Find the square root of -162 and please explain your answer

Describe how the graph of f ( x ) = 1 x + 5 will differ from the graph of g (x) = 1/x

AleksandrR [38]

Answer:

parent function is the simplest form of the type of function given.

The transformation from the first equation to the second one can be found by finding , , and for each equation.

Find , , and for .

The horizontal shift depends on the value of . The horizontal shift is described as:

- The graph is shifted to the left units.

- The graph is shifted to the right units.

Horizontal Shift: None

The vertical shift depends on the value of . The vertical shift is described as:

- The graph is shifted up units.

- The graph is shifted down units.

Vertical Shift: None

The sign of describes the reflection across the x-

5 0

2 years ago

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

2 years ago

Please help. Trig: Laws of Cosines

Nonamiya [84]

Answer:

11.4

Step-by-step explanation:

d² = 6² + 6² - 2(6)(6)cos145

d² = 130.9789472

d = 11.44460341

3 0

3 years ago

What is the smallest value of 122

attashe74 [19]

121.5
121.5 rounded to nearest whole number is 122 --> 121.49 rounded to the nearest whole number is 121

4 0

2 years ago

On a map the distance from Fort Collins to Cheyenne is 3.2 inches. The angle formed at Laramie has measure 43.6º, and the angle

MArishka [77]

We can solve this by drawing a triangle with three points. The first point at Fort Collins (F), the second at Cheyenne (C) and the third at Laramie (L).

The angle at F = 46.5, the angle at L = 43.6. We know the side opposite angle L = 3.2 (side FC), now we must solve for the side opposite angle F (side LC).

We can use the law of sines to solve this where:

sinA/a = sinB/b
sin43.6/ 3.2 = sin46.5/LC
LC = 3.2 (sin46.5/sin43.6)
LC = 3.37 inches

We are told 1 in = 10.6 miles, therefore:

3.37 inches x 10.6 miles/in = 36 miles from Laramie to Cheyenne.

7 0

3 years ago