You would like to retire 25 years from now and have a retirement fund from which you can draw
an income of $50,000 per year – forever! How can you do it? Assume a constant APR of 7%.
(What balance do you need to earn $50,000 from interest? How can you get to that balance?)

The exponential function that passes through (-2,6) and (3,1) is y = 2.93(0.6988)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

An exponential equation is in the form:

y = abˣ

where a is the initial value and b is the multiplier.

Given that an exponential function that passes through (-2,6) and (3,1). At the point (-2, 6):

6 = a(b)⁻²

a/b² = 6

a = 6b²   (1)

At the point (3, 1):

1 = ab³

substitute a = 6b²:

1 = 6b²(b³)

1/6 = b⁵

b = 0.6988

a = 6(0.6988)²

a = 2.93

The exponential function is y = 2.93(0.6988)ˣ

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We can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

What is Line point postulate ?

The line-point postulate, also known as the incidence postulate, is a fundamental axiom in geometry that states that for any two points in a plane, there exists exactly one line that contains both points.

In other words, the line-point postulate asserts that a line can be uniquely determined by two distinct points that lie on it. This is one of the most basic and intuitive principles in geometry, and it is essential for building a foundation for more advanced concepts such as angles, triangles, circles, and more.

The Line-Point Postulate states that a line can be uniquely determined by any two distinct points on the line. In this diagram, we can see an example of this postulate in action.

For instance, we can say that line $q$ passes through points $J$ and $K$, so according to the Line-Point Postulate, this is enough information to uniquely determine the line $q$. Similarly,

Therefore, we can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

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110 is the value of x in function .

What exactly are function and example?

A function is a type of rule that produces one output from one input.   This is illustrated by the equation y=x2. You only get one output for y if you enter anything for x.

                        Considering that x is the input value, we would state that y is a function of x.

f(x) = {  5;  x< 1 }

        { -1/2x + 4 ; x≥ 1 }

 f(4) =  { -1/2  * 4 + 4 }

         =  { -2 + 4 }

         = { 2 }

f( -2) =  { -1/2 * -2 + 4 }

         =  { 1 + 4 }

          = 5

3f(0) = { -1/2 * 0 + 4 }

       = { 0 + 4}

        = 4 * 3 = 12

10f(14) = ( -1/2 * - 14 + 4 )

        =  7 + 4

         = 10 * 11  = 110

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The integer to represent the profit of php 100.00 is +100.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

Given that, a profit of php is 100.00​.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

So, here the integer is +100

Therefore, the integer to represent the profit of php 100.00 is +100.

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Answer:

Step-by-step explanation:

1500+7y > 4700 can be solved algebraically to find the value of y that satisfies the inequality.

First, we need to isolate the variable y on one side of the inequality by subtracting 1500 from both sides:

1500 + 7y - 1500 > 4700 - 1500

Simplifying the left-hand side:

7y > 3200

Finally, we isolate y by dividing both sides by 7:

y > 3200/7

Therefore, the solution to the inequality is y > 457.14 (rounded to two decimal places).

Using the unitary method and the conversion factor, we found the value of 2748 yards in km as 2.512 km.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.

We are given the length as 2748 yards.

Now, this is to be converted to km.

This can be done using the unitary method.

The unitary method uses the single unit's value to find the value of multiple units.

But first, we must find the conversion factor.

1 yard = 0.000914 km

So the value of 2748 yards in km is

2748 * 0.000914 = 2.512 km

Therefore using the unitary method and the conversion factor, we found the value of 2748 yards in km as 2.512 km.

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Answer:

the slop is 2

Step-by-step explanation:

i just calculated it a minute ago

The inequalities that are represented by the given graph are expressed as;

y - x > 0 and y ≥ 1

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

For the dashed line, shading is above the line, the y-intercept is 0.

Slope is 1. Thus, equation is;

y - x > 0

For the horizontal line, the inequality is expressed as;

y ≥ 1

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The company is searching for a fill amount of  12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given mean of 12.23 ounces and a standard deviation of 0.04 ounces.

