please compare the lotka integral equation and the mckendrick-von foerster model. are they based on the same assumptions? how these models are related? how these models are different?

Answer:

u=5/6

Step-by-step explanation:

Answer:

u = 5/6

Step-by-step explanation:

u - 1/12 = 3/4        

  +1/12   +1/12

u=5/6

in order to get 5/6 :

3/4 + 1/12

must get common denominator

3*3/4*3  + 1/12

9/12 + 1/12

10/12

simplify by dividing by 2

5/6

Answer:

1) 81.4×32.1 = (80)(30)=2,400

2) 32.9×4.81 = (30)(5)= 150

3) 29.3×5.9 = (30)(6)= 180

4) 46.7×31.7 = (50)(30)= 1,500

5) 59.3×3.57 = (60)(4)= 240

Hope this helps!

The function f(x) is a logarithmic function with a vertical asymptote at x = -8. The range of the function is from negative infinite to positive infinity, and it is increasing on it's entire domain. The end behavior of the function on the left side is that as x -> -8^+, y -> -∞, and to the right side, is that as x -> +∞, y -> +∞.

The function starts being defined at x = -8, hence the vertical asymptote of the function is given as follows:

x = -8.

The range of the function is the set containing all values assumed by y on the graph, hence it is in fact from negative infinity to positive infinity, and the function is increasing on it's entire domain.

The end behavior is the values on the extreme left and extreme right of the graph.

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(x - (a+48))² + (y - (b+19))² = 24.5² This is the equation for all possible positions (x,y) on the boundary of the cell tower's service coverage.

To write an equation for all possible positions (x,y) on the boundary of the cell tower's service coverage, we first need to determine the coordinates of the center of the coverage.

We know that the cell tower is located 48 miles east and 19 miles north of the center of the small town, so we can add these distances to the coordinates of the town's center. If we let (a,b) be the coordinates of the town's center, then the coordinates of the cell tower would be (a+48,b+19).

Next, we know that the cell tower services everything within a radius of 24.5 miles from it. This means that any point (x,y) on the boundary of the coverage circle would be exactly 24.5 miles away from the cell tower. We can use the distance formula to write an equation for this:

√[(x - (a+48))² + (y - (b+19))²] = 24.5

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Simplify the given expression as follows:

The missing numbers are - 5 and - 4.

The spares should be kept to maintain a 90% or more probability of system success is 35

Let λ be the normal number of component disappointments per year, at that point the disappointment rate (or rate parameter) is given by λ/52 since there are 52 weeks in a year. Let's signify this by μ = λ/52.

The framework victory likelihood can be modeled utilizing the Poisson dissemination since the disappointments happen haphazardly and freely over time. Let X be the number of component disappointments in a year, at that point X takes after a Poisson conveyance with cruel λ.

To preserve a 90% or more likelihood of system victory, we got to guarantee that the number of saves is adequate to cover at the slightest 90% of the potential disappointments. This implies that the likelihood of having more than k disappointments in a year ought to be less than or break even with 0.1, where k is the number of saves.

Let Y be the number of component disappointments amid the two-week conveyance time. At that point, Y too takes after a Poisson conveyance with cruel μ/26, since there are 26 weeks in a half-year (i.e., two quarters). The likelihood of having more than k disappointments amid the conveyance time is given by:

P(Y > k) = 1 - P(Y ≤ k) = 1 - ∑_\({i=0}^k (e^(-μ/26) (μ/26)^i\)/ i!)

where e is the base of the common logarithm.

To preserve a 90% or more likelihood of system victory, we ought to select k such that P(Y > k) ≤ 0.1. Able to solve for k numerically, employing a spreadsheet or a computer program.

For example, utilizing Microsoft Exceed expectations or Go-ogle Sheets, ready to utilize the taking after an equation to compute P(Y > k) for distinctive values of k:

=1-POISSON(k,μ/26,TRUE)

where POISSON is the Poisson total conveyance work, with the moment contention being the cruel and the third contention being Genuine to indicate an aggregate conveyance.

