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3 years ago

Find the product of each pair of complex conjugates. (3 + 8i)(3 – 8i) =

Mathematics

1 answer:

VMariaS [17]3 years ago

8 0

Step-by-step explanation:

By Difference of Squares,

a² - b² = (a + b)(a - b).

=> (3 + 8i)(3 - 8i) = 3² - (8i)²

= 9 - 64i² = 9 - 64(-1) = 73.

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40% of Oatypop cereal boxes contain a prize. Hannah plans to keep buying cereal until she gets a prize. What is the probability

aleksley [76]

Answer:

$(0.6)^{n}+n(0.4)(0.6)^{n-1}+\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}$

Step-by-step explanation:

We will use the binomial distribution. Let X be the random variable representing the no. of boxes Hannah buys before betting a prize.

Our success is winning the prize, p =40/100 = 0.4

Then failure q = 1-0.4 = 0.6

Hannah keeps buying cereal boxes until she gets a prize. Then n be no. times she buys the boxes.

P(X ≤ 3) = P(X=0) +P(X=1)+P(X=2)+P(X=3)

= $\binom{n}{0}p^{0}q^{n-0}$ + $\binom{n}{1}p^{1}q^{n-1}$ + $\binom{n}{2}p^{2}q^{n-2}$ + $\binom{n}{3}p^{3}q^{n-3}$

= $q^{n}+npq^{n-1}$ + $\frac{n(n-1)(p)^{2}q^{n-2}}{2}$ + $\frac{n(n-1)(n-2)p^{3}q^{n-3}}{6}$

= $(0.6)^{n}+n(0.4)(0.6)^{n-1}+[tex]\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}$

7 0

3 years ago

Read 2 more answers

Phillip's Soup Kitchen charges the same price, $8.95, for a bowl of any of their soups. The Rag-dale Family Reunion was being he

777dan777 [17]

P = 8.95R Hope this helps!!

8 0

4 years ago

7/2x+1/2x = 18+ 9/2x

chubhunter [2.5K]

Answer:

x=-36

Step-by-step explanation:

Add the 7/2x +1/2x to be 8/2x which means that it'll be 4x=18=9/2

then subtract 9/2x on both sides so itll be

$4x=18+\frac{9}{2} x$

-9/2x -9/2x

$-\frac{1}{2} x=18$ because if you do 8/2-9/2 it's -1/2

then multiply the reciprocal to both sides so

$(\frac{2}{-1})(-\frac{1}{2}x)=(\frac{2}{-1})(18)$

which then cancels out -1/2 and makes it

x=-36

4 0

4 years ago

OAB is a sector of a circle <br>what is the area of the sector

oee [108]

Answer:

12.56 square cm

Step-by-step explanation:

$Central \:angle \:(\theta) = 40°\\Radius \: (r) = 6 cm$

Let A be the area of the sector of circle.

$\therefore \: A = \frac{\theta }{360 \degree} \times \pi {r}^{2} \\ \\= \frac{ 40 \degree}{360 \degree} \times 3.14\times {6}^{2} \\ \\ = \frac{ 1}{9} \times 3.14 \times 36 \\ \\ = 3.14 \times 4 \\ \\ = 12.56 \: {cm}^{2}$

6 0

3 years ago

Read 2 more answers

What is the inverse of f(x)=(4x-3)/7

iragen [17]

Answer:

f(x)^-1 = $\frac{1}{28} x + \frac{3}{4}$

Step-by-step explanation:

f(x) = (4x - 3) / 7

y = (4x - 3) / 7

x = (4y - 3) / 7

x / 7 = 4y - 3

x/7 + 3 = 4y

y = $\frac{1}{28} x + \frac{3}{4}$

5 0

2 years ago