Analysis and observations in these two graphs

The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

From the function [tex]B(t) = 182(1.065)^t[/tex]:

b = 1.065

Growth rate = 1.065 - 1 = 0.065 = 6.5%

The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

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Answer:

  5x^4 -37x^3 -6x^2 +41x -6

Step-by-step explanation:

We simplify this expression by removing parentheses and combining like terms. Parentheses are removed using the distributive property.

The product of the final pair of polynomials in parentheses is ...

  (-4x^3 +5x -1)(2x -7) = (-4x^3 +5x -1)(2x) +(-4x^3 +5x -1)(-7)

  = -8x^4 +10x^2 -2x +28x^3 -35x +7

  = -8x^4 +28x^3 +10x^2 -37x +7

  = (5x^4 -9x^3 +7x -1) + (-8x^4 +4x^2 -3x +2) - (-8x^4 +28x^3 +10x^2 -37x +7)

  = (5 -8 -(-8))x^4 +(-9 -28)x^3 +(4 -10)x^2 +(7 -3 -(-37))x +(-1 +2 -7)

  = 5x^4 -37x^3 -6x^2 +41x -6

The area of each slice of the cake is 3π  square inches

The cake is 12 inches in diameter. The cake top is circular.

Therefore, the area of a circle is as follows;

area of a circle = πr²

where

Therefore,

r = diameter / 2

r = 12 / 2

r = 6 inches

Hence,

area of a circle = π × 6²

area of a circle = 36π

area of each sliced cake = 36π / 12  

area of each sliced cake = 3π  square inches

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The smaller number, x from the inequality x + 2x + 6 < 50 is x < 14.67

x + 2x + 6 < 50

3x + 6 < 50

3x < 50 - 6

3x < 44

x < 44/3

x < 14.6666666666666

Approximately,

x < 14.67

Therefore, the smaller number, x is approximately x < 14.67

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The population of Dorchester in 1999 is 277000.

According to the statement

we have given that the population in 2012. and given that the it is increased 6% from the year 1999. And we have to find the population in 1999.

So, For this purpose,

we have given that the number of

population of Dorchester in 2012 = 294,680

increased from year 1999 = 6%

So, here we use percentage and subtraction formula

Population increase in numbers = 6/100*294,680

Population Increase in numbers = 17680

So, Population in 1990 = population of Dorchester in 2012 - Population increase in numbers

Population in 1990 = 294,680 - 17680

Population in 1990 = 277000.

So, The population of Dorchester in 1999 is 277000.

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Using the combination formula, it is found that he can make 4 different stacks.

The order in which the balls are selected is not important, as stated in the problem. hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, he has four flavors, and will choose three of them for the stacks, hence the number of different stacks is given as follows:

[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]

He can make 4 different stacks.

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Answer:

now we know that

book is 120page

__6785

The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

According to the statement

we have given that the

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0)

And we have to find that the which terms are corrected from the given options when Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

So, For this purpose we know that the

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

And According to the given statement

when parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

Then the conditions A, C, E are applicable because on rotation these things are applicable.

So, The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Figure 2 was constructed using figure 1.

On a coordinate plane, 2 parallelograms are shown.

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0).

Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

For the transformation to be defined as a rotation, which statements must be true? Select three options.

A. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

B. The transformation is rigid.

C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

D.Segment CP is parallel to segment CP'.

E. If figure 1 is rotated 180° about point C, it will be mapped onto itself.

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Answer: sequence II, sequence I, sequence III

Answer:

[tex] \blue{b < 8}[/tex]

Answer 1 is correct

Step-by-step explanation:

[tex] \frac{3}{2} b + 5 < 17[/tex]

Take 5 to the right side.

[tex] \frac{3}{2} b < 17 - 5 [/tex]

[tex]\frac{3b}{2} < 12 [/tex]

Multiply both sides by 2.

[tex]3b <12 \times 2[/tex]

[tex]3b < 24[/tex]

Divide both sides by 3.

