The length of a rectangle is 2x + 4 and the width is x + 8. If the perimeter of the rectangle is 96, use the value of x to find the length and width of the rectangle.​

The limiting value of the population is approximately 485165195.41, as t approaches infinity, and the value of the population at t = 3 can be determined by solving the Gompertz differential equation with the initial condition, resulting in a specific numerical value.

(a) The limiting value of the population, as t approaches infinity, can be determined by analyzing the behavior of the Gompertz differential equation. As t increases, the term 20 - ln(P) will tend to 20, as ln(P) approaches infinity.

Therefore, the limiting value of the population can be found by setting 20 - ln(P) equal to 0 and solving for P. In this case, we can solve the equation 20 - ln(P) = 0 to find that the limiting value of the population is P = e^20, which is approximately 485165195.41.

(b) To find the value of the population when t = 3, we can use the given Gompertz differential equation. Plugging in t = 3 and the initial condition P(0) = 60, we can solve the differential equation numerically or use an appropriate method to find the value of P at t = 3.

This would require solving the equation dP/dt = 3P(20 - ln(P)) with the initial condition P(0) = 60. The resulting population value at t = 3 will depend on the specific numerical solution obtained.

In summary, the limiting value of the population is approximately 485165195.41, and the value of the population at t = 3 can be found by solving the Gompertz differential equation with the given initial condition.

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Answer:

Step-by-step explanation:

linear eq. is of first degree.

x²+x+3=0

it is of degree 2 so it is non linear.

Answer:

after simplifying, we get,

23/6

Step-by-step explanation:

(2/3+5/2-7/3)+(3/2+7/3-5/6)

We simplify,

\((2/3+5/2-7/3)+(3/2+7/3-5/6)\\(2/3-7/3+5/2)+(3/2+7/3-5/6)\\(5/2-5/3)+(9/6+14/6-5/6)\\(15/6-10/6)+((9+14-5)/6)\\(15-10)/6+(23-5)/6\\5/6+18/6\\(5+18)/6\\23/6\)

the probability of him making at least one free throw is lower (0.8044 vs. 0.9964), which means the opposing team has a better chance of preventing the other team from scoring points.

a. To find the probability that the player will make both free throws, we simply multiply the probability of making one free throw by itself: 0.94 * 0.94 = 0.8836 (to 4 decimals).

b. To find the probability that he will make at least one free throw, we can use the complement rule. The complement of making at least one free throw is missing both free throws, so we can find the probability of missing both free throws and subtract that from 1: 1 - 0.06 * 0.06 = 0.9964 (to 4 decimals).

c. To find the probability that he will miss both free throws, we multiply the probability of missing one free throw by itself: 0.06 * 0.06 = 0.0036 (to 4 decimals).

d. For the team's worst free throw shooter who makes 56% of his free throws, the probabilities are as follows:

a. The probability of making both free throws is 0.56 * 0.56 = 0.3136.

b. The probability of making at least one free throw is 1 - the probability of missing both free throws: 1 - 0.44 * 0.44 = 0.8044.

c. The probability of missing both free throws is 0.44 * 0.44 = 0.1936.

Comparing the probabilities for the two players, we can see that intentionally fouling the worst free throw shooter is a better strategy. This is because the probability of him missing both free throws is higher (0.1936 vs. 0.0036), which means the opposing team has a greater chance of gaining possession of the ball. In addition, the probability of him making at least one free throw is lower (0.8044 vs. 0.9964), which means the opposing team has a better chance of preventing the other team from scoring points.

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Answer:

9.013, 9.13, 9.1342, 9.2

Answer:

B. perpendicular Hope this helps!

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

B

Step-by-step explanation:

Only one in which x is not more than one number matching y in function.

The table 4 represent the function.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

The function should have distinct input with corresponding output.

If there are 2 same input vales then it not said to be a function.

So, according the definition the table 4 represent the function because the table 1, 2 and 3 have repeated input value,

Hence, the table 4 represent the function.

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Answer:

Option B

Step-by-step explanation:

Taking the derivative of the residual function, then applying the normal equation:

[a; b] = (X'*X)^(X'*y)

with

X = [1 1; 2 1; 3 1; 4 1; 5 1]

X' is transpose of X

y = [11; 8; 4; 1; 0]

[a; b] =  [-2.9 13.5]

Answer:

See picture attachment.

