A marine biologist is studying the growth of a particular species of fish. she writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 4(1.08)m
what is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent? (4 points)

The domain of the given rational function R(x) = 6x/(x + 1) include the following: A. the domain of R(x) is {x|x ≠ 1}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.

In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the graph as follows:

Domain = (-∞, 1) U (1, ∞)

By using set builder notation, the domain of this rational function R(x) = 6x/(x + 1) can be re-written as follows;

Domain = {x|x ≠ 1}.

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The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Now, According to the question:

600 [tex]u^2[/tex] of land to be enclosed by fence

Area inside plot should be maximized, amount of fence should be minimized

If we draw a quick sketch, we get something like this:

_____ _____

|        |         |

|        |         |

|        |         |

|        |         |

The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.

Let's put some variables into our picture so we can define our constraints.

       y        y  

  |         |        |

x |      x |      x |

  |         |        |

  |         |        |

Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.

A = x × 2y = area = 600

P = 3x + 4y = perimeter = a minimum

First we solve the area equation for y:

y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]  

and then we substitute that result into our perimeter equation:

P = 3x + 4 (300/x)

P = 3x + 1200/x

Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]

We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.

In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is

P'(x) = 3 - 1200[tex]x^-^2[/tex]

When set equal to zero, we can solve for x:

3 - 1200[tex]x^-^2[/tex]= 0

1 - 400[tex]x^-^2[/tex] = 0

1 = 400/[tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 400

x = ± 20

Our fence length can't be a negative number so our answer must be 20u.

If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.

The y length is 300/(20) = 15

Let's put all of our numbers into our picture to see if it make sense.

      15      15    

    |        |         |

20 |    20 |    20 |

    |        |         |

    |        |         |

       15      15

Sure enough our area is 600.

Here's what we have right now:

A(20, 15) = 600

P(20, 15) = 120

How about we try something a little bigger like 20.5 for x and 14.63 for y?

A(20.5, 14.63) = 600

P(20.5, 14.63) = 120.02

How about we try something a little smaller like 19.5 for x and 15.38 for y?

A(19.5, 15.38) = 600

P(19.5, 15.38) = 120.02

It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.

You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.

Each rectangle is 300 u^2. We want a square so each side would be √(300) = 17.32

              17.32         17.32    

        |                |                 |

17.32 |       17.32 |        17.32 |

        |                |                 |

             17.32          17.32

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

Hence, The dimensions of the rectangular plot that require the least amount of fencing is :

A(17.32, 17.32) = 600

P(17.32, 17.32) = 121.24

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Answer:

500 > 40 + 5t

Step-by-step explanation:

At least 500

40 intro = initial, constant

t = time in seconds

5 words per second

Please mark as brainliest

The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

What is amount and example?

amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.

To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:

wood (m) = (wood (ft) x 0.3048) / 6

Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:

wood (m) = (6 ft x 0.3048) / 6

wood (m) = 1.8288 m      

Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

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Answer: In five days, there will be around 2,476 bacteria.

Step-by-step explanation: Using the hint given, simply plug in the numbers to calculate the predicted amount of bacteria. Hope this helps!

[tex]100(1+0.9)^{5}=2,476.099[/tex]

Answer:

2476

Step-by-step explanation:

Given formula:

[tex]\textsf{Future Amount}=\sf I(1+r)^t[/tex]

Given values:

Substitute the given values into the given formula and solve:

[tex]\begin{aligned}\implies \textsf{Future Amount}& =\sf 100(1+0.9)^5\\& =\sf 100(1.9)^5\\& =\sf 100(24.76099)\\& =\sf 2476.099\\& =\sf 2476\;(nearest\;whole\;number)\end{aligned}[/tex]

Answer:

Step-by-step explanation:

1. Identify the equation and its variables.

The equation can be any type of equation, such as a linear equation, quadratic equation, or polynomial equation. Identify the variables in the equation and label them.

