Set up and evaluate the optimization problem. You are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions (in m) of the box with the largest volume

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

Answer:

Option (c).

Step-by-step explanation:

It is given that, I paid twice as much by not waiting for a sale and not ordering online.

Let the cost of items ordering online be x.

So, now i am paying twice of x = 2x

Now, we have find 2x is what percent of x.

[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]

It means, I paid 200% of what I could have online and on sale.

Therefore, the correct option is (c).

Answer:

Mean = 30, Median = 29.5, Range = 9 and Mid-range = 29.5.

Step-by-step explanation:

We are given that a local doctor’s office logged the number of patients seen in one day by the doctor for ten days.

Arranging the given data in ascending order we get;

24, 25, 27, 27, 28, 31, 33, 35, 35, 35.

(a) Mean is calculated by using the following formula;

         Mean, [tex]\bar X[/tex]  =  [tex]\frac{\text{Sum of all values}}{\text{Total number of observations}}[/tex]

                          =  [tex]\frac{27+ 31+ 27+ 35+ 35+ 25+ 28+ 35+ 33+ 24}{10}[/tex]

                          =  [tex]\frac{300}{10}[/tex]  = 30

So, the mean of the given data is 30.

(b) For calculating the median, we have to first have to observe that the number of observations (n) in the data is even or odd.

                     Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                     Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations is even, i.e. n = 10.

So,  Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{(\frac{10}{2})^{th} \text{ obs.}+ (\frac{10}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{(5)^{th} \text{ obs.}+ (6)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{28+31}{2}[/tex]

                     =  [tex]\frac{59}{2}[/tex]  =  29.5

So, the median of the data is 29.5.

(c) The range of the data is given by = Highest value - Lowest value

                                                        = 35 - 24 = 9

So, the range of the data is 9.

(d) Mid-range of the data is given by the following formula;

                   Mid-range  =  [tex]\frac{\text{Highest value}+\text{Lowest value}}{2}[/tex]

                                      =  [tex]\frac{35+24}{2}[/tex] = 29.5

Answer:

1/5

Step-by-step explanation:

The number 5 or greater than 4 is 5.

1 number out of 5 total parts.

= 1/5

P(5 or greater than 4) = 1/5

Answer:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Step-by-step explanation:

For this case we know that a coin is toss 100 times and we got 65 heads and 35 tails.

We can calculate the empirical probabilities for each outcome and we got:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Answer:

prime factors in ascending order of 1729 is 7 , 13 , 19

relation between  consecutive prime factors is 6

Step-by-step explanation:

given data

number = 1729

solution

we get here factors of 1729

1729 = 7 × 13 × 19

so that required prime factors in ascending order of 1729 is 7 , 13 , 19

and

now we get relation between these prime factors is the difference between consecutive prime factors is

13 - 7 =  6

19 - 13 = 6

so relation between  consecutive prime factors is 6

Step-by-step explanation:

Prime factors of the number 1729 are 7,13,19

i.e. 1729 =7×13×19

The factors in ascending order are 7,13,19.

Clearly we can see that each consecutive prime factors​ have difference of 6.

13-7=6

19-13=6

Answer:

The given equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Step-by-step explanation:

The given equation is

[tex]3v^2 - 84 = 0[/tex]

Let’s solve the equation

[tex]3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = \frac{84}{3} \\\\v^2 = 28 \\\\[/tex]

Take the square root on both sides

[tex]\sqrt{v^2} = \sqrt{28} \\\\v = \sqrt{28} \\\\v = \pm 5.29 \\\\[/tex]

So the equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Also refer to the attached graph of the equation where you can verify that the equation has two solutions.

Note:

It is a very common mistake to consider only the positive value and not the negative value.

Consider the square root of 25

[tex]\sqrt{25} = \pm 5 \\\\Since \\\\5 \times 5 = 25 \\\\-5 \times -5 = 25 \\\\[/tex]

That is why we have two solutions for the given equation.

