Why is the graph in the photo misleading?

The first five coefficients are explained.

Given is power series, f(x) = eˣ about x = 4 as [tex]\sum_{\infty}^{n=0}C_n}(x+4)^n[/tex]

f(x) = eˣ

a = 4,

The general form of a Taylor series is:

f(x) = [tex]\sum_{n=0}^{\infty}\frac{f'(a)}{n!} (x-a)^n[/tex]

Note that since the function is a basic exponential function, its derivative is:

f'(x) = eˣ

That is, the function is the same for whatever order of differentiation. So, let us substitute our values here,

f(x) = [tex]\sum_{n=0}^{\infty}\frac{e^4}{n!} (x-4)^n[/tex]

The general expression for the coefficients is: [tex]C_n = \frac{e^4}{n!}[/tex]

The first coefficient is: [tex]C_0 = e^4[/tex]

The second coefficient is: [tex]C_1 = e^4[/tex]

The third coefficient is: [tex]C_2 = 1/2e^4[/tex]

The fourth coefficient is: [tex]C_3 = 1/6e^4[/tex]

And lastly,

[tex]C_4 = 1/24e^4[/tex]

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We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).

We have,

To show that the solution to the differential equation dp/dt = -0.1P is

P = 495e^(1.1t),

we can use separation of variables and integration.

Starting with the differential equation:

dp/dt = -0.1P

We can separate the variables by dividing both sides by P and multiplying both sides by dt:

dp/P = -0.1 dt

Integrate both sides:

∫ dp/P = -0.1 ∫ dt

Integrating the left-hand sid.

ln|P| = -0.1t + C

where C is the constant of integration.

To solve for C, we can use an initial condition.

Suppose that when t = 0, P = P0.

Then we have:

ln|P0| = -0.1(0) + C

ln|P0| = C

Substituting this value of C back into the equation for P.

ln|P| = -0.1t + ln|P0|

ln|P/P0| = -0.1t

Taking the exponential of both sides.

P/P0 = e^(-0.1t)

Multiplying both sides by P0.

P = P0 e^(-0.1t)

We can substitute P0 = 495 (since P(0) = 495 is given in the solution) and e^(-0.1t) = e^(1.1t)/e^t.

P = 495 e^(1.1t)/e^t

Simplifying the expression by combining the exponentials.

P = 495 e^(0.1t)

which is the same as the given solution.

Therefore,

We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).

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A line of reflection, also known as a line of symmetry, is a line that divides a figure into two congruent parts that are mirror images of each other.

When a figure is reflected across a line of reflection, every point on one side of the line has a corresponding point on the other side of the line that is equidistant from the line.

To determine the line of reflection for the given graph:

- Reflection across the x-axis: The line of reflection is the x-axis.

- Reflection across x = -6: The line of reflection is a vertical line passing through x = -6.

- Reflection across the y-axis: The line of reflection is the y-axis.

- Reflection across y = -6: The line of reflection is a horizontal line passing through y = -6.

Thus, the line of reflection is the perpendicular bisector of every segment joining a point to its image after reflection.

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By using the substitution method, the value for (x,y) = (-2, 2)

The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.

In essence, from the given system of equations; let's make x the subject of the formula in the first equation.

5x + 3y = -4

5x = -4 - 3y

Divide both sides by 5;

x = -4/5 - 3y/5

Now, we are going to substitute this value for x into the second equation. The second equation says:

y - 2x = 6

y - 2(-4/5 - (3y/5)) = 6

By solving for y;

y = 2

Now, let's replace the value of y with any of the given equation (2);

y - 2x = 6

2 - 2x = 6

-2x = 6 - 2

-2x = 4

Divide both sides by -2

-2x/-2 = 4/ -2

x = -2

Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)

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Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes (coefficients of x) of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 1 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 3 into slope-intercept form (y = mx + b):

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.

Line 2 and Line 3:

To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):

2y = 3x + 5

y = (3/2)x + 5/2

Next, we can rearrange Line 3 into the slope-intercept form:

6x - 4y = 4

-4y = -6x + 4

y = (3/2)x - 1

Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.

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Emma has $5,000 total invested.

Let's call the total amount Emma has invested "x".

Emma has half of her investments in stock paying a 10% dividend, so that portion of her investment earns 0.10(x/2) = 0.05x in annual interest.

The other half of her investments are in a stock paying 14% interest, so that portion of her investment earns 0.14(x/2) = 0.07x in annual interest.

The total annual interest Emma earns is $600, so we can set up the following equation:

0.05x + 0.07x = 600

0.12x = 600

x = 5000

Therefore, Emma has a total of $5000 invested.

