Jamie knows that Atmospheric Fixation contributes to the Nitrogen Cycle,


but doesn't remember what exactly it creates. Can you remind her?

Since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

If every term of the sequence is either greater than or equal to (≥) some number M or less than or equal to (≤) some number N (finite numbers), then the sequence is said to be bounded.

Otherwise, the sequence is said to be unbounded. And, if a sequence has a convergent subsequence, then the sequence is called bounded.

Let’s look at the example to answer the question.

Example of an unbounded sequence that has a convergent subsequence:

Let {an} = 1, 2, 3, 4, 5, 6, 7, …It is an unbounded sequence since there is no number that can be defined as M or N, that will make every term of the sequence less than or equal to (≤) or greater than or equal to (≥) this number (M or N).

However, {an} = 1, 2, 3, 4, 5, 6, 7, … has a convergent subsequence which is {an} = 1, 2, 3, 4, 5, 6, 7, … itself.

And, since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

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The solution is 15 3/4 pages

The number of pages Matthew will read in one hour is 15 3/4 pages

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pages Matthew reads in an hour be = A

Now , the number of pages Matthew reads = 26 1/4 pages

26 1/4 pages = 105/4 pages

The time required to read 26 1/4 pages = 1 2/3 hour

1 2/3 hours = 5/3 hours

Now , the equation will be

The number of pages Matthew can read in 1 hour A = number of pages Matthew reads / time required to read 26 1/4 pages

Substituting the values in the equation , we get

The number of pages Matthew can read in 1 hour A = ( 105/4 ) / ( 5/3 )

The number of pages Matthew can read in 1 hour A = 105/4 x 3/5

The number of pages Matthew can read in 1 hour A = ( 21 x 3 ) / 4

The number of pages Matthew can read in 1 hour A = 63/4 pages

The number of pages Matthew can read in 1 hour A = 15 3/4 pages

Therefore , the value of A is 15 3/4 pages

Hence ,

The number of pages Matthew will read in one hour is 15 3/4 pages

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The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:

Step 1: Symbolic Expression

The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.

Step 2: Removing Radical

To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).

So, the expression becomes (57^(1/8))^6.

Step 3: Simplifying Exponents

To simplify the exponent, we multiply the powers:

(57^((1/8)*6))

Simplifying further:

(57^(6/8))

Step 4: Fractional Form

The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(57^(3/4))

Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).

This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.

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Answer:

Step-by-step explanation:

tan28=h/150

h=150tan28

h=79.8ft

x/(12+8)=5/8

x/20=5/8

x=100/8

x=12.5

Answer:

t = -3

Step-by-step explanation:

The side lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

For the equilateral triangle, all the sides have the same length of 12, and x is half of a side length, hence:

x = 12.

For the square, we have the sides of x with a diagonal, representing the hypotenuse, of 4, hence:

x² + x² = 4²

2x² = 16

x² = 8

\(x = 2\sqrt{2}\)

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(a) The VW Beetle takes approximately 22.98 seconds to reach a speed of 54.0 m/h.

(b) The acceleration of the top-fuel dragster is approximately 90 m/h/s.

(a) The time it takes for the VW Beetle to reach a speed of 54.0 m/h with an acceleration of +2.35 m/s^2 can be calculated using the formula:

Time (t) = (Final velocity (v) - Initial velocity (u)) / Acceleration (a)

Given that the initial velocity (u) is 0 m/h and the final velocity (v) is 54.0 m/h, and the acceleration (a) is +2.35 m/s^2, we can substitute these values into the formula:

t = (54.0 m/h - 0 m/h) / 2.35 m/s^2

Simplifying the equation, we get:

t ≈ 22.98 seconds

Therefore, it takes approximately 22.98 seconds for the VW Beetle to reach a speed of 54.0 m/h.

