A group of marine biologists tags 45 great white sharks off the coast of Mexico to study migratory patterns. All of the tag numbers are unique. Weeks later, the marine biologists travel to Hawaii. While there, they randomly capture and release 20 great white sharks per day, for three consecutive days. On the first day, 3 of the sharks have the original tags. On the second day, 2 of the sharks have the original tags. On the third day, 4 of the sharks have the original tags. Based on the data, what is the estimated population of great white sharks that have migrated from Mexico to Hawaii?​

The linear function changes at a rate of [tex]5/4[/tex]. This implies that [tex]y[/tex] grows by [tex]5/4[/tex] units for every unit increase in [tex]x[/tex].

The graph of a linear function is a direct line. The following is the form of a linear function. a + bx = y = f(x). One independent variable one and dependent variable make up a linear function.

A linear relation on the reference system is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) => 3x - 2 since y could be substituted with f(x).

slope = (change in y) / (change in x)

slope [tex]= (1 - (-4)) / (4 - 0)[/tex]

slope [tex]= 5 / 4[/tex]

Therefore, the rate of change of the function is [tex]5/4[/tex]. This means that for every [tex]1[/tex] unit increase in [tex]x[/tex], [tex]y[/tex] increases by [tex]5/4[/tex] units.

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Answer:

  9000 feet altitude

Step-by-step explanation:

Given that the y-value for this situation represents altitude in thousands of feet, you want to know what the y-value of the point of intersection represents.

The problem statement tells you the meaning of the y-value anywhere. It is "altitude in thousands of feet."

The point of intersection is (2, 9), where the x-value is time in minutes.

The y-value of 9 at the point of intersection represents an altitude of 9000 feet.

__

Additional comment

This  is an exercise in reading comprehension.

Answer:80

Step-by-step explanation:

Area is multiple from 20 and 4 so the answer is 80

The remaining customer advance at the end of 2025 is $16,592,000.

To determine the amount of customer advance remaining at the end of 2025, we need to subtract the amount collected in 2025 from the customer advances balance at the end of 2024:

Customer advances balance at the end of 2024 = $12,518,000

Amount collected in 2025 = $30,256,000

Customer advances recognized in income in 2025 = $26,182,000

Customer advances balance at the end of 2025 = Customer advances balance at the end of 2024 + Amount collected in 2025 - Customer advances recognized in income in 2025

Customer advances balance at the end of 2025 = $12,518,000 + $30,256,000 - $26,182,000

Customer advances balance at the end of 2025 = $16,592,000

Therefore, the remaining customer advance at the end of 2025 is $16,592,000.

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The proportion of the pool that will be filled when the first pump works for 2 hours and the second pump works for 3 hours is given as follows:

100%.

The fraction of the pool that will be filled when the first pump works for 2 hours and the second pump works for 3 hours is obtained applying the proportions in the context of the problem.

One pump can fill a swimming pool in 4 hours, hence the proportion filled in two hours is given as follows:

2/4 = 50%.

A second pump can fill the pool in 6 hours, hence the proportion filled in three hours is given as follows:

3/6 = 50%.

Then the total proportion is given as follows:

50 + 50 = 100%.

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There are 84 calories from alcohol in a margarita containing 12 grams of alcohol.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The formula to calculate the calories from alcohol in a drink is:

Calories from alcohol = (Grams of alcohol) x (7 calories per gram)

Therefore, to calculate the calories from alcohol in a margarita containing 12 grams of alcohol, we use this formula:

Calories from alcohol = 12 grams x 7 calories/gram = 84 calories

Therefore, there are 84 calories from alcohol in a margarita containing 12 grams of alcohol.

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Answer:

x = -60

Step-by-step explanation:

1/4x - 3 = 1/2x + 12

add three to both sides

1/4x = 1/2x + 15

subtract 1/2x from both sides

-1/4x = 15

divide by -1/4

x = -60

Answer:

11%

Step-by-step explanation:

find the price of the shirts before markup by dividing 10800 by 400

You get 27, which you will subtract 30 by, getting you 3.

