Which pair of addends form compatible numbers in the expression 6.1 + 8.4 + 1.6

The gates of an amusement park are closely monitored to determine whether the number of

fredd [130]

Answer:

Maybe how many people are in the park

3 0

2 years ago

A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.

Montano1993 [528]

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

area = xy +2(xz +yz)

volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

L = xy +2(xz +yz) +λ(xyz -8788)

partial with respect to x: 0 = y+2z +λyz

partial with respect to y: 0 = x +2z +λxz

partial with respect to z: 0 = 2x+2y +λxy

partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

λ = (y +2z)/(yz) = 1/z +2/y

λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

1/z +2/y = 1/z +2/x ⇒ x = y

The third equation then tells us ...

λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

1/z +2y = 2/x +2/y ⇒ z = x/2

This is the result we started the answer with:

x = y = 2z = ∛(2·8788 cm³)

7 0

2 years ago

The larger nail is a dilation of the smaller nail.

Sergeeva-Olga [200]

Answer: the scale factor is 3/4

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

In ACME PUBLISHING SWEEPSTAKES, the chance of winning a car is 1 in 1,000. What percent of tickets to ACME PUBLISHING SWEEPSTAKE

Yuri [45]

Answer:

0.1% of tickets to ACME PUBLISHING SWEEPSTAKES win a car

Step-by-step explanation:

Given :The chance of winning a car is 1 in 1,000.

To Find : What percent of tickets to ACME PUBLISHING SWEEPSTAKES win a car?

Solution:

The chance of winning a car is 1 in 1,000.

The percent of tickets to ACME PUBLISHING SWEEPSTAKES win a car:

= $\frac{1}{1000} \times 100$

= $\frac{1}{10}$

= $0.1\%$

Hence 0.1% of tickets to ACME PUBLISHING SWEEPSTAKES win a car.

8 0

2 years ago

Pls pls help:( ASAP

katrin [286]

Answer:

The answer is 12.64 ft.

Step-by-step explanation:

From the figure it is clear that slope is the hypotenuse which we have to find while the other two sides are legs of the triangle whose lengths are known.

so the pitch of the roof is 12.64 ft. i explained in the figure below as well.

4 0

2 years ago