Graph the line passing through (−5,−4) whose slope is m=1/5.
Answer:
[tex]y=\frac{1}{5}x-3[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)\\y-(-4)=\frac{1}{5}(x-(-5))\\y+4=\frac{1}{5}(x+5)\\y+4=\frac{1}{5}x+1\\y=\frac{1}{5}x-3[/tex]
Plot that into Desmos and you got your graph :)
The answer is:
below
Work/explanation:
First, we need to find the equation of the line. We're given that:
its slope = 1/5
a point it goes through = (−5,−4)
Plug the data into point-slope
[tex]\rm{y-y_1=m(x-x_1)}[/tex]
where m = slope and the point is (x₁, y₁).
Plug in:
[tex]\rm{y-(-4)=\dfrac{1}{5}(x-(-5)}[/tex]
Simplify fully
[tex]\rm{y+4=\dfrac{1}{5}(x+5)}[/tex]
Now let's graph it. I'll use Desmos - the graphing calculator.
What does 3x+2y equal
Based on the information, it should be noted that the value of 3x + 2y when x = 4 and y = 7, 3x + 2y equals 26.
How to calculate the equationTo find the value of 3x + 2y when x = 4 and y = 7, we substitute these values into the expression and perform the calculations.
3x + 2y = 3(4) + 2(7)
= 12 + 14
= 26
Therefore, when x = 4 and y = 7, 3x + 2y equals 26.
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What does 3x+2y equal if x = 4 y = 7
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $1,070.00, and the tax rate in the area is 7%, what was the pre-tax subtotal?
The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.To calculate the pre-tax subtotal, we need to reverse-engineer the calculation based on the given after-tax total and tax rate.
Let's denote the pre-tax subtotal as "x." The tax rate is 7%, which can be written as 0.07 in decimal form. The after-tax total is $1,070.00.
We know that the tax amount is calculated by multiplying the tax rate by the pre-tax subtotal. So, the tax amount can be expressed as 0.07x.
The after-tax total is obtained by adding the pre-tax subtotal and the tax amount:
After-tax total = Pre-tax subtotal + Tax amount
$1,070.00 = x + 0.07x
To solve for x, we can combine like terms:
$1,070.00 = 1.07x
Now, let's isolate x by dividing both sides of the equation by 1.07:
$1,070.00 / 1.07 = x
Simplifying the calculation:
$1,000.00 = x
Therefore, the pre-tax subtotal is $1,000.00.
To verify the result, we can calculate the tax amount by multiplying the pre-tax subtotal by the tax rate:
Tax amount = 0.07 * $1,000.00 = $70.00
Adding the tax amount to the pre-tax subtotal:
$1,000.00 + $70.00 = $1,070.00
The result matches the given after-tax total, confirming that the pre-tax subtotal is indeed $1,000.00.
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NEED HELP!!!
1. What does it mean for two angles to be supplementary? What does it mean for two angles to be complementary? Draw an example of a pair of supplementary angles and a pair of complementary angles.
Answer:
Two angles are supplementary if the sum of their measures is 180°. For example, two angles whose measures are 35° and 145° are supplementary angles.
Two angles are complementary if the sum of their measures is 90°. For example, two angles whose measures are 35° and 55° are complementary angles.
angle b in the triangle above is 30 degrees. What do the properties of dilations tell you about angle B?
Answer:
Step-by-step explanation:
that it is 30 degrees above and its a triangle
Please help!!!! Thank you so much (don’t mind what’s already typed in the answer box, I’m confused with the whole thing)
A polynomial f(x) has the given zeros of 6, -1, and-3
Part A: Using the Factor Theorem, determine the polynomial f(x) in expanded form. Show all necessary calculations (3 points)
Part B: Divide the polynomial f(x) by (x²-x-2) to create a rational function gox) in simplest factored form. Determine gox) and find its stant asymptote (4 points)
Part C: List all locations and types of discontinuities of the function g(x). Be sure to check for all asymptotes and holes. Show all necessary calculations (
Answer:
Part A:
Using the Factor Theorem, we know that f(x) can be written as:
f(x) = a(x - 6)(x + 1)(x + 3)
where a is a constant that we need to determine.
To find the value of a, we can use one of the given zeros of f(x), for example, x = 6. When x = 6, we know that f(x) = 0, so we can substitute these values into the equation above:
0 = a(6 - 6)(6 + 1)(6 + 3)
Simplifying, we get:
0 = 189a
Therefore, a = 0.
