Asha, wants to invest $345678 today. He found an investment that provides 5% interest per year, compounded annually. The investment is locked in for 10 years and all interest is reinvested. What is the Future Value of this investment?​

Answer:

\(y = -(0.03(x-90)^2)+240\)

Step-by-step explanation:

I hope you already understand how parabolas work, so here are the steps/equations you need:

\(y=\ -\left(a\left(x-c\right)^{2}\right)+\ b\)

\(a=\frac{H}{\left(\frac{T}{2}\right)^{2}}\)

\(c=\frac{T}{2}\)

\(b\ =\ H\)

\(H = 240\)

\(T = 180\)

\(a= 0.0296296296296\)

\(c= 90\)

\(b=240\)

Now that you have "a", "c", and "b", plug them into the very first formula. This is the final result you get:

\(y = -(0.03(x-90)^2)+240\)

Answer:

Let us assume the two numbers be x and y  

From the above condition we can write, x + y = 26 equation 1  

second condition first no x = 2 more 5 times of the second no. that is 5y + 2  

                  then  we can write,               x = 5y + 2..... eqation (2)

  from equation 1  x + y = 26  

                        subtracting y from each side ,     x+ y - y = 26 - y  

                                                                            x = 26 - y  

                             plugging this value of x in eqn. no (2 )  we get,

                                                                   26-y = 5y + 2  

                                                  subtracting 5y on both sides,

                                                                   26 - y - 5y = 5y - 5y + 2  

                                                                    26 - 6y = 2  

                                                  subtracting 26 from both sides,  

                                                              26 -26 -6y = 2- 26  

                                                                          -6y = -24  

                                                eliminating minus sign from both sides,

                                                                            6y = 24  

                                                   dividing by 6 on both sides,

                                                                           y = 24/6 = 4  

                                         substituting this value of y in equation 1 we get,  

                                                                          x + 4 = 26  

                                                       subtracting 4 from both sides,

                                                                             x = 26- 4 = 22

Step-by-step explanation:

so we solve the 2 eqns we get x = 22 and y = 4  

the two numbers will be 22 and 4  

Answer:

Step-by-step explanation:

1.

by using Pythagoras law

h²=p²+b²

17²=6²+x²

x=√{17²-6²)=√253=15.9=16approx

2.

by using Pythagoras law

h²=p²+b²

x²=9²+15²

x=√306=17.49=17.5approx

Answer:

1 is 16.                    2 is 17.49 or 17.5 or 17          depends on how you're rounding.

Step-by-step explanation:

The series Σ(cos(15)k) from k=1 to infinity is convergent.

Σ\((cos(15)k)\) from k=1 to infinity

To determine if this series converges or diverges, we can use the Ratio Test. The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If it's greater than 1, it diverges. If it's equal to 1, the test is inconclusive.

Step 1: Find the ratio of consecutive terms, a(k+1)/a(k)

a(k+1) = cos(15)(k+1)
a(k) = cos(15)k

Ratio: |a(k+1)/a(k)| = |cos(15)(k+1) / cos(15)k|

Step 2: Simplify the ratio

|cos(15)(k+1) / cos(15)k| = |cos(15)|

Since the ratio doesn't depend on k, the limit will just be the absolute value of the ratio itself.

Step 3: Compare the limit to 1

|cos(15)| < 1, since 0 < cos(15) < 1

According to the Ratio Test, since the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges.

Your answer: The series Σ(cos(15)k) from k=1 to infinity is convergent.

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Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.

An algorithm in math is a procedure, a description of a set of steps that can be used to solve a mathematical computation.

Now,

Hence, Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.

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The given problem provides two points (-3, r) and (1, 18) on a line with a known slope of 4. The task is to find the missing coordinate r.

