1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]​

Answers

Answer 1

We should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

What is linear optimization?

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

This is a linear optimization problem that can be solved using the graphic method.

To begin, we can set up the problem as follows:

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints are:

y = 2x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

The objective function is: -3x - 2y (because you lose $3 on every hat sold and $2 on every pair of sunglasses sold)

To graph the constraints, we can start by plotting the inequality y <= 100. This creates a line that goes from the origin (0,0) to (50,100) and is shaded in below the line. Next, we can plot the inequality x+y >= 210 which creates a line that goes from (0, 210) to (210, 0) and is shaded in above the line.

Finally, we can plot the equation y = 2x, which represents the relationship between the number of hats and sunglasses sold.

The feasible solution for this problem is the point where the lines intersect and that lies within the feasible region. In this case, the point where the three lines intersect is (70, 140) which is the optimal solution.

Therefore, you should order 70 hats and 140 pairs of sunglasses to lose the least amount of money in the sales promotion.

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Related Questions

The average of 5 numbers is 8.5. Four of the numbers are 9.2, 3.4, 6.5 and 7.4. What is
the fifth number?

Answers

Answer:5

Step-by-step explanation:

What comes next 17,18,22,31,47

Answers

The number comes after the sequence 17,18,22,31,47 is 72.

What is Number system?

A number system is defined as a system of writing to express numbers.

In the sequence 17,18,22,31,47

We have to find the next number of the sequence.

18–17 =1=1×1

22–18=4=2×2

31–22=9=3×3

47–31=16=4×4

72–47=25=5×5

Hence, the number comes after the sequence 17,18,22,31,47 is 72.

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Ill give brainlyest for the answer

Answers

Step-by-step explanation:

it has answer is square because it has four sides

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

Answers

The two options that represent the equation of the circle are:

x² + (y – 3)² = 36

x² + (y + 8)² = 36

Options A and E are the correct answer.

What is a circle?

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle is (x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius.

Now,

Diameter of the circle = 12 units

This means,

Radius = 12/2 units = 6 units

Now,

Center of the circle = y-axis.

This means,

x = 0,

y = a

Center = (0, a)

Now,

The equation of the circle.

(x - 0)² + (y - a) = 6²

x² + (y - a)² = 36

Where a can be any number.

Thus,

The equation of the circle can be:

x² + (y – 3)² = 36

x² + (y + 8)² = 36

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please help with this

Answers

Answer:

your answer will be (D)

which is 80

Step-by-step explanation:

If the quadrilateral is a trapezoid, then we have:

[tex]\it x+80^o+x = 180^o \Rightarrow 2x+80^o=180^o\bigg|_{-80}\ \Rightarrow 2x=100^o\bigg|_{:2} \ \Rightarrow x= 50^o[/tex]

Find the distance between the two points in simplest radical form. ( 6 , 9 ) and ( − 3 , 7 ) (6,9) and (−3,7)

Answers

Answer:

The distance between the two points (6, 9) and (−3, 7) can be found using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

d = √((-3 - 6)^2 + (7 - 9)^2)

d = √((-9)^2 + (-2)^2)

d = √(81 + 4)

d = √85

So the distance between the two points in simplest radical form is √85.

Step-by-step explanation:

Review the table of values.

Answers

When only non-negative integer powers or only positive integer exponents of a variable are used in a function, the function is called a polynomial. The enclosure's largest area is 562500 square feet.

How can I calculate the maximum area?

When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.

One polynomial with an exponent of 1 is 2x+5, for instance.

As stated, the function is:

V(x) = 1500x - x^2

Differentiate

V'(x) = 1500 -2x

Set to 0

2x = 1500

Multiply by 2

x = 750

Put x = 750 in place of V(x) = 1500x - x2.

V(x) = 1500*750 - 750^^2

Evaluate

V(x) = 562500

Consequently, the enclosure's largest possible area is 562500 square feet.

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Which behavior can help increase savings?
A.
shopping for items at convenience stores
B.
making purchases using credit
C.
identifying and removing discretionary expenses from a financial budget
D.
taking out a loan to make a down payment for a purchase

Answers

The answer is C

Identifying and removing discretionary expenses from a financial budget

how many miles are in 19.09 kilometers

Answers

Answer:

Miles in 19.08 km =11.925 miles

You mis-typed the value asked for in the question in original screenshot. It is asking for 19.08km in the screenshot but you used 19.09 when you typed the question

Step-by-step explanation:

The relationship between miles and kilometers is linear

To determine how many miles there are in 1 kilometer divide the km value on the right by the corresponding mile value on the left

Take the first entry

18.2/29.12 = 0.625

So 1 km = 0.625 miles

The same operation with the other entries should give the same result of 0.625

Therefore number of miles in 19.08 (NOT 19.09 as you wrote in your question) = 0.625 x 19.08 = 11.925 miles

Answer:

11.8619761

Step-by-step explanation:

multiply the value in kilometers by the conversion factor '0.62137119223677'.

