The average rate of change of the function, [tex]f(x) = 10\sqrt[3]{x}-5[/tex] over the interval of x=8 to x=64 is calculated as: 0.357.
How to Find the Average Rate of Change of a Function?The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
The average rate of change = f(b) - f(a) / b - a.
Given the following:
The function is: [tex]f(x) = 10\sqrt[3]{x}-5[/tex]
Interval is: x = 8 to x = 64
Therefore:
a = 8
b = 64
f(a) = f(8) =
[tex]f(x) = 10\sqrt[3]{8}-5\\\\f(x)=10*(2)-5\\\\f(x)=20-5\\\\f(x)=15[/tex]
f(a) = f(8) = 15
f(b) = f(10)
[tex]f(x) = 10\sqrt[3]{64}-5\\\\f(x)=10*(4)-5\\\\f(x)=40-5\\\\f(x)=35[/tex]
f(b) = f(64) = 35
Therefore:
Average rate of change =
[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{35-15}{64-8} \\\\=\frac{20}{56} \\\\=0.357[/tex]
Learn more about average rate of change on:
brainly.com/question/11627203
#SPJ1
Part III: Use the point given for line p and the slope you found in Part II to write an
equation for line p in point-slope form: Y-Y₁ = m(x-x₁). (1 point)
The slope of line q is equal to 3.
The slope of line q is equal to -1/3.
An equation for line p in point-slope form is y + 5 = -1/3(x - 6).
An equation for line p in slope-intercept form is y = -1/3x - 3.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c ....equation 1.
Where:
m represents the slope.x and y are the points.c represents the y-intercept or initial value.From the information provided, we have the following linear equation in slope-intercept form for line q:
y = 3x + 5 ....equation 2.
By comparing equation 1 and equation 2, we can logically deduce the following:
Slope (m) = 3
Since line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q;
m₁ × m₂ = -1
3 × m₂ = -1
Slope, m₂ of line p = -1/3.
At data point (6, -5), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = -1/3(x - 6)
y + 5 = -1/3(x - 6)
By simplifying further, the slope-intercept form is given by;
y + 5 = -1/3(x - 6)
3y + 15 = -x + 6
3y = -x - 9
y = -1/3x - 3
Read more on slope here: https://brainly.com/question/27534065
#SPJ1
Complete Question:
Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.
Find the slope of line q.
Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)
Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)
Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b.
find the value of x. SIMPLEST RADICAL FORM
Answer:
Step-by-step explanation:
56
The lines represented by the equations 9 � − 6 � = − 18 9y−6x=−18 and 3 � − 2 � = 24 3y−2x=24 are
The lines are parallel because they have the same slope in the equation of lines
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first equation be 9y - 6x = -18 be equation (1)
Let the second equation be 3y - 2x = 24 be equation (2)
On simplifying the equation , we get
Adding 6x on both sides of the equation , we get
9y = 6x - 18
Divide by 9 on both sides of the equation , we get
y = ( 2/3 )x - 2
So , the slope of line 1 is m = 2/3
And , for the second equation ,
Adding 6x on both sides of the equation , we get
3y = 2x + 24
Divide by 3 on both sides of the equation , we get
y = ( 2/3 )x + 8
So , the slope of line 2 is m = 2/3
Since the slopes of the lines are same , they are parallel lines
Hence , the equation of lines are solved
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ9
The complete question is :
The lines represented by the equations 9y - 6x = -18 and 3y - 2x = 24 are
a) perpendicular
b) parallel
c) none of the above
suppose [tex]\frac{x^{2} }{25} +\frac{y^{2} }{64} =1[/tex] and y(3)=6.40000. find y^(derivative sign) (3) by implicit differentiation.
Answer:
To find y'(3), we need to use implicit differentiation to differentiate both sides of the equation with respect to x and then solve for y'.
