Last year, scientists claimed there were 10,000 different species of ants around the world. Since then, the number of different species have decreased by 5.1%. How many different species of ants are estimated currently? Round to the nearest whole number.
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Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and  the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

To find the fifth power of the matrix A, we can simply multiply A by itself five times:

A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

To find the probability that state 2 changes to state 4 after five repetitions of the experiment, we need to look at the element in the fifth power matrix A^5 that corresponds to state 2 and state 4. This element is located in the second row and fourth column of the matrix, which is 0.14.

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

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A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

Answer:

Step-by-step explanation:

Let us solve the equation for X-

-1+log 6 (2x+3)-log 6 (2x)=0

adding +1 to both sides-

-1+1+log 6(2x+3)-log 6 (2x)=0+1

log 6(2x+3)-log 6 (2x)=1 . . . (1)

using logarithmic rule,

log a - log b= log(a/b)

equation (1) becomes,

log [6(2x+3)/6(2x)]=1 . . .(2)

equation (2) becomes,

log[(2x+3)/2x]=1....(3)

Again using the logarithmic rule,

log a = b

is equivalent to 10∧b = a

hence equation 3 becomes,

10∧1= (2x+3)/2x

i.e. 10 = (2x+3)/2x. . .(4)

multiplying both sides by 2x, considering x is not 0.

equation( 4) becomes

20x = 2x+3. . .(5)

subtracting 2x from both sides

equation (5) becomes,

18x=3

dividing both sides by 3,

we get,

x=6

Hence value of x is 6.

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Answer:

6(12), multiplication

Step-by-step explanation:

Since it takes 12 minutes to mow one lawn, multiplying would give you the answer of how long 6 lawns would take, which is 72

Answer:

A

Step-by-step explanation:

The problem is a little unclear with its format(random bracket) but given the following it should be A even though a parenthesis is missing but with going from left to right with parenthesis first depending on where the extra parenthesis is placed it is either A or B but it looks like there should be one grouping ((-8)+6) so it should be A

Answer:

Below in bold.

Step-by-step explanation:

Let the height be h in.

Area of a triangle = 1/2 * base * height

= 1/2 * (h + 6) * h = 600

Multiply both sides by 2:

h(h + 6) = 1200

h^2 + 6h = 1200

(h + 3)^2 - 9 = 1200

(h + 3)^2 = 1209

h + 3 = +/- sqrt(1209

h = -3 +/-sqrt(1209)

  = 31.77 in  (we ignore the negative root).

So, the height is 31.77 in and the base is 37.77 in

Answer: 1/4,2/5,3/10

Step-by-step explanation:

The x and y values for the given equation are x= -20 and y=8

One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.

Given,

-1/4[ x 12 -32 ] = [ 5  -3  y ]

[(-1/4)x    (-12/4)    (-32/-4)]=[5  -3  y]

-x/4=5

-x=20

x= -20

-32/-4=y

y=8

Therefore, the x and y values for the given equation are x= -20 and y=8

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The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

Given,

In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°

We know that,

The angles sum in a triangle is 180°.

m∠X+m∠Y+m∠Z=180°

m∠X+71.02°+29.6°=180°

m∠X=180°-100.62°

m∠X=79.38°

Therefore, the measure of exterior angle to ∠X is 79.38°.

So, option 4 is correct.

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Step-by-step explanation:

the ancient Greeks used the system know as the attic numerals

Answer:

When a block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest, their velocity after the collision is equal to the original velocity of the first block. This is because, in a collision where the two objects stick together, the final velocity of the combined system is equal to the initial velocity of the first object.

To calculate the final velocity of the combined system, we can use the formula vf = vi + (2mv)/(m1+m2), where vf is the final velocity, vi is the initial velocity, m is the mass of the first object, v is the velocity of the first object, and m1 and m2 are the masses of the two objects. Plugging in the values from the problem, we get:

vf = V + (2 * M * V)/(M + 2M) = V + (2 * M * V)/(3M) = V + (2/3) * V = (5/3) * V

Therefore, the final velocity of the combined system is (5/3) * V, which is equal to the original velocity of the first block.

The velocity of the mass 2M after the collision will be V/2 which is half of the velocity of mass M.

An elastic collision is one during which the system does not experience a huge reduction of kinetic energy as a result of the collision. In elastic collisions, mass and kinetic energy are both preserved. Imagine two trolleys that resemble one another moving in the same direction at the same pace.

A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest.

Let 'v' be the velocity after the collision. Then the velocity of the mass 2M after the collision will be calculated as,

MV = 2Mv

v = V / 2

Thus, the velocity of the mass 2M after the collision will be V/2 which is half of the velocity of the mass M.