So, 19.09 kilometers = 19.09 × 0.62137119223677 = 11.8619760598 miles.

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Problem No. 6 Tamsin is saving up for a smartwatch and puts all of her 50 cent and 20 cent coins in a jar each night. She thinks that she has saved enough and empties the 620 coins to count the money. 286 of the coins are 50 cent. If the cost of the smart watch is €230, how much more must she save to allow her buy the watch?

Answers

Answer: She must save €230 - €209.8 = €20.2 more to buy the watch.

Step-by-step explanation:

Tamsin has saved 286 * €0.50 = €143 from 50 cent coins.

The remaining coins are 620 - 286 = 334 which are 20 cent coins

So the total amount she has saved from 20 cent coins is 334 * €0.20 = €66.8

Therefore, the total amount she has saved is €143 + €66.8 = €209.8

So she must save €230 - €209.8 = €20.2 more to buy the watch.

Maria has a cylindrical container that she uses to store craft supplies. The measurements of the container are shown.

She wants to cover the entire container with paper. Approximately how much paper will she need? Use 3.14 for π. PLEASE HELP TYYY DUE

A) 583cm squared

B) 704cm squared

C) 1.83cm squared

(D) 2, 210cm squared

Answers

Maria will need approximately 2209.6 square cm of paper to cover the entire container.

What is the surface area of a cylinder?

The formula for the surface area of a cylinder is A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.

To find the surface area of the container, we can plug in the given values for r = 11 and h = 21:

A = 2π(11²) + 2π(11)(21)

A = 2π(121) + 2π(231)

A = 242π + 462π

A = 704π

We can approximate π as 3.14, then

A ≈ 704 × 3.14

Apply the multiplication operation, and we get

A = 2,210 square cm

Thus, the surface area of a cylinder is approximately 2,210 square cm.

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What is the value of f(x) = -x2 + 3 when x = 1? -2 -1 2 4

Answers

Answer:

f(x) = g(x)

3(2) - 4 = (2)² - 2

6 - 4 = 4 - 2

2 = 2

Step-by-step explanation:

I just substituted all the values in the domain to see which one would work. That's not really the quickest way but that's the only way I know

the answer is 4

Step-by-step explanation:

1²+ 3

1+3=4.

Solve for x.
9x-18- (12x+48)

Answers

Answer:-3(x - 10)

Step-by-step explanation:1. Add the numbers

9x-18-12x+48

9x+30-12x

2. Combine the terms:

9x+30-12x

9x+30-12x

3. Common factor:

-3x+30

-3(x - 10)

End. Solution:

-3(x - 10)

So yeah basically that's it! Bye!

Which expressions are equivalent to ln6/ln3?

Answers

The expressions that are equivalent to ln6/ln3 given below:

log₃6 log6/log3 log₅6/log₅3

What is a logarithmic function?

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a logarithmic function ln6/ ln3

From the general properties of log

log(xy) = log(x) + log(y).logb(x/y) = logbx - logby.logb(xn) = n logbx.          logbx = logax / logab.    

thus, from the fourth property option, 1 is correct

ln6/ ln3 = log₃6

Also in the ratio of the log, the base doesn't matter

Thus,

ln6/ ln3 =  log6/log3

ln6/ ln3 = log₅6/log₅3

therefore, The expressions equivalent to ln6/ln3 are:

log₃6 log6/log3 log₅6/log₅3

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Hak Young has accumulated some credit card debt while he was in college. His total debt is now $23,864.00 and his credit card charges 18% interest compounded monthly. He is getting worried about his debt and is determined to pay it off completely. What would Hak Young’s minimum monthly payment have to be in order to pay off his debt in 5 years?

Answers

Answer: To find the minimum monthly payment, we need to calculate the monthly interest rate and the total number of payments over 5 years.

Calculate the monthly interest rate: 18%/12 = 1.5%

Calculate the total number of payments: 5 years * 12 months/year = 60 payments

Use the formula for the present value of an annuity:

P = (R * (1 + r)^n) / (((1 + r)^n) - 1)

where P is the payment, R is the debt, r is the monthly interest rate, and n is the number of payments.

Plug in the values:

P = ($23,864 * (1 + 0.015)^60) / (((1 + 0.015)^60) - 1)

The minimum monthly payment would be $547.68.

Step-by-step explanation:

Someone pls solve this for me

Answers

the length is 100

Step-by-step explanation:

I'm that good

i still neeed help for my math homework

Answers

By solving the equation, we can see that the question is the one in option C.

"How many times is 1/8 in 3"

Which question can be represented by the equation?

