what is 62/25 - 5/4 and find the

Answer:

The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.

Step-by-step explanation:

Geometrically speaking, the volume of the rectangular box ([tex]V[/tex]), in cubic feet, is represented by this formula:

[tex]V = l^{2}\cdot h[/tex] (1)

Where:

[tex]l[/tex] - Side length of the box, in feet.

[tex]h[/tex] - Height of the box, in feet.

In addition, the total cost of the box ([tex]C[/tex]), in monetary units, is defined by this formula:

[tex]C = (c_{b}+c_{t})\cdot l^{2} + 4\cdot c_{s}\cdot l\cdot h[/tex] (2)

Where:

[tex]c_{b}[/tex] - Unit cost of the base of the box, in monetary units per square foot.

[tex]c_{t}[/tex] - Unit cost of the top of the box, in monetary units per square foot.

[tex]c_{s}[/tex] - Unit cost of the side of the box, in monetary units per square foot.

By (1), we clear [tex]h[/tex] into the expression:

[tex]h = \frac{V}{l^{2}}[/tex]

And we expand (2) and simplify the resulting expression:

[tex]C = (c_{b}+c_{t})\cdot l^{2}+4\cdot c_{s}\cdot \left(\frac{V}{l} \right)[/tex] (3)

If we know that [tex]c_{b} = 0.34\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{s} = 0.05\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{t} = 0.16\,\frac{m.u.}{ft^{2}}[/tex] and [tex]V = 40\,ft^{3}[/tex], then we have the resulting expression and find the critical values associated with the side length of the base:

[tex]C = 0.5\cdot l^{2} + \frac{8}{l}[/tex]

The first and second derivatives of this expression are, respectively:

[tex]C' = l -\frac{8}{l^{2}}[/tex] (4)

[tex]C'' = 1 + \frac{16}{l^{3}}[/tex] (5)

After equalizing (4) to zero, we solve for [tex]l[/tex]: (First Derivative Test)

[tex]l-\frac{8}{l^{2}} = 0[/tex]

[tex]l^{3}-8 = 0[/tex]

[tex]l = 2\,ft[/tex]

Then, we evaluate (5) at the value calculated above: (Second Derivative Test)

[tex]C'' = 3[/tex]

Which means that critical value is associated with minimum possible total costs. By (1) we have the height of the box:

[tex]h = 5\,ft[/tex]

The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.

Part (a)

Answers:  

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Work Shown:

Refer to figure 1 in the screenshot attached below.

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Part (b)

Answers:  

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Work Shown:

Refer to figure 2 in the screenshot attached below.

Correction:

The derivative for h should be

[tex]h(x) = f(x)*(x-1)^{-1}\\\\h'(x) = \frac{d}{dx}[f(x)*(x-1)^{-1}]\\\\h'(x) = \frac{d}{dx}[f(x)]*(x-1)^{-1}+f(x)*\frac{d}{dx}[(x-1)^{-1}]\\\\h'(x) = f'(x)*(x-1)^{-1}+f(x)*(-1(x-1)^{-2})\\\\[/tex]

I had a -2 in there instead of -1 as the coefficient.

You should find that h ' (2) = -2

That would then lead to y = -2x+9

The steps shown in figure 2 are effectively the same, just with different numbers of course.

Answer:

no te entiendo

yo también la busco

Answer:

it's less than

Step-by-step explanation:

12/8 simplified is 3/2

11/6 cannot be further simplified

3/2<11/6

Answer:

10, 8, -5. Pls tell me if wrong i will retry. Im doing this mentally to be fast.

Step-by-step explanation:

A. 12 - |1 + -3 | = 12 - 2 = 10

B. 6 - -2 = 8

C. 18 -3/-3 = 15/-3 = -5

Answer:

14,8,-5

Step-by-step explanation:

1. 12-{1+(-3)}

12-{1(-3)} 1-3=-2

12-(-2) -×-=+

12+2

14

2. 6-{1+(-3)}

6-(1-3)

6-(-2)

6+2

8

3. 3×6+(-3)

________

-3

18-3

______

-3

15

_____

-3

=-5

Answer:

Factors of 16: 1, 2, 4, 8, 16

Factors of 56: 1, 2 , 4, 7, 8, 14, 28, 56

GCF: 8

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

55-23=32

Answer:

16

Step-by-step explanation:

shorter piece measures x  

longer piece measures x +23

Together they measure 55 ft

x + (x+23)  =  55

2x + 23 =  55

      -23 = -23

____________________

2x          = 32

x = 16

Answer:

x = 9

Step-by-step explanation:

According to Pythagoras theorem a² + b² = c²

Given that

a = x

b = x

c = 9√2

Substitute'

x² + x² = (9√2)²

2x² = 81 * 2

x² = 81

x = √81

x = 9

Hence the value of x is 9

Answer:

[tex]\theta=41.18^{\circ}[/tex]

Step-by-step explanation:

Given that,

The height of the tree, h = 14 ft

The height of the shadow, b = 16 ft

We need to find the angle of elevation of the sun from the ground. Let the angle be θ. We can use trigonometry to find it. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{14}{16}\\\\\theta=41.18^{\circ}[/tex]

So, the required angle of elevation of the sun is equal to [tex]41.18^{\circ}[/tex].

Answer:

36c2-81

Step-by-step explanation:

It's a difference of squares so you Florida it (FL) do first and last to get 36c2-81

Answer:

is two more than the row before

Step-by-step explanation:

i hope i help\

Answer:

42.9% are girls

Step-by-step explanation:

Answer:

the answer is

9(2p+1)

Answer:

18p +9

Step-by-step explanation:

Because you add the numbers in front of the p's (10+8) and then you add 10 plus -1, which is 9.

