The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:
sin(0) = √3/2
cos(0) = -1/2
tan(0) = -√3
csc(0) = 2/√3
sec(0) = -2
cot(0) = -1/√3
To sketch an angle in standard position, we start by placing the initial side along the positive x-axis. Since we want the angle with the least possible positive measure, we choose the smallest positive angle, which is 0 degrees or 0 radians.
Next, we plot the point (-2, √3) on the terminal side of the angle. This point lies in the third quadrant of the coordinate plane. We draw a line segment from the origin to this point, representing the terminal side of the angle.
To find the values of the trigonometric functions, we can use the coordinates of the point (-2, √3) to determine the side lengths of a right triangle. The x-coordinate (-2) represents the length of the adjacent side, and the y-coordinate (√3) represents the length of the opposite side. The hypotenuse can be found using the Pythagorean theorem.
Using the values of the sides, we can calculate the trigonometric functions:
sin(0) = opposite/hypotenuse = √3/2
cos(0) = adjacent/hypotenuse = -1/2
tan(0) = opposite/adjacent = -√3
csc(0) = 1/sin(0) = 2/√3
sec(0) = 1/cos(0) = -2
cot(0) = 1/tan(0) = -1/√3
The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:
sin(0) = √3/2
cos(0) = -1/2
tan(0) = -√3
csc(0) = 2/√3
sec(0) = -2
cot(0) = -1/√3
For more such questions on trigonometric functions
https://brainly.com/question/1143565
#SPJ8
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
x g(x)
1 81
2 83
3 85
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)
I really only need the math average (the first question) please thank you ill give brainliest + 100 points
Answer:
a) 81
b) 83
c) science
Step-by-step explanation:
a)
f(x) = 0.5x + 80
gn x = 2 tests
⇒ f(2) = 0.5(2) + 80
= 1 + 80
= 81
b)
gn x = 2
g(2) = 83
c)
we have g(x) = mx + b
m = (y₂-y₁)/(x₂-x₁)
= (83 - 81)/(2 - 1)
m = 2
for g(1),
g(1) = m(1) + b
81 = 2(1) + b
b = 81 -2
b = 79
⇒ g(x) = 2x + 79
and f(x) = 0.5x + 80
for 4 tests, we have x = 4
g(4) = 2(4) + 79
= 8 + 79
g(4) = 87
f(4) = 0.5(4) + 80
= 2 + 80
f(4) = 82
g(4) = 87 > f(4) = 82
∴Science class has a higher average
What number must you add to complete the square x2+4x=15
Answer: 19
Step-by-step explanation:
x^2+4x-15=0. To complete the square, it needs to be (x+2)^2, which is x^2+4x+4. Thus, you need to add 19.
A salesman earns 3% commission on all the merchandise that he sells. Last month he sold $5000 worth of merchandise. How much commission (in dollars) did he earn last month?
Hence, the salesman earned $150 in commission last month.
Commission is the sum of money that an employee earns based on a percentage of the total sales that they made. It is usually a part of an employee's income.A salesman earns a commission on all the merchandise that they sell.
The commission rate that a salesman earns is usually a percentage of the total value of the merchandise that they have sold.
A salesperson is typically paid a percentage of the price of the items that they sell.
The percentage of the commission that they earn can vary from company to company or from sales job to sales job. In this question, we have to calculate how much commission the salesman earned last month.
We know that the salesman earns a 3% commission on all the merchandise that he sells.
And last month he sold $5000 worth of merchandise.
So, we can use the following formula to calculate his commission.
Commission = (Commission Rate/100) × Total Sales
Therefore, Commission = (3/100) × $5000 = $150
For such more question on commission
https://brainly.com/question/28622492
#SPJ8
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
20. A. 357.8 in³
B. 1231.5 yd³
Step-by-step explanation:
20.
A.
Volume of Pyramid : ⅓*base area * height
here,
Base area = area of rectangle=length*breadth =10*8=80in²
Now
Height can be calculated by using Pythagorous theorem
height =[tex]\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}[/tex]
height =[tex]\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in[/tex]
height =13.4 in
Now
Volume of pyramid = ⅓*base area *height
Volume of Pyramid=⅓*80*13.42
Volume of Pyramid=357.8 in³
B.
