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 + 20.1t2. 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)? Give your answer to the nearest whole number.
(b) What is the average number of fish that leave the lake per hour over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)?
(c) At what time t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify your answer.
(d) Is the rate of change in the number of fish in the lake increasing or decreasing at 5 A.M. (t = 5)? Explain your reasoning.

In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

learn more about positive growth from

https://brainly.com/question/1437549

#SPJ1

The solution to the inequality algebraically is -9 < x < 12

From the question, we have the following parameters that can be used in our computation:

negative 2 less-than startfraction x over 3 endfraction 1 less-than 5

Express the statement using numbers and expressions

So, we have the following representation

-2 < x/3 + 1 < 5

Subtract 1 from all sides of the inequality

This gives

-3 < x/3 < 4

Multiply through the inequality by 3

So, we have

-9 < x < 12

Hence, the solution is -9 < x < 12

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Answer:

b. Negative 9 less-than x less-than 12

Step-by-step explanation:

True. In compound time signatures, the top number represents the number of beats per measure. Compound time signatures are typically used for music that has a more complex rhythmic structure, and they are characterized by the subdivision of each beat into three equal parts (known as triplets).

The most common compound time signatures are 6/8, 9/8, and 12/8, with each representing six, nine, and twelve beats per measure respectively.
In 6/8 time, for example, there are two beats per measure, each of which is subdivided into three equal parts. This results in a feeling of two larger beats, each consisting of three smaller beats. In 9/8 time, there are three beats per measure, each of which is subdivided into three equal parts. This results in a feeling of three larger beats, each consisting of three smaller beats. Similarly, in 12/8 time, there are four beats per measure, each of which is subdivided into three equal parts, resulting in a feeling of four larger beats, each consisting of three smaller beats.
Overall, the top number in a compound time signature represents the number of larger beats per measure, while the bottom number represents the duration of each beat (usually an eighth note).

To learn more about time signatures, refer:-

https://brainly.com/question/29729191

#SPJ11

The value of x as required to be determined in the task content is; 10.7°.

It follows from the task content that the value of x is to be determined from the task content.

Since the given figure is such that the lines MN and MP are tangents to the circle; the assertion which holds is that <MLP and <MNP are supplementary angles.

On this note, it follows that;

73° + x° = 180°.

On this note;

x = 180 - 73

x = 107°.

Read more on supplementary angles;

https://brainly.com/question/98418

#SPJ1

Answer:

A) 8inches long and 4 inches wide

Step-by-step explanation:

perimeter is the measurement of the outside of the shape. So for a quilt that'd be 2 lengths and 2 widths. 8+8=16 4+4=8, 16+8=24

Answer:

Lateral surface area = 154cm²

Step-by-step explanation:

h = 10cm

pi = 22/7

base area = 154cm²

2πrh = 154cm²

2 × 22/7 × r × 10 = 154

440/7 × r = 154

r = 154 ÷ 440/7 = 2.45

r = 2.45

LSA of right circular cylinder = 2πrh

2 × 22/7 × 2.45 × 10

44/7 × 24.5 = 1078/7

1078/7 = 154

Therefore, lateral surface area = 154cm²

Hope it helps:)

Answer:

I don't think there would be any asymptotes because there are no denominators.

Step-by-step explanation:

The probability that a student makes more than 7 mistakes on the exam is 0.39.

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. T

Now, let X be the number of mistakes a student makes on the exam. Then, the X follows a binomial distribution with n=16 and some unknown probability of success p (i.e., the probability of answering a question correctly).

We know that P(X<5) = 0.47 and P(5<=X<=7) = 0.14. Using the complement rule, we can find P(X>7) as follows:

P(X>7) = 1 - P(X<=7)

= 1 - P(X<5) - P(5<=X<=7)

= 1 - 0.47 - 0.14

= 0.39. Therefore, the probability that a student makes more than 7 mistakes on the exam is 0.39.

