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noname [10]
3 years ago
11

Use sets A and B to answer the question.

Mathematics
1 answer:
olganol [36]3 years ago
6 0

A\cap B=\{2,4\}

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Find the coordinates of the midpoint of (x,y) for A(9,1) and B(3,7)
tekilochka [14]

9514 1404 393

Answer:

  (6, 4)

Step-by-step explanation:

The midpoint is found as the average of the coordinates of the end points.

  M = (A +B)/2

  M = ((9, 1) +(3, 7))/2 = (9+3, 1+7)/2 = (12, 8)/2

  M = (6, 4)

The midpoint of segment AB is (x, y) = (6, 4).

5 0
3 years ago
6 high school seniors choose from among 20 quotes for their yearbook. What is the probability that at least 2 of them choose the
shusha [124]

Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem, we have that:

  • There are 6 students, hence n = 6.
  • There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.

The probability of one quote being chosen at least two times is given by:

P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1).

Then:

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

P(X = 0) = C_{6,0}.(0.05)^{0}.(0.95)^{6} = 0.7351

P(X = 1) = C_{6,1}.(0.05)^{1}.(0.95)^{5} = 0.2321

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9672 = 0.0328

0.0328 = 3.28% probability that at least 2 of them choose the same quote.

More can be learned about the binomial distribution at brainly.com/question/24863377

6 0
2 years ago
The constant value of the ratio of two proportional quantities
Kitty [74]
Think it of a fraction problem,
5 0
3 years ago
Please please please help!
lys-0071 [83]

Answer:

6 pounds

Step-by-step explanation:

every 16 ounces =1 pound

so 96/16 = 6

6 *1 = 6

therefour 6 pounds

4 0
3 years ago
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals
Alekssandra [29.7K]

Answer:

(0.767,0.833)

Step-by-step explanation:

The 95% confidence interval for population proportion p can be computed as

p-z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }

The z-value associated with 95% confidence level is 1.96.

whereas p=x/n

We are given that x=440 and n=550.

p=440/550=0.8

0.8-1.96\sqrt{\frac{0.8(0.2)}{550} }

0.8-1.96\sqrt{\frac{0.16}{550} }

0.8-1.96\sqrt{0.00029 }

0.8-1.96(0.01706)

0.8-0.03343

0.76657

Thus, the required confidence interval is

0.767<P<0.833  (rounded to 3 decimal places)

Hence, we are 95% confident that our true population proportion will lie in the interval (0.767,0.833)

3 0
3 years ago
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