In how many ways can we choose a 12 member jury from 30 possible people?

Answers

Answer 1

Answer: This is a problem dealing with permutations and combinations.
Order does not matter in this problem.
Since order doesn't matter, it is a combination.
Repetition matters, since you can't have the same person count as two people.

There are twelve slots.

_ _ _ _ _ _ _ _ _ _ _ _

Each slot needs to be multiplied by the next.

_*_*_*_*_*_*_*_*_*_*_*_

Now we have to fill in the slots.
Each slot will be filled with a number one less than the one before it. It has to be one less, since repetition matters.
The numbers will be decreasing from 30, since there are 30 possible people.

30 * 29 * 28 * 27 * 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19

Multiply these numbers together and you get your answer.

41,430,393,164,160,000 ways

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Which value must be added to the expression x2 + x to make it a perfect-square trinomial?

Answers

it need a lone number. so something like x2+x+3

Answer:

The answer is A.) 1/4

Step-by-step explanation:

Got it right on Edge.

What is slope (what does it mean) for anyone who answers they will get a brainliest

Answers

slope basically directs how steep a line is. it’s formula is rise/run of y2-y1/x2-x1

Answer:

rise over run

One of the most important things to understand about lines is the definition of slope. Slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the y-value between two points over the change in the x-value.

Step-by-step explanation:

Which of the following best explains why tan 5pi/6 does not equal to tan 5pi/3?A. The angles do not have the same reference angle.
B. Tangent is positive in the second quadrant and negative in the fourth quadrant.
C. Tangent is negative in the second quadrant and positive in the fourth quadrant.
D. The angles do not have the same reference angle or the same sign.

Answers

Option A. The angles do not have the same reference angle.

Explanation:

1) Angle 5π / 3 radians:

Convert radians to degrees: 5π/3 × 180° / π = 300°
300° is in the fourth quadrant
The reference angle for angles in the fourth quadrant is 360° - angle ⇒ 360° - 300° = 60°.
∴ The reference angle for this angle is 60°.

2) Angle 5π / 6 radians:

Convert radians to degrees: 5π/6 × 180° / π = 150°
150° is in the second quadrant
The reference angle for angles in the second quadrant is 180° - angle ⇒ 180° - 150° = 30°.
∴ The reference angle for this angle is 30°.

3) Conclusion:

Since the reference angles are different, the tangent ratios have different values.
tan (5π/3) = - tan(60°) = - √3
tan (5π/6) = - tan(30°) = - (√3)/3

Note that the tangent is negative in both second and fourth quadrants.

Answer:

The correct option is A.

Step-by-step explanation:

The first expression is,

$\tan ((5\pi)/(6))$

$\tan ((6\pi-\pi)/(6))$

$\tan (\pi-(\pi)/(6))$

The reference angle is $(\pi)/(6)$ . In second quadrant the sign of tangent is negative.

$-\tan ((\pi)/(6))$

$-(1)/(√(3))$

The second expression is,

$\tan ((5\pi)/(3))$

$\tan ((6\pi-\pi)/(3))$

$\tan (2\pi-(\pi)/(3))$

The reference angle is $(\pi)/(3)$ . In fourth quadrant the sign of tangent is negative.

$-\tan ((\pi)/(3))$

$-√(3)$

Since the sign are same but the reference angle is are different, therefore the correct option is A.

Let f(x)=8x and g(x)=8x+5+1.Which transformations are needed to transform the graph of f(x to the graph of g(x)?

Select each correct answer.

horizontal translation 1 unit left

vertical translation 1 unit down

vertical translation 5 units up

vertical translation 1 unit up

horizontal translation 5 units right

horizontal translation 5 units left

Answers

Transformation involves changing the form of a function

The transformations are:

vertical translation 1 unit up .
horizontal translation 5 units left.

The functions are given as:

$\mathbf{f(x) = 8x}$

$\mathbf{g(x) = 8(x + 5) + 1}$

Considering f(x), we have:

$\mathbf{f(x) = 8x}$

Start by translating the function 5 units left.

The rule of this translation is:

$\mathbf{f'(x) = f(x + 5)}$

So, we have:

$\mathbf{f'(x) = 8(x + 5)}$

Next, translate the function 1 unit up

The rule of this translation is:

$\mathbf{f''(x) = f'(x) + 1}$

So, we have:

$\mathbf{f''(x) = 8(x + 5) + 1}$

Rewrite as:

$\mathbf{g(x) = 8(x + 5) + 1}$

Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left

Answers

the equation above is a "pythagorean identity", and therefore, the left-side is indeed equal to the right-side.

what are the values of θ that make the equation true? well, all possible angles.

Determine the type and number of solutions of 4x^2-5x+1=0.A. Two real solutions
B. One real solution
C. Two imaginary solutions

Answers

4x² - 5x + 1 = 0
a = 4; b = - 5, c = 1
Δ = b² - 4.a.c
Δ = (-5)² - 4.4.1
Δ = 25 - 16
Δ = 9

x = - b ± √Δ / 2.a
$x = (-5\± √(9) )/(2*4)$
$x = (-5\±3)/(8)$
$x' = (-5-3)/(8) = (-8)/(8) = -1$
$x' = (-5+3)/(8) = (-2)/(8) (/2) = (-1)/(4)$

A. Two real solutions (x' = -1 and x'' = -1/4)

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