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Alenkinab [10]
2 years ago
10

A.)23 B.)60 C.)53 D.)30

Mathematics
1 answer:
olga_2 [115]2 years ago
6 0

Answer:

ABC = 30

Step-by-step explanation:

The two angles are complementary so they add to 90 degrees

2x+14  + x+7  = 90

Combine like terms

3x+21 = 90

Subtract 21 from each side

3x+21-21 = 90-21

3x = 69

Divide by 3

3x/3 = 69/3

x = 23

ABC = x+7 = 23+7 = 30

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Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg sm
GuDViN [60]
Answer: 0.951%

Explanation:

Note that in the problem, the scenario is either the adult is using or not using smartphones. So, we have a yes or no scenario involved with the random variable, which is the number of adults using smartphones. Thus, the number of adults using smartphones follows the binomial distribution.

Let x be the number of adults using smartphones and n be the number of randomly selected adults. In Binomial distribution, the probability that there are k adults using smartphones is given by

P(x = k) = \frac{n!}{k!(n-k)!}p^k (1-p)^{n-k}

Where p = probability that an adult is using smartphones = 54% (since 54% of adults are using smartphones). 

Since n = 12 and k = 3, the probability that fewer than 3 are using smartphones is given by

P(x \ \textless \  3) = P(x = 0) + P(x = 1) + P(x = 2)
\\ \indent = \frac{12!}{0!(12-0)!}(0.54)^0 (1-0.54)^{12-0} + \frac{12!}{1!(12-1)!}(0.54)^1 (1-0.54)^{12-1} + \\ \indent \frac{12!}{2!(12-2)!}(0.54)^2 (1-0.54)^{12-2}
\\
\\ \indent = \frac{12!}{(1)(12!)}(0.46)^{12} + \frac{12(11!)}{(1)(11!)}(0.54)(0.46)^{11}+ \frac{12(11)(10!)}{(2)(10!)}(0.54)^2(0.46)^{10}
\\
\\ \indent = (1)(0.46)^{12} + (12)(0.54)(0.46)^{11}+ (66)(0.54)^2(0.46)^{10}
\\ \indent \boxed{P(x \ \textless \  3) \approx 0.00951836732 }


Therefore, the probability that there are fewer than 3 adults are using smartphone is 0.00951 or 0.951%.


5 0
3 years ago
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