We want to see which question can be represented by the equation:

?*(1/8) = 3

So, a number times (1/8) is equal to 3.

Solving the equation we get:

? = 3/(1/8)

? = 3*8

? = 24

The solution is 24.

So it is "how many times we have (1/8) in 3"

And thus, the correct option is C

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Can I get a step by step on this type of problem? this is the only probability problems that I currently struggle with.​

Answers

Answer:

Step-by-step explanation:

Total students in the class=18

Girls=10

Boys=8

a.  Pr(Girl, Girl)= 10/18*9/17=90/306.

b.   Pr ( at least one is a boy) = BG* BB* GB*GGB*BBG*BBB*BGG*GBG*GBB*BGB*

Answer:

Question 1  : 0.44

Question 2: 0.853

Step-by-step explanation:

We should use combinatorics to solve this problem

Combinations

The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed

The formula for finding the number of ways you can pick r items from a set of n items where duplicates are eliminated is given by the combinations formula:

[tex]C(n,r) = \dfrac{n!}{( r! (n - r)! )}[/tex]

where the ! stands for the factorial of the number

Let's take simple example to illustrate this

Suppose we have 3 books labeled A, B. C and we are asked to randomly pick 2 books in one shot. There are 3 possible picks:

AB, AC, BC

Note that though there are six possible arrangements of 2 items from a set of 3, we have to eliminate duplicates because AB is the same as BA.

In the above case, r = 2, n = 3 so using the formula we get

[tex]C(3,2) = \dfrac{3!}{( 2! (3 - 2)! )}\\\\= \dfrac{3!}{2! \times 1! }\\\\\\= \dfrac{3 \times 2 \times 1}{(2 \times 1)(1)}\\\\\\= 3\\\\[/tex]

Now to the actual problem

There are a total of 18 students in the class

Number of ways of picking 3 students is
[tex]C(18,3) = \dfrac{18!}{( 3! (18 - 3)! )}\\\\= \dfrac{18!}{3! \times 15! }\\\\\\=816[/tex]

So there are 816 possible ways to pick 3 students from 18 students

There are calculators to perform this gruesome task so I will omit the actual steps and just show the result

Let's consider the first question
Out of the 3 students picked 2 are girls. That means the other one is a boy

Number of ways of picking 2 girls out of 10 is C(10, 2)

C(10, 2) = 45

Then we have to consider the lone boy. Number of ways of picking 1 boy out of 8 is

C(8, 1) = 8

Total number of ways of picking 2 girls and 1 boy

= 45 x 8 = 360

Therefore P(2 girls, 1 boy) :

[tex]\dfrac{360}{816} = 0.44[/tex]

Second question
To find the number of ways that at least 1 boy can appear in the group is the sum of the number of ways 1, 2 or 3 boys can appear in the group.

Rather than do this, let's approach it in a easier fashion

The probability of at least 1 boy appearing in the group is the complement of no boys on the group, i.e. all volunteers are girls

Number of ways of selecting a volunteer group of all 3 girls:

C(10, 3) = 120

P(no boys in group) = P(all 3 girls in group)
[tex]=\dfrac{120}{816} = 0.147[/tex]

Therefore P(at least 1 boy) = 1 - P(no boys)

= 1-0.147

= 0.853

Could you please let me know if correct? This is a tough subject area for me too :)

Lynn is taking a trip in her car. She spent $387.00 on gasoline and snacks. Lynn spent $35.80 on snacks for the entire trip. Gasoline costs $2.54 per gallon.

How many gallons of gasoline did Lynn purchase on her trip?

Enter your answer in the box rounded to the nearest gallon.

Answers

She got 142 gallons of gas on her trip

Answer: she got 138 gallons of gas on her trip

Step-by-step explanation:

Fourteen people are entered in a race. If there are no ties, in how many ways can the first two places come out? Order is important.

A.364
B.7
C.150
D.182

Answers

Answer:

D) 182

Step-by-step explanation:

there are 14 possibilities for first place and 13 possibilities for second place because one person has already gotten first. 14*13 = 182

mark brainliest if this is correct thx

4.1 (Probability, Law of Large Numbers, Simulation)
1. The MARTA claims that their 5:30 am Red Line Train from Airport Station to College Park
Station has a probability of .95 of arriving on time. Assume for now that this claim is
true.
a. Explain what the probability .95 means in context.
b. If the 5:30a.m. train has arrived on time 6 days in a row, what is the probability
that it will arrive on time the next day? Why?
c. A student takes the 5:30am train to school 22 days in a month. They are
surprised when the train is late to Airport Station on 9 out of 22 days. Should
they be surprised? Describe how you would create a simulation that to estimate
the probability to see if their claim is true.

Answers

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.

What is meant by Probability?

