Please help me with this!!!!

Vesna [10]

$2\frac{2}{3}=\frac{2\cdot3+2}{3}=\frac{6+2}{3}=\frac{8}{3}$

6 0

2 years ago

Suppose that 7 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at ra

katen-ka-za [31]

Answer:

(a) 350

(b) 175

(c) 21

(d) 196

Step-by-step explanation:

Number of females = 7

Number of males = 5

Total ways of selecting r items from n items is

$^nC_r=\dfrac{n!}{r!(n-r)!}$

(a)

Total ways of selecting 3 females and 2 males.

$\text{Total ways}=^7C_3\times ^5C_2$

$\text{Total ways}=\dfrac{7!}{3!(7-3)!}\times \dfrac{5!}{2!(5-2)!}$

$\text{Total ways}=35\times 10$

$\text{Total ways}=350$

(b)

Total ways of selecting 4 females and 1 male.

$\text{Total ways}=^7C_4\times ^5C_1$

$\text{Total ways}=32\times 5$

$\text{Total ways}=175$

(c)

Total ways of selecting 5 females.

$\text{Total ways}=^7C_5\times ^5C_0$

$\text{Total ways}=21\times 1$

$\text{Total ways}=21$

(d)

Total ways of selecting at least 4 females.

Total ways = 4 females + 5 females

$\text{Total ways}=175+21$

$\text{Total ways}=196$

6 0

3 years ago

A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it doe

Bond [772]

The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet

<h3>What dimensions would guarantee that the garden has the greatest possible area?</h3>

The given parameter is

Perimeter, P = 520 feet

Represent the shorter side with x and the longer side with y

One side of the garden is bordered by a river:

So the perimeter is:

P = 2x + y

Substitute P = 520

2x + y = 520

Make y the subject

y = 520 - 2x

The area is

A = xy

Substitute y = 520 - 2x in A = xy

A = x(520 - 2x)

Expand

A = 520x - 2x^2

Differentiate

A' = 520 - 4x

Set to 0

520 - 4x = 0

Rewrite as:

4x= 520

Divide by 4

x= 130

Substitute x= 130 in y = 520 - 2x

y = 520 - 2 *130

Evaluate

y = 260

The area is then calculated as:

A = xy

This gives

A = 130 * 260

Evaluate

A = 33800

Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet