The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.
How did get the formula?We can use the method of finite differences to find a possible recursive formula for this sequence.
First, let's compute the first few differences:
f(4) - f(1) = 6
f(7) - f(4) = 6
Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:
f(1) = a(1)^2 + b(1) + c = 6
f(4) = a(4)^2 + b(4) + c = 12
f(7) = a(7)^2 + b(7) + c = 18
Solving for a, b, and c, we get:
a = 1
b = 5
c = 0
Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.
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The 8th grade class of City Middle School has decided to hold a raffle to raise money to fund a trophy cabinet as their legacy to the school. A local business leader with a condominium on St. Simons Island has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The students plan to sell 2500 tickets for $1 each.
1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning ticket? (Assume that all 2500 tickets are sold. )
2) After thinking about the prize, you decide the prize is worth a bigger investment. So you buy 5 tickets. What is the probability that you have a winning ticket now?
3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that if any of the 25 tickets is selected, you’ll share the prize. What is the probability of having a winning ticket now?
4) At the last minute, another business leader offers 2 consolation prizes of a week-end at Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a winning ticket changed? Explain your reasoning. Suppose that the same raffle is held every year. What would your average net winnings be, assuming that you and your 4 friends buy 5 $1 tickets each year?
1) If there are 2500 tickets sold, and you buy 1 ticket, then the probability of your ticket being the winning ticket is 1/2500 or 0.04%.
2) If you buy 5 tickets, then the probability of having a winning ticket is 5/2500 or 0.2%.
3) If you and your 4 friends each buy 5 tickets, then there will be a total of 25 tickets. The probability of having a winning ticket in this scenario is 5/25 or 20%.
4) The chances of holding a winning ticket have not changed. This is because the consolation prizes are separate from the main prize, and the probability of winning the main prize is still the same.
The addition of consolation prizes does not affect the probability of winning the main prize.
Assuming the same raffle is held every year and you and your 4 friends buy 5 tickets each year, the average net winnings would be calculated as follows:
Total cost of tickets = $1 x 5 x 5 = $25
Total prize money = $1200 + ($400 x 2) = $2000
Probability of winning = 5/2500 = 0.2%
Expected value of winning = $2000 x 0.2% = $4
Average net winnings = ($4 - $25)/year = -$21/year
This means that on average, you and your friends would lose $21 per year if you participate in the raffle every year.
However, it is important to note that this is just an average and there is a chance of winning a larger prize which would make the net winnings positive.
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PLEASEEEEEEEEEEEEEEEEEEE
Answer:
< 3 = 3x + 105°
Step-by-step explanation:
There is remot angle theory which is the exterior angle is congrent to the other non adjecent angle in triangle.
so <1 + <EDF = <3
(3x + 15 ) ° + 90° = <3
3x°+ 105° = <3
< 3 = 3x + 105° .... so the measur of angle 3 interms of x is 3x + 105°
Check each set of side lengths to see if it would be a
right triangle.
Remember plug the numbers into the Pythagorean
Theorem to see if they work!
Select ALL that are right traingles!
A 5,8, and 9
B 20, 21, and 29
C 9, 12, and 15
D 5, 6, and 11
Where the above figures are given, The right triangles are: B and C.
What is the explanation for the above response?Using the phythagoren theorem, we can determind the options that represent a right ttriangle.
A 5,8, and 9:
5^2 + 8^2 = 25 + 64 = 89
9^2 = 81
Not a right triangle.
B 20, 21, and 29:
20^2 + 21^2 = 400 + 441 = 841
29^2 = 841
It is a right triangle.
C 9, 12, and 15:
9^2 + 12^2 = 81 + 144 = 225
15^2 = 225
It is a right triangle.
D 5, 6, and 11:
5^2 + 6^2 = 25 + 36 = 61
11^2 = 121
Not a right triangle.
The right triangles are: B and C.
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13, 9, 17, 12, 18, 12, 17, 7, 16, 19
so what is the Mean Median_____ Range
Use cylindrical coordinates to evaluate the triple integral ∫∫∫√(x^2 + y^2) dV where E is the solid bounded by the
circular paraboloid z = 9 - (x^2 + y^2) and the xy-plane.
