Please help! The table below shows the elevations of the three animals that Fernanda can see from her boat.

The value of the function when differentiated w.r.t "x" is -2 / 1+x^2.

To differentite the function \(f(x) = tan^{-1}(\frac{1-x}{1+x}) - tan^{-1}(\frac{x+2}{1-2x})\) w.r.t "x", we have to make use of chain rule and the derivative of the inverse tangent function. By applying both the methods, we have to find out the differentiated value of the function.

Chain rule is basically a fundamental rule in calculus that allows us to find the derivative of a function. The chain rule comes out to be very usefull when the functions are layered. On the other hand, inverse tangent function is a mathematical function that takes an input value and returns the angle whose tangent is equal to that value.

We know that;

\(tan^{-1}a - tan^{-1}b = tan^{-1}(\frac{a-b}{1+ab} )\)

So, by following the above method we get the function as:

\(f(x) = (tan^{-1}1 - tan^{-1}x) - (tan^{-1}x + tan^{-1}2)\)

\(f(x) = tan^{-1}1 - tan^{-1}2 - 2tan^{-1}x\)

Now, differentiating both the sides w.r.t "x":

f'(x) = 0 - 0 - 2/1+x^2

f'(x) = 2/1+x^2

Therefore, the value of the function when differentiated w.r.t "x" is

-2 / 1+x^2.

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Answer:

a) The student's overall average for the class is 87.97.

b) He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.

Step-by-step explanation:

Weighed average:

To solve this question, we find the student's weighed average, multiplying each of his grade by his weights.

Grades and weights:

Scored 82.5 on the midterm, worth 30%.

Scored 88.6 on the final exam, worth 30%.

Scored 91.6 on the homework, worth 40%.

a. On a 100-point scale, what is the student's overall average for the class?

Multiplying each grade by it's weight:

\(A = 82.5*0.3 + 88.6*0.3 + 91.6*0.4 = 87.97\)

The student's overall average for the class is 87.97.

b. The student was hoping to get an A in the class, which requires an overall score of 93.5 or higher. Could he have scored high enough on the final exam to get an A in the class?

Score of x on the final class, and verify that the average could be 93.5 or higher. So

\(A = 82.5*0.3 + 88.6*0.3 + 0.4x\)

\(A \geq 93.5\)

\(82.5*0.3 + 88.6*0.3 + 0.4x \geq 93.5\)

\(0.4x \geq 93.5 - (82.5*0.3 + 88.6*0.3)\)

\(x \geq \frac{93.5 - (82.5*0.3 + 88.6*0.3)}{0.4}\)

\(x \geq 105.425\)

He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.

Answer: 40% OUT OF 100

Answer:

  y ≈ 15272.9(1.06306^x) . . . . from regression tool

  y = 15300(1.0624^x) . . . . calculated "by hand"

Step-by-step explanation:

An exponential model is one that uses the exponential function ...

  f(x) = a·b^x

to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.

__

An exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...

  y ≈ 15272.9(1.06306^x)

__

We can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...

  average rate of growth =

  ((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624

Using the first table value as the initial value, the model formed this way is ...

  y = 15300(1.0624^x)

__

For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:

  average rate of growth = (220/153)^(1/6) ≈ 1.0624

This gives the same growth factor as above, hence the same model.

The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.

The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.

__

The values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:

Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Step-by-step explanation:

the manufacturing costs are defined by

m(x) = 25x + 150

the selling revenue is defined by

s(x) = 50 + 30x = 30x + 50

clearly, the selling amount is bigger than the manufacturing amount (also supported by the fact that 30x > 25x). otherwise the company is going bankrupt in no time.

so,

a)

the profit is (as usual) revenue minus manufacturing :

p(x) = 30x + 50 - 25x - 150 = 5x - 100

b)

x = 150

p(150) = 5×150 - 100 = 750 - 100 = $650

since the result is positive, yes, they are making a profit. and it is $650.

