If f(x) = 5x + 40, what is f(x) when x = -5?

charle [14.2K]

Obtuse angle. If wrong I’m sorry lol

5 0

3 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

3 years ago

Please help timed question (question included in photo). I'll mark as brainiest!

Shtirlitz [24]

Answer:

Step-by-step explanation:

This is a right triangle trig problem. Picture a right triangle. The height of the triangle is the height of the lighthouse, your distance from the base of the lighthouse is what we are solving for, and the reference angle is 2 degrees, which is the angle of inclination from where you stand to the top of this lighthouse. We have the reference angle, the side opposite the reference angle, and we are looking for the side adjacent to the reference angle. This is the tangent ratio: the side opposite the reference angle over the side adjacent to the reference angle. We know the measure of the reference angle and we know the value of the side opposite the reference angle. Filling in:

$tan(2)=\frac{200}{x}$ and

$x=\frac{200}{tan(2)}$ so

x = 5727.25 feet, the third choice down

8 0

3 years ago

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In Figure 1, the area of square A is 9 square units, the area of square B is 16 square units, and the area of square C is 25 squ

weqwewe [10]

Answer:

C. The sum of the areas of the two smaller squares is equal to the area of the larger square.

Step-by-step explanation:

9 + 16 = 25

36 + 64 = 100

25 + 144 = 169

The relations "less than" and "greater than" can be ruled out. These observations are consistent with selection C.

The triangle area is half the product of the square roots of the squares on the legs, so the areas of the triangles are (respectively) 6, 24, 30. These are not related to the sum of the smaller squares, so the last selection can also be ruled out.

7 0

3 years ago

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2x 5 The area of the rectangle shown is given by the function A()- 2 -5x lfthe width of the rectangle is 13, then the area is 42

PIT_PIT [208]

If you let x = 13:
Then, Area = 2(13)^2 - 5(13)
= 338 - 65
= 273 sq ft

If you let 2x-5 = 13:
2x = 18
x = 6

Then, Area = 2(6)^2 - 5(6)
= 72 - 30
= 42 sq ft

Therefore, your options are A or C. Your answer can be chosen based on what you assume the width to be. Good luck!

7 0

3 years ago