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3 years ago

Which is the equation of the parabola?

Mathematics

1 answer:

Umnica [9.8K]3 years ago

4 0

Answer: $y=-\dfrac{1}{8}(x - 2)^2 - 3$

Step-by-step explanation:

The vertex form of a parabola is: y = a(x - h)² + k where

(h, k) is the vertex
$a=\dfrac{1}{4p}$

NOTE: p is the distance from the vertex to the focus

The vertex (h, k) is (2, -3)

$p=-2\quad \implies\quad a = \dfrac{1}{4(-2)}=-\dfrac{1}{8}$

Insert those values into the vertex formula to get:

$y=-\dfrac{1}{8}(x - 2)^2 - 3$

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4 years ago

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

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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:

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

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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

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

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

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P(x=5) = 0.215

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3 years ago

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3 years ago

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Sedbober [7]

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So we want to find the midpoint of the two number: 145.809 and 144.809, what we want to do it to find the difference between the two numbers and then divide it by 2 so we can find the halfway point:

145.809 - 144.809 = 1

^ So from this, we just have to add half of 1 or 0.5 to the smaller number:

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