To find the fill amount for the highest 1.5% of the fill amounts

we need to find the z-score corresponding to the 98.5th percentile

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98.5th percentile is  1.81.

The formula for converting a z-score to a raw score is:

x = μ + zσ

where x is the raw score we want to find, μ is the mean, z is the z-score, and σ is the standard deviation.

x = 12.23 + 1.81(0.04)

x = 12.305 ounces

Therefore, the company is searching for a fill amount of  12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.

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Answer:

-x.

Step-by-step explanation:

1) the equation of the line in slope-interception form is: y=slope*x+interception;

2) according to the graph and data in the condition slope=-1, interception=0, then the requred equation is:

y=-x.

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

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Answer:

4, 15, 16, 17, 19, 21, 22

Step-by-step explanation:

Answer:

6 x (9 + 9), (6 x 9) + (6 x 9), 54 + 54 = 108

Those are the answers for the blanks, hope this helped! :)

The slope of the line of fit is 7.5% per hour.

In mathematics, slope refers to the measure of steepness or incline of a line. It is the ratio of the vertical change between two points on the line (the rise) to the horizontal change between the same two points (the run).

To find the slope of the line of fit, we need to use the formula:

slope = change in y / change in x

In this case, the change in y represents the change in the predicted grade on the test, and the change in x represents the change in the number of hours studied. From the given data, we can see that:

The predicted grade for a student who studies for 0 hours is 80%.

The predicted grade for a student who studies for 1 hour is 90% (80% + 10%).

The predicted grade for a student who studies for 2 hours is 95% (90% + 5%).

Using this information, we can calculate the slope of the line of fit:

slope = (95% - 80%) / (2 hours - 0 hours) = 15% / 2 hours = 7.5%/hour

The slope of the line of fit is 7.5% per hour. This means that for each additional hour a student studies, their predicted grade on the test is expected to increase by an average of 7.5%. The slope represents the rate of change of the predicted grade with respect to the number of hours studied. In this case, a positive slope indicates that there is a positive correlation between the number of hours studied and the predicted grade on the test. The higher the slope, the steeper the line of fit, and the greater the impact of studying on the predicted grade.

Therefore, the slope of the line of fit is 7.5% per hour

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Answer: 35

Step-by-step explanation:

So we already know he sold $40 worth jacket so lets subtract that from 92.50

92.50-40= 52.5

So he sold $52.5 worth of notebooks

since we know each notebook costs 1.50 all we have to do is divide

52.5 / 1.50 = 35

He sold 35 notebooks

C. A changing amount of money spent on different categories each year

Amount is a term used to describe a quantity of something, typically money. It is often used to refer to the total value of a financial transaction or the sum of multiple payments. Amount can also refer to any other quantifiable measure, such as a number of items, units of time, or a volume or quantity of something.

Discretionary government spending is a type of government spending that is determined each year by the Congress, and typically includes funds for defense, education, infrastructure, and other government programs. The amount of money spent on each category can vary from year to year, making it a type of changing, or discretionary, spending.

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Polynomials consist of variables, constants and exponents.

(6x - 1)/ 6x is not a polynomial.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The expression is given as:

⇒ (6x - 1)/ 6x

Hence, We can Split the expression as;

⇒ (6x - 1)/ 6x

⇒ 6x/6x - 1/ 6x

⇒ 1 - 1/6x

Simplify as;

⇒ 1 - (1/6)x⁻¹

Thus, The smallest exponent of a polynomial is 0.

And, The above expression has a negative exponent of x.

Hence, The expression is not a polynomial.

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Answer:

492

Step-by-step explanation:

The GCF is found through p.i.g method.

6-2=3

Schedule K-1 (Form 8865) is used to report the partner's share of income, deductions, credits, and other items for the tax year of a foreign partnership.

Identification information: Fill out the partnership's name, employer identification number (EIN), and address.

Partner's identifying information: Fill out the partner's name, identifying number (usually their taxpayer identification number or TIN), address, and their percentage of ownership in the partnership.

Income items: Report the partner's share of ordinary income, net rental income, gain or loss from the sale of property, and other income items on lines 1-7. Make sure to also include any foreign source income or deductions.

