If $900 is invested at 3%, compounded monthly, the future value S at any time t (in years) is given by the following.S = 900(1.0025)^12tHow long (in years) will it take for the amount to double? (Round your answer to one decimal place.)

x = 12, using the concept of absolute value equation.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.

To answer an absolute value problem, isolate the absolute value on one side of the equation. Then, resolve both equations by setting their respective contents to the positive and negative values of the integer on the other side of the equation. 

Given that,

4|x+6| = 24

either |x+6| = 6 or,  |x+6| = -6

x = 0. -12

So, x = 12                           [here as negative sign is already present]

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Answer:  AB || DC   (1st choice)

Reason:

We have two pairs of consecutive interior angles that are supplementary. We then use the converse of the consecutive interior angles theorem to conclude side AB is parallel to DC. This means ABCD is a trapezoid.

Refer to the diagram below.

If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Conversion means converting the same thing into different units.

Home Depot sells boards in 3-meter lengths. If you only need 1 meter and 45 cm. Then the length that you need is calculated as,

⇒ 1 meter and 45 centimeters

Convert the centimeters into a meter. Then we have

⇒ 1 + 45 / 100

⇒ 1 + 0.45

⇒ 1.45

Then the length of the board left will be calculated as,

⇒ 3 - 1.45

⇒ 1.55 meters

If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.

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(a) As time goes on and approaches infinity, the level of oxygen in the pond approaches normal, therefore;

The oxygen level will eventually approach its  normal level in the long-run

(b)  The number of weeks after which the oxygen level becomes 60% of its normal level are 0.5, 2 weeks

The rational polynomial function  in which the numerator and denominator have the same power and the coefficient of the highest power are the same indicates that the value of f(t) approaches 1 (normal) as t approaches infinity.

The function with which the oxygen level in the pond can be found is presented as follows;

[tex]f(t) = \dfrac{t^2-t + 1}{t^2+ 1}[/tex]

f(0) = 1, therefore

The end behavior of the function as the value ot t approaches infinity is therefore the asymptote;

y = 1/1 = 1

The  value of the function f(t) as the value of t approaches infinity is that the f(t) approaches 1, which is the normal level of oxygen in the pond

(b) When the oxygen level is 60%, we get;

[tex]f(t) = \dfrac{t^2-t + 1}{t^2+ 1} = 60\% = 0.6[/tex]

0.6·(t² + 1) = t² - t + 1

0.6·t² + 0.6 = t² - t + 1

0.4·t² - t + 0.4 = 0

t² - 2.5·t + 1 = 0

Therefore;

(t - 2)·(t - 0.5) = 0

t = 2 or t = 0.5

The times when the oxygen level is 60% is 0.5 and 2 weeks after the organic waste is dumped in the pond.

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The linear regression for the given data is y = 0.8x + 12.78 and the test grade will be 44.

What is linear regression?

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Based on the given data

Using the graphing calculator, the linear regression will be,

y = 0.8x + 12.78

For a homework grade of 39, x = 39

Then, y = 0.8*39 + 12.78 = 43.98 ≈ 44

Hence, the test grade will be 44.

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Answer:

Step-by-step explanation:

0.0395 m, -0.486 ms⁻¹ and -4725.791 ms⁻² are the position, velocity and acceleration of the particle are  respectively

Given that:

A particle moves so that position in meters is given as a function of time in seconds by the equation x(t)=Acos(wt+l), where A=0.0395 m, w=346 s⁻¹, and l=1.00

The position of the particle at 3.00 ms

Substitute t = 3.00 ms = 0.003 s into the function:

x(t) = Acos(wt+l)

x(0.003) = 0.0395cos(346×0.003 + 1.00)

x(0.003) = 0.0395cos(2.039)

x(0.003) = 0.0395 m

The velocity of the particle at 3.00 ms

To get the velocity function, take the derivative of x(t) = Acos(wt+l):

x'(t) = -Awsin(wt+l)

Then substitute t = 3.00 ms = 0.003 s into the velocity function:

x'(t) = -Awsin(wt+l)

x'(0.003) = -0.0395 ×346sin(346×0.003 + 1.00)

x'(0.003) = -13.667sin(2.038)

x'(0.003) = -0.486 ms⁻¹

The acceleration of the particle at 3.00 ms

To get the acceleration function, take the derivative of x'(t) = -Awsin(wt+l):

x''(t) = -Aw²cos(wt+l)

Then substitute t = 3.00 ms = 0.003 s into the  function:

x''(t) = -Aw²cos(wt+l)

x''(0.003) = -0.0395 ×346² cos(346×0.003 + 1.00)

x''(0.003) = -4728.782 cos(2.038)

x''(0.003) = -4725.791 ms⁻²

Therefore, the position, velocity and acceleration of the particle are 0.0395 m, -0.486 ms⁻¹ and -4725.791 ms⁻² respectively

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The solution set for absolute value inequalities are presented as follows;

(b) (i) -∞ < x ≤ 2

(ii) 1.25 ≤ x < 3, or x > 3

An absolute value inequality is an inequality with an absolute value expression containing a variable.