So, the polynomial f(x) is:
f(x) = 0(x - 6)(x + 1)(x + 3)
Simplifying, we get:
f(x) = 0
Part B:
To divide f(x) by (x² - x - 2), we can use long division:
0
___________
x² - x - 2 | 0x³ + 0x² + 0x + 0
- (0x³ - 0x² - 0x)
_______________
0x² + 0x
- (0x² - 0x - 2)
_______________
2x + 2
Therefore, the rational function g(x) in simplest factored form is:
g(x) = (2x + 2)/(x² - x - 2)
To find the vertical asymptotes, we need to find the roots of the denominator:
x² - x - 2 = 0
(x - 2)(x + 1) = 0
Therefore, the vertical asymptotes are x = 2 and x = -1.
To find the horizontal asymptote, we can use the fact that the degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is y = 0.
Part C:
The function g(x) has two vertical asymptotes at x = 2 and x = -1.
To check for any holes, we can simplify the function by factoring the numerator:
g(x) = 2(x + 1)/(x - 2)(x + 1)
Since we factored the numerator and denominator of g(x), we can see that there is a hole in the graph at x = -1. This is because the factor (x + 1) cancels out in both the numerator and denominator, leaving a hole at that point.
To find the x-intercepts, we need to solve for when the numerator is equal to zero:
2x + 2 = 0
x = -1
Therefore, the x-intercept is (-1, 0).
To find the y-intercept, we can substitute x = 0 into the equation for g(x):
g(0) = 2(0 + 1)/(0 - 2)(0 + 1)
g(0) = -1
Therefore, the y-intercept is (0, -1).
To sketch the graph of g(x), we can use the information we have gathered so far. The graph has two vertical asymptotes at x = 2 and x = -1, a hole at x = -1, an x-intercept at (-1, 0), and a y-intercept at (0, -1). The horizontal asymptote is y = 0.
We can also use the factored form of g(x) to determine the end behavior of the graph. As x approaches positive or negative infinity, the function approaches zero. Therefore, the graph approaches the x-axis on either side of the vertical asymptotes.
Putting all of this information together, we can sketch the graph of g(x) as follows:
[insert graph of g(x) here]
What is the solution set for StartAbsoluteValue x + 3 EndAbsoluteValue = 5? s = negative 8 and s = 8 s = negative 2 and s = 2 s = negative 8 and s = 2 s = 2 and s = 8
Answer::x= -2x= 2Step-by-step explanation:First, identify the problem.l x+3 l = 5Secondly, plug in the value for x. l -
Step-by-step explanation:
Find the missing side. 37° Z 25 z = [?] Round to the nearest tenth. Remember: SOHCAHTOA
Answer:opposite side has side length of 11. One of the angle is 27 degrees.
Step-by-step explanation:
Given the following quadratic equation:
x² - 4x + 4
Find the vertex:
(h,k) = (
Find the roots as points:
Root 1: (
Root 2: (
Answer:
x² - 4x + 4 = (x - 2)²
The vertex is (2, 0). It follows that 2 is a double root (a root of multiplicity 2).
Please answer correctly (the answer is not 48)
Answer:
There are 72 ways to order AI meals.
Step-by-step explanation:
1. Calculate the number of ways Al could order his lunch: 2 x 3 = 6 ways.
2. Calculate the number of ways Al could order his dinner if he orders a different appetizer than he did for lunch: 1 x 2 x 4 = 8 ways.
3. Calculate the number of ways Al could order his dinner if he orders the same appetizer as he did for lunch: 1 x 1 x 4 = 4 ways.
4. Calculate the total number of ways Al could order his meals: 6 x (8 + 4) = 72 ways.
The number of people contacted at each level of a phone tree can be
represented by f(x) = 3*, where x represents the level.
What is x when f(x) = 27?
A. x = 24; At level 24, 27 people will be contacted.
B. x= 2; At level 2, 27 people will be contacted.
C. x= 9; At level 9, 27 people will be contacted.
OD. x= 3; At level 3, 27 people will be contacted.
.Write the equation of a line that passes through the points (2,6) and (2,4) write the equation in slope intercept-form.
Find (0,2) similar steps to the top question^^
Write the equation of a line parallel to the line 2x 5y =10 with a y intercept of (0,1). Write your answer in standard form.
The equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.
Equation of a line passing through (2,6) and (2,4) in slope-intercept form:
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
Given points:
Point 1: (2,6)
Point 2: (2,4)
Since the x-coordinate is the same for both points, we can conclude that the line is vertical, and its equation will be in the form x = c, where c is the x-coordinate of any point on the line.
