Answers
The recursive formula is 5/6
What is recursive formula?You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.
The given parameters are
aₓ = a(n-1) + 2
Where aₓ = 2aₓ₋1
= 2*5(₃₋₁) = 5(3-1) + 2
= 10₂ = 10 + 2
Taking the log of both sides
Log₂10 - Log12 = 0
Dividing by 10 we have
10/12 = 5/6
therefore the recursive formula is 5/6
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Related Questions
1. Define, compare and contrast common stock and preferred stock.
2. Define, compare and contrast dividends and dividends in arrears.
3. Define, compare and contrast bond premium and discount.
4. What are the 3 main fee structures of mutual funds?
5. What is NAV and how is it calculated?
Answers
Common Stock:
- Represents ownership in a company and a claim on a portion of the company's assets and earnings.- Has voting rights, allowing shareholders to participate in corporate decision-making.- Dividends are not guaranteed and can fluctuate.- In the event of liquidation, common stockholders are paid after preferred stockholders.Preferred Stock:
- Represents partial ownership in a company but typically does not carry voting rights.- Typically has a fixed dividend rate, which is paid before dividends to common stockholders.- In the event of liquidation, preferred stockholders have priority over common stockholders.- Can be converted to common stock or have a callable feature, allowing the company to redeem shares at a predetermined price.Comparison:
- Common stockholders have voting rights, while preferred stockholders generally do not.- Preferred stock usually has a fixed dividend rate, while common stock dividends can fluctuate.- Preferred stockholders have priority in receiving dividends and in the event of liquidation.2. Dividends vs Dividends in Arrears:Dividends:
- Payments made by a corporation to its shareholders, usually in the form of cash or additional shares.- Typically paid from a company's profits or retained earnings.- Can be regular (e.g., quarterly) or special (one-time) dividends.Dividends in Arrears:
- Unpaid dividends owed to preferred stockholders.- Occur when a company does not pay the full dividend amount it has committed to for preferred stockholders.- Must be paid before any dividends can be paid to common stockholders.Comparison:
- Dividends are regular or special payments to shareholders, while dividends in arrears are unpaid dividends owed to preferred stockholders.- Dividends in arrears must be paid before any dividends can be paid to common stockholders.3. Bond Premium vs Bond Discount:Bond Premium:
- Occurs when a bond's market price is higher than its face value.- Usually results from a decrease in market interest rates, making the bond's fixed interest payments more attractive to investors.- Bond premium is amortized over the life of the bond, reducing the bond's book value.Bond Discount:
- Occurs when a bond's market price is lower than its face value.- Usually results from an increase in market interest rates, making the bond's fixed interest payments less attractive to investors.- Bond discount is amortized over the life of the bond, increasing the bond's book value.Comparison:
- A bond premium represents a bond selling for more than its face value, while a bond discount represents a bond selling for less than its face value.- Bond premiums typically occur when market interest rates decrease, while bond discounts occur when market interest rates increase.4. 3 Main Fee Structures of Mutual Funds:1. Sales Loads: Fees paid when buying or selling shares of a mutual fund. They can be front-end loads (charged when buying shares) or back-end loads (charged when selling shares).
2. Expense Ratio: The annual fee that covers the fund's operating expenses, including management fees, administrative fees, and other costs. It is expressed as a percentage of the fund's average net assets.
3. 12b-1 Fees: Annual fees charged by some mutual funds to cover marketing and distribution expenses. These fees are included in the fund's expense ratio.
5. NAV (Net Asset Value):- NAV represents the per-share value of a mutual fund, calculated by dividing the fund's total net assets by the number of outstanding shares.- Total net assets are calculated by subtracting the fund's liabilities from its total assets.- NAV is typically calculated at the end of each trading day and is the price at which investors can buy or sell shares of the mutual fund.Two train tracks run parallel leaving a station. Train A leaves the station heading east at 55 mph. Train B leaves the station 2 hrs and 15 minutes later also traveling east but at 120 mph. The equation below gives the distance, D, between the two trains as a function of the number of hours, T, that have passed since train B left the station.
For which two values of T will D = 40? Round to the nearest tenth.
A.
0.1 and 0.3
B.
12.9 and 25.2
C.
-1.3 and 1.3
D.
1.3 and 2.5
Answers
Answer: Answer choice C: -1.3 and 1.3.