Differentiating both sides with respect to x, we get:
(2x/25) + (2y/64) * (dy/dx) = 0
Now we can solve for dy/dx:
(2y/64) * (dy/dx) = -(2x/25)
dy/dx = -(2x/25) / (2y/64)
dy/dx = -32x/25y
To find y'(3), we need to substitute x=3 and y=6.4 into the expression for dy/dx:
y'(3) = -32(3)/(25)(6.4)
y'(3) = -0.3
Therefore, the value of y'(3) is -0.3
The value of y'(3) in (2x/25) + (2y/64) = 1, is - 0.3
What is implicit differentiation?Finding the derivative of an implicit function is the process of implicit differentiation.
In other words, this method is utilized to discover the implicit derivative.
To find y'(3), After differentiating both sides of the equation with respect to x using implicit differentiation, we must next solve for y'.
Differentiating both sides with respect to x we get,
(2x/25) + (2y/64)×(dy/dx) = 0
Solving for dy/dx
(2y/64)×(dy/dx) = -(2x/25)
dy/dx = -(2x/25) / (2y/64)
dy/dx = -32x/25y
To find y'(3), Replacing x=3 and y=6.4 into the expression for dy/dx:
y'(3) = -32(3)/(25)(6.4)
y'(3) = -0.3
Therefore, the value of y'(3) is - 0.3
learn more about implicit differentiation here :
https://brainly.com/question/11887805
#SPJ1
Evaluate 4y ÷ x if x = 2 and y =5
Which problem situation could be solved using the open sentence below?
24 - k = ?
A.Mrs. Garcia took 24 science papers home to grade. She graded k science papers before dinner. How many science papers did she have to grade after dinner?
B.Mrs. Garcia took 24 science papers and k reading papers home to grade. How many papers did she have to grade?
C.Mrs. Garcia had k science papers to grade. She now has 22 left to grade. How many papers did she grade already?
D. Mrs. Garcia has 22 science papers and 22 reading papers to grade. If she has k papers to grade in all, how many papers does she have to grade?
-5 < 9 -6x???????????
Answer:
7/3>x
Step-by-step explanation:
-5<9-6x
subtract 9 from both sides
-14<-6x
divide by 6
14/6<x
simplified its 7/3<x
but since we divided by a negative we switch the sign
final answer is 7/3>x
the number is divisible by 6, 8, and 10 and has no repeated digits
120 is the number divisible by 6, 8, and 10.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The common multiples to 6, 8, and 10.
6 x 20 = 120
8 x 15 = 120
10 x 12 = 120
So,
120 is divisible by 6, 8, and 10.
Thus,
120 is the number.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ9
Which is true about an equilateral triangle?
no sides have equal measure
one angle is obtuse
all angle measures are equal
only two sides have equal measure
Answer: all angles are equal
Step-by-step explanation:
in a equilateral triangle all angles will be 60°
Suppose x is a normally distributed random variable with μ=10 and σ=2. Find each of the following probabilities.
a. P(x ≥ 12.5) b. P(x ≤ 9) c. P(10.88 ≤ x ≤ 15.3) d. P(4.72 ≤ x ≤ 12.46)
The value of the probabilities are
a. P(x ≥ 12.5) is 6.68%
b. P(x ≤ 9) is 2.28%
c. P(10.88 ≤ x ≤ 15.3) is 61.38%
d. P(4.72 ≤ x ≤ 12.46) is 99.45%
Probability is the measure of the likelihood of an event occurring. It is a way of quantifying uncertainty and predicting the likelihood of an outcome. In this question, we will use the normal distribution to calculate probabilities.
The mean is the center of the distribution, and the standard deviation measures the spread of the distribution.
a. P(x ≥ 12.5):
Using a standard normal distribution table, we find that the area to the right of 12.5 is 0.0668. This means that the probability of x being greater than or equal to 12.5 is 0.0668 or 6.68%.
b. P(x ≤ 9):
Using a standard normal distribution table, we find that the area to the left of 9 is 0.0228. This means that the probability of x being less than or equal to 9 is 0.0228 or 2.28%.
c. P(10.88 ≤ x ≤ 15.3):
Using a standard normal distribution table, we find that the area to the left of 15.3 is 0.9987 and the area to the left of 10.88 is 0.3849. Therefore, the area between 10.88 and 15.3 is
=> 0.9987 - 0.3849 = 0.6138.