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Answer:c

Step-by-step explanation:

Answer: B 1585

took the test

The quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

The quadratic equation is the polynomial having the highest power of 2. If 5i and -5i are the solutions to the quadratic equation, then the quadratic equation can be written as:

(x - 5i)(x + 5i) = 0

Expanding this equation, we get:

x² - (5i)² = 0

x² - 25i² = 0

Since i² = -1, we can substitute -1 for i², giving us:

x² - 25(-1) = 0

x² + 25 = 0

Therefore, the quadratic equation that has 5i and -5i as solutions is:

x²+ 25 = 0

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The coordinates of the vertices for the image if the preimage is translated 3 units up is : A′(−3, 6), B′(0, 10), C′(−3, 3).

The correct option is (B)

If we are given the translated image of something, we need to work backwards given the translation rules. For example, if we have a general translation of (x +a, y +b), then to find pre-translation coordinates, we do: (x−a, y−b).

We have the Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0).

Now, let's consider the translation that moves the triangle 3 units up. This means that we need to add 3 to the y-coordinate of each vertex to get the coordinates of the image.

So, the coordinates of the vertices of the image triangle, let's call it A'B'C', will be:

A' = (-3, 3+3) = (-3, 6)

B' = (0, 7+3) = (0, 10)

C' = (-3, 0+3) = (-3, 3)

The coordinates of the vertices for the image if the preimage is translated 3 units up is : A′(−3, 6), B′(0, 10), C′(−3, 3)

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Step-by-step explanation:

Draw a rectangle.  If the length is 3 inches longer than its width, we can write the width as "w" and the length as the width + 3

Area is (width)(Length) = (width)(width+3)

    W

 ----------

 |         |

 |         |

 |          |  L = w+3

 |         |

 |          |

 -----------

A = (w+3)(w)

A = w2 + 3w = 108.

(Problem states that area is 108 sq in)

Need to solve this quadratic equation

w2 + 3y - 108 = 0

Factor:

(w - 9) (w + 12) = 0

So

w - 9 = 0.    or.    w + 12 = 0

Solve these and get

w = 9. or. w = -12

Only one that makes sense in real life is the poitive one.

So the dimensions are

Width = 9 inches

Length = 12 inches

hope this helped-nia.

Answer:

Step-by-step explanation:

45

Answer:

Step-by-step explanation:

1. the initial population at t=0 is 1

2. 16

Answer:

  30°

Step-by-step explanation:

You want the measure of angle AEF in regular hexagon ABCDEF.

The interior angles of a regular hexagon are ...

  180° -(360°/6) = 120°

Angle AEF is 90° less than this, so is ...

  angle AEF = 120° -90°

  angle AEF = 30°

__

Additional comment

Angle AEF is also a base angle of isosceles triangle AEF, which has angle F = 120°. The base angles are (180° -120°)/2 = 30°.

Answer:

119

Step-by-step explanation:

Firstly, we need to solve the expression inside the parentheses, which is 23-11. This gives us 12. Then we need to carry out the division to get 48 divided by 12, which is 4. We can then multiply 4 by 14 to get 56. Finally, we add 56 to 63 which gives us the answer of 119. Therefore, the solution to the expression 63+48÷(23-11)×14 is 119.

The number of hours Penn volunteer in one week is 8hours

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Representing the number of hours volunteered in a week by Penn by x

therefore for 12 weeks , the number of hour will be;

12×x = 12x

12x = 96

divide both sides by 12

x = 96/12 = 8 hours

therefore the number of hour volunteered by Penn in a week is 8 hours

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(a) The range for the graduates is 86760 hours.

(c) The graduates had the greater median number of hours.

(a) The range is the difference between the maximum and minimum values in a set of data. We are given the following data:

Graduates: 9641 hours, 6655432 hours, 93310 hours, and 92501 hours

Non-graduates: 2138 hours, 3 hours, 4 hours, and 13445559 hours

The range for the graduates is 9641 - 92501 = 86760 hours.

The range for the non-graduates is 2138 - 13445559 = 13443421 hours.

(c) To find the median, we need to arrange the data in order from smallest to largest and find the middle value. If there are an even number of data points, we take the average of the two middle values.

Graduates: 9641 hours, 93310 hours, 92501 hours, 6655432 hours

The median is the average of 93310 hours and 92501 hours, which is (93310 + 92501)/2 = 92905.5 hours.

Non-graduates: 2138 hours, 3 hours, 4 hours, 13445559 hours

The median is the average of 3 hours and 4 hours, which is (3 + 4)/2 = 3.5 hours.

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Answer: so if it cosst 25,000,000 dollars to market a car and they sell it for 30,000 dollars they would need to sell 167 cars to get 5.1 million dollars or 166 for 5.0 million

The two numbers are 4 and 1.

To solve the problem, we will use algebraic equations.

