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Inessa [10]
3 years ago
7

You and a friend each roll two dice. what is the probability that you both have the same two numbers

Mathematics
1 answer:
valentina_108 [34]3 years ago
5 0
Each dice has 6 sides
two will be 12
both together will be 24
same two numbers
there is only 4 equal numbers in 4 dices (12 pairs)
so 24/4 could be the answer
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A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,
tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0
3 years ago
For the function f(x) = 3x ^ 2 - 8 what is the average rate of change on the interval from to 10?
denis-greek [22]

Answer:

C

Step-by-step explanation:

Start from left to right

7 0
3 years ago
Read 2 more answers
Find the product.<br><br> 1/2 - y (2y * 3 - 8)<br> a) -y 4 + 4y<br> b) y 4 + 4y<br> c) -2y 3 + 4
aivan3 [116]
1/2 - y (6y - 8)
1/2 -6y2 - 8y

the answer is A
5 0
3 years ago
Which equation would you use to find how high the bird is flying
lisov135 [29]
Hi there! The fourth answer is correct.

In the picture we have to deal with facts:
1. The angle of 45°
2. The length of the opposite side
3. The length of the adjacent side.

Since we have to use the opposite and the adjacent side, we have to use the tangent of the angle. In a formula:
\tan( \alpha ) = \frac{opposite}{adjecent}

Filling in this formula, brings us to the following answer.
\tan(45) = \frac{x}{1100}
6 0
3 years ago
Complete this quiz to f<br> -<br> Add 521 + 111.
Llana [10]

Answer:

632

Step-by-step explanation:

6 0
3 years ago
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