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3 years ago

12

Hello can anyone answer this for me please ? I will give brainliest

1 answer:

puteri [66]3 years ago

4 0

Answer:

Your answer will be A have a good day :)

Step-by-step explanation:

A - 1 = 1 and B is 1

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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

A train leaves a station and travels north at a speed of 105105 km/h. twotwo hours later, a second train leaves on a parallel

hram777 [196]

Let x = hours to meet

train one has a 2 hour head start or 210 km head start

210 + 105x = 135x
30x = 210
x = 7 hours to meet

6 0

3 years ago

Given the right triangle shown below.if Cos A =15/17 and tan A=8/15 which of the following represents the length of BC

otez555 [7]

Answer:

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.

Step-by-step explanation:

Given:

Consider a right triangle ABC, Such that

$\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}$

To Find:

BC = ?

Solution:

In Right Angle Triangle ABC, Cosine and Tangent identity

$\cos A = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\$

$\tan A= \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}$

BUT,

$\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}$ ....Given

On Comparing,

Adjacent side to angle A = AB = 15

Opposite side to angle A = BC = 8

Hypotenuse = AC =17

Also Pythagoras theorem is Satisfies,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

$(\textrm{Hypotenuse})^{2} = 17^{2}=289$

$(\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}=15^{2}+8^{2}=289$

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.

7 0

3 years ago

In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 45) and matching the

777dan777 [17]

Answer:

39,096,288

Step-by-step explanation:

as we know that

The number of ways to pick 5 numbers from 45 are

$45C_5$

$\frac{45\times44\times43\times42\times41}{5\times4\times3\times2\times1}|$

= 1,221,759.

There are 32 ways to pick a gold ball so total number of ways to get 6 matching numbers is

1221759×32

= 39,096,288

6 0

4 years ago

In Eduardo's collection, the number of butterflies is 12 more than twice the number of moths. If there are x moths, write an exp

galina1969 [7]

Answer:

12x

Step-by-step explanation:

Multiply 12 times another number.

4 0

3 years ago