Write (2i(1+i)+5)/(1+3i) as a complete number in standard form.

Point A(1,9) and point B(−4,−3) are located within the coordinate plane.

AlekseyPX

Answer:

The answer to your question is 13 units

Step-by-step explanation:

Data

A (1, 9)

B (-4, -3)

distance = ?

Formula

distance = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}$

Substitution

distance = $\sqrt{(-4 - 1)^{2} + (-3 - 9)^{2}}$

Simplification

distance = $\sqrt{(-5)^{2} + (-12)^{2}}$

distance = $\sqrt{25 + 144}$

distance = $\sqrt{169}$

Result

distance = 13

8 0

2 years ago

Read 2 more answers

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au

Marta_Voda [28]

Answer:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:

$X \sim Binom(n=8, p=0.9)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

And for this case we want to find this probability:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

7 0

3 years ago

Read 2 more answers

Which of the below descriptions shows a possible HAMILTON PATH?

Vadim26 [7]

Option B: FECBAD is the Hamilton path

Explanation:

Given that ABCDEF is a graph with vertices A,B,C,D,E and F

We need to determine the Hamilton path.

Since, we know that a Hamilton path is a path that touches every vertex in a graph exactly once.

Option A: EFADECBA

The path touches the vertices E and A twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

The path touches every vertex in the graph exactly once.

Hence, the path FECBAD is a Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBD

The path touches the vertex A twice because when the path travels from F to B the only way to travel through A.

Hence, the path ADEFBD is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

The path touches the vertices E and A twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

8 0

3 years ago

The picture shows the Alamillo bridge in Seville, Spain. In the picture m<1=58 and m<2=24. Find the measure of the supplem

Anna11 [10]

Answer:

Supplement of <1 = 122°

Supplement of <2 = 156°

Step-by-step explanation:

Two pairs of angles are said to be supplementary, if their measures in degrees add up to give us 180°. A supplement of am angle is simply 180° - the measure of that angle.

Given that meadure of angle 1 = 58°, the supplement of angle 1 = 180° - 58° = 122°

Also, if the measure of angle 2 = 24°, the supplement of angle 2 = 180° - 24° = 156°.

Thus:

Supplement of <1 = 122°

Supplement of <2 = 156°

6 0

3 years ago

Tavon has a gift card for $45 that loses $2 for each 30-day period it is not used. He has another gift card for $35 that loses

leva [86]

Answer:

1

Step-by-step explanation:

7 0

3 years ago