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. In this problem, we are given the slope (m = 4) and two points (-3, r) and (1, 18) on the line. Using the slope formula, which states that the slope (m) is equal to the change in y divided by the change in x, we can calculate the slope between the two points:

m = (y₂ - y₁) / (x₂ - x₁)

Plugging in the coordinates, we get:

4 = (18 - r) / (1 - (-3))

Simplifying further:

4 = (18 - r) / 4

Multiplying both sides of the equation by 4:

16 = 18 - r

To solve for r, we can isolate it by subtracting 18 from both sides:

16 - 18 = -r

-2 = -r

Finally, multiply both sides of the equation by -1:

2 = r

Therefore, the missing coordinate r is 2. The point (-3, r) is (-3, 2).

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Basedon the given graphs, we can find that:

To find the slope, linear equation, and y-intercept, we have to identify 2 points on each graph first.

Graph 1: (6, 7) and (0, -1)

Graph 2: (0, 5) and (4, 2)

Graph 3: (2, 2) and (7, 5)

Graph 4: (1, 4) and (3, 1)

The slope of the graph can be calculated using formula of:

slope (m) = y₂ - y₁

                  x₂ - x₁

m = [7 - (-1)] / [6 - 0]

m = 8/6

m = 4/3

We take one point and put it into the linear equation formula to find the value of constant C:

(6, 7)

y = mx + C

7 = 4/3 (6) + C

7 = 8 + C

C = -1 --> y = 4/3 x - 1

Y-intercept equals to the y-axis value when x = 0; we can find it on the graph that (0, -1). Y-intercept is -1

The slope of the graph can be calculated using formula of:

slope (m) = y₂ - y₁

                  x₂ - x₁

m = [5 - 2] / [0 - 4]

m = 3/(-4)

m = - 3/4

We take one point and put it into the linear equation formula to find the value of constant C:

(4, 2)

y = mx + C

2 = - 3/4 (4) + C

2 = -3 + C

C = 5 --> y = - 3/4 x + 5

Y-intercept equals to the y-axis value when x = 0; we can find it on the graph that (0, 5). Y-intercept is 5.

The slope of the graph can be calculated using formula of:

slope (m) = y₂ - y₁

                  x₂ - x₁

m = [5 - 2] / [7 - 2]

m = 3/5

We take one point and put it into the linear equation formula to find the value of constant C:

(7, 5)

y = mx + C

5 = 3/5 (7) + C

---------------------- x 5

25 = 21 + 5C

4 = 5C

C = 4/5 --> y = 3/5 x + 4/5

Y-intercept equals to the y-axis value when x = 0; we can find by using our linear equation:

x = 0

y = 3/5 x + 4/5

y = 3/5 (0) + 4/5

y = 4/5 --> Y-intercept = 4/5

The slope of the graph can be calculated using formula of:

slope (m) = y₂ - y₁

                  x₂ - x₁

m = [1 - 4] / [3 - 1]

m = -3/2

We take one point and put it into the linear equation formula to find the value of constant C:

(3, 1)

y = mx + C

1 = -3/2 (3) + C

---------------------- x 2

2 = -9 + 2C

2C = 11

C = 11/2 --> y = -3/2 x + 11/2

Y-intercept equals to the y-axis value when x = 0; we can find it using our linear equation:

x = 0

y = -3/2 x + 11/2

y = -3/2 (0) + 11/2

y = 11/2 --> Y-intercept = 11/2

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Answer:

3x-x+2=4

Step-by-step explanation:

A C and E are the answers!

Answer:

7.2

Step-by-step explanation:

good luck hope it helps

Step-by-step explanation:

To find 9% of 80 you multiply 80 and 0.09(I converted 9% to 0.09).

80x0.09=7.2

Hope it helps!

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The price per $1,000 face value of the zero-coupon bond issued by the Lewiston Company is approximately $288.12.

To calculate the price of the zero-coupon bond, we can use the present value formula:

Price = Face Value / (1 + Interest Rate)^(Number of Years)

In this case, the face value is $1,000, the interest rate is 6.7%, and the number of years is 23.

Price = 1000 / (1 + 0.067)^23 = 1000 / 2.871 = $348.35

However, this value represents the future value of the bond. To determine the present value, we need to discount it to today's value. To do that, we can divide the future value by (1 + Interest Rate).

