Hannah is working two summer jobs, making $18 per hour lifeguarding and $9 per hour clearing tables. Last week Hannah worked twice as many hours clearing tables as she worked hours lifeguarding hours and earned a total of $144. Graphically solve a system of equations in order to determine the number of hours Hannah worked lifeguarding last week, x,x, and the number of hours Hannah worked clearing tables last week, yy.

Answer:

The length of 'x' is 4

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

The pythagorean theorem is:

[tex]a ^{2} + b^{2} = {c}^{2} [/tex]

[tex]a ^{2} + b^{2} = c^{2} \\ {3}^{2} + {b}^{2} = 5^{2} \\ 9 + {b}^{2} = 25 \\ \frac{ - 9 \: \: \: \: \: \: \: \: = - 9}{b ^{2} = \sqrt{16} } \\ b = 4[/tex]

Therefore x = 4

Complete Question

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).

a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?

b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.

c. Please state whether the following statement is always true, and give a brief explanation. If [tex]C_o =C_i[/tex], the news vendor solution is the mean.

Answer:

a

   [tex]N = 46728[/tex]

b

  [tex]n = 47728[/tex]

c

  Yes it is always true  

Step-by-step explanation:

From the question we are told that

   The regular price of the jersey is  [tex]P_r = \$ 80[/tex]

    The cost of producing a jersey is [tex]C= \$ 40[/tex]

  The left-over price of the jersey is [tex]P_o = $ 30[/tex]

   The mean is  [tex]\mu = 40000[/tex]

   The standard deviation is [tex]\sigma = 8000[/tex]

   The cost of lost customer goodwill is [tex]C_g = \$ 10[/tex]

Generally the fund that LCF will loss for one jersey if they order for too many  jersey (i.e more than they need )is mathematically represented  

           [tex]C_o = P_o - C[/tex]

=>        [tex]C_o = 40 - 30[/tex]

=>        [tex]C_o = \$ 10[/tex]

Generally the fund that LCF will loss for one jersey if they order lesser amount  jersey (i.e less than they need )is mathematically represented  

           [tex]C_i = P_r - C[/tex]

=>        [tex]C_i = 80 - 40[/tex]

=>        [tex]C_i = \$ 40[/tex]

Generally the critical ratio is mathematically represented as

             [tex]Z = \frac{C_i }{ C_i + C_o}[/tex]

=>           [tex]Z = \frac{40}{ 40 + 10}[/tex]

=>           [tex]Z = 0.8[/tex]

Generally the critical value of  [tex]Z = 0.8[/tex] to the right of the normal curve is

         [tex]z = 0.841[/tex]

Generally the optimal quantity of jersey to order is mathematically represented as

             [tex]N = \mu * [z * \sigma][/tex]

=>          [tex]N = 40000 * [0.841 * 8000][/tex]

=>          [tex]N = 46728[/tex]

Considering question b

  Generally considering the factor of customer goodwill  the fund that LCF will loss for one jersey if they order lesser amount  jersey (i.e less than they need )is mathematically represented  as

           [tex]C_k = C_i + C_g[/tex]

=>        [tex]C_k = 40 + 10[/tex]

=>        [tex]C_k = \$ 50[/tex]

Now   the critical ratio is mathematically represented as

             [tex]Z = \frac{C_k }{ C_k + C_o}[/tex]

=>           [tex]Z = \frac{50}{ 50 + 10}[/tex]

=>           [tex]Z = 0.833[/tex]

Generally the critical value of  [tex]Z = 0.833[/tex] to the right of the normal curve is

         [tex]z = 0.966[/tex]

Generally the optimal quantity of jersey to order is mathematically represented as

             [tex]n = \mu * [z * \sigma][/tex]

=>          [tex]n = 40000 * [0.966 * 8000][/tex]

=>          [tex]n = 47728[/tex]

Considering question c

    When [tex]C_o =C_i[/tex] then

The critical ratio is mathematically represented as

             [tex]Z = \frac{C_k }{ C_k + C_k}[/tex]

