the states of nature are defined so that they are which of the following, meaning that at least one state of nature must occur at a given time for a chance event? mutually exclusive optimistic outcomes collectively exhaustive certain events

i don't know specifically what you are looking for but:

Direction: Opens Up

Vertex: (1, -1)

Axis of Symmetry: x = 1

and i attached the graph

Answer:  x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)

Step-by-step explanation:

Solve for x:

F x = 2 x^2 - 4 x + 1

Subtract 2 x^2 - 4 x + 1 from both sides:

-2 x^2 + F x + 4 x - 1 = 0

Collect in terms of x:

-1 + x (F + 4) - 2 x^2 = 0

Divide both sides by -2:

1/2 + 1/2 x (-F - 4) + x^2 = 0

Subtract 1/2 from both sides:

1/2 x (-F - 4) + x^2 = -1/2

Add 1/16 (-F - 4)^2 to both sides:

1/16 (-F - 4)^2 + 1/2 x (-F - 4) + x^2 = 1/16 (-F - 4)^2 - 1/2

Write the left hand side as a square:

(1/4 (-F - 4) + x)^2 = 1/16 (-F - 4)^2 - 1/2

Take the square root of both sides:

1/4 (-F - 4) + x = √(1/16 (-F - 4)^2 - 1/2) or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)

Subtract 1/4 (-F - 4) from both sides:

x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)

Subtract 1/4 (-F - 4) from both sides:

Answer: x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)

Answer:

The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression is

In the above expression we have common base 3 but the exponents are different.

According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.

Use this rule in the given expression.

Therefore the correct option is d.

Answer:

d or Keep the base the same and then subtract the exponents.

Step-by-step explanation:

Answer:

9. 471.7 square units

10. 827.0 square units

Explanation:

If you're going to have someone else solve your problem for you, it is much quicker and easier to use an appropriate computer or graphing calculator app. (See the attached.)

9. There are at least a couple of ways to approach this. The law of sines can be used to find the length of another side. Given two sides and the angle between them, a formula gives area.

Law of Sines

... a/sin(A) = c/sin(C)

Multiplying by sin(C) gives

... c = sin(C)·a/sin(A) = 19·sin(64°)/sin(20°) ≈ 49.9301

The angle between sides a and c is B, which has the value ...

... B = 180° -A -C = 180° -20° -64° = 96°

Then the area of the triangle is ...

... Area = (1/2)ac·sin(B) = (1/2)(19)(49.9301)(0.994522) ≈ 471.737 ≈ 471.7

10. Heron's formula will give the area of a triangle from its side lengths.

... s = (a+b+c)/2 = (51+38+45)/2 = 67

... Area = √(s(s-a)(s-b)(s-c)) = √(67·16·29·22) = √683936 ≈ 827.004 ≈ 827.0

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

and you can see how the exponential growth is much faster than the linear one.

Answer:

D. 11.6 cm

Step-by-step explanation:

The missing length of the right angled triangle can be calculated using Pythagorean Theorem as shown below:

Where,

a = x cm

b = 11 cm

c = 16 cm

Thus:

(nearest tenth)

Answer:

Step-by-step explanation:

11.16