Answer:

Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

BAG A:

P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

BAG C:

P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375

= 0.1375 + 0.1 + 0.375 = 0.6125

At Lincoln elementary school there are 88 students in grade 1 and 116 students in grade 2 grade 3 has 164 students is the number of students in grade 1 and grade 2 greater than the students in grade 3mn

Im still stuck.... help? :',)

Using both the rotation matrices earlier in this lesson and your matrix calculator, find each determinant.

4y-x=2x-4=x+ysolve for x

(c) Is it possible for an n × n matrix A to satisfy A3 = In without A being invertible? Explain

Im still stuck.... help? :',)

Using both the rotation matrices earlier in this lesson and your matrix calculator, find each determinant.

4y-x=2x-4=x+ysolve for x

(c) Is it possible for an n × n matrix A to satisfy A3 = In without A being invertible? Explain

72

**Answer:**

72 = {2,2,2,3,3}

**Step-by-step explanation:**

**72**

**8****9**

**2****4****3****3**

**2****2**

B: New radius=?

New height=?

**Answer:**

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

**Step-by-step explanation:**

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

To solve this, we can express h in function of r:

And replace it in the surface equation

To optimize the function, we derive and equal to zero

The radius that minimizes the surface is r=3.44 cm.

The height is then

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

We derive and equal to zero

The radius that minimizes the real surface is r=2.73 cm.

The height is then

The height that minimizes the real surface is h=10.92 cm.

The minimal surface area for a **cylindrical **can of 256cm^3 is achieved with radius 3.03 cm and height 8.9 cm under uniform thickness, and radius 3.383 cm and height 7.14 cm with double thickness at top and bottom. Real cans deviate slightly from these dimensions possibly due to practicality.

For a **cylinder** with given volume, the surface area A, radius r, and height h are related by the formula A = 2πrh + 2πr^2 (if the **thickness **is uniform) or A = 3πrh + 2πr^2 (if the top and bottom are double thickness). By taking the derivative of A w.r.t r and setting it to zero, we can find the optimal values that minimize A.

For a volume of 256 cm^3, this gives us r = 3.03 cm and h = 8.9 cm with uniform thickness, and r = 3.383 cm and h = 7.14 cm with double **thickness **at the top and bottom. Comparing these **optimal dimensions** to a real soda can (r = 2.8 cm, h = 10.7 cm), we see that the real can has similar but not exactly optimal dimensions. This may be due to practical considerations like **stability **and ease of holding the can.

#SPJ3

**Answer:**

14= 1, 2, 7, 14

6= 1, 2, 3, 6

5 will go into everything. That is one of the factors.

x^3 is in everything as well.

The highest common factor is 5x^3

So **the greatest common factor (**determined by the last term) is **5x^3**

And the left over polynomial is x^3 + 7x + 3

square root of 61 is it rational or irrational ?

square root of 62 is it rational or irrational ?

square root of 101 is it rational or irrational ?

square root of 105 is it rational or irrational ?

Each square root of a number that does not generated as a square of an integer is irrational. This means that none of the given numbers is rational, that is, they are all irrational.

Good luck!!!!

Good luck!!!!

The answer would be 7