=>           [tex]Z = \frac{1}{ 2}[/tex]

=>           [tex]Z = 0.5[/tex]          

Generally the critical value of  [tex]Z = 0.5[/tex] to the right of the normal curve is

         [tex]z = 0[/tex]

So

The optimal quantity of jersey to order is mathematically represented as

             [tex]n = \mu * [z * \sigma][/tex]

=>          [tex]n = 40000 * [0* 8000][/tex]

=>          [tex]n = 40000 = \mu[/tex]

Hence the statement in c is true        

Answer:

Let's assume that Susan's graph is linear. Then, we can do linear interpolation. Let y be the amount charged for 10 hours of work done:

(7-10)/(7-11) = (168-y)/(168-264)

y = $240

For Jim's Lawn care, let's find the constant slope using points (1,20) and (2,40):

m = (20 - 40)/(1-2) = 20

Then, since the y-intercept is zero, the linear equation is:

y = 20x

Substituting x = 10 hours,

y = 20(10) = $200

The difference between the two would then be:

Difference = $240 - $200 = $40

Answer:

The measure of the angle labeled d

Step-by-step explanation:

I took the quick check for "angle angle side postulate"

Answer:

-1

Step-by-step explanation:

not sure if the equation is 3-4m or 3-4 but it's -1 if the equation is 3-4

Answer:

A or B

Step-by-step explanation:

Its more likely B

Answer:

false

Step-by-step explanation:

5/9 is .5 repeating

Answer:

I think it's E, F, H

Step-by-step explanation:

Hope you got it.

Merry Christmas...

Answer:

WY = 30

XZ = 10.5

Step-by-step explanation:

Paralellogram's diagonal's bisect eachother

Therefore,

[tex]n + 7 = 3 n[/tex]

Move the n over,

2n = 7

Divide both sides by 2,

n = 3.5

WY = 2(ZY) because definition of bisector

Simplify...

WY = 2(4n+1)

WY = 2(4(3.5)+1)

WY = 2(15)

WY = 30

You asked for XY, but the question asks for XZ, so I'm going to give XZ.

With n = 3.5 from above,

XZ = 3n

XZ = 3(3.5)

XZ = 10.5

The measure of XY and WY are; WY = 30 and XZ = 10.5

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Since Paralellogram's diagonal's bisect each other

Therefore,

2n = 7

Divide both sides by 2;

n = 3.5

WY = 2(ZY)

because definition of bisector

Simplify;

WY = 2(4n+1)

WY = 2(4(3.5)+1)

WY = 2(15)

WY = 30

we asked for XY,

With n = 3.5 from above,

XZ = 3n

XZ = 3(3.5)

XZ = 10.5

The measure of XY and WY are; WY = 30 and XZ = 10.5

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Answer:

Step-by-step explanation:

The basic technique to isolate a variable is to “do something to both sides” of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number. By repeating this process, we can get the variable isolated on one side of the equation.

Answer:

$13.50

Step-by-step explanation:

5 bags is 22.50 so 22.50/5 = 4.50 for 1 bag. Multiply that by 3 for 3 bags and get $13.50

Answer:

$26.43

Step-by-step explanation:

A pound = $1.81. Multiply the price per pound by however many pounds Shelly is buying.

Answer:

26.426

Step-by-step explanation:

1.81x14.6=26.426

Question:

What is the elevation of the deck where Winston ate dinner?

Answer:

The surf shop was higher and the distance would be 12.8 feet above the oceans surface.

12.8

Step-by-step explanation:

9514 1404 393

Answer:

  y = 1/4x^1 -x -4

Step-by-step explanation:

Same question as previous parts. The working is identical, using different numbers.