Step-by-step explanation:
We can start by using the formula for the distance, D, between the two trains as a function of time, T:
D = 55(T + 2.25) - 120T
Simplifying this equation, we get:
D = 55T + 123.75 - 120T
D = -65T + 123.75
To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:
40 = -65T + 123.75
-85 = -65T
T = 1.31
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.31) + 123.75
D = 40.0375
Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:
40 = -65T + 123.75
-83.75 = -65T
T = 1.29
Plugging this value back into the original equation, we can see that D is equal to 40:
D = -65(1.29) + 123.75
D = 40.0375
Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.
Write the standard form of the equation of the circle with radius 7 and center at (0, 0).
Answers
The standard form of the equation of the circle with a radius of 7 and center at (0, 0) will be x² + y² = 49.
Given that:
The center is at the origin.
Radius, r = 7
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
Substitute h = 0, k = 0, and r = 7, then we have
(x - 0)² + (y - 0)² = 7²
x² + y² = 49
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PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
Answers
The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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Help!
The surface area of this rectangular prism is __ square centimeters.
Answers
The surface area of the rectangular prism is 216 square cm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 cm by 3 cm by 6 cm
The surface area of the rectangular prism is calculated as
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square cm
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the sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19° to the highest part of the sunken ship. how many meters must the submarine rise to pass over the sunken ship?
Answers
Step-by-step explanation:
Tan Φ = opposite leg / adjacent leg
tan 19 = height / 1500
1500 * tan 19 = height = 516 m <==== must rise this much
Question 10: The graph below shows a company's profits f(x), in dollars, depending on the price of 8.01 & 8.04
pens x, in dollars, sold by the company.
Part A (2pts): Highlight your answer below
150
90
00
30
f(x)
What does the maximum value represent?
A The point where no profit is made
B.
C.
D.
The point where the most profit is made
The point where the most pens are made
The point where no pens are made.
Part B (2 pts) Highlight/circle your answer What do the x-intercepts represent?
A.
The price per pen where the most profit is made
B.
The price per pen where no profit is made.
C.
D.
The point where the most pens are made.
The point where no pens are made.
Part C (3 pts): What is an approximate average rate of change of the graph from
x=3 to x = 6? Show your work.
Part D (3 pts) Drag & Drop into the blanks to describe the constraints of the
domain.
The domain of this graph given the situation is
because
beyond those points.
+
Z
Answers
The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.
Part A:
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
The function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
Part B:
An approximate average rate of change of the graph from x=3 to x=5 represents the reduction in profit from 3 to 5.
Part C:
Simply, the domain is constrained by x=0.
We are obliged at x=6 .
This is because we have to avoid a negative profit.
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Complete the ratio table
Answers
Answer: do u need help
Step-by-step explanation: ask a teacher dont cheat
How many centimeters are in x meters
Answers
Answer:
multiply the number of meters by 100
the diagram shows a right angled triangle
Answers
Answer:
34.8°
Step-by-step explanation:
You want the angle opposite a side of length 8 cm in a right triangle with hypotenuse 14 cm.
SineThe sine relation is the one of interest in this geometry:
Sin = Opposite/Hypotenuse
sin(x°) = (8 cm)/(14 cm)
The angle can be found using the inverse sine function:
x° = arcsin(8/14) ≈ 34.8°
The size of the angle x° is 34.8°.
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6+3(-2x - 3y). Please help mee
Answers
You currently have $6,500 that you would plan to deposit into an investment account that has an anticipated growth factor of 1.03 per year. Use guess and check to estimate the number of years that it will take for this investment to grow to $10,000. Show your work.
Answers
Answer:
Using guess and check, we can estimate the number of years it will take for the investment to grow to $10,000 as follows:
First, we'll assume that it will take 5 years for the investment to grow to $10,000.
After 5 years, the investment would grow to:
$6,500 x 1.03^5 = $7,960.35
Since this is still less than $10,000, we need to increase the number of years.
Next, we'll assume that it will take 10 years for the investment to grow to $10,000.
After 10 years, the investment would grow to:
$6,500 x 1.03^10 = $9,020.14
Since this is still less than $10,000, we need to increase the number of years again.
Finally, we'll assume that it will take 15 years for the investment to grow to $10,000.
After 15 years, the investment would grow to:
$6,500 x 1.03^15 = $10,005.58
Since this is slightly more than $10,000, we can estimate that it will take around 15 years for the investment to grow to $10,000.
Therefore, the estimated number of years it will take for the investment to grow to $10,000 is about 15 years.
Jacob is standing 112 m from a building. The angle of elevation from where he is standing on the ground to the top of the building is 62°.
How tall is the building?
Round the final answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Let h(x) = x² - 8x.