Answer:

The answer to this equation is 3 5/6

Step-by-step explanation:

in order to solve this problem, we must first turn these fractions into improper fractions. We can do this by multiplying the base number with the denominator and adding the numerator to that number.

6 1/2 = 13/2

2 2/3 = 8/3

Now, set up your equation.

13/2 - 8/3

Change the denominators to the same number so it will be easier to subtract.

39/6 - 16/6

Now subtract.

23/6 = 3 5/6

Answer:

3 5/6

Step-by-step explanation:

6 1/2 - 2 2/3 = 13/2 - 8/3

(39 - 16)/6 = 23/6 = 3 5/6

Answer:

Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time, and making calculations during travel.

Sorry if this is a little wordy, I can get carried away with this sort of thing

anyway, hope this helped and answered your question :)

Answer:

46

Step-by-step explanation:

Answer:

270 tiles.

Step-by-step explanation:

The kitchen is 15 x 18 feet. If we multiply we find the area is 270 square feet. one square foot is a 12 x 12 inch square, so we can fit one tile per square foot, giving us 270 tiles.

Answer:

  x = 2.4

Step-by-step explanation:

We assume you intend ...

  [tex]\sqrt{x^2+49}=x+5\\\\x^2+49=x^2+10x+25\qquad\text{square both sides}\\\\24=10x\qquad\text{subtract $x^2+25$}\\\\\boxed{2.4=x}\qquad\text{divide by 10}[/tex]

Answer:

x=∛4 x

Step-by-step explanation:

Let the number be x.

According to the question,

x^3=4 x

x=∛4 x

This is the only answer we can conclude from the information given in the question.

The required expression is x³ + 4x.

Given that,

The cube of a number increased by 4 times the same number is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
cube of number = x³
4 time of number = 4x
The cube of a number increased by 4 times the same number, which implies,
x³ + 4x

Thus, the required expression is x³ + 4x.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

H=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

S=4lw+2wh

Put S as 136, l as 6, w as 4, and solve for h.

136 = 4(6)(4)+2(4)H

136 = 8h + 96

-8h = 96 - 136

-8h = -40

h = -40/-8

h = 5

Answer:

6

Step-by-step explanation:

12*5=60

6*3=18

1*7=7

hope this help

Answer

h = 5m

Step-by-step explanation:

area of a parallelogram is b * h

base = 14 m

h = ?

Area = 70 m²

Area = b * h

70 = 14 * h

h = 70 / 14

h = 5 m

Answer:

V lies in the exterior of <STU.

Step-by-step explanation:

V lies in the exterior of <STU.

Answer:

If we have a growing exponential relation, we can write it as:

f(x) = A*r^x

Where A is the initial amount, r is the rate of growth, in this case, r > 1 (because is a growing exponential relation)

Now, the "slope" of the graph in x, is equal to the derivate of f(x) in that point, and we have:

f'(x) = A*(r^x)*ln(r)

Now, remember that r > 1, then ln(r) > 0.

then, f'(x) is a growing function as x grows, and f'(x) grows exponentially, this means that the slope of the graph also grows exponentially as x grows.

Answer:

Option B

Step-by-step explanation:

We are given the following system of equations -

[tex]\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}[/tex]

Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -

[tex]\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}[/tex]

Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -

[tex]\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}[/tex]

Now solve through Cramer's Rule -

x = Dx / D = - 6,

y = Dy / D = - 1,

z = Dz / D = 1

Solution = ( - 6, - 1, 1 ) = Option B

-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21

Answer is x=-6,\:z=1,\:y=-1

Answer:

31.4 inches

Step-by-step explanation:

The circumference of a circle has the formula 2πr.

2 × π × 5

= 10 × 3.14

= 31.4

31.4 inches of ribbon is needed to go once around the rim.

Answer:

15.7 inches of ribbon.

Step-by-step explanation:

This question is basically asking for the circumference of the glass vase's rim. We can calculate that by multiplying the diameter by π, which in this case, is 3.14.

The diameter is 5 inches, so all you need to do is 5 * 3.14 = 15.7 inches of ribbon.

