A marine biologist wants to determine the impact of warming oceans on the coral in Great Barrier Reef. Which option below best describes the population he will study?

The result is 45a^3b^4+4b

The given expression is 45a^3b^4+36a^2b^5 ÷ 9a^2b^4 First, we will simplify the term 36a^2b^5 ÷ 9a^2b^4 by dividing the coefficients and subtracting the exponents of the variables.

36 ÷ 9 = 4

a^2 ÷ a^2 = a^(2-2) = a^0 = 1

b^5 ÷ b^4 = b^(5-4) = b^1 = b

So, 36a^2b^5 ÷ 9a^2b^4 = 4b

Now, we can substitute this value back into the original expression:

45a^3b^4+4b

We cannot simplify this expression any further since the terms do not have the same power of the variables.

So, the final answer is: 45a^3b^4+4b

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The surface area of the prism is 60 sq meters.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

We know, The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given prism has 9 m of length, 6 m of width, and 2 m of height.

Therefore, The surface area of the prism is,

= 2(9 + 6)×2 sq meters.

= 2×15×2 sq meters.

= 60 sq meters.

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The answers to all parts are shown below.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

Given:

The polynomial zeros are given as:

x = 7, x = -1 and x = -3

x - 7 = 0, x + 1 = 0 and x + 3 = 0

So, f(x) = (x - 7)(x + 1)(x + 3)

f(x) = (x - 7)(x² + 4x +3)

f(x) = x³ -3x² -25 x -21

Now, Rational function g(x)

g(x) = f(x) / (x² - x + 2)

After Factorizing

g(x) = (x-2) - 25x+ 25 /  (x² - x + 2)

The slant asymptote is the quotient i.e. x - 2

Hence, the slant asymptote of the function g(x) is x - 2

So, the discontinuities of g(x)

g(x) = (x³ -3x² -25 x -21) /  (x² - x + 2)

Set the denominator to 0

x² - x + 2 = 0

(x - 2)(x + 1) = 0

x= 2 or x= -1.

So, the discontinuities and their types are:

Essential discontinuity at x = 2

Removable discontinuity at x = -1

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(-3, 4) is the solution to the given system of simultaneous equation

Given the system of equation

y = -x + 1

y = -1/3x + 3​

When solving graphically, the point of intersection of both lines on an xy plane is the solution to the system of equation.

According to the graph attached, the solution to the system of equation is (-3, 4).

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Answer:

She must score an 87 to obtain an average of 75.

Step-by-step explanation:

(66+72+x) / 3 = 75

x = 87

The value of the fraction is A = 20 / 9

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the first fraction is p = 5/6

Let the second fraction be q = 3/8

Now , the equation is A = p/q

On simplifying , we get

A = ( 5/6 ) / ( 3/8 )

A = ( 5/6 ) x ( 8/3 )

On further simplification , we get

The fraction A = ( 20 / 9 )

Hence , the fraction is A = 20/9

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The area of the enclosure is approximately 128.6 acres

To find the area of the trapezoid ABCD, we first need to find the lengths of its parallel sides. Let's use the fact that the angles of a quadrilateral add up to 360 degrees:

Angle ABC = 124 degrees

Angle BCD = 85 degrees

Angle CDA = 96 degrees

Angle DAB = 360 - 124 - 85 - 96 = 55 degrees

Now we can use the tangent function to find the lengths of the sides:

tan(2 degrees) = (height of AB) / (distance between Anna and Benito)

(height of AB) = (distance between Anna and Benito) × tan(2 degrees)

(distance between Anna and Benito) = (713 - 690) / tan(2 degrees) ≈ 18490.3 ft

(height of AB) ≈ 429.4 ft

Similarly, we can find the height of CD:

tan(3 degrees) = (height of AD) / (distance between Anna and Deon)

(height of AD) = (distance between Anna and Deon) × tan(3 degrees)

(distance between Anna and Deon) = (725 - 690) / tan(3 degrees) ≈ 8639.5 ft

(height of AD) ≈ 459.6 ft

Now we can use the trapezoid area formula:

Area = (height of AB + height of CD) × (sum of the parallel sides) / 2

Area = (429.4 + 459.6) × ((18490.3 + 8639.5) / 2) / 5280 ≈ 128.6 acres

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The area of the polygon will be equal to 58.1 square units.

A polygon's area is the region that it occupies. Polygons can be both regular and irregular in shape. Triangles, squares, rectangles, pentagons, hexagons, and other basic polygons are used in geometry. Each of these polygons has its own area.

A pentagon is a given polygon. The apothem is the perpendicular line drawn from the octagon's midpoint to the base of one of its sides.

The formula for determining the area of a regular polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 5

Area = 4² × 5 × tan(180/5)

Area = 80 × tan 36

Area = 58.1 Square units

Hence, the polygon will have an area of 58.1 Square units.

The missing image is attached with the answer below.

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Since the two parallel lines are cut by a transversal and m∠3 = 41°, the measure of angles m∠6 and m∠8 include the following:

m∠6 = 139°.

m∠8 = 139°.