Deductions: Report the partner's share of partnership deductions, such as business expenses, depreciation, and depletion, on lines 8-15.

Credits: Report the partner's share of any foreign taxes paid or other credits on lines 16-21.

Other items: Report any other items that are required to be reported on Schedule K-1, such as guaranteed payments, charitable contributions, and Section 743(b) adjustments, on lines 22-27.

At-risk limitation: If the partnership is engaged in an activity subject to the at-risk rules, report the partner's share of the at-risk limitation on line 28.

Passive activity limitation: If the partnership is engaged in a passive activity, report the partner's share of the passive activity limitation on line 29.

P.S Your question is incomplete, so I gave a general overview of the tax form for better understanding.

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Answer:

c. The numbers must have a sum of 12.

Step-by-step explanation:

Given a polynomial [tex]x^2+cx+d[/tex], in its factored form, [tex](x+a)(x+b)[/tex], the following must be true:

[tex]a + b = c[/tex]

[tex]a \cdot b = d[/tex]

In the given polynomial, we can assign the following values:

[tex]c = -12[/tex]

[tex]d=20[/tex]

Using these values, we can go through the answer choices:

Remember: we are finding the statement that is NOT true.

a) "the numbers must have a product of 20"

If we look at the equation [tex]ab = d[/tex], we can see that this statement is correct; therefore, we should not check it.

b) "the numbers must both be negative"

This is not necessarily true, as a positive plus a negative can still result in a negative; however, in this case, it is true (if we factor, we get a = -2, b = -10).

c) "the numbers must have a sum of 12"

This is false, since c = -12. The numbers (a and b) must add to negative 12, not positive 12; therefore c) is the correct answer.

Answer: (see attached file/screenshot)

Step-by-step explanation: You didn't specify the question so im guessing we solve with the quadratic formula

Answer:

Modus Tollens

Step-by-step explanation:

Consider the following argument: If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses. We do not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase. Hence, the bookcase does not collapse.

The logical form of this argument is Modus Tollens.

Modus Tollens is a mode of argumentation that involves affirming the consequent of a conditional statement. In this argument, the conditional statement is "If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses." The antecedent of this statement is "we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase," and the consequent is "the bookcase collapses."

Modus Tollens is used to prove the negation of the consequent by negating the antecedent. In other words, if the consequent is not true, then the antecedent must also not be true. Thus, in this argument, since we know that the bookcase does not collapse, we can conclude that we did not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase.

Therefore, the logical form of this argument is Modus Tollens.

PART 1: (a)The value of x in the pie graph is x = 30°

PART 2: (a)The value of x is 36°

(c) percentage of students for soccer is 25%

PART 3: (a)The value of Art is 165°

PART 1

(a) The value of x in the pie graph can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 180 - 60 - 45 - 45 = 30°

(b) frequency = (angle of the part)/360 * 20

Baksket ball = 162/360 * 20 = 12

Bus        12

Car         4

Train       3

Walk       2

Bicycle   3

PART 2

(a) The value of x can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

x = 360 - 150 - 45 = 36°

(b) frequency = (angle of the part)/360 * 24

Basketball = 180/360 * 24 = 9

Basketball  9

Tennis        2

Hurling       4

Soccer       5

(c) percentage of student for soccer = 5/20 * 100 = 25%

PART 3

(a) The value of Art can be found by subtracting the other values from 360° because the sum of angles in a circle is 360°. That is:

Art = 360 - 162 - 90 - 72 = 165°

(b) frequency = (angle of the part)/360 * 120

Technology = 150/360 * 120 = 50

Technology  50

Music            15

Art                 55

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Any amount of time greater than or equal to 85 to 90 seconds is a possible amount of time it takes to run around the baseball field at a rate of at least 10 feet per second.

What is area of circle ?

For calculating the amount of space occupied by a circular field or plot, use the area of the circle formula. If you already have a plot that needs fencing, using the area formula will allow you to determine how much fencing is needed. Or, if you need to purchase a tablecloth, how much cloth would be required to completely cover it?