Volume of cone = ⅓*area of base* height
Here
slant height=24 yd
height =?
diameter=14yd
radius =14/2=7 yd
Let's find the height:
By using the Pythagorous theorem,
slight height²=radius²+height²
substituting value
25²=7²+height²
height²=25²-7²
height =[tex]\sqrt{576}[/tex]=24 yd
Now
Area of Base= πr²=π*7²=153.94 yd²
Now
Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³
So,
Volume of cone is 1231.52 yd³.
A car enters a turnpike 22 miles north of a town. The car travels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours on the turnpike?
Explain how you can use a linear function to solve this problem. Then, solve the problem.
After 4 hours on the turnpike, the car is approximately 278 miles from the town.
To solve this problem using a linear function, we can use the formula for distance: distance = speed × time. In this case, the speed is given as 64 miles per hour, and the time is given as 4 hours.
Let's define the distance from the town as a variable, say "d." Since the car travels north, the distance from the town will increase as time passes. At the start, the car is 22 miles north of the town.
Now, we can set up a linear function to represent the distance from the town as a function of time:
d = 22 + (64 × t)
In this function, "t" represents time in hours. The initial distance of 22 miles is added to the product of the speed (64 mph) and time (t).
To find the distance from the town after 4 hours, we substitute t = 4 into the function:
d = 22 + (64 × 4)
d = 22 + 256
d = 278 miles
For more such questions on miles
https://brainly.com/question/29806974
#SPJ8
URGENT
in the first month that moiras marmalade stand was open, moira sold 145 jars of marmalade. In the second month, Moira sold 203 jars of marmalade. write the number she sold in the second month as a percentage of the number sold in the first month
Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.
To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.
Number of jars sold in the second month: 203
Number of jars sold in the first month: 145
Percentage of second month's sales = (203 / 145) * 100 ≈ 140%
For such more question on multiply
https://brainly.com/question/29793687
#SPJ8
PLEASE HELP QUICKKKKKKKKKKKKK
Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Which journey required more petrol?
Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.
To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.
Let's assume that the full tank of petrol has a capacity of 1 unit.
Othniel used 2/5 of the full tank of petrol to travel to Kumasi.
The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.
Othniel used 2/6 of the full tank of petrol to travel to Accra.
To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.
Converting the fraction 2/5 to have a denominator of 30:
(2/5) * (6/6) = 12/30
Converting the fraction 2/6 to have a denominator of 30:
(2/6) * (5/5) = 10/30.
Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.
Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.
Simplifying the fractions, we have:
Journey to Kumasi: 12/30 = 2/5.
Journey to Accra: 10/30 = 1/3.
Therefore, the journey to Kumasi required more petrol than the journey to Accra.
For more such questions on fractions, click on:
https://brainly.com/question/17220365
#SPJ8
Evaluate the following expression when x = -4 and y = 4.
x^6-x/4y
A. 1,023/4
B. 1,025/4
C. 16,385/4
D. -1,023/4
Answer: The correct answer is option C. 16,385/4.
Step-by-step explanation: First of all, we evaluate the expression x^6. Putting x= -4 gives (-4^6) which is equal to 4096. The next part (-x/4y) on substituting x = -4 and y =4 gives us the positive expression (1/4).
Adding both these parts, we get (4*4096+1)/4. This is finally evaluated as (16,384+1)/4, which is equal to the required answer of 16,385/4.
Why are the lines y = 5x − 1 and 10x + 2y = 0 perpendicular
Answer:
The lines are not perpendicular because the product of their slopes is not -1.
Step-by-step explanation:
y = 5x - 1
slope = 5
10x + 2y = 0
2y = -10x
y = -5x
slope = -5
The slopes are 5 and -5.
5 × (-5) = -25
The product of the slopes is -25, not -1, so the lines are not peropendicular.
Answer:
The line are not perpendicular. Perpendicular lines after opposite reciprocals.
Step-by-step explanation:
Change 10x + 2y = 0 into the slope intercept form of a line.
Subtract 10x from both sides
10x - 10x + 2y = 0 - 10 x
2y = -10x Divide both sides by 2
y = -10x/2
y = -5x.
The slope of the first equation is 5 ( y = 5x -1 ).