This means that the probability of x being between 10.88 and 15.3 is 0.6138 or 61.38%.
d. P(4.72 ≤ x ≤ 12.46):
Using a standard normal distribution table, we find that the area to the left of 12.46 is 0.9946 and the area to the left of 4.72 is 0.0001. Therefore, the area between 4.72 and 12.46 is
=> 0.9946 - 0.0001 = 0.9945.
This the probability of x being between 4.72 and 12.46 is 0.9945 or 99.45%.
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
Which of the following is/are assumptions for linear regression? Please select all that apply. It's possible that there is only one correct answer. Y| X = x (the conditional distribution of Y given X = x) is a normal distribution. X and Y are independent. The errors e1,e2, e; have the same variance. The expectation of each error e; is O
As per the information provided, option B) The errors e1,e2, e; have the same variance is the assumptions for linear regression.
Regression analysis is a linear technique used to model the relationship between a scalar response and/or one or more explanatory variables, also known as the dependent and independent variables here.
Simple linear regression and multiple linear regression are two terms used to describe the process when there is only one explanatory variable present. This statement is different from multivariate linear regression, which thus predicts multiple correlated dependent variables as opposed to a single scalar variable present.
The first regression analysis technique that attracted a lot of research attention and was frequently applied in practical situations was linear regression. This is because models with linear rather than non-linear dependence on their unknown parameters are easier to fit, and it is also easier to determine the statistical properties of the resulting estimators.
To learn more about linear regression: https://brainly.com/question/29665935
#SPJ4
I will give brainliest and ratings if you get this correct
Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].
What is derivative?Derivatives refers to the instantaneous rate of change of a quantity with respect to the other. That is, the amount by which a function is changing at one given point.
Given, [tex]x=b-\sqrt{ap-c}[/tex]
To find [tex]\frac{dx}{dp}[/tex]:
⇒[tex]\frac{dp(b-\sqrt{ap-c)}}{dx}[/tex]
⇒0- [tex]\frac{1}{2} (ap-c)^{-1/ 2} .\frac{d}{dp}(ap-c)[/tex]
⇒[tex]-\frac{ a.dp/dp+\frac{d}{dp}(-c) }{2\sqrt{ap-c} }[/tex]
⇒[tex]-\frac{a}{\sqrt{ap-c} }[/tex]
Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].
Learn more about derivative here:
https://brainly.com/question/29144258
#SPJ1
PLEASE HELP FAST!!!! IT IS URGENT!!!! The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the level that the mean salary for the baseball players on the East Coast is different from $3.2 million? What hypotheses should the analyst use to conduct a significance test?
The hypothesis tested are given as follows:
[tex]H_0: \mu = 3.2, H_a: \mu \neq 3.2[/tex]
What are the null and alternative hypothesis?The claim for this problem is given as follows:
"The mean salary for the baseball players on the East Coast is different from $3.2 million".
At the null hypothesis, we test if the claim is false, that is, if the mean salary is equals to 3.2 million, hence:
[tex]H_0: \mu = 3.2[/tex]
At the alternative hypothesis, we test if the claim is true, that is, if the mean salary is different of 3.2 million, hence:
[tex]H_a: \mu \neq 3.2[/tex]
The [tex]\mu[/tex] symbol, without the bar, is used, as we are testing for the population mean, not sample mean, hence the first option is the correct option.
More can be learned about the test of an hypothesis at brainly.com/question/13873630
#SPJ1
1) A system of equations is shown. What is the solution to the system of equations? Show all work. (3 points) 2 + 2 = 17 {4 − = 25
The value of x for the system of equations will be x=6.7.
What is a system of equations?
A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.
Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.
Multiply the second equation by 2 and subtract from the first equation,
2x+2y=17.
8x-2y=50.
10x=67.
x= 67/10
x = 6.7.
Therefore, the value of x for the system of equations will be x=6.7.
\
-gress:
The movement of the progress bar may be uneven because questions can be worth more or less (including z
Multiply: 4.000329 × 1000
O 400.0329
O 4,000.329
O40.00329
O 4.329
The product of 4.000329 × 1000 is the second option 4,000.329.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have to find the product of 4.000329 × 1000.