Beginning with k = 26 (i.e., one save per week), able to increment k until we discover the littlest esteem that fulfills P(Y > k) ≤ 0.1. In this case, we discover that k = 35 saves are required to preserve a 90% or more likelihood of framework victory. 

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To find the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7, let's analyze the given information.

The sum of the second term (s2), fifth term (s5), and seventh term (s7) themselves form an arithmetic sequence.

Let's denote the second term as a + 2d, the fifth term as a + 5d, and the seventh term as a + 7d, where 'a' is the first term and 'd' is the common difference.

Using the arithmetic sequence formula for the sum of terms, we have:

s2 = (2/2) * (2a + (2-1)d) = 2a + d

s5 = (5/2) * (2a + (5-1)d) = 5a + 6d

s7 = (7/2) * (2a + (7-1)d) = 7a + 12d

Since the sums s2, s5, and s7 themselves form an arithmetic sequence, we can express their differences:

s5 - s2 = (5a + 6d) - (2a + d) = 3a + 5d

s7 - s5 = (7a + 12d) - (5a + 6d) = 2a + 6d

Now, equating the differences, we have:

3a + 5d = 2a + 6d

Simplifying the equation, we find:

a = d

Therefore, the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7 is 'd'.

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Answer:

I think it's A

Step-by-step explanation:

225x + 400 ≥ 2200

225x ≥ 1800

x ≥ 8

I can help you with that problem i just did that on my own.

The z-score for a weekly rental of $423.00 will be 2.45.

A z-score is defined as the fractional representation of data point to the mean using standard deviations.

Given the average cost to rent a car for a week is $276

And the standard deviation is $60

To determine the Z-score for a weekly rental of $423.00

Here,

ц = 276

σ = 60

X = 423

⇒ z-score = (X-ц )/σ

Substitute the values,

⇒ z-score =  (423 - 276)/60

⇒ z-score = 147/60

⇒ z-score = 2.45

Hence, the z-score for a weekly rental is 2.45.

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Answer:

a) Steve

b)0.3

Step-by-step explanation:

1 1/5 is 1.2

1.5 - 1.2= 0.3

Answer:

The bigger avocado will be a better deal if the ratio of the sizes of the bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.

Step-by-step explanation:

Given that two sizea of avocados are being sold, since the regular size is being sold for $0.84 each, let the price for the bigger avocado be $x.

Then note the following:

1. How bigger than the smaller avocado is the bigger one?

This would determine if the price for the bigger one is a bargain, or a mistake.

If for instance, the bigger avocado is double the size of the smaller one, then for any price, $x less that $1.68 (twice of $0.84), it is a bargain.

The bigger avocado will be a better deal if the ratio of the sizes bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.

Answer:

The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.

Step-by-step explanation:

The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.

The shapes of the curves in the AS/AD (Aggregate Supply/Aggregate Demand) model are based upon the relationship between the price level and the output level in an economy.

The AD curve shows the relationship between the overall price level and the quantity of goods and services demanded by all buyers in an economy. It has a negative slope, indicating that as the price level increases, the quantity of goods and services demanded decreases.

The AS curve shows the relationship between the overall price level and the quantity of goods and services that firms are willing and able to supply. In the short run, the AS curve is upward sloping, indicating that as the price level increases, firms are willing to supply more output due to higher profits. In the long run, the AS curve becomes vertical, indicating that the level of output is determined by the factors of production and technology, not the price level.

Thus, the shapes of the curves in the AS/AD model are based on the behavior of buyers and sellers in an economy and their response to changes in the overall price level.

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Answer:

Y=70

X=110

Step-by-step explanation:

if the inside of a triangle equals 180, than 70 plus 40 equals 110 which mean Y =70. if a straight line eguals 180 as well 180-70= 110 X= 110

Answer:

Step-by-step explanation:

Dividend = 24x³ - 14x² + 20x + 6

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Answer:

W=4 l=16

Step-by-step explanation:

Let w = width

Let l = length

Since the length is 4 times the width, l=4w

Perimeter of rectangle = 2l + 2w

= 2(4w)+2w

=10w

The perimeter of the rectangle =40, so

40=10w and w=4

Plug w into the length equation : l=4w=4(4)=16

The correct answer to the question "z scores that fall below the mean are" is "negative". Z-scores are measures of relative standing that can be used to make comparisons among the scores in the distribution by transforming raw data into standardized units.