In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

m∠3 = m∠5 (alternate interior angles)

m∠5 + m∠6 = 180° (linear pair postulate).

41° + m∠6 = 180°.

m∠6 = 180° - 41°

m∠6 = 139°

m∠6 = m∠8 (vertical angles theorem).

m∠8 = 139°.

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For the function y = 3x - 1, the correct conclusion is C.As the value of x increases, the value of y increases.

As the value of x increases, the value of y increases.

In this function, y is dependent on the value of x. The variable x is multiplied by 3 and then subtracted by 1 to find the value of y. As the value of x increases, the value of y will also increase because it is being multiplied by 3.

For example, if x = 1, then y = 3(1) - 1 = 2. If x = 2, then y = 3(2) - 1 = 5. As you can see, as the value of x increases, the value of y also increases.

Therefore, the correct conclusion for this function is C. As the value of x increases, the value of y increases.

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Answer:

Each crust is 1.2 inches

Step-by-step explanation:

12/10 is 1.2

Answer:

Each crust is 1.2 inches.

Step-by-step explanation:

12 ÷ 10 = 1.2

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Answer:

180

Step-by-step explanation:

since both triangles are 90 degrees 90 plus 90 make 180

Answer:

d. 1/36

Step-by-step explanation:

as total outcomes is 36

and we can get 1 on both the dice just once

Answer: look at the image for the answers and solutions

Step-by-step explanation:

Answer:

If 68.3% of Americans believe that some psychics can help solve murder cases, then the percentage of Americans who do not believe this is:

100% - 68.3% = 31.7%

Therefore, the probability of randomly selecting someone who does not believe that some psychics can help solve murder cases is 31.7%.

Step-by-step explanation:

Since, 1 Tablespoon is equal to 15 Gram.

Therefore, 2 Tablespoon is equal to 1/8 cups or 29.5 grams.

Gram:

The gram (originally gram; SI unit symbol g) is a unit of mass in the International System of Units (SI), equal to one thousandth of a kilogram.

Originally defined in 1795 as "the absolute weight of a volume of pure water equal to one hundredth of a meter at the temperature at which ice melts." The positive temperature (~0 °C) was later changed to 4 °C, the temperature of maximum density of water.

However, towards the end of the 19th century, attempts were made to make the kilogram the base unit and the gram the derived unit. In 1960, the new International System of Units defined the gram as one thousandth of a kilogram (i.e., 1 gram equals 1 × 10-3 kg. As of 2019, the kilogram is defined by the International Bureau of Weights and Measures based on the fixed value of Planck's constant (h),  

6.62607015 × 10-34 kg⋅m2⋅s-1.

According to the Question:

Convert from tablespoons to grams by multiplying the volume by 14.786765 times the density of the ingredient or material.

Using this simple formula, it can be converted to:

Grams = Tablespoons × 14.786765 × Ingredient Density

Therefore,

Grams = 02 × 14.786765

           = 29.57353

So the volume in grams is equal to the number of tablespoons times the density of the material or material times 14.786765.

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Answer

lines passing through the midpoint of each side which are perpendicular to the given side

Step-by-step explanation:

The formula for the volume of a square prism is given as V = s^2 * h. V = s^2 * h = 1.5^2 * 8 = 2.25 * 8 = 18 cm^3 So the volume of the square prism is 18 cubic centimeters.

this is what weegy answered

Answer:

for 8x + 9 Y = 0  

for xsmall2 + 4x + 13  y = 6x + 13

Step-by-step explanation:

The required derivative of f(x) = ln(1 - x) is f'(x) = -1 / (1 - x).

A derivative is a two-party contract whose price or value is based on an underlying asset. Futures, options, forward contracts, and swaps are the four most popular types of derivatives. It is a financial instrument whose price and value are determined by the underlying assets.

The derivative of the natural logarithmic function is given by:

d/dx [ln(u(x))] = 1/u(x) * du/dx

So, to find the derivative of f(x) = ln(1 - x), we need to find the derivative of the inside function, which is 1 - x:

f'(x) = 1/[1 - x] * d/dx [1 - x]

= 1/[1 - x] * (-1)

= -1 / (1 - x)

So the derivative of f(x) = ln(1 - x) is f'(x) = -1 / (1 - x).

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⇒ The general formula of a geometric sequence is [tex]ar^{n-1}[/tex] where a is the first term and r is the common ratio, now in the given a which is 3 and the common ratio r which is 3.

to get the 10th term we use the same general formula

[tex]a_{n} =ar^{n-1}[/tex]

where [tex]T_{n}[/tex] is the nth term that is then output and n is the place of the nth term in the general sequence.

For the 10th term we substitute  10 in the place of n and simplify to find the value of the output.

[tex]a_{10} =ar^{(10-1)} \\a_{10} =ar^{9} \\[/tex]

Now since we know which formula to use to get the 10th term we can substitute the known values of the variables to get the output .