The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.
To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:
[tex]z = 9 - (r^2)[/tex]
The limits of integration are:
0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)
0 ≤ θ ≤ 2π
0 ≤ z ≤ 9 - (r^2)
The triple integral becomes:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]
Simplifying, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]
Evaluating the innermost integral, we get:
∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]
Substituting this back into the triple integral, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]
Evaluating the remaining integrals, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]
= 2π [243/5]
= 486π/5
Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.
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Copy and complete the equation of line B below. y = — 84 NWPца - 0 7- 6+ 5- 4- 3- 2- 1/ -11 -2- -8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 ܢܐ ܚ ܩ ܘ ܘ ܢ -3 -4- -5 -6 x +_ -7 -8- Line B 19
The equation of the line passing through the given points is y = 3x-1.
Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),
Therefore, the required equation is =
y+1 = -1-2/-1 (x-0)
y+1 = 3x
y = 3x-1
Hence, the equation of the line passing through the given points is y = 3x-1.
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Answer the following questions for the function
f(x) = x^3/x^2 - 4 defined on the interval (–18, 19) Enter the z-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them separated commas; and if there are nono, enter NONE
There is a vertical asymptote at x = 0.
A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.
In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.
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Only a small percentage of Americans owned cars before the 1940s. By 2017, there were nearly 250 million vehicles for 323 million people, significantly increasing the need for roadways. In 1960, the United States had about 16,000 km of interstate highways. Today, the interstate highway system includes 77,000 km of paved roadways. What percent increase does this represent?
A. 381 percent
B. 792 percent
C. 38 percent
D. 79 percent
The percent increase in the interstate highway system from 1960 to now is 381%.
option A.
What is the percent increase?The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.
percent increase = 100% x (new value - old value) / old value
percent increase = 100% x (77,000 - 16,000) / 16,000
percent increase = 100% x 61,000 / 16,000
percent increase = 381.25%
Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.
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Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
To find the volume of a cone, we use the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.
In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.
First, we need to find the slant height of the cone. We can use the Pythagorean theorem:
[tex]l = \sqrt{(r^2 + h^2)[/tex]
[tex]l = \sqrt{(6^2 + 10^2)[/tex]
[tex]l = \sqrt{\\(36 + 100)[/tex]
[tex]l = \sqrt{136[/tex]
[tex]l = 11.66 ft[/tex]
Now we can substitute the values into the formula for the volume:
[tex]V = (1/3)\pi r^2h[/tex]
[tex]V = (1/3)\pi (6^2)(10)[/tex]
[tex]V = 120\pi /3[/tex]
[tex]V = 40\pi[/tex]
[tex]V= 125.6 cubic feet[/tex]
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Ignacio chooses a plant at random that does not have a white bloom. What is the probability of the complement of the event? Express your answer as a fraction in simplest form
The probability of the complement of the event of Ignacio chooses a plant at random that does not have a white bloom is 0.7692.
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more probable it is that the event will take place.
Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is.
The probability that Ignacio chooses the plant which have white bloom in it is,
P = number of white bloom / total number of flowers
P = 21 / 91
So the probability that the chosen flower is not white is,
1 - P = 1 - 21/91 = 70/91 = 0.7692.
Therefore, the probability of not choosing white is 0.7692.
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[tex]4^3\sqrt{-88}[/tex]
Help I don't know where the negative goes.
if you meant simplification
[tex]4^3\sqrt{-88}\implies 64\sqrt{-88}\implies 64\sqrt{(-1)(2^2)(2)(11)}\implies 64(2)\sqrt{(-1)(2)(11)} \\\\\\ 128\sqrt{(2)(11)}\cdot \sqrt{-1}\implies 128\sqrt{22}~i[/tex]
Select the equivalent expression. \left(\dfrac{4^{3}}{5^{-2}}\right)^{5}=?( 5 −2 4 3 ) 5 =?
(its khan academy)
(4^3/5^-2)^5 = ?
The equivalent expression is $\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = 102400000000000000000$.