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Answer:

The cost of producing 200 units can be calculated by plugging in 200 for q in the equation E = 1.43q + 43,123. This gives us E = 1.43*200 + 43,123 = 286 + 43,123 = $43,409.

Answer: 4/3 of a mile

Step-by-step explanation:

To find the distance that Pepe and Paula ran in 60 minutes, we need to first determine their individual pace in miles per minute. Pepe ran 2/3 of a mile in 5 minutes, so his pace was 2/3 / 5 = 2/15 of a mile per minute. Paula ran 1/4 of a mile in 2 minutes, so her pace was 1/4 / 2 = 1/8 of a mile per minute.

We can now use these values to determine the distance that each of them ran in 60 minutes. Pepe ran at a pace of 2/15 of a mile per minute, so he ran 2/15 * 60 = 8/15 of a mile in 60 minutes. Paula ran at a pace of 1/8 of a mile per minute, so she ran 1/8 * 60 = 3/8 of a mile in 60 minutes.

To find the total distance that Pepe and Paula ran in 60 minutes, we can add their individual distances: 8/15 + 3/8 = 35/60 + 45/60 = 80/60 = 4/3 of a mile. Therefore, Pepe and Paula cumulatively ran a total of 4/3 of a mile on their 60-minute training run.

Option C is correct,4.5 is greater than 3.8, so this solution does work.

If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.

Inequality

In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.  

The first option is having 0.5 liters of water for 4.5 hours of hiking. So will plug 3 in for y and 4.5 in for x:

y > 0.5x + 1.8

3 > 0.5(4.5) + 1.8

3 > 4.05  

But 3 is not greater than 4.05, this solution does not work.

The next option is having 2 liters of water for 2.5 hrs of hiking:

2 > 0.5(2.5) + 1.8  

2 > 3.05

But 2 is not greater than 3.05, so this solution does not work.

Option c is having 4.5 liters of water for 4 hours of hiking:

4.5 > 0.5(4) + 1.8

4.5 > 3.8

So 4.5 is greater than 3.8, this solution does  work.

The last option is having 2.5 liters of water for 3 hours of hiking:

2.5 > 0.5(3) + 1.8

2.5 > 3.3

2.5 is not greater than 3.3, so this solution does not works

Option c is correct,4.5 is greater than 3.8 so this solution does work.

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y > 0.5x + 1.8

3 > 0.5(4.5) + 1.8

3 > 4.05  

But 3 is not greater than 4.05, this solution does not work.

2 > 0.5(2.5) + 1.8  

2 > 3.05

But 2 is not greater than 3.05, so this solution does not work.

4.5 > 0.5(4) + 1.8

4.5 > 3.8

2.5 > 0.5(3) + 1.8

2.5 > 3.3

2.5 is not greater than 3.3, so this solution does not works

Option c is correct,4.5 is greater than 3.8 so this solution does work.

The value of y of the inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

Inequalities can be solved the way a normal algebraic equation is being solved. It is solved by isolating the value of the variable.

The inequality given is, 4y + 1/5 ≤ 4/5. Solve as shown below:

Subtract both sides by 1/5:

4y + 1/5 - 1/5 ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Divide both sides by 4:

4y/4 ≤ 3/5 / 4

y ≤ 3/5 × 1/4

y ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

The value of y is: y ≤ 3/20.

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Answer:

309 chemistry textbooks and 103 math textbooks.

Step-by-step explanation:

Let c be the number of chemistry textbooks sold and m be the number of math textbooks sold. We know that c + m = 412, because the total number of textbooks sold is 412. We also know that c = 3m, because the number of chemistry textbooks sold is three times the number of math textbooks sold.

We can substitute 3m for c in the first equation to get 3m + m = 412. This simplifies to 4m = 412. Dividing both sides by 4 gives us m = 103.

Since we know that c = 3m, the number of chemistry textbooks sold is 3 * 103 = 309. Therefore, the store sold 309 chemistry textbooks and 103 math textbooks.

Answer:

1.6

Step-by-step explanation:

Firstly, we know the rate of change of volume [tex]v'=8[/tex].

The equation for surface area is: [tex]A = 4\pi r^2[/tex].

The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]

The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].

The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].

This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].

We can then plug that into our equation for [tex]A'[/tex] and get:

[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]

After that, we can just plug in:

[tex]2*\frac{8}{10}=1.6[/tex]

Answer:

In modular arithmetic, the modulo operation is used to find the remainder when one number is divided by another. For example, the expression "9 % 3" would evaluate to 0 because 9 divided by 3 leaves a remainder of 0.

