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2 years ago

11

Tom has 4 navy socks and 6 black socks in a drawer. One dark morning he randomly pulls if 2 socks. What is the probability that

he will selects a pair of navy socks ?

2 answers:

andreyandreev [35.5K]2 years ago

4 0

1/5 probably he will choose 2 navy socks.

olganol [36]2 years ago

4 0

Answer:

1/5

Step-by-step explanation:

total number of socks= 10

randomly selects two socks.

2/10=1/5 probability

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Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

2 years ago

Find The Number of Combinations<br> 9C3

tiny-mole [99]

Answer:

Step-by-step explanation:

$9C3=\frac{9*8*7}{3*2*1} =84$

4 0

3 years ago

F the angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of th

Viktor [21]

<u>Given:</u>

The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.

We need to determine the height of the tree.

<u>Height of the tree:</u>

Let the height of the tree be h.

The height of the tree can be determined using the trigonometric ratio.

Thus, we have;

$tan \ \theta=\frac{opp}{adj}$

Substituting the values, we get;

$tan \ 34^{\circ}=\frac{h}{25}$

Multiplying both sides by 25, we have;

$tan \ 34^{\circ} \times 25=h$

$0.6745 \times 25=h$

$16.8625=h$

Rounding off to the nearest tenth of a foot, we get;

$16.9=h$

Thus, the height of the tree is 16.9 feet.

Hence, Option B is the correct answer.

7 0

2 years ago

20 POINS FOR ANSWER!!

inna [77]

Answer: the margin of error is 0.02

Step-by-step explanation:

Confidence interval for population proportion is written as

Sample proportion ± margin of error

If the confidence interval for this population proportion is (0.52, 0.56.), it means that the lower boundary is 0.52 and the upper boundary is 0.56

Let x represent the sample proportion and y represent the margin of error. Therefore,

x - y = 0.52

x + y = 0.56

Subtracting the second equation from the first equation, it becomes

- 2y = - 0.04

y = - 0.04/-2

y = 0.02

7 0

2 years ago

Read 2 more answers

Solve the problem. Round as appropriate.

Monica [59]

Answer:

i need the points

Step-by-step explanation:

8 0

2 years ago