We will call 2 numbers x and y. So, we know that:

------ x + y = 5 (equation 1)

------ xy = 20 (equation 2)

We will solve for y in terms of x:

y = 5 - x

We will substitute for y into equation 2 and simplify:

x(5 - x) = 20

5x - x^2 = 20

x^2 - 5x + 20 = 0

As a quadratic equation which will be solved using the quadratic formula, the solutions are x = 4 and x = 1. We can check that these solutions satisfy both equation 1 and equation 2.

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Answer: B

Step-by-step explanation:

First, you have to know that a straight line is equal to 180 degrees. They gave you 115 degrees in part of a line, so the other part or the angle not given must be equal to 65 degrees. Another thing is that a triangle has 180 degrees. 65+80 degrees is equal to 145 degrees, leaving angle 1 to be equal to 35 degrees. Another thing to know is that reflective angles have the same measurement. If the original angle was equal to 65 after subtraction 115 from 180, we know that the second triangle's angle would also be equal to 65. 65+86 is 150, and 180-150 is 30. Thus, the answer is B.

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Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation:

Answer:

he can make 9 cups of lemonade and he will have 1/3 of a cup of lemonade left over

Step-by-step explanation:

28÷3=9.3333=28/3=9 1/3

Answer:

9.3 or just 9 glasses of lemonade in total.

Step-by-step explanation:

just divide 28 with 3. but just to round it up i would say 9 glasses of lemonade.

The value c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

To find the value of c for which P(z < c) = 0.0234 for a standard normal distribution, we can use a standard normal distribution table or a calculator with a built-in normal distribution function.

Using a standard normal distribution table, we can look up the area to the left of c and find the corresponding z-score. This z-score will be the value of c for which P(z < c) = 0.0234.

Looking up the area 0.0234 in the table, we find that the corresponding z-score is approximately -2.07.

Therefore, c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.

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The limit exists and is equal to 6.

The limit exists and is equal to 4.

Now, let's use this concept to evaluate the limits of the given function F(x). Looking at the graph of F(x), we see that it approaches different values as x approaches different points. We will evaluate each limit separately:

lim F(x) as x → 1

As x approaches 1 from the left side, the function appears to be approaching a value of 2. Similarly, as x approaches 1 from the right side, the function appears to be approaching a value of 4. However, the limit does not exist as the function is not approaching a single value as x approaches 1.

lim F(x) as x → 3

As x approaches 3, the function appears to be approaching a value of 4.

lim F(x) as x → ∞

As x approaches infinity, the function appears to be approaching a value of 6.

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Answer:

487.20

Step-by-step explanation:

1. find the area of a rectangle ( length x width)

14ft x 12ft = 168ft²

2. Multiply the number of feet needed to becovered by the price of one foot of paper

168ft x 2.90 = 487.20

He covered a distance of 5 miles for 5 days of the total days of training. The total distance he covered = 6 miles.

The total number of days Anthony used for training = 8 days.

The number of days he covered 1/4 mile = 2days

The number of days he covered 1/2 mile = 1 day

The number of days he covered 1 mile = 5 days.

Therefore that total distance that he used for the training = 2(1/4)+1(1/2)+5(1)

= 0.5+0.5+5

= 6 miles.

The number of days he covered the highest distance would be for 5 days.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{24}\\ a=\stackrel{adjacent}{22}\\ o=\stackrel{opposite}{MN} \end{cases} \\\\\\ MN=\sqrt{ 24^2 - 22^2} \implies MN=\sqrt{ 92 }\implies MN=2\sqrt{23}[/tex]

The volume of the cone with a diameter of 4ft and height 12ft is approximatelly 50.3 ft³

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The volume of a cone is expressed as;

V = (1/3)πr²h

The figure in the image is a cone.

Diameter of the base of the cone d = 4ft

Radius r = diameter/2 = 4/2 = 2ft

Height h = 12ft

Plug the given values into the above formula and solbr for the volume.

V = (1/3)πr²h

V = (1/3) × π × r² × h

V = (1/3) × π × (2 ft )² × 12ft

V = 50.3 ft³

Therefore, the volume is 50.3 ft³.

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Answer:

Yeeeaaa, no.

Hope this helps!

Step-by-step explanation:

( x, y )

Plug the numbers of the ordered pair into the equation: y = 6x

3 = 6 × ( 0 )

3 = 0

Three does not equal zero...

3 [tex]\neq[/tex] 0

Note the the missing step is: " Total the columns." (Option B) so the completed step with regard to the segmented bar graph is given below.

A segmented bar chart uses vertical or horizontal bars to compare two or more categories. Typically, the stacked bars represent each group's percentage of the whole and are plotted by the proportion of each value inside each group.

This style of chart can be beneficial for comparing total amounts across each split bar or group. It may be an effective method of forecasting a company's profit over a period of months, with the earnings separated into distinct product lines.

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