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VLD [36.1K]
3 years ago
13

Which of the following is perfect square trinomial. Ive asked 4 times. Please Help. Will give brainlilest

Mathematics
1 answer:
Nutka1998 [239]3 years ago
6 0

Answer:

D

Step-by-step explanation:

a perfect square trinomial is

a^2x^2\pm2(ab)xy+b^2y^2

factorized is

(ax\pm by)^2

so as you can see option A and B can't be, because they have -49y^2 and it has to be plus

so the other options are C and D

in the trinomial a=4 and b=\pm 7

the roots of a^2 and b^2

\pm2abxy=\pm2(4)(7)xy\\\\=\pm56xy

so it's option d with b=-7

16x^2-56xy+49y^2

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United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the n
Ivanshal [37]

Answer:

<u><em>a) The probability that exactly 4 flights are on time is equal to 0.0313</em></u>

<u><em></em></u>

<u><em>b) The probability that at most 3 flights are on time is equal to 0.0293</em></u>

<u><em></em></u>

<u><em>c) The probability that at least 8 flights are on time is equal to 0.00586</em></u>

Step-by-step explanation:

The question posted is incomplete. This is the complete question:

<em>United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the number on-time flights is recorded. Round answers to 3 significant figures. </em>

<em>a) The probability that exactly 4 flights are on time is = </em>

<em>b) The probability that at most 3 flights are on time is = </em>

<em>c)The probability that at least 8 flights are on time is =</em>

<h2>Solution to the problem</h2>

<u><em>a) Probability that exactly 4 flights are on time</em></u>

Since there are two possible outcomes, being on time or not being on time, whose probabilities do not change, this is a binomial experiment.

The probability of success (being on time) is p = 0.5.

The probability of fail (note being on time) is q = 1 -p = 1 - 0.5 = 0.5.

You need to find the probability of exactly 4 success on 9 trials: X = 4, n = 9.

The general equation to find the probability of x success in n trials is:

           P(X=x)=_nC_x\cdot p^x\cdot (1-p)^{(n-x)}

Where _nC_x is the number of different combinations of x success in n trials.

            _nC_x=\frac{x!}{n!(n-x)!}

Hence,

            P(X=4)=_9C_4\cdot (0.5)^4\cdot (0.5)^{5}

                                _9C_4=\frac{4!}{9!(9-4)!}=126

            P(X=4)=126\cdot (0.5)^4\cdot (0.5)^{5}=0.03125

<em><u>b) Probability that at most 3 flights are on time</u></em>

The probability that at most 3 flights are on time is equal to the probabiity that exactly 0 or exactly 1 or exactly 2 or exactly 3 are on time:

         P(X\leq 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

P(X=0)=(0.5)^9=0.00195313 . . . (the probability that all are not on time)

P(X=1)=_9C_1(0.5)^1(0.5)^8=9(0.5)^1(0.5)^8=0.00390625

P(X=2)=_9C_2(0.5)^2(0.5)^7=36(0.5)^2(0.5)^7=0.0078125

P(X=3)= _9C_3(0.5)^3(0.5)^6=84(0.5)^3(0.5)^6=0.015625

P(X\leq 3)=0.00195313+0.00390625+0.0078125+0.015625=0.02929688\\\\  P(X\leq 3) \approx 0.0293

<em><u>c) Probability that at least 8 flights are on time </u></em>

That at least 8 flights are on time is the same that at most 1 is not on time.

That is, 1 or 0 flights are not on time.

Then, it is easier to change the successful event to not being on time, so I will change the name of the variable to Y.

          P(Y=0)=_0C_9(0.5)^0(0.5)^9=0.00195313\\ \\ P(Y=1)=_1C_9(0.5)^1(0.5)^8=0.0039065\\ \\ P(Y=0)+P(Y=1)=0.00585938\approx 0.00586

6 0
3 years ago
Sam scored 43, 48, and 42 points on three tests. How many points should he get on the fourth test to get an average score of 50?
tatiyna

So we know that an average is the sum of the scores divided by the number of scores that were added together. In this case we are going to be dealing with 4 tests. So let's say x is the score for our fourth test. We can create this equation:

\frac{x+43+48+42}{4}=50

So then we need to simplify the top:

\frac{x+133}{4}=50

Then multiply by 4 on both sides to get rid of the denominator:

x+133=200

Then solve for x:

x=67

So now we know that Sam needs to score a 67 on the fourth test to have an average score of 50.

6 0
3 years ago
Read 2 more answers
If someone could help it would be great :)
malfutka [58]

Answer:

2.2

Step-by-step explanation:

<u>  -6-5  </u> = -11/-5=2.2

-9-(-4)

3 0
3 years ago
A triangle has an area of 90 and a height of 10. What is the base
Dima020 [189]
The base would be equal to 18

5 0
3 years ago
The Statue of Liberty is approximately 300 feet high, including the base upon
insens350 [35]

Answer:

The state itself is 50% of the total height.

Explanation:

Well, if the height including the base is 300 ft, that'd mean the total height of the statue itself is (300-150) ft = 150 ft.

Thus, it is (150/300)*100% = 50% of the total height.

8 0
2 years ago
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