What is a formula for the nth term of the given sequence?
12, 20, 28...

The evolution of warning calls by some species, despite increasing the risk to the individual providing the alarm, provides evidence for the "kin selection" hypothesis.

The behavior of sounding warning calls, despite the potential risk it poses to the individual, can be understood through the concept of kin selection. According to this hypothesis, individuals are more likely to engage in behaviors that benefit their genetic relatives, even if it comes at a cost to themselves. By sounding the alarm, the individual may attract the predator's attention, increasing their own risk of predation.

However, this behavior benefits their relatives who share similar genes, as they have a higher chance of surviving the predator's attack. Over time, this selfless behavior can be favored by natural selection, as it promotes the survival and reproductive success of genetically related individuals. Thus, the evolution of warning calls despite the increased risk supports the kin selection hypothesis.

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If the HCF of 65 and 117 is expressible in the form of 65 m-117, then the value of m is 2.

To find the value of m, follow these steps:

Therefore, the value of m is 2.

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Answer:

sin θ = 22.62°

cos θ = 22.62°

tan θ = 22.62°

Step-by-step explanation:

From the diagram above

Opposite = 5

Adjacent = 12

Hypotenuse = 13

a) sin θ = Opp/Hypotenuse

sin θ = 5/13

sin θ = 0.3846153846

arc sin 0.3846153846

= 22.619864948°

Approximately = 22.62°

b) cos θ = Adjacent/ Hypotenuse

θ = 12/13

= arccos(0.9230769230769231)

22.619864948°

Approximately = 22.62°

c) tan θ = Opposite/Adjacent

θ = 5/12

= arctan(0.4166666666666667)

= 22.619864948°

= 22.62°

Answer:

12

Step-by-step explanation:

count to 69 and you got 12 lay ups

Answer:

12

Step-by-step explanation:

The surface area of this sphere radius 6 is  452.389

surface area of a sphere formula= 4πr²

plug 6 in for r

4π(6)² =452.389 rounded  to 452.4

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Answer:

true

Step-by-step explanation:

The probability of exactly 1 of the 4 marbles drawn being blue and at least 1 of the 4 marbles drawn being white will be 0.3535 and 0.7454 respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles.

The total number of the marbles will be

Total marble = 3 + 4 + 5

Total marble = 12

Then the probability of exactly 1 of the 4 marbles drawn being blue will be

\(\rm P(B) = \dfrac{^5C_1 \times ^7C_3}{^{12}C_4}\\\\P(B) = \dfrac{35}{99} = 0.353535\)

Then the probability of at least 1 of the 4 marbles drawn being white will be

\(\rm P(W) = \dfrac{^{3}C_1\times \ ^{9}C_3}{^{12}C_4} + \dfrac{^{3}C_2\times \ ^{9}C_2}{^{12}C_4} + \dfrac{^{3}C_3\times \ ^{9}C_1}{^{12}C_4} \\\\\\P(W) = \dfrac{252}{495} + \dfrac{108}{495} + \dfrac{9}{495}\\\\\\P(W) = \dfrac{369}{495}\\\\\\P(W) = 0.745454\)

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Answer:

A. 0.3535.

B. 0.7455.

Step-by-step explanation:

The probability that exactly 1 of the 4 marbles drawn is blue is 0.3535. The probability that at least 1 of the 4 marbles drawn is white is 0.7455.

Answer:

what are those symbols that are by the k

Step-by-step explanation:

To write an absolute value Equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

To write an absolute value equation for a given solution set, we need to first understand what absolute value is. Absolute value is a mathematical function that returns the positive value of a given number, irrespective of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. Now, let's consider the given figures and their respective solution sets:

Figure 1: The solution set for this figure is {2, -2}. To write an absolute value equation for this solution set, we can use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 2.

Figure 2: The solution set for this figure is {5}. To write an absolute value equation for this solution set, we can use the formula |x - b| = a, where b is the midpoint of the solution set and a is the distance from the midpoint to one of the solutions. Therefore, the absolute value equation for this figure is |x - 5| = 0.

Figure 3: The solution set for this figure is {-3, 3}. To write an absolute value equation for this solution set, we can again use the formula |x| = a, where a is the value of the solution set. Therefore, the absolute value equation for this figure is |x| = 3.

In conclusion, to write an absolute value equation for a given solution set, we need to use the appropriate formula depending on the nature of the solution set.

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Answer:

\(6\sqrt{5}-4\sqrt{15}\)

Step-by-step explanation:

\(\sqrt{5} \times (6 - 4\sqrt{3} )\)

\(\sqrt{5}\times 6-\sqrt{5}\times4\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5}\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5 \times 3}\)

\(6\sqrt{5}-4\sqrt{15}\)

Answer:

6\(\sqrt{5}\) - 4 \(\sqrt{15}\)

Step-by-step explanation:

1. Multiply each term in the parentheses by \(\sqrt{5}\)

2. calculate the product

3. solution :)

Answer:

Step-by-step explanation:

area of the aquare = s^2 = 25cm^2

∴ side = √25

side = 5cm

perimeter = 4 × side

= 4 × 5

∴ perimeter = 20 m

hope this helps

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Answer:

20cm

Step-by-step explanation:

area = Length x Width with a square we know the length and width are equal so we just work out the square root of 25 which is 5cm. A square has 4 sides so 5x4 = 20cm

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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The solution to the initial-value problem dy/dx + P(x)y = e^x, y(0) = -4 is:

y(x) = \(\frac{e^x}{2} -\frac{9}{2e^x}\)   ; 0 ≤ x < 1

      = xe^x + Ce^x;   x ≥ 1

Here, the initial-value problem is dy/dx + P(x)y = e^x, y(0) = -4

for 0 ≤ x < 1,

P(x) = 1

So, the differential equation would be,

dy/dx + y = e^x

for which the solution is:

y(x) = (e^x / 2) + C / e^x

where C is constant

The initial value of differential equation is: y(0) = -4

y(0) = (e^0 / 2) + C / e^0

-4 = (1/2) + C

C = -4 - 1/2

C = -9/2

So, we get the solution y(x) = (e^x / 2) -9 / 2e^x

For x ≥ 1,

P(x) = -1

So, the differential equation would be,

dy/dx - y = e^x

for which the solution is: y(x) = xe^x + Ce^x

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The complete question is:

Solve the given initial-value problem.

dy/dx + P(x)y = e^x, y(0) = −4, where

P(x) = 1, 0 ≤ x < 1

       = -1, x ≥ 1

The length of the diagonal of the desktop screen if one side of the desktop screen is 14 inches and the other side is 18 inches is 23 inches so, option B is correct.

A diagonal in geometry is a line segment that connects two polygonal or polyhedral vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.

Given:

The length of the rectangle, l = 18 inches,

The width of the rectangle, b = 14 inches,

Calculate the diagonal of the rectangle as shown below,

Diagonal = √(l² + b²)

Diagonal = √(18² + 14²)

Diagonal = √(324 + 196)

Diagonal = √520

Diagonal = 22.8 or 23

Thus, the diagonal is 23 inches.

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The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).

Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.

The slope-intercept form is y=mx+c

Given points are (2,7) and (-1,-5)

Slope m= (y₂-y₁)/(x₂-x₁)

m=(-5+7)/(-1-2)

m=-2/3

By substituting m value in the above equation we get,

y=(-2/3)x + c

Given that, the above equation is passing through the point (-1,-5)

-5=(-2/3)(-1)+c

c=-5-(2/3)

c=-17/3

y=(-2/3)x-(17/3)

Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)

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The correct Option (B). Succession may be defined as the change in the ecological community of the species with respect to time. Two main types of succession are primary succession and secondary succession.

The living things that accumulate in the succession is from the simple organism to the complex organism. First lichens will evade in the land. After lichens grass then shrubs and finally the trees will cover the area and convert into the forest.

Primary succession occurs in basically dead areas—regions where the soil is incapable of supporting life due to causes such as lava flows, newly created sand dunes, or glacier-left boulders.

Pioneer microorganisms, plants (lichens and mosses), grassy stage, smaller shrubs, and trees are all stages of primary succession. When there is food available, animals begin to return. The climax community stage is reached when the ecosystem is fully functional.

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Full Question :

After a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. What is the most likely order of ecological succession in that area?

A.grass → trees → lichens → moss

B.lichens → grass → shrubs → trees

C.lichens → grass → trees → shrubs

D.shrubs → grass → trees → lichens

The momentum magnitude observed in frame s' is √(15m^2c^4).

In special relativity, the relationship between energy (E) and momentum (p) is given by the equation:

E^2 = (pc)^2 + (mc^2)^2

where m is the rest mass of the particle, c is the speed of light, and p is the momentum of the particle.

In frame of reference s, the energy of the electron is given as 4mc^2. Plugging this into the equation, we have:

(4mc^2)^2 = (pc)^2 + (mc^2)^2

Simplifying this equation, we get:

16m^2c^4 = p^2c^2 + m^2c^4

Canceling out the common terms, we have:

15m^2c^4 = p^2c^2

Taking the square root of both sides, we get:

pc = √(15m^2c^4)

The momentum magnitude observed in frame s', denoted as p', is related to the momentum in frame s (p) by the relativistic velocity addition formula:

p' = γ(p - βE/c)

where γ is the Lorentz factor and β is the velocity of frame s' relative to frame s. Since the electron is moving along the x-axis, the velocity β is zero, and the Lorentz factor γ is equal to 1.

Therefore, the momentum magnitude observed in frame s' is the same as the momentum magnitude in frame s:

p' = p

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Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question the original line is

y = 2/3x - 7

Comparing with the general equation above

Slope = 2/3

Since the lines are parallel their slope are also the same

Slope of parallel line = 2/3

So the equation of the line using point

(12 , 2 ) and slope 2/3 is

\(y - 2 = \frac{2}{3} (x - 12) \\ y - 2 = \frac{2}{3} x - 8 \\ y = \frac{2}{3} x - 8 + 2\)

We have the final answer as

\(y = \frac{2}{3} x - 6 \\ \)

Hope this helps you

An inscribed circle is tangent to

all 3 sides of the triangle it is inscribed in.