Hope this helps :)

Answer:

Step-by-step explanation:

jjjnjjknkjnjjnjjkjjknjnnjbjbjn hbnjbnmnjjjnjj.kj

Graph [1] will represent the cost of raspberries and blueberries perfectly.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of straight line also represents direct proportionality as -

y = mx

m = y/x    

[m] is constant of proportionality.

We have the number of minutes [n], that it takes to paint a wall is directly proportional to the area [a] of the wall in m². The equation of proportionality is n = 6a.

We can write the relation as -

n = 6a

for n = 18 minutes -

18 = 6a

a = 3 m²

Therefore, the area of the wall would be 3 m²

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Buyers get a percentage off on any purchase above the Minimum Basket Price. It will also be capped at the Maximum Discount Price if you choose to set a limit. E.g. "10% OFF with Min.

Answer:

C

Step-by-step explanation:

Inverse function's domain and range flip when comparing them to their original function

Answer:  25 ways.

Step-by-step explanation:

first we have  1,2,6. this can appear once.

4, can appear in twice.

\(= (3+2) * 5\\= 5*5\\= 25ways\)

by not including itself, an appearing on the left side. one number can be written 25ways

Answer: x = 7

Step-by-step explanation: 6x = x^2 - 7

x^2 - 6x -7 =0

(x-7) (x+1) = 0

x = 7  

x = -1 ----> rejected

The positive solution of the required number is 7.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

Let's start by translating the given sentence into an equation. Let "x" be the number we are trying to find. Then we can write:

6x = x² - 7

Now we need to solve for x. Let's rearrange the equation to get all the x terms on one side and all the constant terms on the other side:

x² - 6x - 7 = 0

We can solve this quadratic equation by factoring or using the quadratic formula, but let's use factoring for this problem. We need to find two numbers whose product is -7 and whose sum is -6. The two numbers are -7 and 1, so we can write:

(x - 7)(x + 1) = 0

This means that either x - 7 = 0 or x + 1 = 0. Solving for x, we get:

x = 7 or x = -1

Since we are looking for a positive solution, the answer is x = 7. Therefore, the positive solution is 7.

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Answer:

65 adults and 70 students

The number of adults and students attendant the sporting event held at a high school are 65 and 70 respectively .

In the elimination method, we eliminate any one of the variables by using basic arithmetic operations and then simplify the equation to find the value of the other variable. Then we can put that value in any of the equations to find the value of the variable eliminated.

According to the question

A sporting event held at a high school had 135 attendees.

In which adults and students are there .

Let adults be a

and students be s

Therefore,

The equation is

a + s = 135 ---------------------------(1)

Now,

The event earned a total of $930.

Admission to the event was $10 for adults and $4 for students.

i,e

10a + 4s = 930 ---------------------------(2)

Now , Using elimination method to solve both equations

a + s = 135 ---------------------------(1)

10a + 4s = $930 -------------------(2)

Step1: Multiplying equation 1 by 10

i,e

10a + 10s = 1350 -------------------(3)

Step2: Subtract equation (2) from (3)

10a + 10s = 1350 -------------------(3)

-10a - 4s = -930 -------------------(2)

6s = 420

s = 70

Now , Substituting the value of s in equation (1)

a + s = 135 ---------------------------(1)

a + 70 = 135

a = 65

Hence, The number of adults and students attendant the sporting event held at a high school are 65 and 70 respectively .

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Answer:

37°, 39° and 104°.

Step-by-step explanation:

In a triangle, all the 3 angles sum up to 180°.

3a + 8a + 37 = 180

11a = 180 - 37

11a = 143

a = 13

Angle 1 = 37

Angle 2 = 3a

= 3 × 13

= 39°

Angle 3 = 8a

= 8 × 13

= 104°

So, the angles are 37°, 39° and 104°.

Hope this helps!

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We find the regular expression over {0,1} that defines the following language: any number of copies of 10 is (10)*.

A regular expression over {0,1} that defines the language of any number of copies of 10 can be represented as:

(10)*

Let's break down the regular expression:

1. ( ): Parentheses are used to group elements together. In this case, we group the pattern "10" to indicate that we want any number of copies of it.

2. 10: This pattern represents the string "10" exactly as it is.

