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3 years ago

Sum of Two Dice

Mathematics

1 answer:

stellarik [79]3 years ago

5 0

Answer:

a) Most frequent outcome of the experiment is 7

b) Least frequent is 2

Step-by-step explanation:

x= value of dice =7 is with highest frequency = 21

(b)

x = Value of dice = 2 is with least frequency = 1

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Complete the Square <br><br> y= 3x^2+12x+20

stepan [7]

Answer:

$y = 3({x + 2)}^{2} + 8$

Step-by-step explanation:

The given function is

$y = 3 {x}^{2} + 12x + 20$

Factor

$y = 3({x}^{2} + 4x )+ 20$

Create a perfect square trinomial

$y = 3({x}^{2} + 4x + 4 ) - 3 \times 4+ 20$

Factor the the perfect square

$y = 3({x + 2)}^{2} - 12+ 20$

The vertex form is:

$y = 3({x + 2)}^{2} + 8$

8 0

4 years ago

The roots of \[z^7 = -\frac{1}{\sqrt{2}} - \frac{i}{\sqrt{2}}\]are $\text{cis } \theta_1$, $\text{cis } \theta_2$, $\dots$, $\te

stepan [7]

Decoding the LaTeX that didn't render, we seek sum of the angles of the seventh roots of

$- \frac 1 {\sqrt 2} - \frac i {\sqrt{2}}$

That's on the unit circle, 45 degrees into the third quadrant, aka 225 degrees.

The seventh roots will all be separated by 360/7, around 51 degrees. The first seventh root has

$\theta_1 = 225^\circ / 7$

That's around 32 degrees.

The next angle is

$\theta_2 = \frac{1}{7}( 225^\circ + 360^\circ)$

The next one is

$\theta_3 = \frac{1}{7}( 225^\circ + 720^\circ)$

and in general

$\theta_n = \frac{1}{7}( 225^\circ + (n-1)360^\circ) = \frac 1 7(-135^\circ + 360^\circ n)$

$S = \displaystyle \sum_{n=1}^7 \theta_n = \frac{1}{7} \sum_{n=1}^7 -135^\circ + \frac{360}{7} \sum_{n=1}^7 n$

The first sum is just -135° since it's one seventh of the sum of seven -135s.

We have 1+2+3+4+5+6+7 = (1+7)+(2+6)+(3+5) + 4 = 28 so

$S = -135^\circ + 360^\circ (\frac{28} 7) = 4(360)-135 = 1305^\circ$

If I didn't screw it up, that means the answer is

Answer: 1305°

4 0

4 years ago

Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A

sammy [17]

Step-by-step explanation:

( secA + 1)( sec A - 1)

Using the expansion

( a + b)( a - b) = a² - b²

Expand the expression

We have

sec²A + secA - secA - 1

That's

sec² A - 1

From trigonometric identities

So we have the final answer as

As proven

Hope this helps you

7 0

3 years ago

Read 2 more answers

What is the value of n in the equation 1/2(n – 4) – 3 = 3 – (2n + 3)?

ozzi

(1/2)(n - 4) - 3 = 3 - (2n + 3
Distribute the (1/2) on the left and the -1 on the right.
(1/2)n - 2 - 3 = 3 - 2n - 3
Combine like terms.
(1/2)n - 5 = -2n
Add 2n to both sides and add 5 to both sides
2.5n = 5
Divide both sides by 2.5
n = 2

6 0

3 years ago

2 fractions that are the equivalent to 0.400

BaLLatris [955]

4/10 and 8/20 both are equivalent to 0.400

8 0

4 years ago

Read 2 more answers