In the given equation, taking the modulo 9 of both sides gives:

79z % 9 ≡ 92x + 9y % 9

The modulo operation distributes over addition, so we can simplify this to:

(79z % 9) ≡ (92x % 9) + (9y % 9)

Since any number divided by 9 has a remainder of itself, we can simplify this further to:

(z % 9) ≡ (2x % 9) + (y % 9)

This gives us the result:

-2z % 9 ≡ 2x % 9

Multiplying both sides by 5 gives:

(-2z % 9) * 5 ≡ (2x % 9) * 5

Which simplifies to:

-z % 9 ≡ x % 9

Since x is between 0 and 10, we know that x % 9 is between 0 and 9. Therefore, we can conclude that z = 9 - x.

Answer:

25

Step-by-step explanation:

1: Add up the ratio then divide by the number of students.

3+5=8

40/8=5

2: Each count is equal to 5 students.

3: Multiply the ratio of students who stay after soccer practice by Each count

5*5=25

Answer:

D is the answer

Step-by-step explanation:

Using bags that will make the balloon and the stickers have the same number in each bag, mere looking at the answers, 100/2 gives you 50 while 68/2 gives you 34. it means that it was splitted equally into the two bags.

Option of the matrices a, b, and d are non symmetric.

Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.

It is provided that A and B are symmetric n × n matrices.

To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.

Suppose X is a 2 × 3 matrix and Y is a 3 × 2.

Then the product AB will be a n × n matrix.

(a) A= C+CT

Thus the sum of matrix A and B will be a n × n matrix.

Thus, the matrix A is non symmetric.

(b) B = C-CT

So, matrix D will also be a n × n matrix.

Thus, the matrix D is non symmetric.

(c) D = CTC = (CT) × C

Then the product CT will be a n × n matrix.

The next step would be to multiply CT and C.

Both are n × n matrices.

Thus, the matrix D is symmetric.

(d) E = CTC - CCT

Then he product CT will be a n × n matrix.

Similarly, the product CT will be a n × n matrix.

Thus, the matrix E is non symmetric.

Similalry,

(e) F = (I +C)(I + CT

Thus, the matrix F is symmetric.

(f) G = (I +C)(I -CT)

Thus, the matrix G is symmetric.

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deposited some money at 1.7​% annual​ interest, and two equal but larger amounts at 2.2​% and 24​%. The total amount invested was ​$26,000​ and the total annual interest earned was ​$574. How much was invested at each​ rate?

What is an investor?

An investor is an individual or an organization that gives money to A person or entity that invests in another with the hopes of making a profit in the future is known as an investor. According to the rules, anyone can invest: You are an investor if you put money into something.

Answer provided by our tutors

Let

x = the money invested at 1.7%

y = the money invested at 2.2%

y = the money invested at 24%

Since the total money invested was $26,000 we have:

x + 2y = 26000

The total annual interest was $574 means:

0.017x + 0.022y + 0.24y = 574

0.017x + 0.262y = 574

We have the following system of equations:

x + 2y = 26000

0.017x + 0.262y = 574

click here to see the system of equations solved for x and y

x = $24,842

y = $578

$24,842 was invested at 1.7%

$578 was invested at 2.2% and another $578 was invested at 24%.

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Answer:

"the circumference divided by the diameter"

Step-by-step explanation:

Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).

Answer:

B

Step-by-step explanation:

First, we compute the exponent (3² = 9).

Next, we compute the multiplication and division (from left to right), so we have (40 - 2 × 9) = (40 - 18) = 22.

Thus, the number sentence 40 -2 × 3² = 22 is true.

B is true .22 is the real answer

Answer 34

...................................................................................

Answer:  its 18 im pretty sure

Step-by-step explanation:

The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.

a. A rational function with a hole at x = 1 and a vertical asymptote at x = -3 can be written as:

(x-1)/(x+3)

b. A rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 3 can be written as:

(x+2)/(x+2) = 3

c. A rational function with an oblique asymptote y = x+1 but no vertical asymptote can be written as:

(x-1)/(x-1) = x+1

d. A rational function with a vertical asymptote at x = 3 and f(x) > 0 can be written as:

(x-3)/(x-3) > 0

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It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.

To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:

Q(t) = Pe^(rt)

where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the values, we get:

Q(t) = 10 * e^(-432.2t)

This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.

To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.

[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]

t = approximately 7.66 years

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The perimeter of the shape is 12.82 units

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

A = (0, 2.76)

B = (3.65, 2.76)

C = (3.65, 0)

D = (0, 0)

Because the point D is at the origin, and the shape is a rectangle.

The perimeter of the shape can be represented as

P = 2 * (Bx + By)

Substitute the known values in the above equation, so, we have the following representation

P = 2* (3.65 + 2.76)

Evaluate

P = 12.82

Hence, the perimeter is 12.82 units

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An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.

Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."

Give the null hypotheses a name.

Negative hypothesis:

H. There is no correlation between gender and election participation.

Other possibilities:

H: Gender and participation in the most recent election are linked.

Rule of rejection:

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