(i) |2·x + 7| + 1 ≥ 6·x

Solving for when |2·x + 7| is positive, we get;

2·x + 7 + 1 ≥ 6·x

7 + 1 ≥ 6·x - 2·x = 4·x

8 ≥ 4·x

Dividing both sides by 4, we get;

8 ÷ 4 ≥ 4·x ÷ 4 = x

2 ≥ x

Therefore; x ≤ 2

The solution of the absolute value inequality can be found as follows;

|2·x + 7| + 1 ≥ 6·x

|2·x + 7| ≥ 6·x - 1

Therefore, we have the following compound inequality;

2·x + 7 ≤ -(6·x - 1), 2·x + 7 ≥ (6·x - 1)

The solution for the inequality, 2·x + 7 ≤ -(6·x - 1) is found as follows;

2·x + 7 ≤ -(6·x - 1) = 1 - 6·x

2·x + 6·x ≤ 1 - 7 = 6

8·x ≤ 6

x ≤ 6/8 = 3/4

x ≤ 3/4

The solution for the inequality, 2·x + 7 ≥ (6·x - 1) is found as follows;

2·x + 7 ≥ (6·x - 1)

7 + 1 ≥ 6·x - 2·x = 4·x

8 ≥ 4·x

x ≤ 2

Combining the solution, we get;

-∞ < x ≤ 2

(ii) [tex]\left|\dfrac{2\cdot x+ 1}{x - 3} \right| \geq 2[/tex]

Therefore, we get;

[tex]\dfrac{2\cdot x+ 1}{x - 3} \leq -2[/tex]

[tex]\dfrac{2\cdot x+ 1}{x - 3} + 2 \leq 0[/tex]

[tex]\dfrac{4\cdot x - 5}{x - 3} \leq 0[/tex]

x < 3, or x ≥ 1.25

1.25 ≤ x < 3

[tex]\dfrac{2\cdot x+ 1}{x - 3} \geq 2[/tex]

[tex]\dfrac{2\cdot x+ 1}{x - 3} -2 \geq 0[/tex]

[tex]\dfrac{7}{x - 3} \geq 0[/tex]

Therefore, x > 3,

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Answer:its 30 ft

Step-by-step explanation:

easyyy

Ask a question action correctly completes this graphic organizer.

Option A is correct .

A graphic organizer is a visual and graphic display that depicts the relationships between facts, terms, and or ideas within a learning task.Graphic organizers are also sometimes referred to as knowledge maps, concept maps, story maps, cognitive organizers, advance organizers, or concept diagrams

.Ask a question action correctly completes this graphic organizer.

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The points on the coordinate grid are been labelled in the image attached with solution.

A pair of integers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. The terms abscissa and ordinate are used to describe the x- and y-coordinates, respectively. A point in a plane is represented by both coordinates (x, y).

Here,

The picture showing the answer is labeled with the coordinate grid's points.

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The function that describes the exponential growth is P(t) = 21100 [tex]e^{0.09t}[/tex] and the population in 2008/ will be 43348.54.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

(a)

As per the given,

Growth rate r = 9 % = 0.09

Population in 2000 (t = 0)  is 21100

The formula for exponential growth is given as,

P(t) = P₀e^(rt)

P(t) = 21100 e^(0.09 x t)

P(t) = 21100 [tex]e^{0.09t}[/tex]

(b)

The number of population in 2008 (t = 8) will be as.,

P(8) = 21100 e^(0.09 x 8)

P(8) = 43348.54

Hence "The function that describes the exponential growth is P(t) = 21100 [tex]e^{0.09t}[/tex] and the population in 2008/ will be 43348.54".

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Answer:

  (7, -2)

Step-by-step explanation:

You want a graphical solution to the equations ...

The graph is shown in the attachment. The solution is (x, y) = (7, -2).