The formula for z-score is:z = (X-μ)/σz-scores can be negative, zero, or positive numbers. A negative z-score tells us that the corresponding score is below the mean and vice versa.In addition to this, the mean of all z-scores is always zero. If the mean of all z-scores is zero, that means that z-scores are measuring deviation from the mean. If a z-score is below the mean, it means that the corresponding raw score is below the mean, which results in a negative z-score.

Z-scores that fall below the mean are negative. Z-scores are statistical values that allow analysts to transform raw data into standardized units that make comparisons possible among scores in the distribution. The formula for calculating the z-score is: z = (X-μ)/σThe z-score can be either negative, zero, or positive, depending on whether the value is below, equal to, or above the mean, respectively. Because the mean of all z-scores is always zero, z-scores can be used to measure deviation from the mean, with a negative z-score indicating that the corresponding raw score is below the mean. Z-scores allow us to compare the scores in the distribution by converting them into standard units. Negative z-scores are associated with scores that are below the mean. Conversely, positive z-scores are associated with scores that are above the mean.

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The linearization of the function f(x, y, z) = x²y + 4z at the point (1, -1, 2) is L(x, y, z) = -1 - 2(x - 1) + y + 4(z - 2). This linearization provides an approximation of the function's behavior near the given point by considering only the first-order terms in the Taylor series expansion.

To find the linearization, we need to compute the partial derivatives of f with respect to each variable and evaluate them at the given point. The linearization is an approximation of the function near the specified point that takes into account the first-order behavior.

First, let's compute the partial derivatives of f(x, y, z) with respect to x, y, and z:

∂f/∂x = 2xy,

∂f/∂y = x²,

∂f/∂z = 4.

Next, we evaluate these derivatives at the point (1, -1, 2):

∂f/∂x = 2(-1)(1) = -2,

∂f/∂y = (1)² = 1,

∂f/∂z = 4.

Using these derivative values, we can construct the linearization L(x, y, z) as follows:

L(x, y, z) = f(1, -1, 2) + ∂f/∂x(x - 1) + ∂f/∂y(y + 1) + ∂f/∂z(z - 2).

Substituting the computed values, we have:

L(x, y, z) = (1²)(-1) + (-2)(x - 1) + (1)(y + 1) + (4)(z - 2).

Simplifying this expression yields the linearization L(x, y, z) = -1 - 2(x - 1) + y + 4(z - 2).

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Answer:

15

Step-by-step explanation:

given solution

x=4 20-(3y-4x) substitute

y=7 20-(3(7)-4(4))

20-(21-16)

20-5

answer =15

The maximum point is located at the coordinates (1/63, 98/63).  Assuming that the grid is a coordinate plane with an x-axis and a y-axis, the product can be expressed as a quadratic function and graphed as a parabola on the coordinate plane.

To find the product, one would use the distributive property of multiplication to expand the expression:

(1 - 7x) (1 + 9x) = 1 + 9x - 7x - 63x^2 = -63x^2 + 2x + 1

The resulting expression represents a quadratic function with a concave down shape and a maximum point. To graph this function on the coordinate plane, one would need to determine the coordinates of the maximum point.

One way to find the maximum point is to use the formula x = -b/2a, where a = -63, b = 2, and c = 1 are the coefficients of the quadratic function in standard form. Plugging these values into the formula, one gets:

x = -2 / (2 * (-63)) = 1/63

To find the corresponding y-value, one would substitute x = 1/63 into the quadratic function:

y = -63(1/63) ^2 + 2(1/63) + 1 = 98/63

Therefore, the maximum point is located at the coordinates (1/63, 98/63). By plotting additional points and connecting them with a smooth curve, one can graph the quadratic function and locate the product on the coordinate plane.

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This problem is an example of a balanced transportation problem since the total supply of goods is equal to the total demand.