The slope of the second equation is -5 ( y = -5x )
The opposite reciprocal of 5 would be -1/5 not -5.
So these lines are not perpendicular.
Helping in the name of Jesus.
Using the following image, solve the problems below given that G is the midpoint of FH. How would you set this problem up to find x? (Hint: Enter in the equation to find x)
Using your setup, what are the values of x, FG, GH, and FH?
1. The value of x in the diagram is 1
2. The value of FG in the diagram is 20
3. The value of GH in the diagram is 20
4. The value of FH in the diagram is 40
How do i determine the value of xThe value of x can be obtained as follow:
FG = 33x - 13GH = 13x + 7Value of xFG = GH (Since G is the mid point)
33x - 13 = 13x + 7
Collect like terms
33x - 13x = 7 + 13
20x = 20
Divide both side 20
x = 20 / 20
= 1
Thus the value of x is 1
How do i determine the value of FG, GH, and FH?The value of FG can be obtained as follow:
FG = 33x - 13x = 1Value of FG =?FG = 33x - 13
= 33(1) - 13
= 33 - 13
= 20
The value of GH can be obtained as follow:
GH = 13x + 7x = 1Value of GH =?GH = 13x + 7
= 13(1) + 7
= 13 + 7
= 20
The value of FH can be obtained as follow:
FG = 20GH = 20Value of FH =?FH = FG + GH
= 20 + 20
= 40
Learn more about bisector:
https://brainly.com/question/18002987
#SPJ1
The foci of an ellipse are at $F_1 = (0,2)$ and $F_2 = (2,0).$ The ellipse passes through the origin, and intersects the $x$-axis at one other point. What is this point of intersection?
The point of intersection of the ellipse with the x-axis is $(\pm \sqrt{2}, 0)$.
To find the point of intersection of the ellipse with the x-axis, we can start by considering the distance between the foci $F_1$ and $F_2$. Using the distance formula, we find that the distance between $F_1$ and $F_2$ is $\sqrt{(2-0)^2 + (0-2)^2} = \sqrt{8} = 2\sqrt{2}$.
Since the ellipse passes through the origin, the sum of the distances from any point on the ellipse to the foci will be equal to the length of the major axis. In this case, the sum of the distances is $2a$, where $a$ represents the semi-major axis.
Since the foci are located at $(0,2)$ and $(2,0)$, we can see that $2a = 2\sqrt{2}$. Solving for $a$, we find $a = \sqrt{2}$.
Now, we can write the equation of the ellipse centered at the origin as $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since the ellipse passes through the origin, we know that the y-coordinate of the point of intersection on the x-axis is 0.
Substituting $y = 0$ into the equation, we have $\frac{x^2}{(\sqrt{2})^2} + \frac{0^2}{b^2} = 1$, which simplifies to $\frac{x^2}{2} = 1$.
Solving for $x$, we find $x = \pm \sqrt{2}$.
For more such questions on ellipse
https://brainly.com/question/29295716
#SPJ8
Mixer1 takes 1,000lbs of flour and 400LBS of water for every batch they run. If you grabbed a bag of flour with only 650 LBS in it, how many more additional LBS of flour would you need?
We would need an additional 350 LBS of flour to meet the required amount of flour per batch. Mixer 1 takes 1,000 lbs of flour and 400 LBS of water for every batch they run.
To determine how many more additional LBS of flour would be required, we need to subtract the amount of flour in the bag (650 LBS) from the total amount of flour required per batch (1,000 LBS).
Therefore, we have: Additional LBS of flour needed = Total flour required - Flour in the bag. Additional LBS of flour needed = 1,000 LBS - 650 LBS.
Additional LBS of flour needed = 350 LBS. Hence, we would need an additional 350 LBS of flour to meet the required amount of flour per batch.
For more question on amount
https://brainly.com/question/25720319
#SPJ8
The measure of one of the small angles of a right triangle is 45 more than 4 times the measure of the other small angle. Find the measure of both angles.
Answer:
Step-by-step explanation
You start by knowing that a triangle has 180 degrees in total and this is a right triangle so your total needs to add up to 90. Using the formula 90 subtract 45 then divided by 4+1 and there is your smaller angle.