Read more about probability

brainly.com/question/24756209

#SPJ1

Answer:

7. m=3 b=-4

Equation y=3x-4

8. m=-6/4 b=7

Equation y=-6/4x+7

Step-by-step explanation:

Answer:

7. m=3 b= -4 , Equation y=3x-4

8. m= -6/4 b=7 , Equation y=-6/4x+7

Step-by-step explanation:

look in the chart

Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

Answer:

4

Step-by-step explanation:

2/3 = 4/6

1/3 = 2

2/3 = 4

3/3 = 6

Yes, it can be concluded that attending the 3 months exercise program will significantly reduce weight. As the confidence interval doesn't contain zero, which means the difference in weight before and after the exercise program is statistically significant.

a) Statistical analysis used for this study is Paired sample t-test.

b) A is 1.980 and B is 6.858

c) A 95% confidence interval is defined by the formula, CI = (X-Y) ± tα/2 * (S/√n)

Where, X = Mean of weight before starting the exercise program,

Y = Mean of weight after the exercise program,

S = Standard deviation,

tα/2 = t-distribution at alpha level of 0.05,

n = Number of sample pairs

CI = (6.858) ± 2.201 * (1.759/√12)

CI = (6.858) ± 1.784CI = (5.074, 8.642)

Therefore, the 95% confidence interval for the mean difference in weight before and after the 3 months exercise program is (5.074, 8.642).

a) Yes, it can be concluded that attending the 3 months exercise program will significantly reduce weight. As the confidence interval doesn't contain zero, which means the difference in weight before and after the exercise program is statistically significant.

To know more about Statistical analysis visit: https://brainly.com/question/30154483

#SPJ11

Answer:

Area of the rhombus ABCD = 16 square units

Step-by-step explanation:

Area of a rhombus = \(\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})\)

From the graph attached,

Diagonal 1 = Distance between the points A and C

Diagonal 2 = Distance between the points B and D

Length of a segment between (x₁, y₁) and (x₂, y₂) = \(\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }\)

Diagonal 1 (AC) = \(\sqrt{(4-0)^2+(-1+1)^2}\) = 4 units

Diagonal 2(BD) = \(\sqrt{(2-2)^2+(3+5)^2}\) = 8 units

Now area of the rhombus ABCD = \(\frac{1}{2}(\text{AC})(\text{BD})\)

                                                       = \(\frac{1}{2}\times 4\times 8\)

                                                       = 16 units²

Therefore, area of the given rhombus is 16 units².

Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

Learn more about the equation of a line having 2 points:

brainly.com/question/16137599

#SPJ1

Answer:

C

Step-by-step explanation:

AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.

The given triangles ΔABC and ΔLMN are similar by AA postulate.

A triangle is a three sided polygon that consist of three edges and three vertices .

Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.

Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.

Hence two triangles are similar by AA postulate.

Thus two triangles are similar by AA postulate. So option (C) is correct.

To learn more about triagles click here:

https://brainly.com/question/24147586

#SPJ7

Answer:

A) 14

Step-by-step explanation:

Nuts:

\(\frac{6}{\frac{1}{3} }\) = \(\frac{6}{1}\) ÷ \(\frac{1}{3}\)  Get a common denominator of 3 and divide

\(\frac{18}{3}\) ÷ \(\frac{1}{3}\) = \(\frac{\frac{18}{1} }{\frac{3}{3} }\) = \(\frac{18}{1}\) = 18

We can make 18 bags with the amount of nuts given.

Raisins:

\(\frac{8}{\frac{1}{4} }\) = 8 ÷\(\frac{1}{4}\)  Gert a common denominator of 4 and divide

\(\frac{32}{4}\) ÷ \(\frac{1}{4}\) = \(\frac{\frac{32}{1} }{\frac{4}{4} }\) = \(\frac{32}{1}\) = 32

We can make 32 bags with the amount of raisins given.

32 - 18 = 14

14 more bags need nuts agged.

1/5 cups of sugar.

have a nice day

We can make the conclusion that the series ∑ 3cos(n)/n is convergent.

The series ∑ 3cos(n)/n satisfies the conditions of the integral test if we consider the function f(x) = 3cos(x)/x.