The answer to this Question based on pH is 8.12

What is pH?

pH is a measure of acidity or basicity in a solution. It is measured on a scale ranging from 0 to 14, with 7 being neutral. A pH below 7 is acidic and a pH above 7 is basic. A solution with a pH of 0 is the most acidic, while a solution with a pH of 14 is the most basic. The pH of a solution is an important factor in many chemical and biological processes, as it affects the activity of molecules. For example, enzymes typically only function within a certain pH range, and most biological cells have a preference for a specific pH. pH is also important in determining the solubility of certain substances, and can affect the taste of food.

Here [H] = 7.7 * 10^-9

pH = -log[7.7 * 10^-9]

using some log properties this value comes out to be

pH = 9 - 0.88

pH = 8.12 and pH greater than 7 means solution is Basic

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The quadratic equation is x² - 2x - 24

What is quadratic equation ?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

Given roots of quadratic equation are 6 and -4.

Also given here leading coefficient is 1.

We know that, the formulae for forming quadratic equation when its roots are given is as follows: x² - (α+β)x + αβ

Here α and β are the roots of the quadratic equation.

Let  α = 6 and β = -4

Putting the value of  in the above formulae we get,

x² - (6-4)x - 24

x² - 2x - 24

But remember here 1 is the leading coefficient of the quadratic equation with roots 6 and -4 (given in question),so we have to multiply the equation by 1 to get the final answer.

So, Hence the required quadratic equation is x² - 2x - 24

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The  average rate of change of the function from x = 1 to x = 4 is 14.90

A function can be defined as an expression, law or rule that shows the relationship between two variables.

The variables are;

Given the function;

f(x) = 10x^2 + x

For x = 1, let's substitute the value of x as 1

f(1) = 10(1)^2 + 1

f(1) = 10 + 1

f(1) = 11

For  x = 4, let's substitute the value of x as 4

f(4) = 10(4)^2 + 4

f(4) = 10(16) + 4

f(4) = 160 + 4

f(4) = 164

The rate of change = 164/11 = 14. 90

Hence, the value is 14. 90

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18.5 is correct for part (a) since t = 0 leads to A = 18.5

=====================================================

Part (b)

Your teacher is asking for the value of t when A = 26.6

A = 18.5*e^(0.1708t)

26.6 = 18.5*e^(0.1708t)

26.6/18.5 = e^(0.1708t)

1.437838 = e^(0.1708t)

Ln(1.437838) = 0.1708t

t = Ln(1.437838)/0.1708

t = 2.126116 approximately

t = 2 when rounding down to the nearest integer

Therefore, 2 years after the year 2000, the year 2002, is when the population reaches roughly 26.6 million. The actual population will be slightly less than 26.6 million, but it's close enough.

Note that:

which helps confirm the correct value of t is between t = 2 and t = 3.

The number of races that were 10-kilometer long is 102.

An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.

Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.

32×15 + 10x = 1,500

480 + 10x = 1,500

10x = 1,500 - 480

10x = 1,020

x = 1,020/10

x = 102

Hence, the number of races that were 10-kilometer long is 102.

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Answer: 8 Five point questions

Step-by-step explanation:

Hope this helps you!

The value of variable x is 19.20.

Let's find the value of variable x in the equation.

A variable is a number represented with letters in an equation.

Therefore,

x / 6 + 4 / 10 = 3 + 6 / 10

Therefore, let's find the variable x.

10x + 24 / 60 =  30 + 6 / 10

10x + 24 / 60 = 36 / 10

60 × 36 = 10(10x + 24)

2160 = 100x + 240

2160 - 240 = 100x

1920 = 100x

divide both sides by 100

x = 1920 / 100

x = 19.20

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Answer: its A 23.04

Step-by-step explanation:

a) The best estimate of the probability of rolling a "6" with this die is

0.2 (100/500).

My best estimate of the probability of rolling a “6” is 20%. This is calculated by taking the number of “6”s rolled in the 500 trials (100) and dividing it by the total number of trials (500).

b) If you roll this die 30 times, you can expect to get 6 "6"s (0.2 x 30).

If I roll this die 30 times, I expect to get 6 “6”s. This is calculated by taking the probability of rolling a “6” (20%) and multiplying it by the number of trials (30).

c) If you roll a fair die 30 times, you can expect to get 5 "6"s (1/6 x 30).

If I roll a fair die 30 times instead of the “unfair” die, I expect to get 5 “6”s. This is calculated by taking the probability of rolling a “6” on a fair die (16.7%) and multiplying it by the number of trials (30).

