3. Who set up their equation correctly for the following question?

What is the additive identity of the complex number 14 + 5i?

Naddika [18.5K]

Answer: B) 0

Step-by-step explanation:

1. When you add complex numbers you must add the whole parts and then the imaginary parts.

2. One of the properties of complex numbers is called "Additive identity" which is represented by:

$0+0i$

3. Then, for the complex number $14+5i$ , you have:

$(14+5i)+(0+0i)=(14+0)+(5+0)i=14+5i$

4. Therefore, the answer is the option B.

7 0

1 year ago

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Here are the vertices of rectangle FROG: (−2,5), (−2,1), (6,5), (6,1). Find the perimeter of this rectangle. If you get stuck, t

user100 [1]

Answer:

26

Step-by-step explanation:

Distance between (-2,5) and (-2,1) is 5

Distance between (-2,5) and (6,5) is 8

Distance between (6,5) and (6,1) is 5

Distance between (6,1) and (-2,1) is 8

5+8+5+8=26

5 0

1 year ago

n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

4 0

1 year ago

A bamboo shoot is 20 inches tall at the zero and gross 24 inches each day which functions show below can be used to determine he

ale4655 [162]

It is definitely D because on part 1 n=24n+20 and if n equals 0 than 24 (0) +20= 20 and that is true. on part 2 if n =0 than 24 (0)+ 20 (0-1)=20 than 20 (-1)=20 -20= 20. that statement is false because-20 does not equal 20. AND for part 3 n=1 and f (1-1) + 24= 44 so f (0) + 24 =44 and keep in mind f (0) equals 20 so 44=44 because 24+20 is 44. so that is a true statement too

8 0

1 year ago

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Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks

kati45 [8]

Answer: The probability that the fourth marble Amy picks is black $=\frac{8}{15}$

The probability that in the fifth attempt she will pick a red or a black marble P(R∩B) = $\frac{5}{7}$

Step-by-step explanation:

To find the probability that in the fifth attempt she will pick a red or a black marble P(R∩B) .

The total marble in beginning=6+4+8=18

After 3 attempts, the total marbles left=18-3=15

The number of black marbles =8

The probability that the fourth marble Amy picks is black $=\frac{8}{15}$

As four marble has already picked up, then the total marbles left in the box

=18-4=14

Now, as a red marble is already picked in 1st attempt , the number of red marbles in the box now= 4-1=3

And a black marble is already picked in fourth attempt , the number of black marbles in the box now= 8-1=7

Now P(R∩B)=P(R)+P(B)= $\frac{3}{14}+\frac{7}{14}=\frac{10}{14}=\frac{5}{7}$

7 0

1 year ago