Using integration by parts, we can find that the integral of f(x) from 1 to infinity is equal to 3sin(1) + 3/2 ∫1^∞ sin(x)/x^2 dx.

Since the integral ∫1^∞ sin(x)/x^2 dx converges (as it is a known convergent integral), we can conclude that the series ∑ 3cos(n)/n also converges by the integral test.

Using the Integral Test, we can determine the convergence or divergence of the series ∑ (3cos(n)/n) from n=1 to infinity. The Integral Test states that if a function f(n) is continuous, positive, and decreasing for all n≥1, then the series ∑ f(n) converges if the integral ∫ f(x)dx from 1 to infinity converges, and diverges if the integral diverges.

In this case, f(n) = 3cos(n)/n. Unfortunately, this function is not always positive, as the cosine function oscillates between -1 and 1. Due to this property, the Integral Test is not applicable to the given series, and we cannot draw any conclusions about its convergence or divergence using this test.

Learn more about integration here: brainly.com/question/18125359

#SPJ11

Answer:

yeah its 93 after being rounded

Step-by-step explanation:

already did it and commented i was just wondering what else there was cause it seemed like there was more.

Given that tan(x) = −5/12 and x is in quadrant IV, we can use trigonometric identities to find the exact values of the expressions without solving for x.

We can begin by drawing a reference triangle in the fourth quadrant, with the opposite side equal to -5 and the adjacent side equal to 12. Using the Pythagorean theorem, we can find the length of the hypotenuse to be 13. Therefore, sin(x) = -5/13 and cos(x) = 12/13.

From these values, we can find the other trigonometric functions as follows:

csc(x) = 1/sin(x) = -13/5

sec(x) = 1/cos(x) = 13/12

cot(x) = 1/tan(x) = -12/5

So, the exact values of the expressions are sin(x) = -5/13, cos(x) = 12/13, csc(x) = -13/5, sec(x) = 13/12, and cot(x) = -12/5.

To learn more about Pythagorean theorem : brainly.com/question/14930619

#SPJ11

To sketch a graph of y = f(x) that satisfies the given requirements on the interval 0 <= x <= 10, we need to have more information about the specific requirements of the function.  However, we can make some general suggestions for how to approach the problem.

First, we should determine the type of function we are dealing with. Is it linear, quadratic, exponential, trigonometric, or some other type of function? This will affect the shape of the graph and give us an idea of how to start plotting the points.

Next, we should consider any specific points or features that we need to include in the graph. For example, if the function needs to pass through a certain point or have a certain slope, we can use this information to determine additional points on the graph.

Finally, we should make sure that the graph satisfies the given interval of 0 <= x <= 10. This means that the graph should not extend beyond this range, and any points outside of this interval should be excluded.

Overall, to sketch a graph of y = f(x) that satisfies the given requirements on the interval 0 <= x <= 10, we need to carefully consider the function type and any specific requirements, plot the points accordingly, and make sure the graph is within the given interval.

Learn more about graph:

https://brainly.com/question/17267403

#SPJ11

The rate of each car is 55 miles per hour.

In order to find the rate of each car, we need to follow the given steps :
1. Let's denote the rate of each car as R (in miles per hour).

2. The first car traveled north from 10 a.m. to 4 p.m., which is 6 hours. So, the distance covered by the first car can be represented as 6R.

3. T he second car traveled south from 12 p.m. to 4 p.m., which is 4 hours. So, the distance covered by the second car can be represented as 4R.

4. According to the problem, the total distance between the two cars at 4 p.m. is 550 miles. Therefore, the sum of the distances covered by both cars should equal 550 miles.

5. Now, we can set up an equation: 6R + 4R = 550

6. Combine the terms: 10R = 550

7. Solve for R: R = 550 / 10 = 55

So, the rate of each car was 55 miles per hour.

