MATHEMATICS COLLEGE

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized. 1. Which of the following differential equations could be used to model this situation, where k is a positive constant?
A. dL/dt = kL
B. dL/dt = 100 - kL
C. dL/dt = k(100 - L)
D. dL/dt = kL - 100

Answers

Answer 1
Answer:

Answer:

C. dL/dt = k(100 - L)

Step-by-step explanation:

We have a list containing 100 words.

L = number of words memorized at time t.

At any time t, the number of words left to be memorized is 100-L.

Therefore:

(dL)/(dt)\propto 100-L\n $Introducing k, a constant of proportion$\n(dL)/(dt)= k(100-L)

The correct option is C.

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Suppose PR = 54, solve for QR
Which statement is true? Step by step.
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive positive that is the probability that the bureau finds a match given that the lead at the crime scene and the lead in the possession of the suspect are actually from two differant melts or sources. To estimate the false positive rate the bureau collected 1851 bullets that the agency was confident all came from differant melts. The using its established ctireria the bureau examined every possible pair of bullets and found 658 matches. Use this info to to compute the chance of a false positive.
The bar diagram represents the ratio of points scored by the home team and the visiting team in a basket ball game. How many points did the visiting team score if the home team scored 84 points?

What is a3 if an=64(12)n−1

Answers

Answer:

\huge\boxed{a_3=9,216}

Step-by-step explanation:

a_n=64(12)^(n-1)\n\n\text{substitute}\ n=3:\n\na_3=64(12)^(3-1)=64(12)^2=64(144)=9,216

Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts?

Answers

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

That's the answer.

Answer:

It will take 40 minutes to make and pack an order for 15 parts.

Step-by-step explanation:

An article in the ASCE Journal of Energy Engineering ("Overview of Reservoir Release Improvements at 20 TVA Dams," Vol. 125, April 1999, pp. 1-17) presents data on dissolved oxygen concentration from streams below 20 dams in the Tennessee Valley Authority system. The sample mean from the observations equals 3.234 and the sample standard deviation is s = 2.121. a) Calculate the 95% two-sided prediction interval on the dissolved oxygen concentration for the next stream that will be tested. (rounded to two decimal places)

Answers

Answer:

95% confidence interval: (2.241,4.227)

Step-by-step explanation:

We are given the following in the question:

Sample mean, \bar{x} = 3.234

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, σ = 2.121

95% confidence interval:

\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))  

Putting the values, we get,  

t_(critical)\text{ at degree of freedom 19 and}~\alpha_(0.05) = \pm 2.093  

3.234 \pm 2.093((2.121)/(√(20)) ) = 3.234 \pm 0.993 = (2.241,4.227)

(2.241, 4.227) is the required confidence interval.

The path of the water in a pond fountain can be modeled by y=-0.1x^2+2.8x , where x and y are measured in feet. The x -axis represents the surface of the pond. Find the width of the path at the surface of the pond and the height of the path.Width: ___ ft
Height: ___ ft

Answers

Answer:

the width of the path at the surface of the pond is 14 feet, and the height of the path above the surface of the pond is 19.6 feet.

Step-by-step explanation:

To find the width of the path at the surface of the pond, we need to find the x-coordinate of the vertex of the parabola y = -0.1x^2 + 2.8x. The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -0.1 and b = 2.8. Substituting these values, we get:

x = -2.8 / 2(-0.1) = 14

So the width of the path at the surface of the pond is 14 feet.

To find the height of the path, we need to find the y-coordinate of the vertex of the parabola y = -0.1x^2 + 2.8x. The y-coordinate of the vertex is given by:

y = f(x) = -0.1(x - h)^2 + k

where (h,k) is the vertex of the parabola. To find the vertex, we can use the formula:

h = -b/2a and k = f(h)

Substituting a = -0.1 and b = 2.8, we get:

h = -2.8 / 2(-0.1) = 14

k = f(14) = -0.1(14)^2 + 2.8(14) = 19.6

So the vertex of the parabola is (14, 19.6), which means the maximum height of the path above the surface of the pond is 19.6 feet.

Therefore, the width of the path at the surface of the pond is 14 feet, and the height of the path above the surface of the pond is 19.6 feet.

PLEASE ANSWER Add. 51.342 + 36.530

Answers

Use the calculator :v nvm the answer is 87.872
87.872 is the answer

Find the equation for the line that passes through the points ( 1 , 1 ) and ( − 5 , 6 ) . Give your answer in point-slope form. You do not need to simplify.

Answers

Answer:

Step-by-step explanation:

Final answer:

The equation of the line passing through (1,1) and (-5,6) is y - 1 = -5/6(x - 1).

Explanation:

To find the equation for the line passing through the points (1, 1) and (-5, 6) in point-slope form, we need to calculate the slope and use one of the given points. The slope, denoted by 'm', can be calculated as the change in y divided by the change in x. Substituting the values (1, 1) and (-5, 6) into the slope formula, we get m = (6 - 1) / (-5 - 1) = 5 / -6 = -5/6. Using the point-slope form, y - y1 = m(x - x1), we can substitute the slope and one of the given points to obtain the equation of the line.

Using the point (1, 1), we substitute x1 = 1 and y1 = 1 into the equation. This gives us y - 1 = -5/6(x - 1).

Therefore, the equation of the line that passes through the points (1, 1) and (-5, 6) in point-slope form is y - 1 = -5/6(x - 1).

Learn more about Equation of a Line here:

brainly.com/question/21511618

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