1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitry [639]
3 years ago
6

Perform the indicated operations. Write the answer in standard form, a+bi. (8 - i)^2 + (8 + i)^2

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
4 0

Answer:

{(8 - i)}^{2}  +  {(8 + i)}^{2}  \\   \\ thank \: you

You might be interested in
Thank you so much, my friend
ss7ja [257]

Answer:

Step-by-step explanation:

This is quite a doozy, my friend. We will set up a d = rt table, fill it in...and pray.

The table will look like this before we even fill anything in:

            d        =        r        *        t

SUV

sedan

Ok now we start to pick apart the problem. Motion problems are the hardest of all story problems ever. This is because there are about 100 ways a motion problem can be presented. So far what we KNOW for an indisputable fact is that the distance from Georgetown to Greenville is 120 km. So we fill that in, making the table:

             d      =      r      *      t

SUV     120

sedan  120

The next part is derived from the sentence "After an hour, the SUV was 24 km ahead of the sedan." This tells us the rate of the SUV in terms of the sedan. If the SUV is 24 km ahead of the sedan in 1 hour, that tells us that the rate of the sedan is r and the rate of the SUV is r + 24 km/hr. BUT we have other times in this problem, one of them being 25 minutes. We have a problem here because the times either have to be in hours or minutes, but not both. So we will change that rate to km/min. Doing that:

24 \frac{km}{hr} × \frac{1hr}{60min}=.4\frac{km}{min} So now we can fill in the rates in the table:

            d      =      r      *      t

SUV    120    =   r + .4

sedan 120    =     r

They left at the same time, so now the table looks like this:

             d      =      r      *      t

SUV    120     =   r + .4  *      t

sedan  120    =      r      *      t

We will put in the time difference of 25 minutes in just a sec.

If d = rt, then the equation for each row is as follows:

SUV:   120 = (r + .4)t

sedan:   120 = rt

Since the times are the same (because they left at the same time, we will set the equations each equal to t. The distances are the same, too, I know that, but if we set the distances equal to each other and then solve the equations for a variable, the distances cancel each other out, leaving us with nowhere to go. Trust me, I tried that first! Didn't work.

Solving the first equation for time:

sedan:  \frac{120}{r}=t  That's the easy one. Now the SUV. This is where that time difference of 25 minutes comes in from the last sentence. Let's think about what that sentence means in terms of the times of each of these vehicles. If the sedan arrived 25 minutes after the SUV, then the sedan was driving 25 minutes longer; conversely, if the sedan arrived 25 minutes after the SUV, then the SUV was driving 25 minutes less than the sedan. The latter explanation is the one I used in the equation. Again, if the SUV was driving 25 minutes less than the sedan, and the equations are solved for time, then the equation for the SUV in terms of time is

\frac{120}{r+.4}=t-25 and we solve that for t:

\frac{120}{r+.4}+25=t

Again, going off the fact that times they both leave are the same, we set the equations equal to one another and solve for r:

\frac{120}{r+.4}+25=\frac{120}{r}

I began by first multiplying everything through by (r + .4) to get rid of it in the denominator. Doing that:

[r+.4](\frac{120}{r+.4}) +[r+.4](25)=[r+.4](\frac{120}{r}) which simplifies very nicely to

120+25(r+.4)=\frac{120}{r}(r+.4)  So maybe it's not so nice. Let's keep going:

120+25r+10=\frac{120r}{r}+\frac{48}{r} and keep going some more:

130+25r=120+\frac{48}{r} and now we multiply everything through by r to get rid of THAT denominator:

r(130)+r(25r)=r(120)+r(\frac{48}{r}) giving us:

130r+25r^2=120r+48 Now we have a second degree polynomial we have to solve by factoring. Get everything on one side and factor using the quadratic formula.

25r^2+10r-48=0

That factors to

r = 1.2 and r = -1.6 and both of those rates are in km/minute. First of all, we cannot have a negative rate (this is not physics where we are dealing with velocity which CAN be negative) so we throw out the -1.6 and convert the rate of 1.2 km/minute back to km/hr:

1.2\frac{km}{min} × \frac{60min}{1hr} and we get

r = 72 km/h, choice B.