2. Find a strategy for solving the equation.

Depending on the type of equation, there are various strategies for solving the equation. For example, a linear equation can be solved using the addition-subtraction method, a quadratic equation can be solved using the quadratic formula, and a polynomial equation can be solved using the synthetic division method.

3. Use the strategy to solve the equation.

Follow the steps of the chosen strategy to solve the equation. This may involve expanding the equation, factoring, or rearranging the equation.

4. Check the solution.

Once the equation is solved, check the solution by plugging the answer back into the equation and verifying that it works.

5. Review and summarize the steps.

Review the steps taken to solve the equation and summarize them in a few sentences. This will help with understanding and remembering the steps.

The quadratic equation y = x² - 2x - 3 have ordered points at (0, -3), (2, -3), (-2, 5) and (4, 5)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Quadratic equation is a polynomial that have a degree of 2. The degree of a polynomial is the highest exponent of the variables.

Given that:

y = x² - 2x - 3

When x = 0; y = (0)² - 2(0) - 3 = -3

When x = 2; y = (2)² - 2(2) - 3 = -3

When x = -2; y = (-2)² - 2(-2) - 3 = 5

When x = 4; y = (4)² - 2(4) - 3 = 5

The equation y = x² - 2x - 3 is a quadratic equation.

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Answer:

4 km wide and 6 km long.

Step-by-step explanation:

Let the width be x, then the length is x+2 km.

Area = width * length

Substituting the given values:

24 = x(x + 2)

24 = x^2 + 2x

x^2 + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

As x must be positive, then x = 4.

So, the dimensions are 4 and 4+2

= 4, 6,

Answer:

width = 3.46 km and length = 6.93 km

Step-by-step explanation:

let the width be : X km

then the length would be: 2X km

as area is length x width

therefore:

2X x X = 24

2X² = 24

X² = 24/2

X² = 12

X = [tex]\sqrt{12}[/tex]

X=  3.46

the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km

Answer:

54 loaves of bread

Step-by-step explanation:

45:5=9 (45 divided by 5 equals 9)

9x6=54 (9 times 6 equals 54)

Answer:

a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.

b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).

The best estimate of the average change in rent each year include the following: C. $40.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):

Rate of change, m = (1200 - 800)/(10 - 0)

Rate of change, m = 400/10

Rate of change, m = 40.

Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.

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Complete Question:

The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.

Which of the following is the best estimate of the average change in rent each year?

answer choices

$0.5

$1

$40

$400

True. A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid, using trigonometry approach.

The sine waves oscillate in a smooth, repetitive manner, defined in terms of distance from the [tex]x[/tex] axis to the point on the unit circle.

The main features of a sinusoidal function are its amplitude, its phase, and its frequency. Let us discuss the features one by one :

Amplitude specifies the maximum distance between the x axis i.e. the horizontal axis and the vertical position of the point or a the waveform. It is denoted by [tex]A[/tex].

Phase of a function refers to the horizontal position of the waveform with correspondence to one rotation. The extent or angle by which, a point or a waveform is shifted, is called the phase difference or phase shift.

Frequency is the measurement which tells us about how quickly the sinusoid completes cycles i.e. it simplifies the movement of the sinusoidal wave per unit time.

The sinusoid functions play key role in modern periodic phenomena such as sound and light waves, oscillators, average temperature variations throughout the year, sunlight intensity ,etc.

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The sides given as 16cm , 12cm and 20cm  forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .

The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;

here the hypotnuse (longest side) is = 20 cm ;

According to Pythagoras theorem ,

⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;

⇒ [tex]400 =144+256[/tex] ;

⇒ [tex]400=400[/tex] ;

So , The condition of Pythagoras theorem is satisfied .

Therefore , the given sides can form a Right Triangle .

The given question is incomplete , the complete question is

Does the sides 16cm , 12cm and 20cm form a right triangle ?