The term "probability" is most commonly used to refer to the likelihood that a specific event (or group of events) will occur, either as a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

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Help here. Im not the smartest

Answers

Answer: Third one

Step-by-step explanation:

a point has a positive x coordinate and a positive y coordinate. What quadrant is it in

Answers

Quadrant 1 because both coordinates are positive

Shantal Jones has a job offer in which she will receive $600 per month plus a commission of 2% of the total price of the cars she sells. At her current job, she receives $1000 per month plus a commission of 1.5% of her total sales.

Use a system of equations to determine the total price of the cars that Ms. Jones must sell each month to make the same income from either dealership.

How much must Ms. Jones sell to make the new job a better deal?

Answers

a) Using a system of equations, the total price of the cars that Ms. Jones must sell each month to make the same income from either dealership is $80,000.

b) For Ms. Jones to make the new job a better deal, she must sell cars worth more than $80,000, for example, $80,500.

What is a system of equations?

A system of equations involves two or more equations solved concurrently.

It is also known as simultaneous equations.

Earning Equations:

New job offer = $600 + 0.02x ... 1

Current job = $1,000 + 0.015x ... 2

where x = sales revenue

For the two jobs to be the same, Equations 1 and 2 should be equal:

$600 + 0.02x = $1,000 + 0.015x

0.005x = 400

x = $80,000

Check:

For instance, at sales of $80,500:

Total earnings =

New job offer = $600 + 0.02x = $600 + 0.02(80,500) = $2,210

Current job = $1,000 + 0.015x = $1,000 + 0.015(80,500) = $2,207.50

Thus, based on simultaneous equations, Ms. Jones needs to sell cars worth more than $80,000 to make the new job a better deal.

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On a test that has a normal distribution, a score of 29 falls two standard
deviations below the mean, and a score of 41 falls two standard deviations
above the mean. Determine the mean of this test.

Answers

The mean of this test is 35.

What is the Mean?

The mean is a measure of central tendency that represents the average of a set of data. It is calculated by summing all the values in a dataset and then dividing the sum by the number of values in the dataset. It is also known as the arithmetic mean or simply the average.

Let X be the mean of the test.

We know that a score of 29 falls two standard deviations below the mean, which means that X- 2 * standard deviation = 29.

Similarly, we know that a score of 41 falls two standard deviations above the mean, which means that X+ 2 * standard deviation = 41.

The mean of a normal distribution is the sum of the two values divided by two.

So:

Mean = (29+41)/2 = 70/2 = 35

The mean of this test is 35.

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Answer: 35

Step-by-step explanation:

Fig. 10.12 On a cartesian plane sketch the region which represents the set of points for which x < 2 and y ≥ 5​

Answers

The graph of the inequality is given below.

The red region represents x < 2.

The blue region represents y ≥ 5.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

x < 2 and y ≥ 5

This means,

x < 2 is the region that contains less than 2.

y ≥ 5 is the region that contains 5 and greater than 5.

The graph is given below.

The red region represents x < 2.

The blue region represents y≥ 5.

Thus,

The graph is given below.

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Requesting urgent help, see image.​

Answers

Answer:

the answer is in the picture


Mita and Sita appear in a interview for two posts; the probability of Mita's selection in the interviwew is 80% and that of Sita is 75%. Find the probability that i) both of them will be selected ii) at least one of them will be selected iii) none of them will be selected iv) only one of them will be selected.​

Answers

The probability of both of them being selected is 0.6, while the probability of at least one of them being picked is 0.95, and the probability of none of them being chosen is 0.05. Only one of them will be selected, with a probability of 0.4.

What is probability?

Probability is the measure of how likely an event is to occur in a given situation. It is expressed as a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The mathematical study of random occurrences is known as probability theory. It is concerned with the investigation of random variables and the development of models and hypotheses to explain their behavior. Probability theory is used to anticipate the results of random occurrences like the roll of a dice or the flip of a coin. It may also be used to predict the likelihood of a certain event, such as the chance that a stock will rise in value or that a patient would respond to a specific therapy.

i) The probability that both of them will be selected is 0.6 (80% x 75%).

ii) The probability that at least one of them will be selected is 0.95 (80% + 75% - (80% x 75%)).

iii) The probability that none of them will be selected is 0.05 (1 - (80% + 75% - (80% x 75%))).

iv) The probability that only one of them will be selected is 0.4 (80% + 75% - (2 x (80% x 75%))).

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Match the definition.
A relationship between two similar things written as a to b,
a : b, or
An equation stating that two ratios are equal.
A multiple of the length of the sides from one figure to the
transformed figure.
:: Scale Factor

Answers

Answer:

you should have studied instead of going to a wed site

Step-by-step explanation:

many people can give u a wrong answer

I NEED SOME HELP KIND PEOPLE :(

Answers

15 i think that’s the answer
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