Divide this number by 27

.11

The experimental probability of rolling a number less than 4 is:

P(less than 4) = 6/12 (in fraction)

P(less than 4) = 0.5 (in decimal)

P(less than 4) = 50% (in percentage)

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

The numbers less than are 1, 2 and 3. Since six of the twelve outcome in the table are less than 4. Thus, the experimental probability of rolling a number less than 4 will be:

P(less than 4) = 6/12 (in fraction)

P(less than 4) = 0.5 (in decimal)

P(less than 4) = 50% (in percentage)

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Answer:

6016920.57

Step-by-step explanation:

First, find (57)^3

= 185193

Then find (5.7)^2

= 32.49

Finally,

multiply both answers:

32.49 .  185193

= 6016920.57

Answer: 6016920.57

Step-by-step explanation:

(57)^3 = 185193

(5.7)^2 = 32.49

32.49 *  185193 = 6016920.57

The third quartile for the given conditions is 224.

Given that a  sample of nine participants is selected and their total cholesterol levels are measured as follows:

185 225 240 196 175 180 194 147 223

The third quartile is the median of the upper half of a data set.

We can calculate the third quartile by arranging the data in ascending order and finding the median of the upper half of the data.

Therefore, the data arranged in ascending order is:

147 175 180 185 194 196 223 225 240

Now, the upper half of the data is:

194 196 223 225 240

There are five data values in the upper half, so the median is the mean of the 3rd and 4th values in the ordered list:

Q3=(223+225)/2 = 448/2 = 224

Hence, the third quartile is 224.

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With the equation solved, we obtain variable x=-3.

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The connection between the phrases displayed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS (left hand side = right hand side) is used. Solving the equations to get the value of an unknown variable that stands in for an unknown quantity.

Given equation: 4⁻²ˣ × 4ˣ=64

Let 4ˣ be y

y⁻² × y=64

Solving the equation, we get

y/y²=64

y=1/64

Putting the value of y, we get

4ˣ=1/64

4ˣ=4⁻³

Hence, value of x=-3.

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Bo would drive 893 miles on 38 gallons of fuel.The number of miles driven by Bo is directly proportional to the number of gallons of fuel he has used.

This means that if we know how many miles Bo has driven for a certain number of gallons of fuel, we can calculate how many miles he would drive with a different number of gallons of fuel. To calculate this, we need to first determine the ratio of miles driven per gallon of fuel used. To do this, we can use the data given in the problem: Bo has driven 188 miles on 8 gallons of fuel, and 799 miles on 34 gallons of fuel.

We can calculate the ratio of miles driven per gallon of fuel used by dividing the number of miles driven by the number of gallons used. In this case, the ratio is 188/8 = 23.5 miles per gallon. We can then use this ratio to calculate the number of miles Bo would drive on 38 gallons of fuel. To do this, we simply multiply the ratio by the number of gallons used, which in this case is 38. This gives us 38 x 23.5 = 893 miles.

Therefore, Bo would drive 893 miles on 38 gallons of fuel.

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Answer: -46

Step-by-step explanation:

First f-g (since its in parenthesis)

  f(x)=3x^5+6x^2-5

-  g(x)=3x^5-5x^4-15

=          0  -5x^4 +6x^2 + 10

then, sub in 2 for x

(-5x^4 +6x^2 + 10); x=2

-5(2)^4 + 6(2)^2 + 10 = -46

*can only subtract terms with the same power

Answer:

i don't know is correct but here The function f(x)f(x) is a cubic function and the zeros of f(x)f(x) are -5−5, 11 and 55. Assume the leading coefficient of f(x)f(x) is 11

by-step explanation:

Answer:

x = 5 , ML = 18

Step-by-step explanation:

the midsegment NP of the trapezoid is half the sum of the bases, that is

NP = [tex]\frac{JK+ML}{2}[/tex]

25 = [tex]\frac{4x-2+6x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

50 = 10x ( divide both sides by 10 )

5 = x

Then

ML = 4x - 2 = 4(5) - 2 = 20 - 2 = 18

The statement "two proofs are required to establish the provable equivalence of two sentences of tfl" is false.