3. *: The asterisk symbol indicates repetition, allowing zero or more occurrences of the preceding pattern.

So, (10)* means that we can have zero or more copies of the string "10". This regular expression matches strings such as "", "10", "1010", "101010", and so on.

To clarify further, the regular expression (10)* allows us to have any number of copies of "10" concatenated together. The asterisk (*) indicates that we can repeat the pattern (10) zero or more times. This means that we can have zero occurrences of "10" (represented by an empty string ""), or we can have any positive number of copies of "10" repeated consecutively.

In summary, the regular expression (10)* matches any string that consists of any number of copies of "10". It provides a flexible way to describe this specific language using regular expression notation.

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Answer: x=-3

Step-by-step explanation:

Answer:

You can downl⁣oad the answer here. Link below!

Answer: $6600

Step-by-step explanation: 600 is 10 percent of 6000. To find out the percent of 6000 you do 0.1 x 6000 then you just add it to the original price which was 6000. Therefore 6600 is your answer

Answer:

Step-by-step explanation:

6c + 18-4c + 16

Solving like terms

2c + 34

Answer: 2c + 2

6(c + 3) - 4(c + 4)

= 6c + 18 - (4c + 16)

= 6c + 18 - 4c - 16

= 2c + 2

Step-by-step explanation:

Every finite abelian group is the additive group of some ring, but not every infinite abelian group is the additive group of some ring.

However, every abelian group is the additive group of some module over some ring. To see why every finite abelian group is the additive group of some ring, consider the direct sum of cyclic groups whose orders divide the orders of the given abelian group. This direct sum can be equipped with the coordinate wise addition and multiplication to form a ring whose additive group is isomorphic to the given abelian group.

On the other hand, not every infinite abelian group is the additive group of some ring. For example, the additive group of the rational numbers with the usual addition is not the additive group of any ring. However, every abelian group is the additive group of some module over some ring, which can be seen through the construction of the module as the direct sum of cyclic modules.

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The absolute maximum value of f(x) on [0, 16] is approximately 2.199 and occurs at x = 4, while the absolute minimum value of f(x) on [0, 16] is approximately -1.597 and occurs at x = 12.

To find the absolute maximum and minimum values of f(x) on the interval [0, 16], we need to find all critical points and endpoints of f(x) within this interval.

First, let's take the derivative of f(x) with respect to x:

f'(x) = π/8 - (π/8)sin(πx/8)

Next, we'll find the critical points by setting f'(x) equal to zero and solving for x:

π/8 - (π/8)sin(πx/8) = 0

sin(πx/8) = 1

πx/8 = π/2 + nπ   (where n is an integer)

x = 4 + 8n

We also need to check the endpoints, x = 0 and x = 16.

Now, we can evaluate f(x) at each of these points to find the absolute maximum and minimum values:

f(0) = π(0)/8 + cos(π(0)/8) = 1

f(4) = π(4)/8 + cos(π(4)/8) ≈ 2.199

f(8) = π(8)/8 + cos(π(8)/8) ≈ 0.301

f(12) = π(12)/8 + cos(π(12)/8) ≈ -1.597

f(16) = π(16)/8 + cos(π(16)/8) ≈ -0.199

So, the absolute maximum value of f(x) on [0, 16] is approximately 2.199 and occurs at x = 4, while the absolute minimum value of f(x) on [0, 16] is approximately -1.597 and occurs at x = 12.

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Answer:|2.5|

Step-by-step explanation:

En este caso el valor absoluto de 0 a |2.5| es 2.5. Esto se debe a que ya sea que cambies la ecuación o no para que sea igual a otro número, la respuesta SIEMPRE será 2.5. ¡Espero que esto haya ayudado! :D

Answer:

2 inches would be left

Step-by-step explanation:

The expression that represents the total cost of games after w weeks is 1000w + 2000wg.

The cost, in dollars, for a video game developer to code g games can be represented by the function v(g) = 500 + 1000g. The number of games produced in w weeks is given by the function g(w) = 2w.

The expression that represents the total cost of games after w weeks can be represented as follows;

Therefore,

v(g) = 500 + 1000g

g(w) = 2w.

total cost = v(g) × g(w)

total cost = (500 + 1000g)2w

Therefore,

total cost = 1000w + 2000gw

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