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3 years ago

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Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) ?

1 answer:

Strike441 [17]3 years ago

5 0

Answer:

all work is shown and pictured

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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

Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than a

Verdich [7]

= 3 × 10-11
(scientific notation)

= 3e-11
(scientific e notation)

= 30 × 10-^12
(engineering notation)
(trillionth; prefix pico- (p))

= 0.0000000000
<span>(real number)</span>

4 0

3 years ago

Read 2 more answers

1. find the actual distance from new york to memphis

Marat540 [252]

Answer:

A=950

B=540

Step-by-step explanation:

$\frac{8}{800} =\frac{9.5}{x} \\8x=7600\\x=950\\\\\frac{8}{800} =\frac{5.4}{x} \\8x=4320\\x=540$

6 0

3 years ago

Read 2 more answers

I need help :) please if you know this I would appreciate it if you can help me

elena-14-01-66 [18.8K]

Step-by-step explanation:

a.

2(3x) - 5x = 4

6x - 5x = 4

x = 4

B. -5(x-4)+8x=29

-5x+20+8x=29

3x+20=29

3x=9

x=3

C. 2y=18+2(3-y)

2y=18+6-2y

2y=24-2y

4y=24

y=6

D. c = -b - 11

3c + 6 = 6b

3( -b - 11) +6 = 6b

-3b-33+6=6b

-3b-27=6b

-27=9b

3=b

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3 years ago

peter uses unit cubes to build a figure in the shape of the letter x. what is the fewest unit cubes that peter can use to the fi

noname [10]

Five cubes.
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3 years ago