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
Answers
(a) Find the average rate of change from 3 to 9.
(b) Find an equation of the secant line containing (3,h(3)) and (9, h(9))
your avatar
(a) The average rate of change from 3 to 9 can be found by calculating the slope of the secant line connecting the points (3, h(3)) and (9, h(9)).
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Applying this formula, we have:
m = (h(9) - h(3)) / (9 - 3)
To find the values of h(9) and h(3), we need to substitute 9 and 3 into the function h:
h(9) = 9² - 8(9) = -27 h(3) = 3² - 8(3) = -9
Substituting into the formula for slope, we have:
m = (-27 - (-9)) / (9 - 3) = -18 / 6 = -3
Therefore, the average rate of change from 3 to 9 is -3.
(b) To find the equation of the secant line containing (3, h(3)) and (9, h(9)), we need to find the slope of the line and its y-intercept.
We've already calculated the slope in part (a) as -3. To find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is a point on the line, and (x, y) are any other points on the line. We can choose either (3, h(3)) or (9, h(9)) as our point.
Let's use (3, h(3)):
y - h(3) = -3(x - 3)
Simplifying, we get:
y = -3x + 18 - 9 y = -3x + 9
Therefore, the equation of the secant line is y = -3x + 9.
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS
Answers
What is the midpoint of line segment Ab (-3,-5) (-1,-7)
Answers
Answer:
(-2, -6)
Step-by-step explanation:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
= (-3 + -1)/2, (-5 + -7)/2
= (-4/2), (-12/2)
= (-2, -6)
how to do I solve this
Answers
Answer:
the answer is 80
Step-by-step explanation:
1pound=16ounces
A right prism with a triangular base has a volume of 195 mm3 . The right prism is 13 mm tall. The triangular base of the prism has a base length of 5 mm .
What is the base height of the triangular base of the right prism? Round your answer to the nearest whole millimeter, if necessary.
Answers
Justify Results Hector was asked to simplify the expression (5^-3/5^-1) He gave the answer 1/25 Did Hector give the correct answer? Explain.
Answers
Answer:
To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.
Using this rule, we get:
(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25
Therefore, Hector gave the correct answer.
Two ramps are placed back to back as shown. What is the length of the ramp labeled x?
Answers
The value of the x as shown in the graph will be 16.61 ft.
From the sine rule in the triangle,
In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]
Use the Law Of Sines to solve this:
(Sin 7)/9 = (Sin 13)/x
Cross multiply...
x(Sin 7) = 9(Sin 13)
Divide both sides by Sin 7
x = [9(Sin 13)]/(Sin 7)
x = 16.61254121
therefore, for the ramp, the value of the x will be 16.612 ft.
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I need help with this problem.
Answers
According to the information, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
How to calculate the elasticity?To evaluate the elasticity at $p=2$, we need to use the formula for price elasticity of demand:
E = (dQ/Q) / (dP/P)
where:
E = price elasticity of demand
dQ = change in quantity demanded
Q = quantity demanded
dP = change in price
P = price
We are given the equation for the demand function:
x = 15000 - 3535√p
So, the quantity demanded at price $p$ is $Q = x(p) = 15000 - 3535\sqrt{p}$.
Taking the derivative of Q with respect to p:
dQ/dp = -3535/(2√p)
Now we can calculate the elasticity at $p=2$:
Q = 15000 - 3535√2
dQ/dp = -3535/(2√2)
P = 2
dP = 0
E = (dQ/Q) / (dP/P)
E = (-3535/(2√2)) / [(15000 - 3535√2)/2]
E ≈ -0.619
According to the above, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.
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A data set contains three points, and two of the residuals are-7 and 4. What is the third residual?
A. 7
B. -3
C. -4
D. 3
Answers
Answer:
D
Step-by-step explanation:
We know that the residual is the difference between the observed value and the predicted value for a given point. Let's assume that the predicted values for the three points in the data set are denoted by ŷ₁, ŷ₂, and ŷ₃, and the observed values are denoted by y₁, y₂, and y₃.
We can write the residuals as:
e₁ = y₁ - ŷ₁
e₂ = y₂ - ŷ₂
e₃ = y₃ - ŷ₃
We are given that two of the residuals are -7 and 4.
Let's assume that e₁ = -7 and e₂ = 4.
We can use these values to find the third residual e₃.Since the sum of residuals is always equal to zero, we have:
e₁ + e₂ + e₃ = 0
Substituting the values of e₁ and e₂, we get
:-7 + 4 + e₃ = 0
Simplifying, we get:
e₃ = 3
Therefore, the third residual is 3, which is option D.