Present Value = Price / (1 + Interest Rate) = 348.35 / (1 + 0.067) = $288.12 (rounded to the nearest cent)

The price per $1,000 face value of the zero-coupon bond issued by the Lewiston Company, using an interest rate of 6.7%, is approximately $288.12. Zero-coupon bonds are sold at a discount to their face value because they do not pay any periodic interest payments. The price reflects the present value of the bond, taking into account the time value of money and the specified interest rate.

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1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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An effective leader is able to balance and integrate both relationship-building and task-oriented aspects of leadership.

Effective leaders recognize that leadership is not solely about achieving tasks and goals; it also involves building and maintaining strong relationships with their team members.

They understand that establishing positive relationships is crucial for fostering trust, collaboration, and engagement within the team.

By prioritizing relationships, effective leaders create a supportive and inclusive work environment where individuals feel valued, heard, and motivated to contribute their best.

At the same time, effective leaders also understand the importance of accomplishing tasks and achieving organizational goals.

They possess the ability to set clear objectives, delegate responsibilities, and monitor progress to ensure that tasks are completed efficiently and effectively.

They are skilled at organizing resources, making decisions, and providing guidance to their team members, all while maintaining a focus on the desired outcomes.

The key to being an effective leader lies in the ability to balance and integrate both relationship-building and task-oriented aspects of leadership.

This means recognizing that strong relationships contribute to improved teamwork, communication, and employee satisfaction, which in turn enhance overall performance and productivity.

By acknowledging and valuing both dimensions, effective leaders create a harmonious work environment that fosters growth, success, and the well-being of both individuals and the organization as a whole.

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To solve the given truth table (p -> q) v q, we will first break it down step by step:

Step 1: Evaluate the conditional statement (p -> q):
To evaluate p -> q, we consider the truth values of p and q. If p is true and q is false, the conditional statement is false; otherwise, it is true. Looking at the truth table, we can see that when p is true (T) and q is true (T), the conditional statement is true (T). When p is true (T) and q is false (F), the conditional statement is false (F). When p is false (F), the conditional statement is true (T) regardless of the value of q.

Step 2: Evaluate the disjunction (v) with q:
To evaluate (p -> q) v q, we consider the truth values of (p -> q) and q. If either (p -> q) or q is true, the disjunction is true. Looking at the truth table, we can see that when (p -> q) is true (T) and q is true (T), the disjunction is true (T). When (p -> q) is false (F) and q is true (T), the disjunction is true (T). When (p -> q) is true (T) and q is false (F), the disjunction is true (T). When both (p -> q) and q are false (F), the disjunction is false (F).

Step 3: Final answer:
Based on the evaluation of the truth table, we can conclude that the expression (p -> q) v q is always true (T).

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This answer breaks down the process step by step, providing a clear explanation and a conclusion that summarizes the truth table for the given expression. To solve the truth table for (p -> q) v q, let's break it down.

1. Start by analyzing the expression (p -> q). This is known as an implication or conditional statement. The truth table for an implication is as follows:
  p | q | p -> q
  t  |  t |   t
  t  |  f |   f
  f  |  t |   t
  f  |  f |   t

2. Next, we need to evaluate (p -> q) v q. The "v" represents the logical OR operation. In this case, (p -> q) v q means either (p -> q) is true or q is true.

3. Let's compare the values of (p -> q) and q, and determine the resulting truth values:
  - When (p -> q) is true (t) and q is true (t), (p -> q) v q is true (t).
  - When (p -> q) is true (t) and q is false (f), (p -> q) v q is true (t).
  - When (p -> q) is false (f) and q is true (t), (p -> q) v q is true (t).
  - When (p -> q) is false (f) and q is false (f), (p -> q) v q is false (f).

4. Therefore, the truth table for (p -> q) v q is:
  p | q | (p -> q) v q
  t  |  t |       t
  t  |  f |       t
  f  |  t |       t
  f  |  f |       f

In conclusion, the truth table for (p -> q) v q is:
p | q | (p -> q) v q
t  |  t |       t
t  |  f |       t
f  |  t |       t
f  |  f |       f

This answer breaks down the process step by step, providing a clear explanation and a conclusion that summarizes the truth table for the given expression.