In this case, x = 2 is the equation of the line passing through the points (2,6) and (2,4).
Equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) in standard form:
To determine the equation of a line parallel to a given line, we need to keep the same slope. The given line has the equation 2x - 5y = 10, which can be rearranged to the slope-intercept form y = (2/5)x - 2.
Since the parallel line has the same slope, the equation will be in the form y = (2/5)x + b, where b is the y-intercept.
Given y-intercept: (0,1)
Substituting the values into the equation, we have y = (2/5)x + 1.
To convert the equation into standard form (Ax + By = C), we multiply through by 5 to eliminate the fraction:
5y = 2x + 5
Rearranging the terms:
2x - 5y = -5
Therefore, the equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.
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X3-x-9=0 bisection method
Step-by-step explanation:
The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].
Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.
Now we can apply the bisection method as follows:
Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.
Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.
Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.
Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.
Evaluate f© ≈ 1.765625.
Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.
We can continue this process until we reach the desired level of accuracy.
A drum of water is 3/4 full. When 9 litres are drawn from it, it is half full. How much water does the drum hold what is the capacity of the drum
Answer:
OK, Here is your answer
Step-by-step explanation:
Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.
Answer:
18 Lieters.
Step-by-step explanation:
found the answer in his answer. ↑↑↑↑
Talwar wants to invest R5800 at simple interest rate of 12,2% per annum. How many years will it take for the money to grow to R26100
It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.
To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:
Time = (Amount - Principal) / (Principal × Rate)
Plugging in the values, we have:
Time = (R26,100 - R5,800) / (R5,800 × 0.122)
= R20,300 / R708.6
≈ 28.67 years
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What is the volume of a hemisphere with a radius of 4.3 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
Expert-Verified Answer
= 166.59 cm³ (approx.)
Step-by-step explanation:
The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units. Where π is a constant whose value is equal to 3.14 approximately.
Answer:
166.5 [tex]cm^{3}[/tex]
Step-by-step explanation:
The volume of a sphere is 4/3 [tex]\pi r^{3}[/tex]. A hemisphere is half of a circle.
V = 1/2(4/3)[tex]\pi[/tex][tex]4.3^{2}[/tex]
v = 2/3 [tex]\pi[/tex] (79.507)
v = 166.519071406
Helping in the name of Jesus.
Quick help pleasae been stuck in brain
Step-by-step explanation:
Given:
f(x) = x² + 3
To find:
f(a + 7),
Replace x with (a + 7) in the function f(x) = x² + 3:
→ f(a + 7) = (a + 7)²+ 3
Now,simplify by expanding the square:
→ f(a + 7) = a² + 14a + 49 + 3
→ f(a + 7) = a² + 14a + 52
Therefore, f(a + 7) = a²+ 14a + 52.
i really need help. Someone please help me
The values of the functions (u + w)(5) and (u - w)(5) are 18 and -32 respectively.
Given that :
u(x) = -2x + 3v(x) = 5x1.)
(u + w)(5) can be calculated thus:
(u + w) = -2x + 3 + 5x = 3x + 3
substitute x = 5 into the equation
Hence,
(u + w)(5) = 3(5) + 3 = 15 + 3 = 18
2.)
(u - w)(5) can be calculated thus:
(u - w) = -2x + 3 - 5x = -7x + 3
substitute x = 5 into the equation
Hence,
(u - w)(5) = -7(5) + 3 = -35 + 3 = -32
Therefore, the values of (u + w)(5) and (u - w)(5) are 18 and -32 respectively.
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Need help with the problem I feel like I understand a bit, yet need further help.
Answer:
Step-by-step explanation:
Remeber, if we have some fraction,
[tex]\frac{x-y}{d}[/tex]
We can rewrite this as a difference of quotients:
[tex]\frac{x}{d} -\frac{y}{d}[/tex]
So essentially,
the first step becomes
[tex]\frac{sec(\alpha )}{sec(\alpha )(tan(\alpha )} -\frac{tan(\alpha )}{sec(\alpha )(tan(\alpha )}[/tex]
Next, remember that we can cancel out common factors in the numerator and denominator.
[tex]\frac{1}{tan(\alpha )} -\frac{1}{sec(\alpha )}[/tex]
Next in order to match the RHS, we would apply the Reciprocal Identity and get
[tex]cot(a)-cos(\alpha )[/tex]
Let me know if you need any further clarification. These types of problems involve math ingenuity so I suggest you to work on recognizing perfect squares, differences of squares, properties of fractions, canceling common factors, etc.
