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Alecsey [184]
3 years ago
8

Fish enter a lake at a rate modeled by the function E given by ( ) 20 15sin 6 t E t          . Fish leave the lake at a

rate modeled by the function L given by 2 0.1 L( ) 4 2 t t   . Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0). a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)? Give your answer to the nearest whole number.

Mathematics
1 answer:
liraira [26]3 years ago
5 0

Answer: The number of fish that enter the lake from midnight (t = 0) to 5 A.M. (t = 5) is 101 fish

Step-by-step explanation:

Given that

Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 2^0.1t2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).

(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)?

Please find the attached file for the solution

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30 is 60% of which of the following numbers?
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Answer:

50

Step-by-step explanation:

30 divided by 0.6 equals 50

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4 0
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3. Assume that the likelihood of a child under the age of ten watching PBS is 0.76. Three children are
natta225 [31]

Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549

More can be learned about the binomial distribution at brainly.com/question/24863377

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4 0
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A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.

<h3>What is a number line?</h3>

A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.

Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:

x + 4 ≥ 9

x ≥ 9 - 4

x ≥ 5.

This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.

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8 0
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What is the answer pls hurry!!
Mkey [24]

Answer:

the answer is 16.3452

Step-by-step explanation:

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Write the equation of the line in fully simplified slope-intercept form.
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Answer:

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Step-by-step explanation:

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