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MOD(-2a a+b c+a) = 4[a+b][b+c][c+a] is an identity that holds true for all values of a, b, and c.

To show that MOD(-2a a+b c+a) = 4[a+b][b+c][c+a], we will simplify the expression

First, let's expand the expression on the left side of the equation:

MOD(-2a a+b c+a) = MOD(-\(2a^2\) - 2ab + ac + aa + bc + ca)

Now, let's simplify the expression further by grouping the terms:

MOD(-\(2a^2\) - 2ab + ac + aa + bc + ca) = MOD(\(a^2\) + 2ab + ac + bc + ca)

Next, let's factor out the common terms from each group:

MOD(\(a^2\) + 2ab + ac + bc + ca) = MOD(a(a + 2b + c) + c(a + b))

Now, let's expand the expression on the right side of the equation:

4[a+b][b+c][c+a] = 4(a + b)(b + c)(c + a)

Expanding further:

4(a + b)(b + c)(c + a) = 4(ab + ac + \(b^2\) + bc + ac + \(c^2\) + ab + bc + \(a^2\))

Simplifying:

4(ab + ac + \(b^2\) + bc + ac +\(c^2\) + ab + bc + \(a^2\)) = 4(\(a^2\) + 2ab + ac + bc + ca)

We can see that the expanded expression on the right side is equal to the expression we obtained earlier for the left side.

Therefore, MOD(-2a a+b c+a) = 4[a+b][b+c][c+a].

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Answer:Rx + Py = RP.

Step-by-step explanation: The x-intercept of the line is (-P, 0), which means that the line passes through the point (-P, 0). Similarly, the y-intercept of the line is (0, -R), which means that the line passes through the point (0, -R).

We can use these two points to find the slope of the line using the slope formula:

slope = (change in y) / (change in x) = (-R - 0) / (0 - (-P)) = -R / P

Now that we have the slope of the line, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the points that the line passes through. Let's use the point (-P, 0):

y - 0 = (-R / P)(x - (-P))

Simplifying this equation, we get:

y = (-R / P)x + R

To write this equation in standard form, we need to move all the variables to one side of the equation:

(R / P)x + y = R

Multiplying both sides by P, we get:

Rx + Py = RP

Therefore, the equation of the line in standard form is Rx + Py = RP.

Answer:

\( \sf \: \frac{4}{3} x - 3\)

Step-by-step explanation:

Let's simplify step-by-step.

2x−2/3x−3

=2x+−2/3x+−3

Combine Like Terms:

=2x+−2/3x+−3

=(2x+−2/3x)+(−3)

=4/3x+−3

The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

x = - 69

Step-by-step explanation:

if its wrong i can help u again

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The equivalent value is ~

\( \boxed{12}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's solve ~

Answer:

0

Step-by-step explanation:

m=y1-y2/x2-x1. Plug in your values. -7-(-7)/1-(-4). Simplifies to 0/5, or 0.

Answer:

It's an irrational number

Step-by-step explanation:

Yes, 8.141141114 is not a rational number . it is a irrational number .generally we can find out a number is rational or irrational by seeing the number. If mentioned number were 8.141141141 then It would be a rational number because after point number 141 is repeated. Hence,Mentioned number is not look like that. so, it is a irrational number

Answer:

evaluate parenthesis first:

67/100(consider 67% out of 100) x 119 = 79.73

Answer:

79.73

Step-by-step explanation:

First, it would be finding 67% of 119

Then we find 10% = 11.9   and 1% = 1.19

The 11.9 multiplied by 6 to equal 71.4 and 1.19 multiplied by 7 to equal 8.33

Then add 71.4 and 8.33 to get the answer of 79.73.

Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

Answer:

D is the answer.

Step-by-step explanation:

Answer:

m = 3.625

Step-by-step explanation:

1.2m + 0.65 = 5

~Subtract 0.65 to both sides

1.2m = 4.35

~Divide 1.2 to both sides

m = 3.625

Best of Luck!