Focus-vertex distance is (y-difference) p = -4-(-5) = 1. Vertex is (h, k) = (2, -5). Putting these values into the vertex form and expanding to standard form, you get ...

  y = (1/(4p))(x -h)^2 +k

  y = 1/4(x -2)^2 -5 . . . . . . . . fill in the values for p, h, k

  y = 1/4(x^2 -4x +4) -5 . . . .  expand the square

  y = 1/4x^2 -x +1 -5 . . . . . . . use the distributive property to eliminate parens

  y = 1/4x^1 -x -4 . . . . . . . . . collect terms

_____

Additional information may be found at ...

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Answer:

11

Step-by-step explanation:

22-11=11

Answer:

[tex]\huge\boxed{\boxed{x=-10}}[/tex]

Step-by-step explanation:

Hello.

The Distributive Property states that

a(b+c)=ab+ac

Simplify:

-1(4+x)=6

-4-x=6

Add 4 to both sides:

-4+4-x=6+4

-x=10

Divide both sides by -1 in order to get rid of the minus sign:

x=-10

And we're done!

I hope it helps & have an outstanding day!

~ST2710 :)

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]

Given:

[tex]y=\log_{\sqrt{x}}x[/tex]

To find:

The value of [tex]\dfrac{dy}{dx}[/tex].

Solution:

We have,

[tex]y=\log_{\sqrt{x}}x[/tex]

It can be written as

[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]

Using property of log, we get

[tex]y=2[/tex]          [tex][\because \log_aa^x=x][/tex]

Now, differentiate both sides with respect to x.

[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]

[tex]\dfrac{dy}{dx}=0[/tex]          [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]

Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.

Answer:

C

Step-by-step explanation:

It has to be either A or C because the function is decreasing as you move left to right, this only occurs when the number inside parenthesis is less than 1.

It isn't A because if you plug in x=0, the value is 2, but on the graph it is greater than 2.

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Answer:

=

Step-by-step explanation:

After the decimal point if the zeros are on the right side they do not have any value.

Answer: = because 0 has no value

Complete the statement with the appropriate symbol.

1.42 ___=__ 1.420

>

<

=

Step-by-step explanation: = because the 0 has no value.

Step-by-step explanation:

Answer

[tex] {a}^{3} - {b}^{2} [/tex]

[tex] = {3}^{3} - { \frac{1}{2} }^{2} [/tex]

[tex] = 27 - \frac{1}{4} [/tex]

[tex] = \frac{107}{4} [/tex]

[tex] = 26 \frac{3}{4} [/tex]

sorry if wrong :)

Answer:

(x, y)

(-1,0)

since the rest of the points aren't in the multiple choice well it's (-1,0)

The solution is :  the correct option is (B) (-1, 0), is an x-intercept of the graphed function.

Here, we have,

We are given to find the x-intercepts of the graphed function.

We know that

x-intercepts of a function are the points on the X-axis through which the graph of the function is crossing.

From the graph, we see that

the curve is crossing the X-axis at the points (-2, 0) and (-1, 0) .

Therefore, the x-intercept of the given function is (-1, 0).

Option (B) is CORRECT.

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Answer:

$28

Step-by-step explanation:

The website charges 20%, so Macy receives 80%.

Then:

80% x 35=.8 x 35=28 ....................

the answer is =10

10

10

10

Answer:

2x+3x-11x-6=0

Combine like x variables

-6x-6=0

Add 6 to the right side

-6x = 6

Divide by -6

x=-1

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Answer:

x = - 1

Step-by-step explanation:

2x + 3x - 11x - 6 = 0

-6x = 6

x = - 1

Answer:

solution

or, (N+1) th item

_

2

or ,8+1 th item

_

2

or,9

_

2

or,4.5 th item hence the median is4

The median of the given numbers will be 8.5.

The Median is the middlemost value of the numbers arranged in ascending orders. If the number of the data is an odd number so the median will be a middle number if the number of the data is even then the median is the mean of the middle two numbers.

The given data is:-

1 , 1.23 , 2 , 3 , 4 , 13 , 22 , 26.8

The total numbers of the data are 8 so the median will be calculated as:-

Median = ( 4 + 13 ) / 2

Median = 17 / 2

Median = 8.5

Therefore the median of the given numbers will be 8.5.

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