The transportation problem is a well-known linear programming problem in which commodities are shipped from sources to destinations at the minimum possible cost. The initial step in formulating a mathematical model for the transportation problem is to identify the sources, destinations, and the quantities transported.
The objective of the transportation problem is to minimize the total cost of transporting the goods. The mathematical model of the transportation problem is:
Let there be m sources (i = 1, 2, …, m) and n destinations (j = 1, 2, …, n). Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
The transportation problem can then be formulated as follows:
Minimize Z = ∑∑cijxij
Subject to the constraints:
∑xij = si, i = 1, 2, …, m
∑xij = dj, j = 1, 2, …, n
xij ≥ 0
where si and dj are the supply and demand of goods at the i-th source and the j-th destination respectively.
Using the given table, we can formulate the transportation problem as follows:
Let A1, A2, and A3 be the sources, and B2, B3, and B4 be the destinations. Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
Minimize Z = 27x11 + 27x12 + 32x13 + 15x21 + 21x22 + 20x23 + 16x31 + 22x32 + 18x33
Subject to the constraints:
x11 + x12 + x13 = 3
x21 + x22 + x23 = 14
x31 + x32 + x33 = 10
x11 + x21 + x31 = 21
x12 + x22 + x32 = 32
x13 + x23 + x33 = 26
xij ≥ 0
In this way, we can construct a mathematical model of the transportation problem using the given table. The model can be solved using the simplex method to obtain the optimal solution.

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The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

The shape of an equilateral triangle is an equilateral triangle.

The word "Equilateral" is formed by combining two words. H. "Equi" means equal, "lateral" means side.

Equilateral triangles are also called regular polygons or equilateral triangles because all sides are equal.

In geometry, an equilateral triangle is a triangle with all sides of equal length.

Three sides are equal, so three angles on the same side are equal. Therefore, it is also called an equilateral triangle with each angle of 60 degrees.

Like other types of triangles, equilateral triangles have formulas for area, perimeter, and height.

According to our question-

AB=OA=BO= 9CM

Hence, Area is,

ONQ-AOB/ONQ x 100

Putting all the values,

Area = 60.3%

Hence, The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%

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Answer

56.6

Explanation

To solve this, we will use one of the principles for the order of operations.

55 + (12 - 4) ÷ 5

BODMAS or PEMDAS indicates that the expression in the bracket is simplified first before the multiplication or division, then, the addition or subtraction follows.

So,

55 + (12 - 4) ÷ 5

= 55 + 8 ÷ 5

= 55 + 1.6

= 56.6

Hope this Helps!!!

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\(\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.\)

\(2x-5y=-13, \: 3x+4y=15 \)

\(2x-5y=-13 \)

\(2x=5y-13 \)

\(x=\frac{1}{2}\left(5y-13\right) \\ \)

\(x=\frac{5}{2}y-\frac{13}{2} \\ \)

\(3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\ \)

\(\frac{15}{2}y-\frac{39}{2}+4y=15 \\ \)

\(\frac{23}{2}y-\frac{39}{2}=15 \\ \)

\(\frac{23}{2}y=\frac{69}{2} \\ \)

\(\large \underline{ \underline{ \sf \: y=3 }}\)

\(x=\frac{5}{2}\times 3-\frac{13}{2} \\ \)

\(x=\frac{15-13}{2} \\ \)

\( \large\underline{ \underline{ \sf \: x=1 }}\)

\( \huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}\)

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

In a case whereby a ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the time the ball is thrown will it strike the​ ground at t = 2.5 or -3.5.

Height of building = 140 ft

Initial velocity, u = 16 ft/sec

the equation given is

h = -16t² -16t +140

h(t) = -16t² -16t +140

AT h(t) = 0 , We can divide by -2 and have

(8t² + 8t - 70) = 0

8t² + 8t - 70 = 0

Then if we solve with quadratic equation formula where  a=8, b=8, c=- 70 then the root will be -7/2 and 5/2 then  t = 2.5 or -3.5

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complete question;

A ball is thrown downward from the top of a 140​-foot building with an initial velocity of 16 feet per second. the height of the ball h in feet after t seconds is given by the equation h equals negative 16 t squared minus 16 t plus 140. how long after the ball is thrown will it strike the​ ground?

When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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