Hope this helps! Have a good day and remember to be tiger fierce!! :)

-9-(-7)

-9--7

-9+7

7-9

-2

---

hope it helps

A fair price for the seller's 1800 square foot house is $183.68 thousand, option B is correct

Two or more expressions with an Equal sign is called as Equation.

The given linear equation represents a relationship between the square footage (x) and the price (y) of houses in the neighborhood.

We can use this equation to estimate the fair price for the seller's house by plugging in the square footage (x) of the house and solving for y:

y = 0.074x + 50

y = 0.074(1800) + 50

y = 133.2 + 50

y = 183.68

Hence, a fair price for the seller's 1800 square foot house is $183.68 thousand, option B is correct

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

24

Step-by-step explanation:

Answer:

ur lame asl

Step-by-step explanation:

Answer:

2:29 PM

Step-by-step explanation:

Answer:

2:30

Step-by-step explanation:

I think sorry if I'm wrong

Answer:

a. Sample  = 1664 adults

b. Parameter= % of poll based on telephone interview

c. Statistic = 66%

d. Population = American adult population

e. Confidence level= 95%

f. Margin of error = +/- 3%

g. Sampling Error

Step-by-step explanation:

The missing part of the question is

The quotation below describes an opinion poll conducted by CBS News and the New York Times. Oneof the questions asked was "Do you favor an amendment to the Constitution that would permitorganized prayer in public schools?" Sixty-six percent answered, "Yes."

a. Sample  = 1664 adults

The number included in the sample

b. Parameter= % of poll based on telephone interviews

The sample chosen on the bases

c. Statistic = 66%

The statistic obtained after applying the formula etc.

d. Population = American adult population

The sample is chosen from the population

e. Confidence level= 95%

f. Margin of error = +/- 3%

g. Sampling Error

It is a sampling error because the areas omitted had a very large religious population and the results were biased.

The sample was not chosen from the areas omitted.

Answer: -2√7

Step-by-step explanation:

Step-by-step explanation:

step 1. a diagram is important and can be uploaded. you will get a quicker answer with a diagram

step 2. triangle RST is a right triangle so we can use trigonometry to find <S

step 3. the adjacent side of <S is ST and the hypotenuse is RS so we will use cos

step 4. cosS = adj/hyp = ST/RS = 2.7/4.9

step 5. <S = 56.6° using inverse cos.

Answer:

42.43

Step-by-step explanation:

This is because you had to divbide by 3

Answer: 505

Step-by-step explanation:

I searched it up

Answer:

Step-by-step explanation:

making all terms have a common denominator of 12

(3(2x-3)+2(2x-5))/12=6(1)/12 now the 12s cancel out

3(2x-3)+2(2x-5)=6

6x-9+4x-10=6

10x-19=6

10x=25

x=2.5

Answer:

180 minutes to cook 9lb turkey.

Step-by-step explanation:

Let the time taken to cook a 9lb turkey be x.

Using proportions,

6/120 = 9/x

6x = 120 x 9

6x = 1080

x = 1080/6

x = 180

Question

If a 6 lb turkey takes 120 minutes to cook, how long would a 9 lb. Turkey take to cook?

Solution

time taken by 6 lb. Turkey to cook = 120 minutes

time taken by 1 lb. Turkey to cook = (120/6 = 20) minutes

time taken by 9 lb. Turkey to cook = ( 20×9= 180 ) minutes

Answer:

8 liters

Step-by-step explanation:

3x+2x+4x=9x

36/9=x

x=4

2x= smallest bucket= 8

Answer:

not it is not aa function

Step-by-step explanation:

Step-by-step explanation:

Given

GPA = NO + B1Study + B2work + B3leisure + B4sleep + u

1. No it makes no sense. There is an intercorellation between these explanatory variables. Changing study while holding the rest variables constant or fixed would not make sense. If study us changed then one or more of the other predictors should be changed so that they can still be equal to 168

2. Study is a perfect linear function of work, leisure and sleep. There is the problem of multicollinearity among these independent variables. One assumption of the MLR is no multicollinearity.

3. To reformulate model, you have to drop the variable that is having the issue. Let's say that leisure is dropped from the model. After this the assumption is satisfied.

GPA = b0 + B1Study + b2sleep + b3work + u

Answer:

The given data does not support the submission that there has been a change in the mean arrival times on Southwest

Step-by-step explanation:

The known mean late arrival time, μ = 72.3

The known standard deviation in late arrival time, σ = 9.8 minutes

The number of flights in the sample, n = 47

The sample mean late arrival time, [tex]\overline x[/tex] = 70.7

The sample standard deviation  late arrival time, s = 7.1

Using a significance level of 0.01

The null hypothesis is, H₀ ; μ = 70.7

The alternative hypothesis is, Hₐ ; μ ≠ 70.7

The test statistic is given as follows;

[tex]z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]z=\dfrac{70.7-72.3 }{\dfrac{9.8 }{\sqrt{47}}} \approx -1.119290547[/tex]

∴ z ≈ -1.12

p-value = 2 × P(z < -1.12)  = 2 × 0.13136 = 0.26272

Given that the p-value of 0.26272 is larger than the significance level, 0.05, we fail to reject the null hypothesis

Therefore, there is not enough statistical evidence to show that there has been a change in the mean arrival times on Southwest