Wow...what a pain THAT was, right?!

5 0
2 years ago
The probability distribution of the amount of memory X (GB) in a purchased flash drive is given below. x 1 2 4 8 16 p(x) .05 .10
Rama09 [41]

Answer:

a) E(X) = 6.45

b) E(X^{2} )= 57.25

c) V(X) = 15.648

d) E(3X + 2) = 21.35

e) E(3X^{2} +2) = 173.75

f) V(3X+2) = 140.832

g) E(X+1) = 7.45

h) V(X+1) = 15.648

Step-by-step explanation:

a) E(X) = \sum xP(x)

E(X) = (1*0.05) + (2*0.10) + (4*0.35) + (8*0.40) + (16*0.10)\\E(X) = 6.45

b)

E(X^{2} ) = (1^{2} *0.05) + (2^{2} *0.10) + (4^{2} *0.35) + (8^{2} *0.40) + (16^{2} *0.10)\\  E(X^{2} )= 57.25

c)

V(X) = E(X^{2} ) - (E(X))^{2} \\V(X) = 57.25 - 6.45^{2} \\V(X) = 15.648

d)

E(3X+2) = 3E(X) + 2\\E(3X+2) = (3*6.45) + 2 \\E(3X+2) = 21.35

e)

E(3X^{2} +2) = 3E(X^{2} ) + 2\\E(3X^{2} +2) = (3*57.25) + 2 \\E(3X^{2} +2) = 173.75

f)

V(3X+2) = 3^{2} V(X)\\V(3X+2) = 9*15.648\\V(3X+2) = 140.832

g)

E(X+1) = E(X) + 1\\E(X+1) = 6.45 + 1\\E(X+1) =7.45

h)

V(X+1) = 1^{2} V(X)\\V(X+1) = 15.648

6 0
3 years ago
For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5
Keith_Richards [23]

Answer:

a) n = 50, p = \frac{1}{6}

b) n = 16, p = \frac{1}{100}

c) n = 26, p = 0.25, \mu = 6.5

Step-by-step explanation:

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 combinatios 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.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so n = 50.

Each roll can have 6 outcomes. So the probability that 5 is rolled is p = \frac{1}{6}

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so n = 16.

1 of 100 are winners. So p = \frac{1}{100}.

(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.

He plays 26 games, so n = 26.

He wins 25% of the time, so p = 0.25

We have that \mu = np. So \mu = 26*0.25 = 6.5

6 0
3 years ago
Round off then estimate 18.9*5.2
Nataly [62]
18.9 rounded is 19
5.2 rounded is 5

19 * 5 = 95
7 0
3 years ago
Mr. Owens' printer can print 55 pages in 30 minutes. How many pages can it print In 1 hour?
miskamm [114]

Answer:

110 pages

Step-by-step explanation:

The rate of 55 pg in 30 minutes is given in "minutes".

Thus,

we need to convert 1 hour to minutes.

We know 1 hour = 60 minutes

Note: 30 mins * 2 = 60 minutes

Logically, 30 minutes makes 55 pages, so 60 minutes (30 * 2) will make 55 * 2 = 110 pages

So, in 1 hour, it can print 110 pages (at this rate)

8 0
3 years ago
Other questions:
  • How would you type out how you showed your work
    11·2 answers
  • How to use the proper formula
    13·2 answers
  • Which of the following sets are continuous?
    9·1 answer
  • What was the value of the third check Tony deposited?
    15·1 answer
  • Can you help with 14 please
    12·1 answer
  • What’s the answer please someone ?
    9·1 answer
  • Assume n is an integer and solve for n.
    10·1 answer
  • *20 POINTS PLEASE HELP!!!!!!*
    9·1 answer
  • What is the measure?
    10·1 answer
  • Please answer these questions: are they rational or irrational numbers?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!