When a number is being multiplied by (10)ⁿ, 'n' number of zeroes will be added to the right of the number.
If the number is decimal number, decimal point is being shifted n digits to the right.
The question here is 4.000329 × 1000.
4.000329 × 1000 = 4.000329 × (10)³
Decimal point is shifted three digits to the right.
4.000329 × (10)³ = 4,000.329
Hence the correct option is B. 4,000.329.
Learn more about Multiplication here :
https://brainly.com/question/14956782
#SPJ1
A radio station broadcasts a signal over an area with a 45-mile radius. What is the area of the region that receives the radio signal to the nearest tenth?
Rounded to the nearest tenth, the area of the region that receives the radio signal is approximately 6,366.2 square miles.
What is the region's signed area?Consider a plane region described by a xy-plane graph. The signed area of the region is defined as the area of the graph on or above the x-axis. The negative area of the graph is defined as the area below the x-axis.
The formula A = πr² gives the area of a circle with radius r. In this case, the radio station broadcasts over a 45-mile radius, so the region that receives the radio signal is:
A = π(45)²
A ≈ 6,366.2 square miles
The area of the region that receives the radio signal is approximately 6,366.2 square miles when rounded to the nearest tenth.
To know more about Area visit:
brainly.com/question/29093313
#SPJ1
6. Write the unit rate for the following: a) Kate sews 100 dresses in a 20 day month. b) Kim runs 5 km in 30 minutes.
a) The unit rate of Kate's sewing productivity can be found by dividing the number of dresses by the number of days:
Kate sews 100 dresses in 20 days.
The unit rate is 100 dresses / 20 days = 5 dresses per day.
b) The unit rate of Kim's running speed can be found by dividing the distance by the time:
Kim runs 5 km in 30 minutes.
The unit rate is 5 km / 0.5 hour = 10 km/hour.
Therefore, the unit rate for Kate's sewing productivity is 5 dresses per day, and the unit rate for Kim's running speed is 10 km/hour.
the base of a triangle is 8 ft less than its height. if the area is 120 ft2, find the base and the height of this triangle. use an equation to solve this problem.
The height of the triangle is 20 and base of the triangle is 12.
"Information available from the question"
The base of a triangle is 8 ft. less than its height.
If the area is 120 [tex]ft^2.[/tex]
We have to find the base and the height of this triangle.
Now, According to the question:
Let the height be x then if the base is 8 ft. less, then the base is x - 8.
We know that:
Area of the triangle is : (b × h)/2
Area of the triangle is : (x (x - 8)) /2
120 [tex]ft^2[/tex] = ([tex]x^{2} -8x[/tex])/2
240 = [tex]x^{2} -8x[/tex]
[tex]= > x^{2} -8x-240=0[/tex]
For solving equation, Use the quadratic formula :
x = (-b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a
a = 1
b = -8
c = -240
x = (-(-8) ± [tex]\sqrt{(-8)^2-4.1(-240)})/2.1[/tex]
By solving, we get
x = (8 ± 32)/2
We get the values :
x = 20 and x = -12
We know x = −12 can't be a solution as length can't be negative.
Base = x - 8
Base = 20 - 8
Base = 12
Hence, The height of the triangle is 20 and base of the triangle is 12.
Learn more about Triangle at:
https://brainly.com/question/16970122
#SPJ4
stuck on this question plsss helpp
Answer:
2 vases of lilacs
3 vases of irises
Step-by-step explanation:
7( lilacs ) × 2( vases) = 14 flowers
5( irises ) × 3( vases) = 15 flowers
14 + 15 = 29 flowers
This figure was created by using two semi-circles and one rectangle. Find the area of the figure in square inches.
The area of the figure is 596.625 in².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
We will consider the figure to have a rectangle and a circle.
Rectangle:
Length = 28 in
Breadth = 15 in
Area = 28 x 15 = 420 in²
Semicircle:
Diameter = 15 in
Radius = 7.5 in
Area = 1/2 πr²
= 1/2 x 3.14 x 7.5²
Area = 176.625/2
Area = 88.3125
There are two semicircles so,
= 2 x 88.3125
= 176.625 in²
Now,
Area of the figure.
