Please help, refer to the picture for information.

Mathematics

1 answer:

aleksklad [387]3 years ago

5 0

Answer:

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)

d = $\sqrt{(4+1)^2+(1-4)^2}$

= $\sqrt{5^2+(-3)^2}$

= $\sqrt{25+9}$ = $\sqrt{34}$ → b

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A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that 5 of the 10

AveGali [126]

Answer:

The probability of drawing 5 gumdrops in 10 picks from the dish is 0.215

Step-by-step explanation:

A hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws with each draw being a success or failure, without replacement from a finite population size that contains exactly the same objects. The general formula is given as:

$h(x) =\frac{({A}C_{x})({N-A}C_{n-x})}{^{N}C_{n} }$

where:

$^{n}C_{r}=\frac{n!}{(n-r)!r!}$

h(x) is the probability of x successes,

n is the number of attempts,

A is the number of successes

N is the number of elements

For this problem:

A = 30, x = 5, N = 50, n = 10

The probability of drawing 5 gumdrops in 10 picks from the dish P(x=5) is

$P(x=5)=\frac{({30}C_{5})({50-30}C_{10-5})}{^{50}C_{10} }\\P(x=5)=\frac{({30}C_{5})({20}C_{5})}{^{50}C_{10} }$

$P(x=5)=\frac{\frac{30!}{(30-5)!5!}*\frac{20!}{(20-5)!5!} }{\frac{50!}{(50-10)!10!} }\\P(x=5)=\frac{\frac{30!}{25!5!}*\frac{20!}{15!5!} }{\frac{50!}{40!10!} }$