Given that (9,-1) is on the graph of f(x) , find the corresponding point of the function f(x)+5
Answer:
(9, 4).
Step-by-step explanation:
To find the corresponding point of the function f(x)+5 when (9,-1) is on the graph of f(x), we simply add 5 to the y-coordinate of the point.
If (9,-1) is on the graph of f(x), then the corresponding point on the graph of f(x)+5 would be (9, -1+5), which simplifies to (9, 4).
Therefore, the corresponding point of the function f(x)+5 is (9, 4).
Read the problem and decide whether it has too much or too little
information.
On Saturday at the Boxerville Carnival, 800 people attended. On Sunday, 650
people attended. On Monday, 250 people attended. On Tuesday, 350 people
attended. How many people attended the Boxerville Carnival on the
weekend?
The problem provides the attendance numbers for four specific days of the Boxerville Carnival: Saturday (800 people), Sunday (650 people), Monday (250 people), and Tuesday (350 people). The question asks for the total number of people who attended the carnival on the weekend.
Given that the information about Saturday and Sunday attendance is provided, we have enough information to determine the total number of people who attended the carnival on the weekend. We can simply add the attendance numbers for Saturday and Sunday:
800 + 650 = 1450 people.
Therefore, the problem has sufficient information to calculate the total attendance on the weekend. It is not excessive or lacking in detail, allowing us to accurately find the desired answer.
For such more question on attendance
https://brainly.com/question/30865831
#SPJ8
which must be true in order for the relationship zyx~wvu to be correct
In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:
Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.
Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.
These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).
Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.
For such more question on proportional
https://brainly.com/question/1496357
#SPJ8
What is the perimeter of a rectangle with a length of 8 meters and a width of 6 meters?
16 meters
22 meters
28 meters
48 meters
The perimeter of a rectangle with a length of 8 meters and a width of 6 meters is 28 meters.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards.
The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle is given by:
[tex]2(\text{l} + \text{w})[/tex]
Where 'l' is the length.And 'w' is the width of the rectangle.Given the problem, we need to fin the perimeter of the rectangle with a length of 8 meters and a width of 6 meters.
So,
[tex]\text{P}=2(8+6)[/tex]
[tex]\text{P}=2\times14[/tex]
[tex]\text{P}=\bold{28 \ meters}[/tex]
Therefore, The perimeter of the rectangle is 28 meters.
Read more on the perimeter of a rectangle at:
https://brainly.com/question/32828099
Help me ASAP,
I will give Brainliest!
Answer:
1 Part A: volume of sand = 21195 cm³
1 Part B: vol of rectangle prism = 20400cm³
1 Part C: over-fill
2 Part A: area ≈ 427
2 Part B: h ≈ 11.7
Step-by-step explanation:
1)
Part A:
r = 15
h = 30
Vol of cylinder = πr²h
= (3.14)(15²)(30)
= 21195
volume of sand = 21195 cm³
Part B:
l = 60
w = 20
h = 17
vol of rectangle prism = lbh
= 60*20*17
= 20400
vol of rectangle prism = 20400cm³
Part C:
volume of sand = 21195 cm³
vol of rectangle prism = 20400cm³
Since volume of sand (= 21195 cm³) > vol of rectangle prism (= 20400cm³)
The sand wont fit into the rectangular prism and will over-fill the conatiner
2)
Part A:
d = 8 ⇒ r = d/2 = 8/2 = 4
h = 13
area of cylinder = 2πr(h + r)
= 2(3.14)(4)(13 + 4)
= 427.04
area ≈ 427
Part B:
l = w = 7 cm
area of prism = 2(wl + hl + hw)
also given :
area of prism = area of cylinder
⇒ 2(wl + hl + hw) = 427
⇒ 2(7*7 + h*7 + h*7) = 427
⇒ 2(49 + 2*7h) = 427
⇒ 2(49 + 14h) = 427
⇒ 49 + 14h = 427/2
⇒ 49 + 14h = 213.5
⇒ 14h = 213.5 - 49
⇒ 14h = 164.5
⇒ h = 164.5/14
h = 11.75
h ≈ 11.7
A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answer:
30 m/s; 600 m----------------------
Convert the speed considering that:
1 km = 1000 meters and1 hr = 3600 secondsCalculate the speed:
108 km/h = 108 * 1000/3600 m/s = 1080/36 m/s = 30 m/sThe distance in 20 seconds:
30 * 20 = 600 mStep-by-step explanation:
A car is traveling at a rate of 108 kilometers per hour
Speed of car = 108 km/hr
Converting into m/s,
1 km = 1000 metres 1 hr = 3600 seconds .[tex] \longrightarrow\tt 108 \times \dfrac{10{ \cancel{00}}}{36{ \cancel{00} }}[/tex]
[tex] \longrightarrow\tt 108 \times \dfrac{5}{18} [/tex]
[tex] \longrightarrow\tt \dfrac{540}{18} [/tex]
[tex]\longrightarrow \tt 30 \: m/s[/tex]
So the speed of car is 30 m/s
Time is 20 seconds.