= 420 + 176.625
= 596.625 in²
Thus,
596.625 in² is the area of the figure.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
Anthony painted 2triangles of the same size on the top corners of his house flag for sports day. What is the total area of both triangles?
The total area of both triangles is the product of the height and base of the flag.
What is a triangle?The connecting of three noncolinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.
Given, Anthony painted 2triangles of the same size on the top corners of his house flag for sports day.
We are aware of A parallelogram can be divided into two comparable triangles by dividing it along its diagonal.
A planar figure with opposite sides that are parallel and of equal length is called a parallelogram.
Since the area of a parallelogram is equal to its base times its height, the combined area of the two triangles will be the same.
learn more about parallelograms here :
https://brainly.com/question/29147156
#SPJ9
What is D(50) − (D(15) ∪ D(20))?
The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).
The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.
What is Set Theory?Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.
In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.
The union of sets, represented by the symbol ∪, is the operation that gives you the set of all elements that are in at least one of the sets being considered.
Learn more about Set Theory:
https://brainly.com/question/16823768
#SPJ1
Use the expression (8x + 2) + (-9x + 7).
a. Find the sum.
b. Reasoning Explain how you know when to combine terms with variables.
Answer:
-x + 9
Step-by-step explanation:
Addition of expression:a)
8x + 2 + (-9x + 7) = 8x + 2 - 9x + 7
= 8x - 9x + 2 + 7
= -x + 9
b) We can combine like terms. Like terms have same variable with same power. Here 8x and (-9x) have same variable 'x'. so, combine the coefficients of the like terms which give (-1).
8x - 9x = -1
Combine the constants. 2 + 7= 9
A group of 6 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: Queen of Clubs, 10 of Hearts. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.)
Recall, while using your calculator, that E10 means to move the decimal place 10 places to the righ
a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.
b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.
Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52
Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,
a) Number of cards are in the deck that are not one of the designated cards
= 52 - 2 = 50
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.
b) Number of cards are in the deck = 52
Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35
Thus total possible number of ways
= ⁵²C₃₅ = 21945588357420
Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards
= 2250829575120/21945588357420
= 0.10256410256
Hence, required probability is 0.1026.
To learn more about probability , visit :
https://brainly.com/question/13604758
#SPJ4
takeAssignment/takeAssignment Main.do?inprogress-true
Sandpiper Company has 25,000 shares of cumulative preferred 2% stock, $150 par and 50,000 shares of $15 par common stock. The following amounts were
distributed as dividends:
20Y1
2012
2013
$150,000
30,000
225,000
Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places. If an answer is zero, enter "0".
Preferred Stock
(dividends per share)
2011
2012
2013
Feedback
X
Common Stock
(dividends per share)
Check My Work
X
Check My Work
Determine what amount of current dividends that preferred stock should receive per year.
< ✰ ✰ O
Keep in mind that the question is asking for a dividend per share for each year and class of stock, rather than the total amount to be distributed to
each class of stock.
Previous
a) The determination of the dividends per share for the cumulative preferred and common stock for each year is as follows:
Preferred StockDividends per share
2011 $3.00
2012 $1.20
2013 $4.80
Common StockDividends per share
2011 $1.50
2012 $0
2013 $2.10
b) The determination of the amount of current dividends that preferred stock should receive per year is $75,000.
What is cumulative preferred stock?Cumulative preferred stock is a special class of preferred stock that enjoys cumulative dividends.
Cumulative dividends imply that any year when sufficient dividends are not declared, the arrears are carried forward to subsequent years.
It is the opposite of non-cumulative preferred stock.
On the other hand, the common stockholders can only receive dividends after the preferred stockholders have been paid, including their cumulative dividends.