Answer:

5.a) p = 5x - 100

b)p = $650

Step-by-step explanation:

5.a)

p - Profit

p - Profitc - Cost

p - Profitc - Cost - revenue

p = r - c

p = (30x + 50) - (25x + 150)

p = 5x - 100

b) The company will make profit.

p = 5x - 100

p = 5(150) - 100

p = 750 - 100

p = $650

or

p = (30×150 + 50) - (25 × 150 + 150)

p = $650

we get that orange points are (0,7) and (9,2). So the slope for the equation is

so the equation for this line is

The equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

here we have given the graph of the

The roots of the given polynomial is

x=-2,x=-1 and x=3

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Therefore the equation of the polynomial is

f(x)=(x+2)(x+1)(x-3)

Therefore the equation of the given polynomial is f(x)=(x+2)(x+1)(x-3).

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The equation for this polynomial graphed will be P(x) = a(x + 2)(x + 1)(x – 3)³.

A polynomial expression is an algebraic expression with variables and coefficients.

The graph of the polynomial is given below.

From the graph, the roots of the polynomial will be -2, -1, and 3.

Then the factor of the polynomial will be

(x + 2), (x + 1), and (x – 3)

Then the polynomial will be

P(x) = a(x + 2)(x + 1)(x – 3)³

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Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Answer:

no 7+2 is 9 so yeah ;)))))))))))))))

Answer:

a cube that is 1 yard long, 1 yard wide, and 1 yard high

Step-by-step explanation:

The dimensions for a unit cube are:

\(1\times1\times1\)

Please note that the units for each side MUST be the same (or if they're different, then the lengths have to be equivalent).

Looking at the answer choices, we can see that the last answer choice is a 1 yd by 1 yd by 1 yd cube, therefore it is a unit cube.

Answer:

I guess 4, because it has only 1 unit in it, and not 9 inches^3.

Step-by-step explanation:

Hope this helps.

Answer:

6

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the missing number in the given sequence, let's analyze the pattern:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, ???

Looking at the sequence, we can identify a few patterns:

The sequence alternates between increasing and decreasing numbers.

The first two numbers, 2 and 4, are increasing.

The next two numbers, 4 and 3, are decreasing.

The following two numbers, 3 and 6, are increasing.

The subsequent two numbers, 6 and 3, are decreasing.

The next two numbers, 3 and 8, are increasing.

The subsequent two numbers, 8 and 9, are increasing.

Based on these observations, it appears that the sequence is following a pattern where it alternates between increasing and decreasing numbers, but the specific values being added or subtracted are not consistent.

Now let's determine the missing number:

From the pattern, the next two numbers should be decreasing. Following the pattern of alternating between increasing and decreasing numbers, the missing number after the last given number (8) should be less than 9.

Let's assume the missing number is x:

8 - x

Since the previous decreasing sequence was 6 - 3, we can assume that x is 1 less than the previous number (3):

8 - (3 - 1) = 8 - 2 = 6

Therefore, the missing number in the sequence is 6.

The complete sequence is:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, 6

answer:

£11.25

explanation:

2.75+1=3.75 this was one third so you have to multiply 3.75 by 3 so you get 11.25.

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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they are not like terms (option B)

Given:

Two radicals: √3 and √2

To find:

the best description of the two radical expressions

a) Perfect squares are numbers that can be written as the product of itself

The given numbers are radicals and their roots give a decimal not a whole number. Hence, they are not perfect squares

b) √3 and √2 give two different results

The two radicals are not like terms. Neither are they equal to each other

Hence, they are not like terms (option B)

Answer:

12/52

Step-by-step explanation:

There are 12 face cards. The probability of picking one is 12/52

which can be simplified to be 3/13

Answer:

See Explanation

Step-by-step explanation:

Given

See attachment for graph

Required

A situation that can be modeled by the graph.

The prompt and the response are as follows:

The type of function:

It is a linear function

The variables modeled in the function

The variables are x and y

The domain and the range

From the graph, we can see that x and y values are not limited to any constraints.

So, the domain and the range are:

\(Domain: \{-\infty \le x \le \infty \}\)

\(Range: \{-\infty \le y \le \infty \}\)

Question that could be \(answered\)

The graph could be used to predict y value, given the x value.

Take for instance, find y when x = 10

The answer can be handpicked directly from the graph. However, the best way is to calculate the graph equation, first.

