-32-(-27)= what is negative 32 minus negative 27?

Suppose there are 4 defective batteries in a drawer with 10 batteries in it. A sample of 3 is taken at random without replacemen

SSSSS [86.1K]

Answer:

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ = $\frac{4!}{1! (4 - 1 )!}$ × $\frac{6!}{2! (6 - 2 )!}$

= $\frac{4!}{(3)!}$ × $\frac{6!}{2! (4)!}$

= $\frac{4.3!}{(3)!}$ × $\frac{6.5.4!}{2! (4)!}$

= $4$ × $\frac{6.5}{2.1! }$

= $4$ × $15$ = 60

Total Number of possibility = ¹⁰C₃ = $\frac{10!}{3! (10-3)!}$

= $\frac{10!}{3! (7)!}$

= $\frac{10.9.8.7!}{3! (7)!}$

= $\frac{10.9.8}{3.2.1!}$

= 120

So, probability = $\frac{60}{120} = \frac{1}{2} = 0.5$

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility = ⁴C₀ × ⁶C₃

= $\frac{4!}{0! (4 - 0)!}$ × $\frac{6!}{3! (6 - 3)!}$

= $\frac{4!}{(4)!}$ × $\frac{6!}{3! (3)!}$

= 1 × $\frac{6.5.4.3!}{3.2.1! (3)!}$

= 1× $\frac{6.5.4}{3.2.1! }$

= 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability = $\frac{80}{120} = \frac{8}{12} = 0.66$

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility = ⁴C₂ × ⁶C₁

= $\frac{4!}{2! (4 - 2)!}$ × $\frac{6!}{1! (6 - 1)!}$

= $\frac{4!}{2! (2)!}$ × $\frac{6!}{1! (5)!}$

= $\frac{4.3.2!}{2! (2)!}$ × $\frac{6.5!}{1! (5)!}$

= $\frac{4.3}{2.1!}$ × $\frac{6}{1}$

= 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility = ⁴C₃ × ⁶C₀

= $\frac{4!}{3! (4 - 3)!}$ × $\frac{6!}{0! (6 - 0)!}$

= $\frac{4!}{3! (1)!}$ × $\frac{6!}{(6)!}$

= $\frac{4.3!}{3!}$ × 1

= 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability = $\frac{100}{120} = \frac{10}{12} = 0.83$

3 0

3 years ago

Consider the figure in the diagram above. ABJK is a rectangle. There are two semicircles cut out of the rectangle. AB=8cm; AJ=18

RUDIKE [14]

First find the area of the rectangle, then remove the circular area.

AB * AJ = 8 * 18 = 144 sq cm

Circle = $\pi r^{2}$
= $\pi 4^{2}$
=3.14 * 16
=50.24 sq cm

144 - 50.24 = 93.76 sq cm shaded area.

3 0

4 years ago

1/3 x 3/4<br> Help me plss

EastWind [94]

Answer:

1/4

Step-by-step explanation:

this should be it

(hope it helps)

8 0

3 years ago

Read 2 more answers

Each time Henry visits the art museum he pays $15 for parking and $25 for admission.

Flauer [41]

Answer:

A

Step-by-step explanation:

Since it says 'each time ' you would say 15x and 25x. Since that isnt an answer you add them together and get 40x. That eliminates B and C. Next you would do the other side of the equation. He only pays the membership one time but pays for parking every time he goes so it would be 110 and 10x

8 0

3 years ago

What is the range of g(x) = 3|x − 1| − 1? A. (-∞, 1] B. [-1, ∞) C. [1, ∞) D. (-∞, ∞)

AVprozaik [17]

Answer:

B. [-1, ∞).

Step-by-step explanation:

g(x) = 3|x − 1| − 1

When x = 1 g(x) = 3(0) - 1 = -1.

As all negative vales of x will give positive values of |x - 1| then g(x) = -1 is its minimum value. The graph will be shaped like a letter V with the vertex at (1,-1).

Therefore the range is [-1, ∞).

6 0

3 years ago