Find the simplified equivalent expression of the following?We can simplify the expression inside the parentheses first:
\begin{aligned} \frac{4^3}{5^{-2}} &= 4^3 \cdot 5^2 \ &= (2^2)^3 \cdot 5^2 \ &= 2^6 \cdot 5^2 \ &= 2^5 \cdot 2 \cdot 5^2 \ &= 2^5 \cdot 10^2 \ &= 3200 \end{aligned}
Now we can substitute this value into the original expression and simplify further:
\begin{aligned} \left(\frac{4^3}{5^{-2}}\right)^5 &= (3200)^5 \ &= (2^8 \cdot 5^2)^5 \ &= 2^{40} \cdot 5^{10} \ &= (2^4)^{10} \cdot 5^{10} \ &= 16^{10} \cdot 5^{10} \ &= (16 \cdot 5)^{10} \ &= 80^{10} \ &= 102400000000000000000 \end{aligned}
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Answer correctly and if you dont know it just dont say anything
the table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 $600
3 $720
6 $840
part a: find and interpret the slope of the function. (3 points)
part b: write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
part c: write the equation of the line using function notation. (2 points)
part d: what is the balance in the bank account after 7 days? (2 points)
Answer:
part a: The slope of the function represents the rate of change of the balance in the bank account per day. To find the slope, we can use the formula: slope = (change in y)/(change in x).
Using the values from the table, we have: slope = (720-600)/(3-0) = 120/3 = 40. Therefore, the slope of the function g(x) is 40.
part b: Using the point-slope form of the equation of a line, we can write: g(x) - 600 = 40(x-0). Simplifying, we get: g(x) = 40x + 600. This is the slope-intercept form of the equation, where the y-intercept is 600 and the slope is 40.
To write in standard form, we can rearrange the equation as: -40x + g(x) = 600.
part c: Using function notation, we can write the equation as: g(x) = 40x + 600.
part d: To find the balance in the bank account after 7 days, we can use the equation we found in part c and substitute x = 7: g(7) = 40(7) + 600 = 880. Therefore, the balance in the bank account after 7 days is $880.
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60 juniors and sophomores were asked whether or not they will attend the prom this year. The data from the survey is shown in the table. Find P(will attend the prom|sophomore).
Attend the prom Will not attend the prom Total
Sophomores 10 17 27
Juniors 24 9 33
Total 34 26 60
The probability of a sophomore attending the prom, given that they were selected from the group of sophomores, is:
P(will attend the prom|sophomore) = (number of sophomores attending the prom) / (total number of sophomores)
From the table, we see that the number of sophomores attending the prom is 10, and the total number of sophomores is 54 (10 + 17 + 27). Therefore:
P(will attend the prom|sophomore) = 10 / 54
Simplifying the fraction, we get:
P(will attend the prom|sophomore) = 5 / 27
So the probability of a sophomore attending the prom is 5/27 (18.519%).
What is the equation of a circle with center (2,3) that passes through the point (5, 3)?
The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.
The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.
Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]
Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]
Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]
So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
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Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer
Alexander stacked 16 unit cubes required to build the rectangular prism.
What is a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
Here we need to find the number of cubes required to build the rectangular prism.
Here first we need to find how many cubes stack in the base layer
Number of unit cubes in the base layer = Number of cubes along the length * Number of cubes along the width
The number of unit cubes in the base layer = 2 * 4 = 8 cubes.
Total number of unit cubes in prism =Number of unit cubes in the base layer *Number of layers = 8 * 2 = 16 unit cubes
So, there are 16 unit cubes are required to build the rectangular prism.
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Complete question :
Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer the question.
How many cubes are required to build the rectangular prism?
The guidance department has reported that of the senior class 2. 3% are members of key club 8. 6% are enrolled in AP physics and 1. 9% are in both
The percentage is 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
We need to find the percentage of seniors who are either members of the Key Club, enrolled in AP Physics, or both. We can use the formula:
Total percentage = Key Club percentage + AP Physics percentage - Both percentage
Step 1: Identify the given percentages
Key Club percentage = 2.3%
AP Physics percentage = 8.6%
Both percentage = 1.9%
Step 2: Apply the formula
Total percentage = 2.3% + 8.6% - 1.9%
Step 3: Calculate the result
Total percentage = 9.0%
So, 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
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Find the error. A class must find the area of a sector of a circle determined by a ° arc. The radius of the circle is cm. What is the student's error?