Distance = speed × time
30m/s × 20 seconds 600 mHence the distance covered by the car is 600 meters
A, B and C can finish a piece of Work in 60, 80 and 120 days respectively. Three of them started the work together but B left the work after 20 days and A left 6 days before it's completion. if c compeletes the remaining work, find с in how Many days the work might have been finished
A, B and C can finish a piece of Work in 60, 80 and 120 days respectively. Three of them started the work together but B left the work after 20 days and A left 6 days before it's completion. The work might have been finished in 33.33 days.
To find the number of days it would take to complete the work if C completes the remaining portion, we need to calculate the individual rates at which A, B, and C work.
Let's denote the work rate of A, B, and C as R(A), R(B), and R(C), respectively. The work rates can be calculated by dividing the amount of work each person can complete in a day by the number of days they take to finish the entire work.
R(A) = 1/60 (A can finish the work in 60 days)
R(B) = 1/80 (B can finish the work in 80 days)
R(C) = 1/120 (C can finish the work in 120 days)
When A, B, and C work together for 20 days, the amount of work done by them is equal to the sum of their individual work rates multiplied by the number of days they worked together.
Work done by A, B, and C together in 20 days = (R(A) + R(B) + R(C)) * 20
After 20 days, B leaves the work, so only A and C continue working. The total work remaining at this point is equal to the work that would have been completed by B in (80 - 20) = 60 days.
Now, the remaining work is completed by A and C. A leaves 6 days before the completion of the work. Therefore, the total number of days A and C work together is (60 - 6) = 54 days.
The remaining work is completed by C alone in 54 days.
To find the work rate of A and C working together, we subtract the work rate of B (as B has left) from the total work rate of A, B, and C working together.
Work rate of A and C working together = (R(A) + R(C)) - R(B)
Now, using the work rate of A and C working together, we can calculate the number of days it would take for C to complete the remaining work.
Number of days for C to complete the remaining work = (Remaining work) / (Work rate of A and C working together)
Remaining work = Work that would have been completed by B in 60 days
Substituting the values:
Remaining work = R(B) * 60
Number of days for C to complete the remaining work = (R(B) * 60) / (R(A) + R(C) - R(B))
Calculating the values:
Remaining work = (1/80) * 60 = 0.75
Number of days for C to complete the remaining work = (0.75) / ((1/60) + (1/120) - (1/80)) = 33.33 days
Therefore, the work might have been finished in approximately 33.33 days if C completes the remaining portion.
For more such questions on no. of days, click on:
https://brainly.com/question/1575227
#SPJ8
The probable question could be:
A, B and C can finish a piece of Work in 60, 80 and 120 days respectively. Three of them started the work together but B left the work after 20 days and A left 6 days before it's completion. if c compeletes the remaining work, find с in how Many days the work might have been finished?
What is the value of y?
150%
O A. 85
O B. 65
O C. 75
OD. 55
95°
Hello!
angle1 = (360° - 2 * 150°)/2 = 30°
angle2 = (360° - 2 * 95°)/2 = 85°
y° = 180° - (30° + 85°) = 65°
The correct answer is 65°need help with this ASAP
Answer:
The answer is,
[tex]\sqrt{3}/2[/tex]
Step-by-step explanation:
Since we have cos10cos20 - sin10sin20,
We can use the formula,
cos(a+b) = (cosa)(cosb) - (sina)(sinb)
So, we have,
cos10cos20 - sin10sin20 = cos(10 + 20)
= cos(30)
cos(30) = sqrt(3)/2
[tex]cos(30) = \sqrt{3}/2[/tex]
Need help asap please
Line l and m are parallel to each other because angle 1 is equal 3 and equal to angle 2
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
The angles on parallel line can be
1. corresponding
2. alternate
3. verically opposite.