The correct option is the second option

Explanation

A circle is inscribed in the triangle if the triangle's three sides are all tangents to a circle. In this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter.

Since the triangle's three sides are all tangents to the inscribed circle, the distances from the circle's center to the three sides are all equal to the circle's radius

Answer:

y = 8x - 8

Step-by-step explanation:

y-8 = 8(x-2)

y-8 = 8x - 16

y = 8x - 16 + 8

y = 8x - 8

Answer:

y=8x-8

Step-by-step explanation:

slope intercept form is y=mx+b

Where m is slope and b is y intercept

We can fill in for m

y=8x+b

Now we can fill the coordinates we know to find b

8=8(2)+b

8=16+b

-16 -16

-8=b

Now  we know b

y=8x-8

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Possible options:

uppercase letter: 26

lowercase letter: 26

number: 10

upper or lowercase letter: 50

Note: I'm interpreting the "no upper or lower case letters can be repeated in the sequence" to mean you could have Aa0b, where A is used as the uppercase and a is used as the lower case letter, but then you can't use A or a for the last character.

26 · 26 · 10 · 50 = 338,000 combinations

Now is using "A" and "a" isn't allowed, then you have:

Possible options:

uppercase letter: 26

lowercase letter: 25

number: 10

upper or lowercase letter: 48

26 · 25 · 10 · 48 = 312,000 combinations

Answer:

5x

Step-by-step explanation:

The rοοts οf the functiοn are x = -6 and x = -1.

A quadratic equatiοn is a type οf pοlynοmial equatiοn οf the secοnd degree, which can be written in the fοrm:

\(ax^2 + bx + c = 0\)

Where "a", "b", and "c" are cοnstants, and "x" is the variable. The cοefficient "a" must nοt be equal tο zerο, as this wοuld result in a linear equatiοn.

The quadratic equatiοn can be sοlved using the quadratic fοrmula, which is:

x = (-b ± sqrt(b² - 4ac)) / 2a

Tο find the rοοts οf the functiοn, we need tο find the values οf x that make y equal tο zerο since the rοοts οf a functiοn are the values οf x that make the functiοn equal tο zerο.

Sο we set y tο zerο and sοlve fοr x:

0 = (x+6)(x+1)

Using the zerο prοduct prοperty, we knοw that if the prοduct οf twο factοrs is equal tο zerο, then at least οne οf the factοrs must be equal tο zerο.

Sο we set each factοr equal tο zerο and sοlve fοr x:

x + 6 = 0 οr x + 1 = 0

x = -6 οr x = -1

Therefοre, the rοοts οf the functiοn are x = -6 and x = -1.

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The price of a pack of balloons is 4. 39

The price of a pack of party favors is 0. 36

We have that;

Let the cost of balloons be x

Let the cost of party favors by y

From the information given, we have that;

3x + 4y = 14. 63   (1)

2x + 4y = 16. 03  (2)

Now, let's make 'x' the subject from equation (1)

x = 14. 63 - 4y/ 3  (3)

Substitute in equation (2)

3( 14. 63 - 4y/ 3) = 16. 03

expand the bracket

43. 69 - 12y /3 = 16. 03

cross multiply

43. 69 - 12y = 48. 09

collect like terms

- 12y =  - 4. 4

make 'y' the subject

y = 0. 36

substitute in equation (3)

x = 14. 63 - 4(0. 36)/ 3

x = 13. 1/ 3

x = 4. 39

Hence, the prices are 4. 39 and 0. 36 respectively.

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a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.

b) The price of the security is $128.31.

a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:

PV = C / \((1+r)^n\)

where PV is the present value,

C is the coupon payment,

r is the zero rate, and

n is the number of years to maturity.

We can solve for r by rearranging the formula:

r = \((C/PV)^{(1/n) }\)- 1

Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:

For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.

For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.

For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.

For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.

For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.

Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:

PV = A × x

where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.

To solve for x, we can use the equation:

x = (\(A^{-1}\)) x PV

where (\(A^{-1}\)) is the inverse of matrix A.

Using this method, we can solve for the zero rates as follows:

[2.01% ]

[2.48% ]

[2.77% ] = x

[1.73% ]

[4.32% ]

PV = \(A^{-1}\) x  [98]

                   [101]

                   [103]

                   [101]

                   [103]

PV =   [-0.0201]

          [ 0.0248]

          [ 0.0277]

          [-0.0173]

          [ 0.0432]

b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:

PV = \(C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4\)

where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.

Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:

PV1 = $10 /(1+2.01 % \()^1\) = $9.80

PV2 = $25/(1+2.48%\()^2\) = $22.15

PV3 = $100/(1+1.73%\()^4\) = $81.36

Then, the price of the security is the sum of the present values:

PV = $9.80 + $22.15 + $81.36 = $128.31

Therefore, the price of the security is $128.31.

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Answer:

constant.

Step-by-step explanation:

like natural constants like pi or e.

Answer:

pi

Step-by-step explanation:

it stays the same 3.14 and so on

Answer:

10

Step-by-step explanation:

2x(+5)=(25)< subtract 5 to each side

2x=20<divide 2 to 20

x=10