Write an equation for a rational function with the given characteristic.

Vertical asymptotes at x = -2 and x = 3, x-intercepts at (-4,0) and (-1,0), y-intercepts at (0,4)

f(x) =

−26am^2 + 26am + 37a

The amount of money that needs to be deposited now into an account to obtain $6,200 in 15 years is $2,928.67.

Mathematically, continuous compounding interest can be calculated by using this mathematical expression:

P(t) = P₀e^{rt}

Where:

Substituting the given parameters into the continuous compounding interest formula, we have;

P(t) = P₀e^{rt}

$6,200 = P₀e^{0.05 × 15}

$6,200 = P₀e^{0.75}

Principal, P₀ = 6,200/e^{0.75}

Principal, P₀ = 6,200/2.11700001661

Principal, P₀ = $2,928.67.

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In circle L with m/KLM = 60 and KL = 18 units, the length of arc KM is approximately 18.85 units.

What is circle?

A circle is a geometrical shape that is defined as the set of all points in a plane that are equidistant from a given point called the center of the circle. The distance between the center of the circle and any point on the circle is called the radius of the circle.

We can use the formula for the length of an arc of a circle:

L = rθ

where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the center of the circle (in radians).

In this problem, we are given the measure of the central angle m/KLM = 60 degrees, which is equal to 60/360 = 1/6 of a full revolution (360 degrees). Therefore, the angle θ subtended by the arc KM is:

θ = (1/6) * 2π = π/3 radians

To find the length of arc KM, we need to know the radius of circle L. Since we are not given this information directly, we can use the fact that KL is a chord of the circle and the perpendicular bisector of KL passes through the center of the circle. Let O be the center of circle L, and let N be the midpoint of KL. Then ON is the radius of the circle, and KN = KL/2 = 9 units.

We can use the Pythagorean theorem to find ON:

ON² = OM² + MN²

where OM is the distance from O to the midpoint of LM. Since OM is perpendicular to LM, it is also the altitude of triangle KLM, and we can use the formula for the altitude of an equilateral triangle to find that OM = ([tex]\sqrt{3}[/tex]/2)KL = 9[tex]\sqrt{3}[/tex] units.

Since MN = KL/2 = 9 units, we have:

ON^2 = [tex](9*\sqrt{3} )^2 + 9^2[/tex] = 243 + 81 = 324

so ON = 18 units.

Now we can find the length of arc KM using the formula:

L = rθ = 18 * (π/3) = 6π units

Rounding to the nearest hundredth, we get:

L ≈ 18.85 units.

Therefore, the length of arc KM is approximately 18.85 units.

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Answer: A) [tex]y=\frac{3}{7}x-2[/tex]

Step-by-step explanation:

its just the answer, and if you want explanation just say...

The longest side of a triangle is always opposite the,

A. angle with the greatest measure.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

We know, The length of the largest side in a triangle is opposite to the largest angle.

The statement, The longest side of a triangle is always opposite the

angle with the greatest measure.

Because A longer angle will be more spread out and hence the opposite side will be longer too.

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Answer: C

Step-by-step explanation:

I am fairly certain this is the right answer. Good luck on your quiz!

Answer:C

Step-by-step explanation:

I remember this from class one time hope it helps:)

a) The distribution of the mean weight of 10 apples picked at random is normally distributed.

b) The mean, μ, is 45 oz.

What is normal distribution and mean?

normal distribution: The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean.

Mean: In mathematics, a mean is the average of a data set, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

a) The distribution of the mean weight of 10 apples picked at random is approximately normally distributed. This is because, according to the Central Limit Theorem, when the sample size is sufficiently large, the distribution of the sample mean becomes normal regardless of the underlying population distribution.

Here, we have a sample size of 10, which is considered large enough to apply the Central Limit Theorem. Also, we know that the underlying population distribution of the weight of a single apple is normal.

b) The mean weight of 10 apples picked at random is simply the mean of the individual weights of those 10 apples. Since the individual weights of the apples are normally distributed with a mean of 45 oz and a standard deviation of 3 oz, the mean weight of 10 apples will also be normally distributed with a mean equal to the mean of the individual weights, which is 45 oz.