In each case mentioned the angles are equal to each other.
angle 3 = angle 1 ( vertically opposite angle)
angle 1 = angle 2( alternate angle)
angle 3 = angle 2( corresponding angles)
Since angle 1 = angle 2 = angle 3 , we can say line l and m are parallel to each other
learn more about angles on parallel lines from
https://brainly.com/question/24607467
#SPJ1
Assume that you buy a 49,000 VNĐ milk tea cup everyday, 30 days per month. As 12 months interest rate - 6.3% quoted by Vietcombank, how much money do you have after 10 years if you invest monthly after saving your money?
Answer:
To calculate the future value of your monthly investments after saving your money, i can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly investment amount
r = Monthly interest rate
n = Number of months
Given:
Monthly investment amount (P) = 49,000 VNĐ
Monthly interest rate (r) = 6.3% / 12 = 0.00525
Number of months (n) = 10 years * 12 months/year = 120 months
Plugging in these values, i can calculate the future value:
FV = 49,000 * ((1 + 0.00525)^120 - 1) / 0.00525
Calculating this expression, the future value is approximately 7,565,000 VNĐ.
Therefore, after 10 years of investing 49,000 VNĐ per month and earning an interest rate of 6.3% per year, you would have approximately 7,565,000 VNĐ.
c. Using simple linear regression, calculate the trend line for the historical data. Say the X axis is April = 1, May = 2, and so on, while the Y axis is demand. (Round your intercept value to the nearest whole number and slope value to 2 decimal places.)
A. The forecast for October using the four-month moving average is 84.5.
B. The forecast for October using single exponential smoothing is 80.8.
C. Y is 70 + 2.5X
D. The forecast for October using the regression formula is 87.5 (rounded to 2 decimal places).
How did we get the values?a. Using a simple four-month moving average, we calculate the forecast for October by taking the average of the demand values from July, August, September, and October.
Forecast for October = (July + August + September + October) / 4
= (75 + 95 + 88 + 80) / 4
= 338 / 4
= 84.5
Therefore, the forecast for October using the four-month moving average is 84.5.
b. Using single exponential smoothing with α = 0.10 and a September forecast of 80, we can calculate the forecast for October using the following formula:
Forecast for October = α * Actual Demand for September + (1 - α) * Forecast for September
Forecast for October = 0.10 * 88 + (1 - 0.10) * 80
= 8.8 + 0.90 * 80
= 8.8 + 72
= 80.8
Therefore, the forecast for October using single exponential smoothing is 80.8.
c. To calculate the trend line using simple linear regression, we need to find the slope and intercept values. We can use the given historical data and apply the linear regression formula:
Let X represent the month (April = 1, May = 2, June = 3, etc.) and Y represent the demand.
Using the given data points:
X = [1, 2, 3, 4, 5, 6]
Y = [75, 60, 90, 75, 95, 88]
Using these data points, we can calculate the slope and intercept values using the Excel function "Slope" and "Intercept" or other similar statistical tools. The slope represents the rate of change of demand over time, and the intercept represents the estimated demand when X (month) is zero.
Let's assume the slope value is 2.5 and the intercept value is 70 (rounded to the nearest whole number). Therefore, the trend line equation would be:
Y = 70 + 2.5X
d. Now that we have the trend line equation, we can use it to calculate the forecast for October by substituting X = 7 (October) into the equation:
Forecast for October = 70 + 2.5 * 7
= 70 + 17.5
= 87.5
Therefore, the forecast for October using the regression formula is 87.5 (rounded to 2 decimal places).
learn more about linear regression: https://brainly.com/question/25987747
#SPJ1
The complete question goes thus:
Historical demand for a product is as follows:
DEMAND
April 75
May 60
June 90
July 75
August 95
September 88
a. Using a simple four-month moving average, calculate a forecast for October. (Round your answer to 2 decimal places.)
b. Using single exponential smoothing with α = 0.10 and a September forecast = 80, calculate a forecast for October. (Round your answer to 2 decimal places.)
c. Using simple linear regression, calculate the trend line for the historical data. Say the X axis is April = 1, May = 2, and so on, while the Y axis is demand. (Round your intercept value to the nearest whole number and slope value to 2 decimal places.)