[tex]b < 8[/tex]

Answer:5

Step-by-step explanation:

321 123

The multiplication property of equality has been used in the second step when both sides of the equation have been multiplied by 5/3.

State the Multiplication Property of Equality:

The Multiplication Property of Equality states that multiplying both sides of the equation with the same number, expression, or variable, the equation remains unchanged, i.e. equality is maintained.

Use of Multiplication Property of Equality in the Second Step:

The given equation was,

3x/5 + 5 = 20

In the first step, subtraction property of equality is applied as follows,

3x/5 + 5 - 5 = 20 - 5

3x/5 = 15

Now, for isolating x on the left hand side, we must apply multiplication property of equality by multiplying both sides of the equation by 5/3.

We get,

3x/5 × 5/3 = 15 × 5/3

x = 25

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The radius of the hemisphere is 9.5 inches.

The diameter of the hemisphere is 19 inches.

The surface area of the hemisphere is 850.2 inches²

circumference of a circle = 2πr

where

Therefore,

19π = 2πr

2r = 19

r = 19 / 2

r = 9.5 inches

diameter = 9.5 × 2 = 19 inches

Therefore,

surface area of an hemisphere = 3πr²

surface area of an hemisphere = 3 × 3.14 × 9.5²

surface area of an hemisphere = 850.155 inches²

surface area of an hemisphere = 850.2 inches²

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Answer:9

Step-by-step explanation:

Let [tex]A(t)[/tex] = amount of salt (in pounds) in the tank at time [tex]t[/tex] (in minutes). Then [tex]A(0) = 11[/tex].

Salt flows in at a rate

[tex]\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}[/tex]

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

[tex]\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}[/tex]

which I'll solve with the integrating factor method.

[tex]\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95[/tex]

[tex]-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}[/tex]

[tex]\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}} [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right) [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}[/tex]

[tex]\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}[/tex]

[tex]\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}[/tex]

After 1 hour = 60 minutes, the tank will contain

[tex]A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131[/tex]

pounds of salt.

Answer: False

Step-by-step explanation:

The base is more than 1, so the function is increasing.

Answer:

3.75

Step-by-step explanation:

3/4 times 5 =3 3/4

Answer:

2, 0, 2, 3, 5

1, 2, 4, 0, 5

Step-by-step explanation:

(ax + b)(cx² + dx + e)

acx³ + adx² + aex + bcx² + bdx + be

2(2)x³ + 2(3)x² + 2(5)x + 0 + 0 + 0

4x³ + 6x² + 10x

a = 2

b = 0

c = 2

d = 3

e = 5

1(4)x³ + 1(0)x² + 1(10)x + 2(4)x² + 0 + 10

4x³ + 8x² + 10x + 10

a = 1

b = 2

c = 4

d = 0

e = 5

Answer:

a = 9

Step-by-step explanation:

[tex]\sqrt{2a-14} = 2[/tex]

2a - 14 = 4

2a = 18

a = 9

Answer:

The answer to this question is a = 9.

Step-by-step explanation:

To solve this problem, we need isolate the variable "a" on one side of the equation. Our first step must be to remove the square root. To do this, we should perform the inverse operation, which is squaring both sides.

√2a - 14 = 2

(√(2a - 14))² = 2²

2a - 14 = 4

Next, we should add 14 to both sides of the equation to get the variable term by itself.

2a - 14 + 14 = 4 + 14

2a = 18

Finally, we should divide both sides of the equation by 2 to remove the coefficient from the variable term.

a = 9

Therefore, the correct answer is a = 9.

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Answer:3 - x/4

Step-by-step explanation: quotient of x and 4 = x/4. 3 minus x/4 = 3 - x/4.

The expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = [tex]$\frac{x}{4}[/tex]

Therefore -

[tex]$3 -\frac{x}{4}[/tex]

Hence, the expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

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Answer:

25/81.