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If a figure can be transformed into another figure by a sequence of translations, rotations, and reflections, and the size and shape remain the same, the figures are congruent.

A congruence transformation is a type of transformation that preserves the size and shape of a figure. The most common congruence transformations are translations, rotations, and reflections.

Translations involve moving a figure a certain distance in a certain direction without changing its size or orientation.

Rotations involve rotating a figure around a certain point without changing its size or shape.

Reflections involve flipping a figure over a certain line without changing its size or shape.

In order to show that two figures are congruent, you can use a combination of these congruence transformations to match one figure to the other. By using these transformation you can map each point of one figure to a corresponding point on the other figure and if the size and shape of figures remain the same, that means that the figures are congruent.

It's important to notice that Congruence is an equivalence relation and it's reflexive, symmetric, and transitive.

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A. The total number of points of intersection of the graphs of the equations y = 5e^x and xy = 20 is two.

To find the points of intersection, we must solve the two equations for x and y.

For the first equation, y = 5e^x, we can solve for x by taking the natural logarithm of both sides and getting x = ln(y/5).

For the second equation, xy = 20, we can solve for y by dividing both sides by x and getting y = 20/x.

We can then substitute the expression for x in terms of y into the expression for y in terms of x and solve for y to get y = 20/(ln(y/5)). This is a nonlinear equation that must be solved numerically.

By using numerical methods, we can solve the equation and find the two points of intersection, which are (x, y) = (3.68, 4.64) and (x, y) = (0.87, 22.95).

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Answer:

real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting

Step-by-step explanation:

The quotient of any two integers is an integer.

A real number is a number that can be measured and represented on a number line; this includes fractions, decimals, irrational numbers, rational numbers, and basically every number you encounter. With that in mind, the quotient of 2 real numbers is not necessary an interger as 2.01/ 1 is not an integer

The surface area of the prism shown in the figure is equal to 480 square inches. (Right choice: B)

In this problem we need to determine the surface area of a prism, that is, the sum of the areas of the five faces of the prism. There are three rectangles and two right triangles as faces of the prism, whose area formulas are described below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Where:

Now we proceed to determine the areas of all faces of the prism:

A = (8 in) · (9 in) + 2 · 0.5 · (15 in) · (8 in) + (9 in) · (15 in) + (17 in) · (9 in)

A = 480 in²

The prism shown in the figure has a surface area of 480 square inches.

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On solving the provide question, we can say that by quadratic equation  number of corn plants in the row are 52 - 4 = 21

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

number of rows be x.

the number of corn plants = x - 4

So,

[tex]x(x - 4) = 525\\x^2 - 4x - 525 = 0\\x = 25, x = -21\\[/tex]

number of corn plants in the row are 52 - 4 = 21

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Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.

Here,

Given : 55=0.1(m-500)+50

where m is the number of minute

=> 55=0.1(m-500)+50

=> 55=0.1m-50+50

=>55=0.1m-0

=>55-0=0.1

=>55=0.1

=>0.1=0.1

=>550=m

Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.

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The radius of the signal is 10 units. The 1st option is the answer

The equation of a circle is a mathematical expression that describes the properties of a circle. It is typically represented in the form of (x - h)²+ (y - k)² = r², where (h, k) is the center of the circle, and r is the radius

Since the border is modeled by the equation (x – 10)² + y²= r² and the boundary is located at (2, 6).

To get the radius of the signal substitute x = 2 and y = 6 into the given equation and solve for r:

(x – 10)² + y²= r²

(2 – 10)² + 6²= r²

(-8)² + 6²= r²

64 + 36 =  r²

100 =  r²

r² = 100

r = √100

r = 10 units

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The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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Answer:

12

Step-by-step explanation:

1) FInd the sides of small triangle. Since it has 2 congruent angles it also has to congruent sides opposite those angles. So the sides adjacent (connected to) the right angle are both 6.