(b) To find the acceleration of the top-fuel dragster, given that it can go from 0 to 54.0 m/h in 0.600 seconds, we can use the formula:

Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)

Given that the initial velocity (u) is 0 m/h, the final velocity (v) is 54.0 m/h, and the time (t) is 0.600 seconds, we can substitute these values into the formula:

a = (54.0 m/h - 0 m/h) / 0.600 s

Simplifying the equation, we get:

a ≈ 90 m/h/s

Therefore, the acceleration of the dragster is approximately 90 m/h/s.

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Answer:

68.57mph

Step-by-step explanation:

with decimals, well, 3/4=0.75 (just divide 3/4 and you'll see) and 1 3/4 = 1.75

Then you divide 120/1.75 and there you go, 68.57mph

If you're supposed to do it with fractions:

1 3/4 = 4/4 + 3/4 = 7/4

Then you divide 120 / 7/4 (remember 120 = 120/1

Which means you have to cross multiply (an important part on fraction division, that is, your division would be 120x4 / 1x7).

Then 120x4= 480

And 1x7 = 7

Then you get 480/7, which is the same as 68 4/7 mph

Answer:

g=Xs+t

Step-by-step explanation:

please love math

to learn math, to look for topics you don't know in the internet

In conclusion: (a) The linear transformation f: M₂x₂ → R₃ given by f(a b; c d) = (b+d, a+b, d-a) is injective (one-to-one). (b) The linear transformation f is surjective (onto) if and only if every value of z can be expressed as the difference d - a for some real numbers d and a.

To determine whether the linear transformation f: M₂x₂ → R₃ is injective (one-to-one) and surjective (onto), we need to analyze its properties and conditions.

Let's define the linear transformation f as:

f(a b; c d) = (b+d, a+b, d-a)

(a) Injective (One-to-One):

A linear transformation f is injective if every distinct input vector in the domain corresponds to a distinct output vector in the codomain. In other words, if f(a₁ b₁; c₁ d₁) = f(a₂ b₂; c₂ d₂), then (a₁ b₁; c₁ d₁) = (a₂ b₂; c₂ d₂).

To test injectivity, we need to compare the outputs of f for two different input matrices and see if they are equal.

Let's assume two different input matrices: A₁ = (a₁ b₁; c₁ d₁) and A₂ = (a₂ b₂; c₂ d₂).

If f(A₁) = f(A₂), then we have:

(b₁+d₁, a₁+b₁, d₁-a₁) = (b₂+d₂, a₂+b₂, d₂-a₂)

Comparing the corresponding elements, we get the following system of equations:

b₁ + d₁ = b₂ + d₂ (1)

a₁ + b₁ = a₂ + b₂ (2)

d₁ - a₁ = d₂ - a₂ (3)

From equation (1), we can deduce that b₁ - b₂ = d₂ - d₁. Let's call this equation (4).

Similarly, equation (2) can be rewritten as a₁ - a₂ = b₂ - b₁. Let's call this equation (5).

Now, subtracting equation (3) from equation (4), we have:

(b₁ - b₂) - (d₁ - d₂) = (d₂ - d₁) - (a₂ - a₁)

(b₁ - b₂) - (d₁ - d₂) = (d₂ - d₁) - (b₂ - b₁)

Simplifying further, we get:

2(b₁ - b₂) = 2(d₂ - d₁)

b₁ - b₂ = d₂ - d₁

Using equation (5), we can substitute b₁ - b₂ = d₂ - d₁:

a₁ - a₂ = b₂ - b₁ = d₂ - d₁

This implies that a₁ = a₂, b₁ = b₂, and d₁ = d₂.

Therefore, we have shown that if f(A₁) = f(A₂), then A₁ = A₂. This confirms that f is an injective (one-to-one) linear transformation.

(b) Surjective (Onto):

A linear transformation f is surjective if every vector in the codomain has at least one corresponding input vector in the domain. In other words, for every vector (x, y, z) in the codomain R₃, there exists an input matrix A = (a b; c d) such that f(A) = (x, y, z).

To test surjectivity, we need to check if every vector (x, y, z) in R₃ can be expressed as f(A) for some matrix A = (a b; c d).