A recycling bin contained 40 pounds of plastic in October and 50 pounds of plastic in
November. By what percentage did the amount of plastic increase from October to
November?
Answers
The percentage increase by the given data is 25%.
We are given that;
Weight of plastic in october= 40
Weight of plastic in november= 50
Now,
To find the percentage increase of the amount of plastic from October to November, we need to find the absolute increase and divide it by the original amount, then multiply by 100 to get the percentage.
The absolute increase is the difference between the final amount and the initial amount, which is 50 - 40 = 10 pounds.
The original amount is the initial amount, which is 40 pounds.
10/40×100=25%.
Therefore, by the percentage the answer will be 25%.
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What is the measure of y (angle AXB)?
1. 90°
2. 60°
3. 45°
4. 30°
Answers
Answer:
4. 30°
Step-by-step explanation:
Sum of interior angles of a triangle = 180
y° + ∠XYZ + ∠YZX = 180
y° = 180 - 90 - 60 = 30°
A circular arc has measure 6cm and is intercepted by a central angle of 40° . Find the radius r of the circle
Answers
The radius of the circle with central angle θ = 40° is r = 8.594 cm
Given data ,
A circular arc has measure 6cm and is intercepted by a central angle of 40°
Now , the radius r of the circle is given by
r = L / θ
where θ is in radians
So , 40° = 0.6981317007977318 radians
On simplifying , we get
r = 40 / 0.6981317007977318
Now , the measure of r = 8.594 cm
Hence , the radius is r = 8.594 cm
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A water park has pools, slides, and rides that, in total, make use of 8.8 × 1 0 5 8.8×10 5 gallons of water. They plan to add a ride that would make use of an additional 51 , 000 51,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
Answers
[tex]9.31*10^5[/tex] gallons are the total gallons of water used by the water park after adding the new ride.
To express the total gallons of water used by the water park after adding the new ride in scientific notation, we need to add the two values together and then convert them to scientific notation.
[tex]8.8*10^5[/tex] gallons + 51,000 gallons = [tex]9.31*10^5[/tex] gallons
Therefore, the total gallons of water used by the water park after adding the new ride is [tex]9.31*10^5[/tex] gallons.
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Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure.
Answers
The null and alternative hypothesis is represented by option A.
The test statistic is 0.153.
How to explain the informationWe want to test the claim that women and men have the same mean diastolic blood pressure.Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men.
The t-statistic value will be:
= (69.81 - 69.53) / (✓10.46²/26 + 11.24²/26)
=0.153
Since p-value for two tail test=0.879 which is greater than =0.05(0.879>0.05) So we do not reject H0.
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Sue likes to skate at a skate park that is due south of her school and due west of her favorite ice cream parlor. If the skate park is 4 miles from her school and the straight-line distance between the school and the ice cream parlor is 5 miles, how far is the skate park from the ice cream parlor?
Answers
The skate park is approximately 6.4 miles from the ice cream parlor.
We can use the Pythagorean theorem to find the distance between the skate park and the ice cream parlor.
As per the information, we can see that the distance we're looking for is the hypotenuse of a right triangle with legs of length 4 miles (distance from school to skate park) and 5 miles (distance from school to ice cream parlor).
Using the Pythagorean theorem, we get:
c² = a² + b²
where c is the distance between the skate park and the ice cream parlor, and a and b are the distances from the school to the skate park and ice cream parlor, respectively.
Substituting the values we know, we get:
c² = 4² + 5²
c² = 16 + 25
c² = 41
Taking the square root of both sides, we get:
c = √41
c ≈ 6.4
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What is the value of x?
34°
(-1/2 x) °
Answers
Answer:
The expression "34° (-1/2 x) °" can be simplified by multiplying 34° by the quantity (-1/2 x):
34° (-1/2 x) ° = (34°) * (-1/2 x)
To multiply two values with units, we can simply multiply the numerical parts and keep the units. Therefore, we get:
(34°) * (-1/2 x) = -17x°
So the value of "34° (-1/2 x) °" is simply -17x°.
Autumn's Pumpkin Patch started the day with 432 pumpkins, each priced at $5. Most of
the pumpkins sold. At the end of the day, there were only 129 pumpkins left. How much
money did the pumpkin patch make today?
Answers
Answer:
It's very simple you just subtract 432 and 129. And you get 303. Then you just multiple 303 by 5 and you get 1515.
1515