Only one proof is required to establish the provable equivalence of two sentences of TFL.

What is TFL? TFL (Truth-Functional Logic) is a form of propositional logic in which the only logical expressions are truth functions. Truth functions are built from a fixed set of truth-functional connectives or operators, each of which operates on one or more sentences to create a compound sentence. TFL's operators are all truth-functional; that is, the truth or falsity of a sentence depends solely on the truth or falsity of its atomic components and how they are combined by the operators.

Here are the five standard truth-functional operators in TFL:

Conjunction: AND (•)

Disjunction: OR (+)

Negation: NOT (~)

Conditional: IF...THEN (→)

Biconditional: IF AND ONLY IF (↔)

Proofs are used to demonstrate the validity of sentences in TFL. It is important to note that a sentence's validity is a property of the sentence itself, not the sentence's meaning. To demonstrate the validity of a sentence in TFL, proofs are created.In TFL, two sentences are provably equivalent if and only if they are logically equivalent. The provable equivalence of two sentences in TFL only requires one proof. Thus, the statement, "Two proofs are required to establish the provable equivalence of two sentences of TFL," is false.

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Answer:

36

Step-by-step explanation:

(2 x 10)+(2 x 8) = 36

The total area is 36 cm squared.

The volume of the cylinder is 6π (18.84) cubic inches.

What is volume in mensuration ?

In mensuration, volume is the measure of the amount of space occupied by a three-dimensional object or a region in space. It is a measure of the capacity of an object and is usually expressed in cubic units, such as cubic meters, cubic centimeters, or cubic inches.

To understand the concept of volume in more detail, we can visualize the cylinder as a three-dimensional object with circular bases and curved sides. The height of the cylinder represents the distance between the circular bases, and the radius represents the distance from the center of the circular bases to their edges. The volume of the cylinder represents the amount of space inside the cylinder, and can be thought of as the product of the area of the circular base and the height of the cylinder.

To find the volume of a cylinder, we use the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height of the cylinder. Since the diameter of the cylinder is given as 2 inches, we can find the radius as:

radius = diameter / 2 = 2 / 2 = 1 inch

Now, we can substitute the values of the radius and height into the formula to find the volume:

V = π(1)²(6) = 6π

Therefore, the volume of the cylinder is 6π cubic inches.

In practical applications, the concept of volume is used in many areas, such as manufacturing, engineering, architecture, and physics. For example, the volume of a cylinder can be used to calculate the amount of liquid it can hold, the amount of material needed to fill it, or the amount of air it can displace.

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To solve the quadratic function -3x² + 5x + 9 = 0, the formula that should be used is Option C: x = (-5 ± √133) / -6.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic formula is used to solve quadratic equations in the form of ax² + bx + c = 0, where a, b, and c are constants.

To use the quadratic formula to solve the equation -3x² + 5x + 9 = 0, we need to identify the values of a, b, and c.

In this case, a = -3, b = 5, and c = 9.

Therefore, we can use these values to plug into the quadratic formula -

x = (-b ± √(b² - 4ac)) / 2a

So the answer that can be used to find the solutions to the equation using the quadratic formula is -

x = (-5 ± √(5² - 4 × (-3) × 9)) / 2 × (-3)

Solving this equation we get -

x = (-5 ± √(25 + 108)) / -6

x = (-5 ± √133) / -6

Therefore, the solution is obtained by the equation x = (-5 ± √133) / -6.

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the value of the given function f(g(1)) is 2 , fog is an even function

A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.

f is even (given)

∴f(−x)=f(x)

g is odd (given)

∴g(−x)=−g(x)

So,

According to question,

fog=f[g(x)]=f(y)             Let [g(x)]=y

and also,

fog=f[g(−x)]        ∵g(x) is odd

       =f[−g(x)]

       =f(−y)

       =f(y)

⇒fog(x)=fog(−x)

∴fog is an even function

f(g(1)) = f(g(1)) = f(3) = 2

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By hypothesis , μ ≤ $200 is the mean cost of science textbooks are no more than $200.