The codomain R₃ consists of 3-dimensional vectors, and the range of f is determined by the values of b, d, and the differences between b and d (b - d).

From the transformation equation f(a b; c d) = (b+d, a+b, d-a), we can observe that the third component z in R₃ is given by z = d - a. Therefore, any vector in R₃ can be expressed as f(A) if and only if z = d - a.

Since a and d are the diagonal elements of the input matrix A, we can conclude that for every vector (x, y, z) in R₃, there exists a matrix A = (a b; c d) such that f(A) = (x, y, z) if and only if z = d - a.

Therefore, f is surjective (onto) if and only if every value of z can be expressed as the difference d - a for some real numbers d and a.

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Answer:

  ASA is correct because segment KL is between congruent angles at K and congruent angles at L, and angle-side-angle arrangement.

Step-by-step explanation:

Segment KL is congruent to itself. At one end of that segment (L) are angles marked with a single arc. Those are congruent.

Aht the other end of that segment (K) are angles marked with a double arc. Those are congruent. So, we have congruent angles, congruent segments, and more congruent angles. That angle-side-angle sequence is sufficient for the triangles to be declared congruent. The associated postulate is abbreviated ASA (for angle-side-angle).

In the triangles of interest angle MLK corresponds to angle JLK. Each of those angles has the single-arc mark. Similarly, angle MKL corresponds to angle JKL, since each of those has the double-arc mark. The naming of the triangles in the congruence statement must be such that these angle names will correspond.

ASA is the correct congruence criterion because the triangles have congruent angles joined by a self-congruent side. The correct congruence statement is ∆JKL ≅ ∆MKL because K and L are self-corresponding vertices in each of the triangles.

The correct answer is D.

The variable of time that could cause a student’s GPA to increase is studying.

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The value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

To solve this problem, let's call the smaller number x and the larger number y.
According to the given information, the sum of the two numbers is 20, so we can write the equation: x + y = 20.
It is also given that one of the numbers (y) is twice the other number (x).

In equation form, we can write: y = 2x.

To find the value of the smaller number (x), we can substitute the value of y from the second equation into the first equation:
x + 2x = 20
Combining like terms, we get:
3x = 20
Dividing both sides by 3, we find:
x = 20/3
So, the value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Step-by-step explanation:

\( \frac{( {m}^{5} \times {m}^{6} \times {n}^{11})}{ {m}^{3} \times {n}^{5} \times n} \\ = \frac{ {m}^{11} \times {n}^{11} }{ {m}^{3} \times {n}^{6} } \\ = {m}^{8} \times {n}^{5} \\ = {m}^{8} {n}^{5} \)

Answer:

\(\frac{m^5 \times m^6 \times n^{11}}{m^3 \times n^5 \times n^1}\)

Step-by-step explanation:

m to the power of 5 = m⁵

m to the power of 6 = m ⁶

n to the power of 3 = n³

n to the power of 11 = n¹¹

      \(m^5 \times m^6 \times n^{11}\)   over  \(m^3 \times n^5 \times n^1\) = \(\frac{m^5 \times m^6 \times n^{11}}{m^3 \times n^5 \times n^1}\)

Simplified form:

\(m^{(5+6-3)} \times n^{(11 - 5- 1)} = m^8 \times n^{6}\)

Answer:

False

Step-by-step explanation:

You can't add without first doing the terms of 2^3---(PENDAS)

Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.

Repeating decimals are those numbers that, following the decimal point, continue to repeat the same value. Recurring numbers is another name for these figures. The term "non-repeating rational numbers" refers to decimal numbers that do not repeat their value after the decimal point.

A repeating decimal can be a rational number, and any integer is a rational number since it can be expressed as a fraction by simply assigning it a denominator of 1. Then, by multiplying and dividing the decimal according to its place values, we can also state that a terminating decimal can be expressed as a fraction.