Hope this helps!

Answer: 12600

Step-by-step explanation:

We are given the function that f(x) = 12000 * 1.05x

the x in f(x) is the amount of years that passed in the city of Peachwood, and the f(x) is the total population of Peachwood

These are two key elements in this function,

Therefore after 1 year the equation would be f(1) = 12000*1.05(1)

or f(1) = 12600

Answer:

x^2-2x+1

Step-by-step explanation:

We can solve this by using FOIL

First, Outside, Inside, Last

Multiply the x with the x to get x^2

Then x times -1 for the outside numbers to get -x

Then -1 times x for the inside numbers to get -x

And finally -1 and -1 for the last numbers to get 1

Add the two -x to get -2x.

Put it all together

x^2-2x+1

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

USING FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

D -price of car wash keeps getting higher

Answer: The price of a car wash keeps getting higher

Step-by-step explanation:

Answer:

1,050 workers

Step-by-step explanation:

25% = 0.25

0.25 × 1400 = 350

1400 - 350 = 1050

Hope this helps.

Answer:

x" means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s . this should help I asked my brother for the answer and he told me to put this happy to help :0

Answer:

Step-by-step explanation:

8P3=8*7*6=336

Answer:

The maximal area will be "1093.5 square feet".

Step-by-step explanation:

Let,

Length = L feet

Breadth = b feet

Given Total fencing = 162 feet

According to the question,

 [tex](2\times L)+(3\times b)=162[/tex]

              [tex]2L+3B=162[/tex]

                         [tex]L=\frac{162-3b}{2}[/tex]

                         [tex]L=81-\frac{3}{2}b[/tex]

As we know,

 [tex]Area=Length\times breadth[/tex]

          [tex]=(81-\frac{3}{2}b)\times b[/tex]

          [tex]=81b-\frac{3}{2}b^2[/tex]

Now, we required to decrease or minimize the are. So for extreme points:

 [tex]\frac{dA}{db}=0[/tex]

or,

 [tex]\frac{dA}{dB}=\frac{d}{db}(81-\frac{3}{2}b^2 )=0[/tex]

       [tex]81-\frac{3}{2}\times 2\times b=0[/tex]

                            [tex]b=\frac{81}{3}[/tex]

                            [tex]b=27 \ feet[/tex]

Now on putting the value of b, we get

 [tex]l=81-\frac{3}{2}\times 27[/tex]

   [tex]=81-40.5[/tex]

   [tex]=40.5 \ feet\\[/tex]

So that the dimensions will be:

⇒  40.5 feet by 27 feet

Therefore when the dimension are above then the area will be:

=  [tex]81\times 27-\frac{3}{2}\times 27\times 27[/tex]

=  [tex]2187-\frac{3}{2}\times 729[/tex]

=  [tex]2187-1093.5[/tex]

=  [tex]1093.5 \ square \ feet[/tex]

Answer:

Length=17 yds, Width=14 yds

Step-by-step explanation:

62=x+x+(x+3)+(x+3)

4x+6=62

4x=56

x=14

x+3=17

Answer:

2 units.

Step-by-step explanation:

In this question we use the Pythagorean theorem which is shown below:

Given that

The right triangle OMP

The hypotenuse i.e OM is the circle radius =5 units.

The segment MP = 4 units length

Therefore

[tex]OP^2 + MP^2 = OM^2[/tex]

[tex]OP^2 + 4^2 = 5^2[/tex]

[tex]OP^2 + 16 = 25[/tex]

So OP is 3

Now as we can see that ON is also circle radius so it would be 5 units

And,

ON = OP + PN

So,

PN is

= ON - OP

= 5 units - 3 units

= 2 units

Answer:

2

Step-by-step explanation:

Answer:

  0 ≤ g(x) < ∞

Step-by-step explanation:

The range is all non-negative numbers.

___

g(x) is an even-degree polynomial with a positive leading coefficient, so it opens upward. There is no added constant, so its minimum value is zero. The function can take on all values zero or greater.

  range: [0, ∞)