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3 years ago

Simplify x + 1/2 (x-5) =20

Mathematics

1 answer:

Aneli [31]3 years ago

5 0

Answer: x=15

Step-by-step explanation: Let's solve your equation step-by-step.

x+ 1 /2

(x−5)=20

Step 1: Simplify both sides of the equation.

x+ 1 /2

(x−5)=20

x+( 1 /2 )(x)+( 1 /2 )(−5)=20(Distribute)

x+ 1 /2

x+ −5 /2 =20

(x+ 1 /2 x)+( −5 /2 )=20(Combine Like Terms)

3 /2 x + −5 /2 =20

Step 2: Add 5/2 to both sides.

3 /2 x + −5 /2 + 5 /2 =20+ 5 /2

3 /2 x= 45 /2

Step 3: Multiply both sides by 2/3.

( 2 /3 )*( 3 /2 x)=( 2 /3 )*( 45 /2 )

x=15

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AveGali [126]

Answer:

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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:

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

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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

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

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

$P(x=5)=\frac{142506*15504}{1.207*10^{10} }=0.215$

P(x=5) = 0.215

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

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