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snow_lady [41]
3 years ago
15

The function f(x) = 25(4)^x represents the growth of a bird population every year in a national park. Kyle wants to manipulate t

he formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Kyle's purposes?
Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
6 0

f(x)=25(4)^{\frac{x}{2}} will be the function to calculate population every half year.

Further explanation:

The given formula is:

f(x) = 25(4)^x

In the given formula, x represents the amount of time in years. So, in order to convert the given function for yearly calculation of population, to find the population every half year the time will be converted into half. This means that instead of x, x/2 will be used.

So the new function will be:

f(x) = 25(4)^{\frac{x}{2}}

Keywords: Population growth, Population growth function

Learn more about population growth at:

  • brainly.com/question/10689103
  • brainly.com/question/118412

#LearnwithBrainly

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Evaluate the expression below when x = 9 and y = 12. <br> 4(x + 6) - 3(y + 4)
Viefleur [7K]
The answer would be 12
8 0
2 years ago
A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day of sharpness. If any dull blade
Alex73 [517]

Answer:

Part a

The probability that assembly is replaced the first day is 0.7069.

Part b

The probability that assembly is replaced no replaced until the third day of evaluation is 0.0607.

Part c

The probability that the assembly is not replaced until the third day of evaluation is 0.2811.

Step-by-step explanation:

Hypergeometric Distribution: A random variable x that represents number of success of the n trails without replacement and M represents number of success of the N trails without replacement is termed as the hypergeometric distribution. Moreover, it consists of fixed number of trails and also the two possible outcomes for each trail.

It occurs when there is finite population and samples are taken without replacement.

The probability distribution of the hyper geometric is,

P(x,N,n,M)=\frac{(\limits^M_x)(\imits^{N-M}_{n-x})}{(\limits^N_n)}

Here x is the success in the sample of n trails, N represents the total population, n represents the random sample from the total population and M represents the success in the population.

Probability that at least one of the trail is succeed is,

P(x\geq1)=1-P(x

(a)

Compute the probability that the assembly is replaced the first day.

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly N = 48.

Number of blades selected at random from the assembly  n= 5

Number of blades in an assembly dull is M  = 10.

The probability mass function is,

P(X=x)=\frac{[\limits^M_x][\limits^{N-M}_{n-x}]}{[\limits^N_n]};x=0,1,2,...,n\\\\=\frac{[\limits^{10}_x][\limits^{48-10}_{5-x}]}{[\limits^{48}_5]}

The probability that assembly is replaced the first day means the probability that at least one blade is dull is,

P(x\geq 1)=1- P(x

(b)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly  N = 48

Number of blades selected at random from the assembly  N = 5

Number of blades in an assembly dull is  M = 10

From the information,

The probability that assembly is replaced (P)  is 0.7069.

The probability that assembly is not replaced is (Q)  is,

q=1-p\\= 1-0.7069= 0.2931

The geometric probability mass function is,

P(X = x)= q^{x-1} p; x =1,2,....=(0.2931)^{x-1}(0.7069)

The probability that assembly is replaced no replaced until the third day of evaluation is,

P(X = 3)=(0.2931)^{3-1}(0.7069)\\=(0.2931)^2(0.7069)= 0.0607

(c)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly   N = 48

Number of blades selected at random from the assembly  n = 5

Suppose that on the first day of the evaluation two of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M  = 2.

P(x=0)=\frac{(\limits^2_0)(\limits^{48-2}_{5-0})}{\limits^{48}_5}\\\\=\frac{(\limits^{46}_5)}{(\limits^{48}_5)}\\\\= 0.8005

Suppose that on the second day of the evaluation six of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M  = 6.

P(x=0)=\frac{(\limits^6_0)(\limits^{48-6}_{5-0})}{(\limits^{48}_5)}\\\\=\frac{(\limits^{42}_5}{(\limits^{48}_5)}\\\\= 0.4968

Suppose that on the third day of the evaluation ten of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M

= 10.

P(x\geq 1)=1- P(x

 

The probability that the assembly is not replaced until the third day of evaluation is,

P(The assembly is not replaced until the third day)=P(The assembly is not replaced first day) x P(The assembly is not replaced second day) x P(The assembly is replaced third day)

=(0.8005)(0.4968)(0.7069)= 0.2811

5 0
3 years ago
1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually.
DaniilM [7]

Answer:

Step-by-step explanation:

a) We would use the formula for exponential growth model which is expressed as

y = b(1 + r)^t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 5655

r = 1.4% = 1.4/100 = 0.014

Therefore, the equation would be

y = 5655(1 + 0.014)^t

y = 5655(1.014)^t

b) in 2022, t = 2022 - 2010 = 12 years

y = 5655(1.014)^12

y = 6682

6 0
3 years ago
How many centimeters are there in 75 meters?
kumpel [21]

Answer:

7500. There are 100 centimeters in a meter therefore 75 meters have 7500 centimeters.

3 0
3 years ago
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Which word describes the unit price​
Pavlova-9 [17]
The last one is right because it’s per 1 unit or in this case day
3 0
2 years ago
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