ALGEBRA 2 - Exponential and Logarithmic Functions

Simone’s parents invested $1,500 in an account such that the value of the investment doubles every seven years. The value of the investment, V, is determined by the equation V= p · t^r/7, where p represents the amount invested and t represents the number of years since the money was deposited. How many years, to the nearest tenth of a year, will it take the value of the investment to reach $1,000,000?

A polynomial of degree 4 is called bi-quadratic polynomial.

Bi-quadratic polynomial

A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

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The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.

When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.

The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.

In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.

There are several methods also present to find the value of the third side of the triangle.

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Sandra needs to score at least 87.67% to get an average score of 85%.

Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).

Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.

Now as per the question she needs 85%.

The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33

Now to get 85%, we have to average out as 82.33+x/2 = 85

x+82.33 = 85*2 = 170

x = 170-82.33 = 87.67

Hence, Sandra needs to score at least 87.67% to get an average score of 85%.

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Answer:

7.5 which rounds to 8

Step-by-step explanation:

2,722 divided by 360 equals 7.56

check if needed <3

The combined gas law for a gas is discussed below.

Given is the combined gas law.

The ideal combined gas law is given by →

PV = nRT

Where -

{P} = pressure     {T} = temperature     {V} = volume    

{n} = number of moles   {R} = gas constant

Non ideal gases are often modelled by the Van der Waals equation as →

(p + n²a/V²)(V - nb) = nRT

Where -

{a} and {b} = constants for a particular gas

{p} = pressure       {v} = volume    

{n} = number of moles       {t} = temperature  

{R} = gas constant

Therefore, the combined gas law for a gas is discussed above.

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The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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A traditional yearbook should have a few pages for the school's administrators, faculty, and other staff members, class or student portraits, several pages for clubs, teams, or other group photos, a section for special awards & superlatives, event pages typically with a collage of school events, and graduating class.

Despite possible differences in size and appearance, school yearbooks all have a similar structure and content makeup. A school yearbook is essentially a "memory book" that emphasizes the pupils, teachers, and activities that took place during the academic year.

Additionally, yearbooks give kids the chance to request the autographs of their friends and professors and give them a place to write personal notes, "inside jokes," and other remarks. Overall, a yearbook gives students a tangible memento of the academic year.

The only thing we are doing is dividing if we require that all of the rows be equal.

20/1= 20

20/2= 10

20/4=5

20/5=4

20/10=2

20/20=1.

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A log graph can be either increasing or decreasing, depending on the function or data being graphed.

A log graph is a type of graph that displays the data on a logarithmic scale. That is, the values of the data are represented on a logarithmic scale, rather than on a linear scale. This type of graph is useful for displaying data or functions that span a wide range of values over a large range of exponents. The direction of the graph depends on the data being graphed or the function being shown. If the values of the data or the function being graphed increase over time, then the graph will be increasing. Conversely, if the values of the data or the function being graphed decrease over time, then the graph will be decreasing.

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Answer:

To find the number of hours you work, you need to set up an equation using the information given. Let's say that the number of hours you work is x. The equation would be:

17(x/2) = 42.50

The parentheses around x/2 indicate that the division should be done before the multiplication. So, x/2 = 2.5. Multiplying both sides of the equation by 2 gives us:

x = 5

So, you work 5 hours.

Step-by-step explanation:

So, we know that you earn $17 per 2 hours. We also know that we earned $42.50. Now, we just need to find the hours! We can do this by using a cross multiply.

$17 is directly correlated to 2 hours of work. Therefore, to find the hourly wage we should divide it by 2:

   $8.5 = 1 hour

$42.50 = x hours?

Now cross multiply:

$8.5x = $42.50

x = 5 hours

Therefore, your answer is 5 hours!

Hope this helps!

The coefficient of expression 5x^2 in 5x^2 5x is 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. In this expression, the number multiplied with 5x^2 is 5, so the coefficient of 5x^2 is 5.

The expanded expression is 5x^2 5x = 5x^3 + 5x^2. The coefficient of 5x^2 in this expression is still 5.

The coefficient of 5x^2 in 5x^2 5x is the number that is multiplied with 5x^2. When we expand the expression 5x^2 5x, it becomes 5x^3 + 5x^2. The number that is multiplied with 5x^2 in this expression is still 5, so the coefficient of 5x^2 is 5.

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We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.

The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.

A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.

The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.

lim/h→0f(x+h)−f(x)h=f'(x).

lim/h→06−6/h=0.

f'(x)=limΔx→0

f'(x)=limΔx→0

f(x+Δx)−f(x)Δx=

f'(x)=limΔx→06−6Δx=0

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To prove a number is irrational we divide the integer by another integer is the decimal is non terminating and non repeating then it will be a irrational number .

What are Irrational Numbers ?

The Irrational numbers can be defined  a number that cannot be expressed as a fraction [tex]\frac{p}{q}[/tex] for any integers p and q.

The Irrational numbers have decimal expansions that do not terminate nor repeat (periodic) . Every transcendental number is an irrational number .

(i) To prove a number irrational  when we divide an integer by another integer, and  if decimal expansion does not terminate and do not  repeat then it is an irrational .

(ii) if the number cannot be expressed in the form of [tex]\frac{p}{q}[/tex] , then also the number will be called as irrational numbers .

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The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

What is the average rate of change?

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval, divided by the difference in the x-values of the endpoints.

In this case, the function is h(x) = -x² + 8x, the interval is 0 ≤ x ≤ 5, and we want to find the average rate of change over that interval.

