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3 years ago

when three different numbers are chosen from the set {-3,-2,-1,4,5) and multiplies the greatest possible product is

1 answer:

5 0

1. We cannot pick both of the positive numbers 4 and 5 because the third one would be negative, and the overall product negative.

2. So we pick 5, the largest of (4, 5) and 2 negative numbers

3. Since the multiplication of the 2 negative numbers is positive, we pick the ones with larger absolute value, so -3 and -2

Answer: 5*(-3)*(-2)=5*6=30

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1.5 g = __?__ kg<br><br> 3 1-4 qt =__?__ pt<br><br> Help Is Appreciated!!!

zysi [14]

The first one is 0.0015

6 0

3 years ago

Two dice are tossed together. What is the probability of getting an odd number on the second die and a total of five?

wolverine [178]

Probability = (number of ways to succeed) / (total possible outcomes) .

The total possible results of rolling two dice is

(6 on the first cube) x (6 on the second one) = 36 possibilities.

How many are successful ? I need you to clarify something first.
You said that the 'second die' shows an odd number. When a pair
of dice is rolled, the problem usually doesn't distinguish between them.
And in fact, you said that they're "tossed together" (like a spinach and
arugula salad ?) so I would understand that they would lose their identity
unless they were, say, painted different colors, and we wouldn't know
which one is the second one.

Oh well, I'll just work it both ways:

First way:
Two identical dice are tossed.
The total is 5 and ONE cube shows an odd number.

How can that happen ?

1 ... 4
4 ... 1
3 ... 2
2 ... 3

Four possibilities. Probability = 4/36 = 1/9 = 11.1% .

=======================================

Second way:
A black and a white cube are tossed together.
The total is 5 and the white cube shows an odd number.

How can that happen:

B ... W
4 .... 1
2 .... 3

Only two possibilities. Probability = 2/36 = 1/18 = 5.6% .

3 0

4 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

3 years ago

What is an equation of the line that passes through the points (2,5) and

harkovskaia [24]

Y-5=-1/2(X-2)
the simplified version of this equation (so you can plug into a calculator) is
Y=-1/2x+6

3 0

3 years ago

5(x 1) − 8 = 5x(2 − 4)

svp [43]

Answer:
5 x (2 - 4)
5x-8= -10x
15x=8
x=8/15

Hope this helps!

3 0

4 years ago