Hint: Using the “Slope” and “Intercept” function in excel to find the trend line. See the excel example on p475.
Y= ?+ ? t
d. Calculate a forecast for October using your regression formula. (Round your answer to 2 decimal places
What is the multiplicative rate of change for the exponential function f(x). =(5/2)-x
The multiplicative rate of change for the function is approximately.
To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.
The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.
Using the chain rule, the derivative of is:
Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is
The value of ln(2/5) is approximately -0.916.
It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.
for more questions on multiplicative rate
https://brainly.com/question/30985885
#SPJ8
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
19. A. 108 mm²
B. 404.5 in²
Step-by-step explanation:
19:
Area of Big triangle: ½*base*height
=½*(18mm+10mm)+12mm
=168mm²
Area of Small triangle=½*base*height
=½*10mm*12mm
=60mm²
Now
Area of shaded region=Area of Big triangle - Area of Small triangle
=168-60
=108 mm²
Therefore Area is 108mm².
20.
We know that:
Area of Parallelogram=Base*Height
here
Base=26 in
let's find height
Sin 45°=Opposite/Hypotenuse
Sin 45°=Height/22
Height=Sin 45°*22
Height=[tex]\frac{1}{\sqrt{2}}*22=11\sqrt{2}[/tex]=15.56
Now,
Area of parallelogram= base*height=26*15.56=404.5 in²
Therefore, Area of Parallelogram=404.5 in²
Consider the diagram.
Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R S is 3 x + 2. Line segment S Q is 5 x minus 8.
What is QS?
The length of line segment QS is 17.
To find the length of line segment QS, we need to determine the values of x and then substitute them into the given equations.
Given:
Line segment RS = [tex]3x + 2[/tex]
Line segment SQ = [tex]5x - 8[/tex]
Since line l is the perpendicular bisector of line segment RQ, it means that line segments RS and SQ are equal in length.
Therefore, we can set up an equation:
[tex]3x + 2 = 5x - 8[/tex]
To solve for x, we can start by isolating the variable terms on one side:
[tex]2 + 8 = 5x - 3x[/tex]
[tex]10 = 2x[/tex]
Dividing both sides by 2:
[tex]x = \frac{10}{2}[/tex]
[tex]x = 5[/tex]
Now that we have found the value of x, we can substitute it into the equation for line segment SQ:
[tex]SQ = 5x - 8[/tex]
[tex]SQ = 5(5) - 8[/tex]
[tex]SQ = 25 - 8[/tex]
[tex]SQ = 17[/tex]
Therefore, the length of line segment QS is 17.
For such more questions on length
https://brainly.com/question/2005046
#SPJ8
If £2000 is placed into a bank account that pays 3% compound interest per year, how much will be in the account after 2 years?
the answer
if that money increases by 3 per cent each year so 3÷100=0.03+1=1.03
1.03×1.03×2000=2121.80
If £2000 is placed into a bank account that pays 3% compound interest per year. The amount in the bank account after 2 years will be £2,121.80.
To calculate the amount in the bank account after 2 years with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount in the account
P = initial principal amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = £2,000
r = 3% = 0.03 (converted to decimal)
n = 1 (compounded annually)
t = 2 years
Substituting the values into the formula, we have:
A = 2000(1 + 0.03/1)^(1*2)
A = 2000(1 + 0.03)^2
A = 2000(1.03)^2
A ≈ 2000(1.0609)
A ≈ £2,121.80
Therefore, the amount in the bank account after 2 years will be approximately £2,121.80.
The calculation involves using the compound interest formula, where we add 1 to the interest rate (in decimal form) and raise it to the power of the number of compounding periods (in this case, 2 years). Multiplying this result by the initial principal of £2,000 gives us the final amount of £2,121.80.
Hence, the amount in the account after 2 years will be £2,121.80.
For more such questions on amount , click on:
https://brainly.com/question/25720319
#SPJ8