Cumulative Preferred Stock:Number of shares = 25,000
Dividend rate = 2%
Par value = $150
Total cumulative preferred stock = $3,750,000 (25,000 x $150)
Annual dividend = $75,000 ($3,750,000 x 2%)
Common Stock:Number of shares = 50,000
Par value = $15
Total common stock = $750,000 (50,000 x $15)
Preferred StockDividends Due (Dividends per share)
2011 $75,000 $3 ($75,000/25,000)
2012 $30,000 $1.2 ($30,000/25,000)
2013 $120,000 $4.8 ($120,000/25,000)
Common StockDividends Available (Dividends per share)
2011 $75,000 ($150,000 - $75,000) $1.50 ($75,000/50,000)
2012 $0 ($30,000 - $30,000) $0
2013 $105,000 ($225,000 - 120,000) $2.10 ($105,000/50,000)
Learn more about cumulative and non-cumulative preferred stocks at https://brainly.com/question/14971141.
#SPJ1
In the ratio of yellow marbles to blue marbles, 6:2, the quantities 6 and 2 are called?
The quantities 6 and 2 are called proportions
How to determine the name of the quantitiesFrom the question, we have the following parameters that can be used in our computation:
In the ratio of yellow marbles to blue marbles, 6:2,
This means that
Yellow : Blue = 6 : 2
Using the above as a guide, we have the following:
For every 6 yellow marbles, there are 2 blue marbles
This means that 6 and 2 are the proportions
Read more about ratio at
https://brainly.com/question/12535721
#SPJ1
For the following exercises, determine whether each of the following relations is a function_ 1.y =2x + 8 2. {(2, 1), (3,2), (-1,1), (0, -2)}
For the following exercises, evaluate the function f(x) = -3x2 + 2x at the given input: 3. f(-2) 4. f(a)
The value of the evaluated function f(x) = -3x² + 2x at
(i) f(-2) is -16 ;
(ii) f(a) is -3a² + 2a .
The Function is represented as : f(x) = -3x² + 2x ;
(i) We have to evaluate the above function at f(-2),
So, we substitute x = -2 into the function:
we get ;
⇒ f(-2) = -3(-2)² + 2(-2)
⇒ f(-2) = -12 - 4 = -16 .
So , f(-2) = -16 .
(ii) Next we have to evaluate f(a),
So , we substitute x = a into the function:
⇒ f(a) = -3a² + 2a
So , f(a) = -3a² + 2a .
Learn more about Function here
https://brainly.com/question/21870221
#SPJ4
The given question is incomplete , the complete question is
For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a) .
What is the y-intercept of the graph of y = 2.5*?
a. 2.5
b. 1
ΟΑ
О в
О с
OD
C. 0
d. -1
OT
Ü
Please select the best answer from the choices provided
Point of y-intercept is (0,1)
What is y-intercepts?In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.
Given the function is [tex]y=2.5^{x}[/tex]
y-intercept is the point where the graph of the function crosses the y-axis.
To find the point of y-intercept put x=0 in the given function, we get
if x=0 then [tex]y=2.5^{0}[/tex] ⇒ y=1.
The function crosses at the point 1 in the y-axis.
Hence, point of y-intercept is (0,1)
Learn more about y-intercepts here:
https://brainly.com/question/14180189
#SPJ9
C
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance (x) between the flagpoles is 12 ft.
The distance (y) from flagpole c to point s is 10 ft.
The height of flagpole a is 13.2 ft.
What is the height of flagpole c?
Show all your work.
The height of flagpole c is given as follows:
66 ft.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For each flagpole, the parameters are given as follow:
Flagpole a: Distance of 12 - 10 = 2 ft, height of 13.2 ft.Flagpole c: Distance of 10 ft, height of h ft.The triangles are similar, hence the proportional relationship to obtain the height of flagpole's c is given as follows:
2/10 = 13.2/h
Applying cross multiplication, the height is obtained as follows:
2h = 10 x 13.2.
h = 132/2
h = 66 ft.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.
The probability she pulls out a purple piece of candy would be 0.22.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is Sam's fathers collection.
We can write the equations for upstream and downstream as -
x - y = 7/2
x + y = 21/10
Solving the equations graphically -
{x} = 2.8
{y} = 0.7
In still water, the speed would be -
S = 3 - 0.7
S = 2.3 Km/h
Distance peddled upstream -
D = 2.8 x 3.5 = 9.8 Km
Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.
To solve more questions on functions & expressions, visit the link below
brainly.com/question/17613163
#SPJ1