In order to solve such problems, the concepts of area and perimeter are introduced in mathematics. But the question of "does a circle have volume?" is one that most people frequently ask. "No" is the response. A circle has no volume because it is a two-dimensional shape. It only has a perimeter and an area.

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Complete Question:

You run around the perimeter of a baseball field at a rate of at least 10 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?

85 seconds

90 seconds

95 seconds

100 seconds

Answer:

Sum: not present

Term: 4(2x + 3), 5y

Product: 4 and (2x + 3), 4 and 2x, 4 and 3, 5 and y

Factor: 4, 2x, 3, 5, y

Quotient: (4(2x + 3)) ÷ 5y

Coefficient: 4, 5

Step-by-step explanation:

The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

This problem can be solved using the probability , where we have a fixed number of trials (10 children) and a fixed probability of success (one-in-two chance of getting the disease).

The probability of getting exactly k successes in n trials, each with probability p of success, is given by the binomial probability formula:

P(k) = (n choose k) * [tex]p^k * (1-p)^{(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of a set of n.

For this problem, we have n = 10, p = 1/2 (since the children have a one-in-two chance of getting the disease), and we want to find P(5) and P(7).

P(5) = (10 choose 5) * ([tex]1/2)^5 * (1/2)^{(10-5)} = 0.2461[/tex] (rounded to four decimal places)

P(7) = (10 choose 7) * [tex](1/2)^7 * (1/2)^{(10-7)} = 0.1172[/tex] (rounded to four decimal places)

Hence, The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.

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The Congruency Postulates for each of the given triangle are:

1) SAS Congruency

2) AAS Congruency

3) HL Congruency

4) Not enough Information

5) AAS Congruency

There are different congruency postulates such as;

SSS: Side Side Side Congruency

SAS: Side Angle Side Congruency

ASA: Angle Side Angle Congruency

AAS: Angle Angle Side Congruency

HL: Hypotenuse Leg Congruency

1) We are given two triangles with two congruent sides and the included angle and as such it is congruent by SAS Congruency Postulate.

2) We are given two congruent angles and the included side and as such they are congruent by AAS Congruency Postulate.

3) We are given the hypotenuse and leg as congruent and as such we can say that they are congruent by HL Congruency Postulate.

4) We are given two congruent sides and the non-included angle and as such they are not congruent by any congruency postulate.

5) We are given two congruent angles and the non-included side and as such they are congruent by AAS Congruency Postulate.

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The numeric values for the composite functions are given as follows:

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

Using the definitions of p(x) and q(x) given in this problem, the composite function of p and q is given as follows:

[tex]p(q(x)) = p(\sqrt{x + 2}) = (\sqrt{x + 2})^2 + 3 = x + 2 + 3 = x + 5.[/tex]

Hence the numeric value at x = 2 is given as follows:

2 + 5 = 7.

The composite function of q and p is given as follows:

[tex]q(p(x)) = q(x^2 + 3) = \sqrt{x^2 + 3 + 2} = \sqrt{x^2 + 5}[/tex]

Hence the numeric value at x = 2 is given as follows:

sqrt(2^2 + 5) = sqrt(9) = 3.

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Check the picture below.

Answer: So it will take 90 hours (which is 3.75 days or 3 days, 18 hours) to eat all the possible cheeseburgers.

Step-by-step explanation:

There are 9 x 6 x 2 x 5 = 540 different cheeseburgers

So...

(540 cheeseburgers)*(10 minutes/1 cheeseburger) = 540 x 10 = 5400 minutes

Convert to hours to get

(5400 min)*(1 hr/60 min) = 5400/60 = 90 hours

Using the variable b for the unknown number, we have the expression 7b + 29 ≤ - 26.

In algebra, a variable is a symbol (typically a letter) used to represent an unknowable numerical value in an equation. The variables x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are frequently used (arc length).

The sum of a number times 7 and 29 is at most -26 .

The inequality in the mathematical form will be written as below:-

7b + 29 ≤ -26.

Therefore, the inequality will be written as 7b + 29 ≤ - 26.

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