The student's error could be in the wrong formula he used. The area of the sector is 245.043 sq.
How do we calculate?The formula for area of a sector is
A = (θ/360) * π * r^2
where:
θ is the central angle of the sector in degrees
r is the radius of the circle
In this case, the central angle θ is 45 degrees and the radius r is 25 cm. So the area of the sector should be:
A = (45/360) * π * (25)^2
A = (1/8) * π * 625
A = 78.125π ≈ 245.043 sq. cm
The student could have made an error during any step of the calculation.
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2. A cylindrical water tank has a diameter of 4.6 feet and a height of 10.0
feet. A cubic foot of water is about 7.5 gallons. About how many gallons
of water are in the tank if it is completely full?
A 1,100 gallons
B. 1,250 gallons
C. 1,725 gallons
D. 3,450 gallons
Answer: Dude, I think its B. but I wouldn't use this site, its not a good rabbit hole to go down.
Step-by-step explanation:
A bee flies for 4.0 min at 32.5 in/min find the bees distance in ft
The distance that the bees cover in feet is 10.84 feet.
The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.
We know that
1 inch=1/12feet.
so 32 inches/min=32.5 *(1/12) feet/min.
which is roughly equal to 2.71 feet/min (rounded to two decimal places).
Now by using the speed, distance, and time formula which is:
distance=speed*time
we can calculate the distance covered by bees at the given speed and time.
Substituting the values in the equation.
distance=2.71 feet/minute * 4.0 minutes.
=10.84 feet
Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).
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need help on this problem
Answer:
a. n < 14
b. n ≥ 14
Step-by-step explanation:
a.
We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14
b.
The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14
Find the value of x that will make aiib.
4x 2x
x=
The value of x that will make a parallel to b is 30. We solved the equation 4x + 2x = 180 and obtained x = 30.
According to the definition of interior consecutive angles, when a transversal intersects two parallel lines, the sum of the measures of the two interior consecutive angles formed on the same side of the transversal is always 180°.
In this case, we are given that lines A and B are parallel, and line q intersects these lines at two distinct points, forming two interior consecutive angles with measures 4x and 2x, respectively.
Since the two angles are consecutive and on the same side of the transversal, their sum is equal to 180°. Therefore, we can set up the following equation
4x + 2x = 180
Simplifying the equation, we get
6x = 180
Dividing both sides by 6, we get
x = 30
Therefore, the value of x that will make a parallel to b is 30.
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--The given question is incomplete, the complete question is given
" Find the value of x that will make a parallel to b.
Lines A and B are parallel lines and a transverse line is intersecting these lines at two distinct points, making the angle 4x and 2x
x= "--
pls help
what is the volume
And total surface area
Debra has these snacks from a birthday party in a bag.
4 bags of chips
5 fruit snacks
6 chocolate bars
3 pieces of bubble gum
Debra will randomly choose one snack from the bag. Then she will put it back and randomly choose another snack. What is the probability that she will choose a chocolate bar and then a piece of gum?
A. 1/2
B. 1/3
C. 1/9
D. 1/18
Your answer is D. 1/18 is the probability that she will choose a chocolate bar and then a piece of gum
First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks
Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.
Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.
Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18
So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.
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√3x^3 BRAINLIEST IF CORRECT!!!!!1
Answer:
[tex] \sqrt{3 {x}^{3} } = x \sqrt{3x} [/tex]
We note that x>0 here.
Answer:
The answer is x√3x
Step-by-step explanation:
√3x³=x√3x
The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2. A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 15, and the box ranges from 8. 8 to 10. 2. A line divides the box at 9. 5. Plot 1 A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 11, and the box ranges from 8. 7 to 10. A line divides the box at 9. 6. Plot 2 How does the mean and median change from plot 1 to plot 2? The mean and median remain the same. The mean decreases, and the median remains the same. The mean remains the same, and the median decreases. The mean and median decrease.
The mean decreases, and the median remains the same from plot 1 to plot 2.