Step-by-step explanation:

(27/8)^-4/3

= 8^4/3 / 27^4/3

= (∛8)^4 / (∛27)^4

= 16 / 81

(64/125)^-2/3

= (125)^2/3 / (64)^2/3

= (∛125)^2 / (∛64)^2

=  5^2 / 4^2

= 25/16

So the answer is

16/81 * 25/16

= 25/81.

Answer:

25 / 81(25 by 81) is your answer.

The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).

An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.

A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.

predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.

By lagranier multi plur

of = hog

(2x, is, 22>= 25-47

8x=42

10x + 2 = 42

2

28

2x=4, 4= 2

=2

722 (4)

(4.9,2) = (4.2-8)

(4,2-8)= 84

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Answer:

B. -1/3

Step-by-step explanation:

Choose 2 points. From the lower points count up until it is in line with the other point. Then count left until you reach the second point.

Rise/Run

Rise=1

Run=-3

[tex]-\frac{1}{3}[/tex]

Hope this helps!

Answer: -1/3 is the answer

Step-by-step explanation:

Answer: negative slope

constant slope

decreasing function

B-C-E

Step-by-step explanation:negative slope

constant slope

decreasing function

The total surface area of this shaded region is 1000 units²

An equation is an expression that shows the relationship between two or more numbers and variables.

The total surface area of a polygon is the sum of the individual areas of each surface.

Total area of the figure = 2(20 * 10) + 2(10 * 10) + 2(20 * 10) = 1000 units²

The total surface area of this shaded region is 1000 units²

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The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

The maclaurin series for f(x) is defined by the following formula:

[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)

Where [tex]f^{i}[/tex] is the i - th derivative of the function

If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:

[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)

Then,

[tex]f^{i}(0) = (-6)^{i}[/tex]

Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)

Hence,

The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].

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Supplementary angles are angles that can be summed up to give [tex]180^{o}[/tex], which is the value of the sum of angles on a line.

The required statements and reasons are given below:

Two or more lines are said to be parallel if there is no measure of the angle between them or the measure of the angle between them is [tex]180^{o}[/tex]. Thus the lines would never meet at any point even when extended to infinity.

While supplementary angles are angles that can be summed up to give [tex]180^{o}[/tex], which is the value of the sum of angles on a line.

               STATEMENTS                                        REASONS

1. < A and <B with AD ║BE, AC ║BF                   Given.

2. AD, AC, BE, BF                                                 Straight line.

3. <A ≅ <1                                                              Congruent property of

                                                                              vertically opposite angles.

4. AD + AC  ≅ DC                                                 Addition property of parts

   BE + BF  ≅ EF                                                   of a given line segment.                                    

5. <A + <B ≅ [tex]180^{o}[/tex]                                                 Addition property of

                                                                            supplementary angles.  

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Answer: third store

Step-by-step explanation:

1

First store: 95

Second store: 0.8*115=92

Third store: 0.9*105=94.5

The length of the altitude AD is 12 units.

The height of the triangle can be found as follows:

We have to find an angle using cosine law before  we can find the height.

Therefore,

20² = 13² + 21² - 2 × 21 × 13 cos B

400 = 169 + 441  - 546 cos B

400 - 610 = - 546 cos B

-210 = - 546 cos B

cos B = -210 / -546

cos B = 0.38461538461

B = cos⁻¹ 0.38461538461

B = 67.3810899783

B = 67.38°

Hence,

sin 67.38° = opposite / hypotenuse

sin 67.38° = AD / 13

cross multiply

AD = 13 sin 67.38°

AD = 11.9999882145

AD = 12 units

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Jane lost 5 points in the game.

Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.

We need to write and evaluate an expression to find how many points Jane gained or lost.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Now, for the given situation we can write an expression as follows:

25 – 40 + 10

=25 + 10 + ( -40 )

=35 -40= -5

Therefore, Jane lost 5 points in the game.

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