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Likurg_2 [28]
3 years ago
8

Which pairs of rational numbers are equivalent? Select all that apply.

Mathematics
2 answers:
Alla [95]3 years ago
5 0

Answer:

-0.5 and Negative one-half

11 over 20 and 0.55

negative 1 over 50 and -0.02

(A,C,D)

Step-by-step explanation:

Airida [17]3 years ago
4 0

Answer:

-0.5 and negative one-half

-1/50 and -0.02

Step-by-step explanation:

-0.5 can be rewritten as -5/10. This can be simplified to -1/2 which is the same as negative one-half.

7/10 isn't equivalent to 11/20. If you multiply 7/10 by 2/2 to get the denominator of 20, it will become 14/20 not 11/20.

-1/50 in decimal form is -0.02 so -1/50 and -0.02  are equivalent.

0.15 and 1/5 aren't equivalent because 1/5 in decimal form is is 0.2, not 0.15.

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A certain restaurant always overbooks. If possible. At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53
oee [108]

Answer:

The probability that the restaurant can accommodate all the customers who do show up is 0.3564.

Step-by-step explanation:

The information provided are:

  • At 7:00 pm the restaurant can seat 50 parties, but takes reservations for 53.
  • If the probability of a party not showing up is 0.04.
  • Assuming independence.

Let <em>X</em> denote the number of parties that showed up.

The random variable X follows a Binomial distribution with parameters <em>n</em> = 53 and <em>p</em> = 0.96.

As there are only 50 sets available, the restaurant can accommodate all the customers who do show up if and only if 50 or less customers showed up.

Compute the probability that the restaurant can accommodate all the customers who do show up as follows:

P(X\leq 50)=1-P(X>50)\\=1-P(X=51)-P(X=52)-P(X=53)\\=1-[{53\choose 51}(0.96)^{51}(0.04)^{53-51}]-[{53\choose 52}(0.96)^{52}(0.04)^{53-52}]\\-[{53\choose 53}(0.96)^{53}(0.04)^{53-53}]\\=1-0.27492-0.25377-0.11491\\=0.3564

Thus, the probability that the restaurant can accommodate all the customers who do show up is 0.3564.

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