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oee [108]
3 years ago
13

www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are footba

ll players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Mathematics
1 answer:
Mazyrski [523]3 years ago
8 0

Answer:

84%

Step-by-step explanation:

The probability that the selected player is a football player, P(F)=19%

The probability that the selected player is a basketball player, P(B)=79%

The probability that the selected player play both football and basketball,

P(B \cap F)=14\%

We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, P(B \cup F)

In probability theory

P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%

The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.

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A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear the
LenKa [72]

Answer:

a) The probability that at least 5 ties are too tight is P=0.0432.

b) The probability that at most 12 ties are too tight is P=1.

Step-by-step explanation:

In this problem, we could represent the proabilities of this events with the Binomial distirbution, with parameter p=0.1 and sample size n=20.

a) We can express the probability that at least 5 ties are too tight as:

P(x\geq5)=1-\sum\limits^4_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\geq5)=1-(0.1216+0.2702+0.2852+0.1901+0.0898)\\\\P(x\geq5)=1-0.9568=0.0432

The probability that at least 5 ties are too tight is P=0.0432.

a) We can express the probability that at most 12 ties are too tight as:

P(x\leq 12)=\sum\limits^{12}_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\leq 12)=0.1216+0.2702+0.2852+0.1901+0.0898+0.0319+0.0089+0.0020+0.0004+0.0001+0.0000+0.0000+0.0000\\\\P(x\leq 12)=1

The probability that at most 12 ties are too tight is P=1.

5 0
3 years ago
A store is having a sale on walnuts and chocolate chips. For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost
Jlenok [28]

Answer:

  • Walnuts  cost $1.75, chocolate chips cost $2.75

Step-by-step explanation:

<h3>Let the costs be:</h3>

  • Walnuts - x
  • Chocolate chips - y

<h3>Set equations as per question</h3>

For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost is $37:

  • 7x + 9y = 37

For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $17:

  • 5x + 3y = 17

<h3>Solve the system by elimination</h3>

Multiply the second equation by 3 and subtract the first equation, solve for x:

  • 3(5x + 3y) - (7x + 9y) = 3(17) - 37
  • 15x + 9y - 7x - 9y = 51 - 37
  • 8x = 14
  • x = 14/8
  • x = 1.75

Find the value of y:

  • 7*1.75 + 9y = 37
  • 12.25 + 9y = 37
  • 9y = 37 - 12.25
  • 9y = 24.75
  • y = 24.75/9
  • y = 2.75
6 0
2 years ago
Some help please? <br><br><br> Which polynomial represents the difference below?
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<em>So</em><em> </em><em>the</em><em> </em><em>right</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>of</em><em> </em><em>option</em><em> </em><em>D</em><em>.</em>

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<em>Hope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em>

4 0
3 years ago
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Lucas is making a banner that has an area of 2,046 square centimeters and has a length of 62 centimeters. Emily is making a bann
UkoKoshka [18]
B and c are correct because you use divison and multiplication to get the right answer and the right answer is 99cm
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zloy xaker [14]

Answer:

45 degrees

Step-by-step explanation:

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