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podryga [215]
3 years ago
8

The number of bacteria in petri dish A doubles every 10 minutes. The number of bacteria in oetri dish B doubles every 6 minites.

If both petri dishes begin with the same number of bacteria, how mmau times greater will the number of bacteria in petri dish b be than the number of bacteria in petri dish A after one hour?
Mathematics
1 answer:
marissa [1.9K]3 years ago
7 0
Givens
Petri Dish A sees a double ever 10 minutes
Petri Dish B sees a double ever 6 minutes

Consequences
A doubles 60 / 10 = 6 times.
B doubles 60 / 6 = 10 times.

Solution
If you work best with numbers then suppose there are 100 bacteria in both dishes at the beginning
A = 100 * 2^6
B = 100 * 2^10

A will have 100 * 64 = 6400 bacteria growing inside A
B will have 100 * 1024 = 102400 bacteria growing inside B

B/A = 102400 / 6400 = 16

There are 16 times as many in B than in A. <<<< Answer

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32​% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a
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Answer:

a) P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

b) P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

c) P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.32)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

Part b

P(X> 2)=1-P(X\leq 2)=1-[P(X=0)+P(X=1)+P(X=2)]

P(X=0)=(10C0)(0.32)^0 (1-0.32)^{10-0}=0.0211  

P(X=1)=(10C1)(0.32)^1 (1-0.32)^{10-1}=0.0995

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

Part c

P(2 \leq x \leq 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X=3)=(10C3)(0.32)^3 (1-0.32)^{10-3}=0.264

P(X=4)=(10C4)(0.32)^4 (1-0.32)^{10-4}=0.218

P(X=5)=(10C5)(0.32)^5 (1-0.32)^{10-5}=0.123

P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

The formula for Percentage increase is

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Increase = Current Amount - Initial Amount

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Increase = $300,000

Percentage Increase =

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The percent increase in home value in those 50 years is 1500%

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