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Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

if x = 1

P(x) = 1/10

if x = 2

P(x) = 2/10

if x = 3

P(x) = 3/10

if x = 4

P(x) = 4/10

a) Corresponding angles are congruent, m<a=139

b) Alternate Interior Angles are congruent, m<b =139

Answer:

A: "The theoretical probability is higher."

Step-by-step explanation:

The theoretical probability of rolling an odd number on a die is 1/2, or 0.5. Since Tami rolled the die 20 times and it landed on an odd number 6 times, the experimental probability of rolling an odd number is 6/20, or 0.3. Since 0.3 is less than 0.5, the theoretical probability is higher. Therefore, the correct answer is option A: "The theoretical probability is higher."

The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."

Given : 40 - 4x > 10 which is an inequality

To find : The value of x

Procedure:

Step 1:  Collect all the terms with x on right side and the constant terms  on the left side of the greater sign.

40 - 4x > 10

When 10 is brought to the left, there will be change in sign for the number 10 and similarly, when -4x is taken to the right, it becomes +4x or simply 4x. So inequality becomes

40 - 10 > 4x

Step 2: On solving the resulting inequality, we get

30 > 4x

Divide both sides by 4. So inequality becomes

[tex]\frac{30}{4} > \frac{4x}{4}[/tex]

7.5 > x

This means, x < 7.5

The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."

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Answer:She can buy from 0 to 7 smoothies, but no more."

Step-by-step explanation:She can buy from 0 to 7 smoothies, but no more." Which is option B

Answer:

y = 14

Step-by-step explanation:

y = k[tex]\sqrt{x}[/tex]  Solve for k

7 = k[tex]\sqrt{9}[/tex]

7 = k3  Divide both sides by 3 to solve for k

[tex]\frac{7}{3}[/tex] = k  

y = kx

y  = [tex]\sqr\frac{7}{3} }[/tex][tex]\sqrt{36}[/tex]

y = [tex]\frac{7}{3}[/tex](6)

y = 14

[tex]\frac{7}{3}[/tex][tex](\frac{6}{1})[/tex] is the same thing as [tex]\frac{7}{1}[/tex][tex](\frac{2}{1})[/tex]  I cross canceled the 3 and the 6

[tex]\frac{14}{1}[/tex] = 14

The lawyer's net worth is $307,331.

Assets are those things the organization or the individual possess. It is a source of income.

Liabilities are those items that are debt or has to pay money for it.

From the list, the assets of the lawyer are:

Car value = $41,450

Savings account balance = $13,547

Season baseball tickets = $19,400

Checking account balance = $16,309

Home Value = $271,345

Total assets = $41,450 + $13,547 + $19,400 + $16,309 + $271,345

                    = $362,051

The liabilities of the lawyer are:

Car loan = $22,890

Student loans = $12,410

Credit card balance = $19,420

Total liabilities = $22,890 + $12,410 + $19,420

                        = $54,720

Net worth = Total assets - Total liabilities

                 = $362,051 - $54,720

                 = $307,331

Hence, the net worth of the lawyer with these assets and liabilities is $307,331.

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a. The population of the state in 2000 is 18.5 million

b. The population will reach 26.6 million in about 2 years

From the question, we are to determine the population of the state in 2000.

From the given information,

The formula that models the population of the US state after 2000 is

A = 18.5e^(0.1708t)

To determine the population of the state in 2000, we will substitute t = 0

That is,

A = 18.5e^(0.1708(0))

A = 18.5e^(0)

A = 18.5(1)

A = 18.5

Thus, the population of the state in 2000 is 18.5 million

b. To determine when the population will reach 26.6 million

Substitute A = 26.6 in the equation

A = 18.5e^(0.1708t)

26.6 = 18.5e^(0.1708t)

Solve for t

26.6/18.5 = e^(0.1708t)

ln(26.6/18.5) = 0.1708t

0.36314048 = 0.1708t

t = 0.36314048/0.1708

t = 2.126

t ≈ 2

Hence, the population will reach 26.6 million in about 2 years

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The values to make up the solution set of inequality are {8,9,10}.

In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality.

A less than symbol (a, b) denotes that one thing is less than the other.

The notation a > b indicates that an is greater than b.

A and b are not equal in either situation. A strict inequality is one in which an is strictly less than or strictly bigger than b in certain connections. Comparability is left out.

First we have to replace m with 8, it becomes:

8+7 =15<18

For 9,  

9+7 =16<18

For 10,

10+7 =17<18

And for 11,

11+7 =18=18

So, The values to make up the solution set of inequality are {8,9,10}.

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