What does "mathematical hypothesis" mean?

A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong. An assertion that will serve as the foundation for hypothesis testing is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

                          The statement "all fours sides of a quadrilateral measure the same, then the quadrilateral is a square" states that if true, the quadrilateral is a square.

Here  n = 143

    the claim that the mean cost of science textbooks are no more than $200.

    H₀  : μ = $200

    H₁  :  μ ≤ $200

Therefore, this problem based on one sample t test for mean .

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Answer:

9

Step-by-step explanation:

1 to 10

Hence,

10 - 1 = 9

Similarly,

20 - 11 = 9

30 - 21 = 9

40 - 31 = 9

Therefore,

Interval is 9

9/1 is the simple form in fraction .

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

1st rectangle = 15 * 45  = 675

2nd rectangle  = 15 * 5 = 75

 1st/2nd = 675/75

             =  9/1

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Madison will require 88 fabric squares, rounded up to the next integer, therefore option B is the correct solution.(d).

A circle's circumference is the distance around its outside boundary.

The following formula can be used to compute it.

C = 2πr

The diameter of the circle is equal to the perimeter of the circular mirror, which is 2r, where r is the radius.

Circumference = 2 x 3.14 x 14 cm = 87.92 cm

Madison will need to cover this area with 1 cm cloth squares.

The number of fabric squares required equals the perimeter / length of each square.

87.92 cm / 1 cm = 87.92 fabric squares required

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[tex](2x-6)(2x-6)[/tex]

[tex]4x^2 - 12x - 12x + 36[/tex]

Answer:

To find the area of the isosceles trapezoid, we can use the formula:

Area = ((upper base + lower base) / 2) x height

First, we need to find the height of the trapezoid. We can use the Pythagorean theorem to find the height, since the legs of the trapezoid form a right triangle with the height as the hypotenuse.

Using the Pythagorean theorem:

height^2 = leg^2 - ((lower base - upper base) / 2)^2

= 5^2 - ((16 - 8) / 2)^2

= 25 - 4^2

= 9

height = 3 cm

Now that we have the height, we can use the area formula:

Area = ((8 + 16) / 2) x 3

= 12 x 3

= 36 cm^2

Therefore, the area of the isosceles trapezoid is 36 square centimeters.

Answer:

The expression 6c + 4d - c - 7d can be simplified by combining like terms. 6c + 4d - c - 7d = (6c - c) + (4d - 7d) Simplifying further, we get: 6c + 4d - c - 7d = 5c - 3d So the simplified expression is 5c - 3d.

To simplify the expression 6c + 4d - c - 7d, we can first combine the like terms, which are the terms that have the same variable and the same exponent:

6c - c + 4d - 7d

Simplifying this expression further by combining the like terms, we get:

5c - 3d

Therefore, 6c + 4d - c - 7d simplifies to 5c - 3d.

a. q-p = 11-3 = 8, which is an even number. b. p+q = 3+11 = 14, which is an even number.

In mathematics, a prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that can only be divided evenly by 1 and itself.

There are various methods for finding prime numbers, such as the Sieve of Eratosthenes, which is a simple algorithm for generating all prime numbers up to a given limit. However, as the numbers get larger, it becomes increasingly difficult to find prime numbers, and there is no known formula for generating all prime numbers.

a. One possible example is:

p = 3

q = 11

Here, q-p = 11-3 = 8, which is an even number. However, if we add 1 to it, we get 9, which is odd but not prime (since it is divisible by 3).

b. One possible example is:

p = 3

q = 11

Here, p+q = 3+11 = 14, which is an even number. However, if we add 1 to it, we get 15, which is odd but not prime (since it is divisible by 3 and 5).

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Answer:

substitute the value of y

y=15-x

3(15-x)=5x+3

45-3x=5x+3

-3x-5x=3-45

-2x=42

X=21