Determine the area of a rugby field with a length of 91.75 metres and a width of 55.25 metres
Answer:
5069.1875
Step-by-step explanation:
Area is found by using Length x Width, for this the length is 91.75 and width 55.25. Thus the answer is 91.75x55.25=5069.1875
Matt looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 19 inches. The length of the diagonal of the floor of the room in the plan is approximately 20.62 inches.
Is the room in the shape of a square? Explain how you determined your answer. Show all your work.
Answer:
no
Step-by-step explanation:
if the room is a square, then all sides are equally long (19 in).
in any case, Pythagoras applies to calculate the length of the diagonal :
(side1)² + (side2)² = diagonal²
if both sides are equally long, that would mean
19² + 19² = 20.62²
361 + 361 = 425.1844
722 = 425.1844
that is not true, so the assumption that the room is a square is not true.
Use the percent formula, A =PB: A is P percent of B, to answer the following question.
22% of what number is 37.4?
22% of _ is 37.4
Use the percent formula, A =PB: A is P percent of B, 22% of approximately 170 is equal to 37.4.
To find the number, let's use the percent formula:
A = P * B
where A is the value we are trying to find, P is the percentage (in decimal form), and B is the total.
In this case, we are given that 22% of a certain number is equal to 37.4. So we have:
A = 0.22 * B
We want to solve for B, so we can rearrange the formula:
B = A / 0.22
Substituting A = 37.4 into the equation:
B = 37.4 / 0.22
Calculating this:
B ≈ 170
Therefore, 22% of approximately 170 is equal to 37.4.
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How do I do these problems? I dont understand.
Answer:
Question 5: <ACB=<DFE
Question 6:AB=DE
Question 1: SSS (side side side)
Question 2: SAS (side angle side)
Step-by-step explanation:
All of these questions are talking about congruency theorems. There are many theorems including SAS, SSS, AAS, etc, that help with congruency.
SAS=side angle side
SSS = side side side
AAS = angle angle side
HL (right triangles only)= hypotenuse and a leg are congruent
ASA=angle side angle
Question 5:
In this case, they are asking for AAS, which stands for Angle-Angle-Side. We are already given 1 angle, and 1 side, so we need another angle. The answer to this would be to show that <ACB and <DFE are congruent.
Question 6:
They are asking for the same thing (triangle congruency), but by using SAS, which is Side-Angle-Side. We are given 1 angle, 1 side, so we need another side. The answer to this would be AB=DE.
Question 1:
We are given 3 sides, which means that the congruence theorem would be SSS (Side-Side-Side).
Question 2:
We are given a side, an angle, and another side. This means that the congruence thorem would be SAS (Side-Angle-Side).
Hope this clarifies! Let me know if you have more questions :)
f the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)
Answer: A ( -4, -7)Step-by-step explanation:if you translate -1, three units to the left u get -4 and then when u go nine units down
Step-by-step explanation:
Which of the following best represents the linear regression equation for the x-values and log(y)-values of the data shown below? X 0 1 2 3 4 5678 y 4 12 22 44 82 150 318 630 1300
Answer:
y = 0.30x + 0.70
Step-by-step explanation:
Assuming that the options are
A.
y = 1.90x + 0.40
B.
y=0.30x +0.70
C.
y= 0.90x + 0.30
D.
y= 1.30x + 1.70
(these might be in a random order for different people)
the answer would be B. y=0.30x +0.70
Ascending orders of 823 345 678
Answer:
345, 678, 823
Step-by-step explanation:
Ascending means increasing (lowest to highest)
Provide four strategies that communities could engage in to protest Gender based violence in their areas
The four strategies that can be effective in raising awareness, promoting change, and addressing the issue are mentioned below.
Awareness Campaigns and Education: Communities can organize awareness campaigns to educate the public about gender-based violence, its impact, and the importance of preventing and addressing it. This can include public rallies, marches, workshops, and community dialogues. Education initiatives can focus on promoting gender equality, challenging harmful gender norms and stereotypes, and fostering empathy and respect.
Support and Empower Survivors: Creating support systems for survivors of gender-based violence is crucial. Communities can establish safe spaces, helplines, or support groups where survivors can share their experiences, access resources, and receive emotional and practical support. Empowering survivors through counseling, legal aid, and vocational training can help them regain control of their lives and raise awareness about the issue.
Advocacy for Policy Change: Community members can engage in advocacy efforts to influence policy changes related to gender-based violence. This can involve lobbying for stricter laws, improved enforcement, and increased funding for support services. Collaborating with local NGOs, women's rights organizations, and other stakeholders can strengthen advocacy efforts and amplify voices.
