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Leona [35]
3 years ago
6

Edurado started a business selling sporting goods.He spent $ 7500 to obtain hos merchandise , and it cost him $300 per week for

general expenses.He earns $850 per week in sales. What is the minimum number of weeks Edurado will take to make a profit?

Mathematics
1 answer:
Alik [6]3 years ago
5 0

Answer:

C)  It will take  14 weeks for Edurado to make a profit.

Step-by-step explanation:

The money spent on obtaining the merchandise = $ 7500

The general expense per week = $300

Let us assume Eduardo has to work for N weeks to break Even.

So, the general expense in N weeks  = N x( Expense per week)

=  N x ( $300)  = 300 N

So, the total expense in N weeks  =  Money spent on merchandise + general expense

or, the TOTAL EXPENSE =  $ 7500 +  300 N     .... (1)

Now, the earning per week = $850

So, the total earning in N weeks = N x ( Earning in 1 week) =  N x ( $850)

or, the TOTAL EARNING  =  850 N    .... (2)

Now, for N weeks ,

TOTAL EXPENSE  = TOTAL EARNING

⇒ $7500 +  300 N = 850 N

or, 7500 = 850 N -  300 N = 550 N

⇒ N  = 7500/550 = 13.63

So, number of weeks should at least be 13.63

Among the given options, N = 14 weeks is the most feasible answer.

Hence, it will take  14 weeks for Edurado to make a profit.

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4 years ago
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Jack finds this list of ingridents needed to make 20 muffins. To make 20 muffins you need 220ml milk, 250g castel sugar, 400g fl
Harlamova29_29 [7]

Answer:

60 muffins

Step-by-step explanation:

Find out how much ml you need for each ingredient.

20 muffins =

220 ÷ 20 = 11 (milk)

250 ÷ 20 = 12.5 (castel sugar)

400 ÷ 20 = 20 (flour)

Find out the greatest number of muffins Jack can make.

1 litre = 1000 ml

1000 ÷ 11 = 90.90 (recurring decimal) (milk)

750 ÷ 12.5 = 60 (castel sugar)

1500 ÷ 20 = 75 (flour)

Find the smallest answer out of the 3 questions.

6 0
3 years ago
10 + 3x < 4 or 2x + 5 > 11 in interval notation​
Stella [2.4K]

Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

7 ≥ 2 x − 5

12 ≥ 2 x

6 ≥ x

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

be any number less than 6, but it could also be 6.

Let's try the second example:

3 x − 2 4 > 4

3 x − 2 > 16    3 x > 18 x > 6

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

( 6 , ∞ )  

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )

6 0
4 years ago
Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (
galben [10]

Answer:

(a) Yes, λ_{A}+λ_{B}

(b) Yes, λ_{A}λ_{B}

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation λ_{A} to denote Lambda(A) sign.

v is an eigenvector of matrix A with eigenvalue λ_{A}

v is also eigenvector of matrix B with eigenvalue λ_{B}

So we can write this in equation form as

Av=λ_{A}v

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector  that is in the same direction as of Av, then this v  is called the eigenvector of A. Av is λ_{A} times the original v. The number λ_{A} is the eigenvalue of A.

λ_{A} this number is very important and tells us what is happening when we multiply Av. Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of Av by using the following equation:

det(A-λI)=0

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that v is an eigenvector of A + B and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)

so,  (A+B)(v)=(λ_{A}+λ_{B})(v)

which means that v is also an eigenvector of A+B and the associated eigenvalues are λ_{A}+λ_{B}

(b) Show that v is an eigenvector of AB and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)

so,  

(AB)(v)=λ_{A}λ_{B}(v)

which means that v is also an eigenvector of AB and the associated eigenvalues are λ_{A}λ_{B}

5 0
3 years ago
A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics
balandron [24]

Answer:

a. 95.4

b. UCL = 96.07

LCL = 94.73

c.  Process is in control

Step-by-step explanation:

a. The computation of estimate mean is shown below:-

Estimate\ mean = \frac{\Sigma X}{N} \\\\ = \frac{1908.000}{20}

= 95.4

b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-

UCL = Mean + \frac{3\times \sigma }{\sqrt{Sample\ size} }

UCL = 95.4 + \frac{3\times (0.5)}{\sqrt{0.5} }

= 95.4 + 0.67082

= 96.07

UCL = Mean - \frac{3\times \sigma }{\sqrt{Sample\ size} }

UCL = 95.4 - \frac{3\times (0.5)}{\sqrt{0.5} }

= 95.4 - 0.67082

= 94.73

c. The explanation is shown below:-

From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,  

The Process is in control

7 0
3 years ago
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