In the first box-and-whisker plot, the hourly wages earned by 20 employees are displayed, with a range from $8.70 per hour to $11.50 per hour. The median, which is the value that separates the higher half of the data from the lower half, is $10 per hour. The mean, which is the average of all the wages, is calculated by adding up all the wages and dividing the total by 20.
When one employee earning $15 per hour quits and is replaced by a new employee earning $8 per hour, the second box-and-whisker plot is created. The range of wages extends from $8 per hour to $15 per hour, with a median of $9.50 per hour. Since the new employee is earning a lower wage, the mean hourly wage decreases.
Therefore, the correct answer to the question is that the mean decreases, and the median remains the same. It is important to note that while the median does not change in this case, it is not always the case in other situations where data is added or removed from a set. It is also important to note that box-and-whisker plots are helpful in visualizing the spread of data and identifying any outliers.
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The money in Maya's college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
A. 0. 0215
B. 11/5
C. 0. 022
D. 11/500
A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.
= 2 1/5% / 100
= (2 + (1/5)) / 100
= 0.022
A value that is less than 0.022 from the given data is 0. 0215.
Therefore, a value less than 2 1/5% is 0. 0215.
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5. A salesman bought a computer from a manufacturer. The salesman then sold the computer for
$15 600 making a profit of 25%. Unfortunately, he suffered a 5% loss due to damages when
assembling
a. What was his actual profit earnings? (10 marks)
The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.
Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.
Let the cost price of the computer be x.
Selling price = 125% of cost price
$15,600 = 1.25x
Solving for x, we get:
x = $12,480
So, the salesman's cost price of the computer was $12,480.
Now, the salesman suffered a loss of 5% due to damages when assembling the computer.
Loss = 5% of cost price
Loss = 5% of $12,480
Loss = $624
So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.
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In ΔLMN, m = 2. 1 inches, n = 8. 2 inches and ∠L=85°. Find the length of l, to the nearest 10th of an inch
The length of l is approximately 6.1 inches to the nearest tenth of an inch.
To find the length of l, we can use the Law of Cosines which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the side opposite angle C, and a and b are the other two sides.
In this case, we want to find the length of l, which is opposite the given angle ∠L. So we can label l as side c, and label m and n as sides a and b, respectively. Then we can plug in the values we know and solve for l:
l^2 = m^2 + n^2 - 2mn*cos(L)
l^2 = (2.1)^2 + (8.2)^2 - 2(2.1)(8.2)*cos(85°)
l^2 = 4.41 + 67.24 - 34.212
l^2 = 37.438
l = sqrt(37.438)
l ≈ 6.118
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Question One:
Zahir bought a house 15 years ago, and it is now valued $548 900.00.
Determine the initial value of the home when Zahir purchased it, if it's value
has grown at a rate of 4.8% compounded annually. (2 marks)
Question Two:
Kiran purchases a sofa for $1791.99 (taxes already included). The
department store offers her a promotion of 0% interest with no payments
for one year. If Kiran does not pay the amount in full within one year,
interest will be charged from the date of purchase at an annual rate of
27.93%, compounded monthly.
a) If Kiran does not make any payments, what will the department store bill
her one year after the date of purchase? Show your work. (2 marks)
b) Describe a different compounding period such that the overall cost of the
sofa is lower than if the annual interest rate were compounded monthly. Use
an example to help your explanation. (2 mark)
A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
B. In this case, the overall cost of the sofa would be approximately $2,284.08
How to solve the problemsTo find the initial value of the home when Zahir purchased it, we can use the compound interest formula:
Future Value = Initial Value * (1 + (interest rate))^years
Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.
548,900 = P * (1 + 0.048)^15
Now, we'll solve for P:
P = 548,900 / (1 + 0.048)^15
P ≈ 305,113.48
a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)
Initial Value = $1,791.99
Interest Rate = 27.93% (0.2793)
Number of periods = 12 (monthly)
Years = 1
Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)
Future Value ≈ 2284.33
Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
b. interest were compounded annually:
Future Value = Initial Value * (1 + interest rate)^years
Future Value = 1,791.99 * (1 + 0.2793)^1
Future Value ≈ 2284.08
In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).
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