Therefore, the mean, μ, is 45 oz.

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The conditional probability P(B|F) of the two way table is; P(B|F) = 0.37 given that the students prefer to write with block letters, there is a 0.37 probability that they have fair dancing skills

Two-way tables are a way of sorting data so that the frequency of each category can be seen quickly and easily.

Conditional probability is defined as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

Now, from the given two way table,

B = the student prefers writing in block letters.

F = the student's dancing skills are fair.

Thus;

P(B|F) = 17/45

P(B|F) = 0.37

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The shape is most specifically a trapezoid because it has a pair of parallel sides

From the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we have the following highlights:

Using the above as a guide, we have the following:

The shape is most specifically a trapezoid

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An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.

The equation of a line with slope m passing through the point (x1, y1) can be written in the form:

y - y1 = m(x - x1)

Since the slope of the line is undefined, the equation of the line would be in the form:

x - x1 = constant

To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:

x - 3 = constant

So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:

x - 3 = constant

or simply:

x = 3.

Answer:

15 cups

Step-by-step explanation:

So we have a ratio, butter:sugar. This ratio is given as 3:5, or 3 parts to 5 parts. Basically, every 3 cups of butter you use, you use 5 cups of sugar.

In order to calculate this, we simply need to divide the amount of butter being used by 3, and then multiply that by 5. This way, we are figuring out how much a singular "part" is in this situation, and then multiplying that by 5 for the 5 parts sugar.

9/3 = 3

3*5 = 15

Therefore, you have 15 cups of sugar.

Answer:

30°

Step-by-step explanation:

360 / 12 = 30°

30 X 1 = 30

According to the information, it can be inferred that the total surface of the figure is 23.18yr². Additionally, the volume would be 7.8 yr³

To calculate the surface of the figure we must perform the following mathematical procedure.

We must find the surface of each of the faces that the figure has, we do this by multiplying base by height; in the case of triangles it is base times height divided in two.

Now we must multiply these values by the number of faces of this dimension:

Then we add all the surfaces to have the total surface

On the other hand, to find the volume of the figure we must multiply height by length by width; in the case of the triangle it is the same formula because it has a rectangular base.

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Answer:

Step-by-step explanation:

The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.

To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.

So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.

The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.

For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.

The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:

±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2

To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:

x = 1/2, x = 1, x = 3/2, x = 2

Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.

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The total distance that Cami walked from home to school, then home, and then library, is 7. 46 miles

The distance walked by Cami, can be found to be :

= Distance from home to school + distance from school to home + distance from home to library

The distance in kilometers is:

= 5 + 5 + 2

= 12 kilometers

In miles, this is:

= 12 / 1. 60934 km per mile

= 7. 46 miles

In conclusion, the distance walked by Cami in miles, was 7. 46 miles.

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There was a 305.1% increase in the value from 2000 to 2010.

What is Percent?

To compute a percentage, divide the value by the entire amount and multiply the result by 100.

To calculate the percent increase, we need to determine the difference between the two values and divide it by the original value, then multiply by 100 to express it as a percentage.

For the year 2000:

Percent increase = (22.5 - 5.53) / 5.53 * 100 = 305.05%

And rounded to the nearest tenth of a percent, this would be 305.1%.

So, There was a 305.1% increase in the value from 2000 to 2010.

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The leading coefficient of the expression is 1

From the question, we have the following parameters that can be used in our computation:

4x² + x4 -8 -5

When written in standard form, we have

x^4 + 4x^2 - 8 - 5

Evaluate the like terms

x^4 + 4x^2 - 13

The leading coeffiicient is the coefficient of the term with highest power

In this case, it is

Coefficient = 1

Hence, the value is 1

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Answer: His debts to income ratio is 35.29%

Step-by-step explanation:

His debts to income ratio is 35.29% ($2,400 / $6,800 = 0.3529).

Answer: no exact answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

a

The equation of the line that contains diagonal AH is  y = -4/7 x + 51/14.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Given;

The endpoints of the diagonal MT are M(0,-1) and T(4,6).