Engaging Men and Boys: Engaging men and boys as allies in the fight against gender-based violence is essential. Community initiatives can promote positive masculinity, challenge harmful attitudes, and encourage men to actively participate in prevention efforts. Engaging men as role models, mentors, and advocates can help shift social norms and contribute to a more inclusive and violence-free community.
These strategies can be interconnected and reinforce each other. Building a strong community network and fostering partnerships with relevant organizations and stakeholders will enhance the impact of these efforts. It is important to tailor strategies to the specific needs and cultural context of the community, ensuring that they are inclusive, respectful, and sustainable in the long term.
The need for engaging in strategies to protest gender-based violence in communities arises from several important reasons: Human Rights: Gender-based violence is a violation of human rights. Every individual has the right to live a life free from violence, discrimination, and harm. By addressing gender-based violence, communities can uphold the principles of human rights and work towards creating a society where everyone can thrive with dignity and equality.
Safety and Well-being: Gender-based violence has severe physical, emotional, and psychological consequences for survivors. It creates an environment of fear, insecurity, and trauma. By protesting gender-based violence, communities aim to create safer environments where individuals can live without the constant threat of violence and can access the support they need for healing and recovery.
Social Justice and Equality: Gender-based violence is rooted in gender inequality and harmful social norms. It perpetuates power imbalances, discrimination, and the marginalization of individuals based on their gender. Protesting gender-based violence is essential for challenging these oppressive structures, promoting gender equality, and working towards a more just and inclusive society.
Prevention and Intervention: By engaging in strategies to protest gender-based violence, communities aim to prevent future acts of violence and intervene in existing cases. Awareness campaigns, education, and support services play a crucial role in creating a culture that rejects violence and promotes respectful relationships.
Addressing gender-based violence is not only a moral imperative but also essential for building healthy, inclusive communities. By raising awareness, supporting survivors, advocating for policy changes, and engaging men and boys as allies, communities can play a vital role in eradicating gender-based violence and creating a more equitable and just society for all.
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20!/1! in binominal distribution
Answer:
The expression 20!/1! is not directly related to the binomial distribution.
The expression 20!/1! represents the number of ways to arrange 20 distinct objects in a specific order, where each object is used exactly once. This is known as a permutation, and the number of permutations of n objects is given by n!.
On the other hand, the binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success. The probability of getting k successes in n trials, each with probability p of success, is given by the binomial probability mass function:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) represents the number of ways to choose k items from a set of n items, and is given by the formula:
(n choose k) = n!/k!(n-k)!
So, while the expression 20!/1! is not directly related to the binomial distribution, the binomial distribution does involve calculating combinations (i.e., choosing k items from a set of n items), which are related to permutations.
please help! It would be great>
The number of years N(r) since two independently evolving languages split off are as follows;
a. N(0.9) = 526.8.
b. N(0.4) = 4581.5.
c. N(0.3) = 6019.9.
d. 2554.1 years have elapsed since the split.
e. r = 0.9.
How to determine the number of years N(r)?Based on the information provided above, the number of years N(r) since two independently evolving languages split off from a common ancestral language can be approximated by the following equation:
N(r) = -5000Inr
Part a.
When r = 0.9, we have:
N(0.9) = -5000In(0.9)
N(0.9) = 526.8 years.
Part b.
When r = 0.4, we have:
N(0.4) = -5000In(0.4)
N(0.4) = 4581.5 years.
Part c.
When r = 0.3, we have:
N(0.3) = -5000In(0.3)
N(0.3) = 6019.9 years.
Part d.
When r = 60% or 0.6, we have:
N(0.6) = -5000In(0.6)
N(0.6) = 2554.1 years.
Part e.
When N(r) = 500 years, we have:
500 = -5000lnr
-500/5000 = lnr
-0.1 = lnr
[tex]r = e^{-0.1}[/tex]
r = 0.9.
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3. An investor plans to invest $500/year and expects to get a 10.5% return. If the investor makes these contributions at the end of the next 20 years, what is the present value (PV) of this investment today?
The present value (PV) of the investment today is approximately $2,965.05.
To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.
The formula for the present value of an annuity is given by:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.
Let's plug in these values into the formula and calculate the present value (PV):
PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]
Using a calculator, we can evaluate the expression inside the brackets:
PV = $500 * [(1 - 0.376889) / 0.105]
Simplifying further:
PV = $500 * [0.623111 / 0.105]
PV = $500 * 5.930105
PV = $2,965.05
Therefore, the present value (PV) of the investment today is approximately $2,965.05.
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