2) Find the hypotenuse (side opposite the right angle) in the small triangle

a^2 +b^2 = c^2

6^2 +6^2 = c^2

36+36 = c^2

72 = c^2

c = [tex]\sqrt{72}[/tex]

In simplified radical form  [tex]\sqrt{72\\[/tex] = 6[tex]\sqrt{2}[/tex]

3) Now find the sides of big triangle. It has 2 congruent angles therefore it has two congruent side opposite those angles. We know that one of the sides is 6[tex]\sqrt{2}[/tex] because it is also the hypotenuse of the small triangle. The other side adjacent to the right angle is also 6[tex]\sqrt{2}[/tex].

4) Now find x which is the hypotenuse of the big triangle.

[tex](6\sqrt{2} )^{2}[/tex]+                    [tex](6\sqrt{2} )^{2}[/tex]= [tex]c^{2}[/tex]

(36*2)+(36*2) = [tex]c^{2}[/tex]

144 = [tex]c^{2}[/tex]

c = 12

so x = 12

Answer:

1000 mitre=1km

1.25 ×1000

Answer:

DIGIT FORM = 13km

DECIMAL FORM: 12.5km

Step-by-step explanation:

DIGIT Form: A digit can only be a whole number, so round 12 and a half (12/5 or 12.5) to the nearest whole number.

DECIMAL Form: It cannot be a whole number and must consist of a number followed by a decimal point (a period) and then another number.

DON'T FORGET TO ADD KILOMETERS (km) AFTER YOUR ANSWER.

Answer:

$7

Step-by-step explanation:

Got it right on a test

The equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3 is equals to the y = 9x-3.

Slope intercept form of an equation : The slope intercept form is one of method to determine the equation of a straight line in the coordinate plane. The equation of a straight line is a relation which:

Let us assume a straight line of slope 'm' and y-intercept 'b'. The equation of slope intercept form for a straight line with slope, say, 'm', and the y-intercept, 'b', is

y = mx + b

Now, the slope of line , m = 9

y-intercept of line, b = - 3

As we know slope intercept form of a line is, y = mx + b , so plugging the known values of slope and y-intercept in it,

=> y = 9x - 3

So, required equation in slope intercept form of line is y = 9x - 3.

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Answer:

  see attached

Step-by-step explanation:

You want the steps in order for constructing a perpendicular to a line through an external point.

Essentially, the procedure identifies two points on the line (P and Q) that are equidistant from the external point (R), then proceeds to draw a perpendicular bisector of the segment between those two points. The external point is already equidistant from P and Q, so we only need to find another equidistant point (S) to complete the construction.

See the attachment for the ordering of the instruction steps. (Note the step numbers are not in order on the left.)

The measurement of length of the car is 2.25m, when the width is 1.5 meter. Thus, option B is correct.

Measurement is the process of relating numerical values to physical quantities and phenomena. The sciences, engineering, construction, and other technical fields, as well as nearly all daily activities, all depend on measurement. The components, circumstances, restrictions, and theoretical underpinnings of measurement have thus been extensively studied.

Measurements can be made using only the human senses, in which case they are frequently referred to as estimates, or, more frequently, by using instruments.

These instruments can range in complexity from straightforward rules for measuring lengths to extremely complex systems built to detect and measure things that are completely outside the range of the senses, like radio waves from a far-off star or the magnetic moment of a subatomic particle.

Given that length : width is  3 : 2

let length be 3x and width be 2x

width is given 1.5m

2x = 1.5

x = 1.5/2

x = 3/4

Length = 3x

= 3 × 3/4

= 9/4

= 2.25 m

Thus, the measurement of length of the car is 2.25m, when the width is 1.5 meter.

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Correct answer:

The flat dimensions of a car is given as 3 : 2, and the width of the car 1.5 metre. which measurement could be the length of a car?

a. 2m

b. 2.25m

c. 2.50m

d. 2.15m

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}[/tex]