[tex]a_{10} =(3)(3)^{9} \\a_{10} =59049[/tex]

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If Keshawn is 1.45 meters tall. At 12 noon, he measures the length of a tree's shadow to be 15.05 meters. the height of the tree to the nearest hundredth of a meter is 2.02 meters.

To find the height of the tree, we can use the similar triangles method. Let's call the height of the tree "h".

Since Keshawn and the tree are standing in the same spot, the same light source is casting their shadows, so the ratios of their shadow lengths to their heights are equal. This means we can set up the following proportion:

1.45 / h = 15.05 / 10.8

We can solve for "h" by cross-multiplying:

h = 15.05 * 1.45 / 10.8

h = 2.02 meters

Therefore, the height of the tree to the nearest hundredth of a meter is approximately 2.02 meters.

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Answer: 5.13

Step-by-step explanation:

Compliment set of set A union set B is {1, 6, 9}.

Sets in mathematics, are simply a collection of distinct objects forming a group. A set can have any group of items, be it a collection of numbers, days of a week, types of vehicles, and so on. Every item in the set is called an element of the set.

The given sets are U={1,2,3,4,5,6,7,8,9,10}, A={4,6,8,10} and B={2,3,7}

Here, (A∪B)={4,6,8,10}∪{2,3,7}

= {2,3,4,5,7,8,10}

(A∪B)'=U-(A∪B)

= {1,2,3,4,5,6,7,8,9,10}-{2,3,4,5,7,8,10}

= {1, 6, 9}

Therefore, (A∪B)' is {1, 6, 9}.

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Answer: B- about 349,471 deer.

To calculate the population after 12 years, we can use the formula:

N = N0 * (1 + r)^t

where N0 is the initial population (15,000), r is the growth rate (3%), and t is the number of years (12).

Plugging in the values:

N = 15,000 * (1 + 0.03)^12 = 15,000 * 1.95863 = 29,379.45 ≈ 349,471

Step-by-step explanation:

The ratio 3:4 into percentage is 75%.

3/4 is expressed as 75% in terms of percentage.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.

According to the Question:

The fraction 3/4 to an equivalent fraction with the denominator equal to 100

(3 × 25) / (4 × 25) = 75/100

Now,

75/100 is expressed as 75% in terms of percentage.

Another simple way to convert a fraction to a percentage is by multiplying the fraction by 100.

In this case, 3/4 × 100 = 75%

Thus, 3/4 is expressed as 75% in terms of percentage.

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The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA).

By using the Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated. The student's letter grades for each subject are then translated into a number value on a 4.0 scale, as seen below:

A = 4.0 A- = 3.67 B = 3.0 B- = 2.67 C = 2.0 C- = 1.67 D = 1.0 F = 0.0

The sum of the products of the credit hours and the numerical values of the letter grades obtained is used to compute the student's GPA after each letter grade has been given a numerical value.

The Grade Point Average at Purdue University is determined using a 4.0 scale (GPA). By allocating each course a specific number of credit hours, which is normally decided by the number of hours the course meets per week, the GPA is generated.

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The statement which is given as , "The product of permutation matrices is again a permutation matrix." is True.

A permutation matrix is a square matrix whose entries are either 0 or 1 and has exactly one "1" in each row and each column. In other words, it is a matrix that represents a permutation of the rows (or columns) of the identity matrix.

When two permutation matrices are multiplied, the result is another square matrix with exactly one "1" in each row and each column. To see why this is true, consider two permutation matrices, A and B. Suppose that A is a m x m matrix and B is a m x m matrix. The product of these two matrices is another m x m matrix, C = AB.

Each entry in the matrix C is given by the dot product of the corresponding row in A and the corresponding column in B. If the row in A has a "1" in the i-th position and the column in B has a "1" in the j-th position, then the i,j-th entry in C will be "1".

Since both A and B are permutation matrices, each row in A and each column in B has exactly one "1". This means that each row in C will have exactly one "1", and each column in C will also have exactly one "1". Hence, C is also a permutation matrix.

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The composite figure has a total area of 258 square centimeters.

The diagram is the made up of a rectangle and two triangles.

A triangle's area is given by the formula

Triangle 1

= 1/2 x base x height.

= 1/2 × 4 × 12

= 24

Triangle 2

=  1/2 × 12 × 3

= 18

Area of a rectangle

= length x width

= 18 × 12

= 216

The total area

= 24 + 18 + 216

= 258 squared centimeter

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The value of the square root of 9 is 3.

The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we want to find the square root of 9.

We can start by finding the perfect squares that are less than 9. The perfect squares less than 9 are 1 and 4. We can see that 3 is between these two numbers, so the square root of 9 must be somewhere between 1 and 3.

We can test whether 3 is the square root of 9 by squaring it: 3 x 3 = 9. This confirms that 3 is indeed the square root of 9.

Another way to find the square root of 9 is to use a calculator or a mathematical formula. The formula for finding the square root of a number is √x = y, where y is the square root of x. In this case, x is 9, so we have √9 = 3.

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