Now, The point that it passes through in this case is the midpoint of the diagonal MT. Using the midpoint formula you get

( (0+4)/2 , (-1+6)/2 ) = (2,2.5).

The slope of MT is (6--1)/(4-0) = 7/4.

We need this because the other diagonal must be perpendicular, which means that the slopes must be negative reciprocals. So the negative reciprocal of 7/4 is -4/7.

Now that we have the slope and the point, we can just use y=mx+b. We have an x and y value as well as the m....so we can substitute them in and calculate b.

2.5 = -4/7 (2) + b

5/2 = -8/7 + b

5/2 + 8/7 = b

35/14 + 16/14 = b

51/14 = b

Therefore, in the rhombus diagonal line has the equation will be y = -4/7 x + 51/14

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In reference to the given focus and directrix, the standard form of the equation of the parabola is (x - 3)² = 12y.

The standard form of the equation of a parabola with a horizontal axis of symmetry and a focus at (p, q) is:

(x - p)² = 4c(y - q)

where, c is the distance from the focus to the vertex.

In this case, the focus is at (3,0), which means that p = 3 and q = 0. The directrix is at x = -3, which means that the vertex is at the midpoint between the focus and the directrix, which is (0,0). The distance from the vertex to the focus (or from the vertex to the directrix) is c = 3.

Substituting these values into the standard form equation, we get:

(x - 3)² = 4(3)(y - 0)

Simplifying, we get:

(x - 3)² = 12y

So the standard form of the equation of the parabola is (x - 3)² = 12y.

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a. This is an example of continuous growth, as the functions for the GDPs of both countries are given as continuous functions of time.

(b) In the function for China's GDP, the parameter 1.35 represents the initial level of GDP in the year 2000, and the parameter 1.076 represents the annual rate of growth of GDP. In the function for the US's GDP, the parameter 10.4 represents the initial level of GDP in the year 2000, and the parameter 1.024 represents the annual rate of growth of GDP.

It should be noted that on order to calculate the projected level of GDP for each country for the years 2011, 2025 and 2047, we can substitute the corresponding values of t into the functions for YChina and YUSA:

For China:

YChina(11) = 1.35 * 1.076^11 ≈ 4.65 trillion dollars

YChina(25) = 1.35 * 1.076^25 ≈ 30.83 trillion dollars

YChina(47) = 1.35 * 1.076^47 ≈ 516.97 trillion dollars

For the US:

YUSA(11) = 10.4 * 1.024^11 ≈ 15.63 trillion dollars

YUSA(25) = 10.4 * 1.024^25 ≈ 30.19 trillion dollars

YUSA(47) = 10.4 * 1.024^47 ≈ 57.17 trillion dollars

So according to these projections, China's GDP has already surpassed the US's GDP as of 2025 and is expected to continue to grow at a much faster rate than the US's GDP in the future.

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The zeros of the given polynomial function are 3

Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.

For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.

In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.  

Here we have a graph

In the given graph the polynomial function meets the x-axis three times at three different points.

Therefore,

The zeros of the given polynomial function are 3

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The truth table for the statement is

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

-------------------------------------

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

From the question, we have the following parameters that can be used in our computation:

~(q↔️~p)

To construct the truth table, we make use of the following notations

p, q, ~p, (q↔️~p) and ~(q↔️~p)

The truth table for the statement ~(q ↔️ ~p) is then represented as follows:

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

-------------------------------------

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

The condition for ↔ is that it is true if both statements are true

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In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:

In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5

If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.

In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.

mean = sum of values ​​/ number of values

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The value of lim x -> -1- f(x)= -1

The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.

Hence,

As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.

As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.

The one-sided limits do not match, so the two-sided limit does not exist.

But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.

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The graph below is the function f(x)

Find lim x -> -1- f(x)=

The battery will last 2.73 hours when it is fully charged

The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity

Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:

rate =   1.5 hours/55% = 3/110 hour per %

When it is fully charged, that is 100%. Thus, it will take:

Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours

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