So, we have:

Pick any two points on the line of the graph

\((x_1,y_1) = (-2,0)\)

\((x_2,y_2) = (0,4)\)

Calculate the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{4 - 0}{0 - -2}\)

\(m = \frac{4}{2}\)

\(m =2\)

The equation of the graph is:

\(y = m(x - x_1) + y_1\\\)

So, we have:

\(y = 2(x - -2) + 0\)

\(y = 2(x +2)\)

Expand

\(y = 2x +4\)

To solve for y when x = 10;

\(y = 2 * 10 +4\)

\(y = 20 +4\)

\(y = 24\)

The value of y when z is 220 is 5.2. This answer is in simplified form, as 5.2 is already in its simplest fractional form.

If two variables vary inversely, it means that their product is always constant. In this case, we are given that y varies inversely as z, and that y is 26 when z is 44. This means that the product of y and z is 26 * 44 = 1144. We are asked to find the value of y when z is 220. To do this, we can use the fact that the product of y and z is constant. Since the product of y and z when z is 44 is 1144, the product of y and z when z is 220 must also be equal to 1144. Setting up the equation y * 220 = 1144 and solving for y, we find that y = 5.2. This means that the value of y when z is 220 is 5.2.

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Answer:

80 km/hr

Step-by-step explanation:

This is asking for speed.

Speed=Distance/Time

Speed=720/9

Speed=80 km/hr

The equation that determines the amount x that Jeremiah still has to spend is given as follows:

c + 2t + 2bi + ba + x = 35

x = 35 - (c + 2t + 2bi + ba).

In which:

The amount that Jeremiah still has to spend is obtained applying the proportions in the context of the problem.

Considering the meaning of each variable given in this problem, the equation modeling his total spending is given as follows:

c + 2t + 2bi + ba + x = 35

The solution is obtained isolating the variable x, as follows:

x = 35 - (c + 2t + 2bi + ba).

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Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.

Answer:

The length of the third side is less than 13.

Step-by-step explanation:

In any given triangle the sum of any two sides is longer than the length of the third side.

This means that the length of the third side has to be less than 13, since that is the sum of the lengths of the two shorter sides.

Não sei te responder amigo!

Answer:

8

Step-by-step explanation:

E is the midpoint of segment BC, so the segment BE would have to be 8.

Answer:

C: EAF Is the correct answer

Answer:

The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.

Step-by-step explanation:

From Geometry, the volume of the cone (\(V\)), measured in cubic centimeters, is defined by:

\(V = \frac{\pi\cdot r^{2}\cdot h}{3}\) (1)

Where:

\(r\) - Radius, measured in centimeters.

\(h\) - Height, measured in centimeters.

Then, we find a formula for the rate of change of the volume of the birth bath (\(\dot V\)), measured in cubic centimeters per minute, by means of differentiation:

\(\dot V = \frac{\pi}{3}\cdot \left(2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h \right)\) (2)

Where:

\(\dot r\) - Rate of change of radius, measured in centimeters per minute.

\(\dot h\) - Rate of change of height, measured in centimeters per minute.

In addition, we have the following relationship:

\(r = 2\cdot h\) (3)

And by Differential Calculus:

\(\dot r = 2\cdot \dot h\) (4)

By applying (3) and (4) in (2), we find the following expanded formula:

\(\dot V = \frac{\pi}{3}\cdot \left[2\cdot (2\cdot h)\cdot (2\cdot \dot h)+4\cdot h^{2}\cdot \dot h\right]\)

\(\dot V = \frac{\pi}{3}\cdot (8\cdot h+4\cdot h^{2})\cdot \dot h\) (5)

If \(\dot V = -8\,\frac{cm^{3}}{min}\) and \(h = 10\,cm\), then the rate of change of the water level is:

\(\dot h = \frac{\dot V}{\frac{\pi}{3}\cdot (8\cdot h + 4\cdot h^{2}) }\)

\(\dot h = \frac{-8\,\frac{cm^{3}}{min} }{\frac{\pi}{3}\cdot [8\cdot (10\,cm)+4\cdot (10\,cm)^{2}] }\)

\(\dot h \approx -0.016\,\frac{cm}{min}\)

The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.

Answer:

0

Step-by-step explanation:

10 to the power of zero is zero

Answer:

1

Step-by-step explanation:

Anything with an exponent of zero always equals 1