To learn more about equations visit : https://brainly.com/question/2972832

#SPJ11

Answer:

A)

7.2 7 * ⇒ correct

8.5 8 9 ⇒ 9 is the correct answer

12.9 13 * ⇒ correct

3.4 3 * ⇒ correct

11.5 11 12 ⇒ 12 is the correct answer

9.5 9 10 ⇒ 10 is the correct answer

B)

When a decimal number is 5 or more, you must round up, e.g. 4.5 must be rounded up to 5. You round down when the number is 4 or less.

Answer:

  H.  48

Step-by-step explanation:

Let p represent the number of coins Pamela has. Then 3p is the number Samantha has. After 6 days of adding coins, we have ...

  2(p +3·6) = 3p +2·6

  2p +36 = 3p +12

  24 = p . . . . Pamela has 24 coins; Samantha has 72.

Now, we can find the number of days (d) before the coin count is the same.

  24 +3d = 72 +2d . . . . coin counts are the same after d days

  d = 48 . . . . . subtract 24+2d

In 48 days from now, Pamela and Samantha will have the same number of coins.

\(\frac{73}{8}\) cups or \(9\frac{1}{8}\) cups or 9.125 cups of flour will be used from new bag.

Flour required for lemon bread = \(4\frac{1}{2}\) cups

Flour required for lemon bread = \(\frac{(4*2)+1}{2}\)

Flour required for lemon bread = \(\frac{9}{2}\) cups

Flour required for pumpkin bread = \(1\frac{1}{2} * \frac{9}{2}\)

Flour required for pumpkin bread = \(\frac{(2*2)+1}{2}* \frac{9}{2}\)

Flour required for pumpkin bread = \(\frac{5}{2}*\frac{9}{2}\)

Flour required for pumpkin bread = \(\frac{45}{4}\) cups

Now, the amount of flour Marvin already has = \(2\frac{1}{8}\)

The amount of flour Marvin already has = \(\frac{(2*8)+1}{8}\)

The amount of flour Marvin already has =\(\frac{17}{8}\) cups

The amount of flour needed from new bag = \(\frac{45}{4}-\frac{17}{8}\)

Taking LCM, we get 8

The amount of flour needed from new bag = \(\frac{(45*2)-17}{8}\)

The amount of flour needed from new bag = \(\frac{90-17}{8}\)

The amount of flour needed from new bag = \(\frac{73}{8}\) cups

Hence, the amount of flour that will be used from new bag is \(\frac{73}{8}\) cups or \(9\frac{1}{8}\) cups or 9.125 cups.

Learn more about mixed number -

https://brainly.com/question/21610929

#SPJ4

The logarithm statement can be written as

log₃9 = log 9/ log 3

log₉ 3 = log 3/log 9

log₂ 8 = log 8/ log 2

log₈2 = log 2/ log 8

What is a logarithm?

The power to which a number must be raised in order to obtain other values is referred to as a logarithm. The easiest way to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be written as multiplication and division of logarithms.

"The exponent by which b must be raised to yield an is the logarithm of a positive real number a with respect to base b, a positive real number not equal to 1"

Given logarithm are log₃9, log₉ 3, log₂ 8, log₈2.

Apply the formula \(log_ab\) = log b/log a:

log₃9 = log 9/ log 3

log₉ 3 = log 3/log 9

log₂ 8 = log 8/ log 2

log₈2 = log 2/ log 8

To learn more about rule of the logarithm, click on the below link:

https://brainly.com/question/16503695

#SPJ1

Answer:

pretty sure this is right

Answer: The two angles are supplementary, meaning they add up to 180 degrees.

Therefore:

82 + x = 180

x = 98

x is equal to 98 degrees.

Step-by-step explanation:

Mark me brainlist

Answer:

x=61 °

Step-by-step explanation:

angle ABE=90 ° (angle in a semi circle), so angle EBD= angle ABD - angle ABE =115-90=25 °

and the angle EDB=180 - angle EDF =180-86=94 °

so in the triangle BED:

x=180-(angle EDB+ angle EBD) =180-(94+25) =61°

Answer:

A) 0.25 miles per minute

Explanation:

edge 2021