Solve. i really need help<br><br><br><br> z =

You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f

postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m and W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L is L - 2*x l = 4 - 2*x

For the side W is W - 2*x w= 2 - 2*x

The height is x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x ⇒ V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0 8 - 24x + 12x² = 0 reordering 12x² - 24x + 8 = 0

or 3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂ = ( 6 ± √36 - 24 ) /6

x₁,₂ = ( 6 ± 3.46) /6

x₁ = 6 + 3,46 /6 x₁ = 1.58 we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂ =( 6 - 3,46 ) / 6

x₂ = 0,42 m

Dimensions of the open box

l = 4 - 2*x l = 4 - 0,85 l = 3,15 m

w = 2 -2*x w = 2 - 0,85 w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0

3 years ago

the number of patients treated dr. martens dentist office each day was recorded for nine days. These are the data; six, six, six

Effectus [21]

Answer:

Mean: 5.5555555555556

Median: 6

Mode: 6

Step-by-step explanation:

8 0

3 years ago

Show that <1+<2+<3=180, if line l and m are parallels cut by two transversals.

Svet_ta [14]

Step-by-step explanation:

Angle 1 2 and 3 are angles that are in a triangle and all the angles in a triangle always add up to 180

so <1 +<2 +<3=180

Hope that helps :)

7 0

3 years ago

Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumte

borishaifa [10]

Answer:

a) 0.3874

b) 0.3874

c) 0.1722

d) Mean and Standard Deviation = 0.9

Step-by-step explanation:

This is binomial distribution problem that has formula:

$P(x=r)=nCr*p^{r}*q^{n-r}$

Here p is probability of success = 10% = 0.1

q is probability of failure, that is 90% = 0.9

n is total number, which is 9, so n = 9

a)

The probability that none requires warranty is r = 0, we substitute and find:

$P(x=r)=nCr*p^{r}*q^{n-r}\\P(x=0)=9C0*(0.1)^{0}*(0.9)^{9-0}\\P(x=0)=0.3874$

Probability that none of these vehicles requires warranty service is 0.3874

b)

The probabilty exactly 1 needs warranty would change the value of r to 1. Now we use the same formula and get our answer:

$P(x=r)=nCr*p^{r}*q^{n-r}\\P(x=1)=9C1*(0.1)^{1}*(0.9)^{9-1}\\P(x=1)=0.3874$

This probability is also the same.

Probability that exactly one of these vehicles requires warranty is 0.3874

c)

Here, we need to make r = 2 and put it into the formula and solve:

$P(x=r)=nCr*p^{r}*q^{n-r}\\P(x=2)=9C2*(0.1)^{2}*(0.9)^{9-2}\\P(x=2)=0.1722$

Probability that exactly two of these vehicles requires warranty is 0.1722

d)

The formula for mean is

Mean = n * p

The formula for standard deviation is:

Standard Deviation = $\sqrt{n*p*(1-p)}$

Hence,

Mean = 9 * 0.1 = 0.9

Standard Deviation = $\sqrt{9*0.1*(1-0.1)}=0.9$

4 0

3 years ago

Multiplying binomials using area model.

Kazeer [188]

Answer:

4x²+35x+24

Step-by-step explanation:

FOIL the binomials and simplify

7 0

3 years ago

Read 2 more answers

Solve. i really need help z =