explanation:

See image below:)

Answer:

The mean time between logons is of 0.3333 minutes.

Step-by-step explanation:

Poisson process with an average of 3 logons per minute.

This means that the time between logons follows an exponential distribution, which mean is given by:

[tex]E(X) = \frac{1}{\lambda}[/tex]

For this question, we have that [tex]\lambda = 3[/tex], and thus:

[tex]E(X) = \frac{1}{\lambda} = \frac{1}{3} = 0.3333[/tex]

The mean time between logons is of 0.3333 minutes.

Answer:

a) 0.9998

b) 0.9979

c) 0.7

d) 0.9155

Step-by-step explanation:

P( people who wear their ties tightly ) = 0.3

P( people who do not wear their ties tightly ) = 1 - 0.3 = 0.7

sample size ( n ) = 30

Given that the events are independent and there are only two outcomes we will apply Binomial distribution

a) P( at least one tie is too tight )

P ( x ≥ 1 ) = 1 - P ( x < 1 ) = 1 - P ( x = 0 )

       = 1 - 0.00002 = 0.9998 ( excel function: 1 - BINOMDIST(0,30,0.3,0) )

b) P( more than two ties are too tight )

P ( x > 2 ) = 1 - P ( x ≤ 2 ) = 1 - BINOMDIST(2, 30, 0.3, 1 )

                                       = 1 - 0.002113178

                                       = 0.9979

c) P ( no tie is tight )

P ( x = 0 ) = 0.7

d) P( at least 18 ties are not too tight )    i.e. ( P = 0.7 )

   P ( x ≥ 18 ) = 1 - P( x ≤  17 )

                     = 1 - BINOMDIST ( 17, 30, 0.7, 1 )

                     = 1 -  0.08447006

                    = 0.9155

Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44

Step-by-step explanation:

Let the cost of adult ticket be 'x' and cost of student ticket be 'y'

From the question, the equations formed are:

[tex]662.5=85x+65y[/tex]                .....(1)

[tex]x=2.5y[/tex]                                ......(2)

Putting value of 'y' from equation 2 to equation 1:

[tex]662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44[/tex]

Now, solving for 'x', we get:

[tex]x=2.5(2.44)=\$ 6.1[/tex]

Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44

Answer:

[tex]\text{A. }y=1.30x+1.50[/tex]

Step-by-step explanation:

The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.

Answer:

210

Step-by-step explanation:

7:5

First add the ratios

7+5=12

Put each ratio over the denominator 12 then multiply each by the total

7/12×1260= 735

5/12 × 1260 = 525

To find how many more winners than losers

735-525= 210

Answer:

(5,20)

Step-by-step explanation:

x+y=25

If you substitute y=4x,

x+4x=25

Now add like terms

5x=25

Divide 5

x=5

Put it back into the equation

5+y=25

Subtract 5

y=20

Answer: (5,20)

Answer:

1) (0,a)

Step-by-step explanation:

f(0) = a. b^0 = a. 1 = a

=> (0,a)

Answer:

153.86 cm²

Step-by-step explanation:

Area circle = πr²

Area = 3.14 * 7²

Area = 3.14 * 49

Area = 153.86

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

PA BRAINLIEST

Answer:

20%

Step-by-step explanation:

Given that

The car is depreciated at a rate of 7% per year

We need to find out the percentage when the car is depreciated after 6 years

So,

Since the car is depreciated by 7% so we can say it can be 0.93 times in a year

Now after 6 years, it would make

= 0.93^3

= 0.80

So, the percentage is

= 1 - 0.80

= 0.20

= 20%

Answer:

The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.

Answer:

EF=4

Step-by-step explanation:

vì diện tích bằng nhau và bằng 28 áp dụng công thức tính diện tích

Answer:

To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.

15 mins x 60 seconds = 900 seconds.

Step-by-step explanation:

In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.

112.5 x 108 = 12150 feet

12150 feet/5280 feet is approximately 2.3 miles.

For your friend you take 900/6 = 150 groups of 6 seconds.

150 x 63 = 9540 feet

9540 feet/5280 feet = 1.79 miles

1.79 miles + 2.3 miles = 2.09 miles

You and your friend are about 2.09 miles apart after 15 minutes.

B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more

3.07 + 2.3 = 5.37 miles after 40 minutes (you).

Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes

0.6 x 5 (5 x 5 = 25 minutes)= 3 miles

1.79 + 3 miles= 4.79 miles (friend)

4.79 + 5.37 = 10.16 miles

You and your friend are about 10.16 miles apart after 40 minutes.

Step-by-step explanation:

1) -5n+10n

= 5n

2) -x-9+2x-10

= 2x-x-9-10

= x-19

3) -5(x-10)-x

= -5x+50-x

= -6x+50

4) 9-5(1-7x)

= 9-5+35x

= 35x+4

5) y^2-x

= 3^2-2

= 9-2

= 7

Do the remain questions by yourself, you can do it!

Answer:

3

Step-by-step explanation:

The perimeter of the rectangle is equal to the doubled sum of the sides, and the area is equal to the product of the sides. So we have the following equation

Answer: A

Step-by-step explanation: Ape x

Answer:

The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200.

This means that [tex]n = 150, \pi = \frac{60}{150} = 0.4[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.3216[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.4784[/tex]

The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).

Answer:

(x, y) = (-2,-5)

Step-by-step explanation:

Multiply the first equation by 3,and multiply the second equation by 1.

3(3x+y=−11)

1(4x−3y=7)

Becomes:

9x+3y=−33

4x−3y=7

Add these equations to eliminate y:

13x=−26

Then solve13x=−26for x:

13x=−26

13x

13

=

−26

13

(Divide both sides by 13)

x=−2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

3x+y=−11

Substitute−2forxin3x+y=−11:

(3)(−2)+y=−11

y−6=−11(Simplify both sides of the equation)

y−6+6=−11+6(Add 6 to both sides)

y=−5

Answer:

x=−2 and y=−5

Answer:

a

Step-by-step explanation:

yes

Answer:

The + 78 :-  it should be + 60.

Step-by-step explanation:

Long division:-

x - 3 )4x^4 - 6x^3 + 0x^2 + 6x + 3 ( 4x^3 + 6x^2 + 18x + 60 <--- Quotient.

         4x^4 - 12x^3

                      6x^3 + 0x^2

                       6x^2 - 18x^2

                                   18x^2 + 6x

                                    18x^2 - 54x

                                                 60x + 3

                                                  60x - 180

                                                              183