So, we can use the following formula:

Average rate of change = (h(5) - h(0)) / (5 - 0)

Now we have to substitute the values into the equation:

h(5) = -5^2 + 85 = -25 + 40 = 15

h(0) = -0^2 + 80 = 0

Average rate of change = (15 - 0) / 5 = 3

Hence, The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

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The most accurate value for AB is 37.699111843077516 (approximately)

The measure of an arc is directly related to the measure of the central angle that intercepts it. The measure of an arc is equal to the measure of its central angle, multiplied by the radius and divided by the degree of the circle.

Since, radius is not given let's assume it 20.

In this case, the central angle AOB has a measure of 110 degrees, and the radius of the circle is 20. Therefore, the measure of the arc AB is:

AB = (110/360) * 20 * 2 * π

or

AB = (110/360) * 20 * π

where π is the mathematical constant (approximately equal to 3.14).

So, the measure of the arc AB is (110/360) times the circumference of the circle, or (110/360) of the total length of the circumference.

The most accurate value for AB is 37.699111843077516 (approximately)

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The statistical model is not good, and this is true for a negatively skewed curve.

It is a statistical term implies that a curve is skewed at the left side.

In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.

In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.

In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.

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She can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter

In the given question, Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter.

We have to find how many pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter.

The radius of a ball of yarn six inches in diameter is

r = 6/2 = 3 inches

The radius of a ball of yarn twelve inches in diameter is

r = 12/2 = 6 inches

Now, the volume of the six inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the six inches yarn = [tex]\frac{4}{3} \pi (3)^3[/tex]

The volume of the six inches yarn = 36π

Now, the volume of the twelve inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the twelve inches yarn = [tex]\frac{4}{3} \pi (6)^3[/tex]

The volume of the twelve inches yarn = 288π

Now we finding the numbers of pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter

= 288π/36π

= 8

Hence, she can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter.

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For the described situation, y  = 6sin ( (π / 10) x )  -  10 is the sine function.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Asin(Bx)+C is the usual sine function formula.

A buoy bobs 6 meters up and down.

That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.

A=6 Amplitude

The x-axis distance that constitutes one complete oscillation is known as the period.

We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).

20 seconds make up the complete oscillation period.

⇒ 20 (B) = 2π

B=2π /20

= π/ 10

Given that the buoy is 10 meters under the ocean's surface, C equals –10.

Using the formula's whole range of values:

⇒y  = 6sin ( (π/ 10) x )  -  10

The midline is the initial point.

x=0 is the first point.

⇒y=6sin(0)-10

y= -10

The line is drawn from the origin at y = -10.

Either the highest or smallest value is at the second point.

Therefore, (5,-4) and (15, -16.)

Therefore, for the described situation, y  = 6sin ( (π / 10) x )  -  10 is the sine function.

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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.      

The slope intercept form of a line is y = mx + c              

Where, c - y-intercept and m - the slope of the line

Given that

The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.

4 minutes of internet costs $ 3

8 minutes of internet costs $ 4  

[ We can represent the given situation as given below ]      

And the coordinates formed are (4, 3) and (8, 4)

The slope of the line formed = (4 - 3)/(8 - 4) = 1/4

Let y = mx + c be the equation to the model situation

=> y = (1/2)x + c

=> 2y = x + c ---- (1)

As we know (1) will pass through (4, 3)

=> 2(3) = 4 + c

=> 6 = 4 + c

=> c = 6 - 4

=> c = 2

=> 2y = x + 2

=> x - 2y + 2 = 0

Therefore,

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

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Answer:

Step-by-step explanation:

3x=24

x=8

On solving the provided question, we can say that - the radicals are as follows be = 3x^2|y| sqrt(7x)  

The square root or nth root symbol is called a radical. Expressions with square roots are referred to as root expressions. A radical's radicand is a number or phrase that appears there. The radicals 7, 2y+1, and so on are examples. The following phrases can also be used to describe radicals: Radical equations are equations contained within of radicals. The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

here,

the radicals will be - 7xy ∛(xy^2)

and   3x^2|y| sqrt(7x)  

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Answer:

Step-by-step explanation:

In 12 hours, the train will travel 487.5 miles

8/325=40.625

40.625 x 12 = 487.5

Answer:

Step-by-step explanation:

you have studied this in grade 8 grade 9 and grade 10 if you are studying under CBSE, so, better call textbook

Answer:

Read below

Step-by-step explanation:

Step 1: Multiply 2 by x: 2x

Step 2: Add 1 to 2x: 2x + 1

Step 3: Substitute x with 7: 2(7) + 1

Step 4: Multiply 2 by 7: 14 + 1

Step 5: Add 1 to 14: 14 + 1 = 15

A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.

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$0, He earned $8798 in net taxable income the previous year. He has a negative amount of taxable income since the exemption and the allowed deduction are larger than his annual gross income.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.

The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.

According to our question-

Last year, a part-time housekeeper earned $8798.

He claimed he was exempt, costing $365.

$570.00 is the standard deduction.

Gross income less the standard deduction and all exemptions equals taxable income.

= 8798 - 3650 - 5700 = $-552

There is a negative number, which indicates that he owes no taxes.

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That means after 6  weeks will Haley have at least the same amount of

money as Kendra

Kendra and Haley are each saving money. Kendra starts with $100 in his savings account and adds $5 per week. Haley starts with $10 in her savings account and adds $20 each week. After how many weeks will Haley have at least the same amount of money as Kendra?

Kendra and Haley are each saving money.

Kendra starts with $100 in his savings

account and adds $5 per week.

After 6 week 6* 5 = 30

Total amount in After 6 week in  Kendra savings

account = $100 + $30

             = $130

Haley starts with $10 in her savings account and

adds $20 each week.

After 6 week 6* 20 =120

Total amount in After 6 week in  Haley savings

account = $10 + $120

             = $130

That means after 6  weeks will Haley have at least the same amount of

money as Kendra

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