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Answer:

34 if i am wrong i  apologies

Step-by-step explanation:

Answer: 1. 64 | 2. 32

Step-by-step explanation:

Formula for a rectangle is Area = Length*Width

Therefore: 8*8 = 64

Formula for a triangle is Area = 1/2*Base*Height, which is also 1/2*length*width

Therefore: 1/2*8*8 = 32

Hope this helps :)

Answer:

Total tickets sales= 8(45) + 15x, or you could do T= 360 + 15x. Whichever one you think is best.

Step-by-step explanation:

We know that each children's ticket costs $8, and there's 45 children tickets sold. So that would make 8(45), 8 x 45, which you could represent as $360 total of kids tickets.

For the adult tickets, we only know that each ticket costs $15 each. With the variable x representing the number of adult tickets, we can multiply that by 15 to make 15x. Since we don't know the amount of adult tickets sold.

With that, we can add both together to get the equation:

T= 8(45) + 15x

or

T= 360 + 15x

Answer:

a

Step-by-step explanation:

the probem said that joe has 3 and we know joe has less than 2 so we know to get to beths origina problem we have to subtract 2 from x while 3 is being represented as less sorry i picked the wrong option before

Answer:

y=4x-1

Step-by-step explanation:

We know that the slope equation is y=mx+b. M is the slope and B is the y-intercept. M is provided to be 4 and B is provided to be -1, so all we have to do is plug them in to get the answer.

Answer:

y = 4x - 1

Step-by-step explanation:

Slope-intercept form:

y = mx + b

So, input all the values...

y = 4x - 1

Hope this helps :)

Let me know if there are any mistakes!!

The answer is:

\(\sf{y-12=-\dfrac{3}{4}(x+4)}\)

Work/explanation:

The point slope equation is:

\(\rm{y-y_1=m(x-x_1)}\)

where m = slope;

(x₁, y₁) is a point on the line.

Plug in the data accordingly.

\(\sf{y-12=-\dfrac{3}{4}(x-(-4)}\)

Simplify

\(\sf{y-12=-\dfrac{3}{4}(x+4)}\)

Answer:

24

Step-by-step explanation:

x is hypotenuse

so 16 is adjacent to 49 degrees angle

then cos (49) = 16/x

x = 16/cos(49) = 16/0.6561 = 24

Rays AB and BE are part of line BE.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

To find the rays which are part of line BE.

Here,, By figure, we have;

Rays AB and BE are part of line BE.

Thus, Rays AB and BE are part of line BE.

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Answer: x=-5

Step-by-step explanation:

The probability of a success gets closer to zero is 15.

What is behavior of the standard deviation ?

The average squared difference between data points and their mean value is called variance, and it is the variance's square root that is used to calculate standard deviation. The symbol for standard deviation can be seen below.

Both the standard deviation and the variance are indicators of dispersion, but the standard deviation is more explicitly the typical distance between a data point and the mean. The majority of the data will be within one standard deviation of the mean. While the variance is not measured in the same units as the actual data, the standard deviation is

If mean deviation is 12, what is its standard deviation?

Lets look the problem .

Given ,

Mean deviation (MD) =12

Here is the inequality to calculate the standard deviation.

6QD=5MD=4SD ,

Where ,QD stands for the Quartile deviation.

SD stands for the standard deviation.

So,

Standard deviation =(5/4)*MD

=(5/4)*12

=15

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Answer:

6cm square

Step-by-step explanation:

There is 35.135 percentage  of dogs are male .

What is percentage?

In mathematics, a percentage is a number or rate expressed as a bit of 100. It's frequently denoted using the percent sign % .A percentage is a dimensionless number; it has no unit of dimension.

Main body:

since we have given that

Total number of dogs = 37

Number of dogs that are female = 24

Number of dogs that are male  is given = 37-24 = 13

We need to find the percentage of dogs are male:

So, Percentage of the dogs are male is given by

(13/37)*100

=  35.135%

Hence, there is 35.135% of dogs are male .

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Answer:

You need 2.11 quarts of strawberries

and 3.17 pints of blueberries

Step-by-step explanation:

2.11 quarts of strawberries

3.17 pints of blueberries