Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.
How to calculate the valueTo find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.
To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).
This gives us:
1 part of the ratio = 1225 / 35 = 35
To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.
For the part that corresponds to 8, we have:
8 parts of the ratio = 8 x 35 = 280 items
For the part that corresponds to 27, we have:
27 parts of the ratio = 27 x 35 = 945 items
Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.
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Please help me solve these question(giving 50 points)
The restrictions on the polynomial expression [tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex] are at x = -5, -2, 1 and 6
Simplifying the expressionFrom the question, we have
[tex]\frac{27x^2y^3}{45x^4}[/tex]
Divide the variables
So, we have
[tex]\frac{27y^3}{45x^2}[/tex]
Divide 27 and 45 by 9
So, we have
[tex]\frac{3y^3}{5x^2}[/tex]
Hence, the solution is [tex]\frac{3y^3}{5x^2}[/tex], x ≠ 0
The simplest form of a rational expressionGiven that
[tex]\frac{x + 2}{x^2 - 5x - 14}[/tex]
Factorize the numerator
So, we have
[tex]\frac{x + 2}{(x + 2)(x - 7)}[/tex]
Divide
[tex]\frac{1}{x - 7}[/tex]
So, the solution is [tex]\frac{1}{x - 7}[/tex] , where x ≠ 7
The possible functionThe hole is given as (2, 1/3)
This means that the graph is undefined at (2, 1/3)
One possible equation from the list of options is
[tex]f\left(x\right)\:=\:\frac{x\:-\:2}{x^2\:-\:x\:-\:2}[/tex]
Restrictions on the polynomialThe expression is given as
[tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex]
The restrictions on the polynomial is the domain
When solved graphically, we have the restrictions to be at x = -5, -2, 1 and 6
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Let a =⟨–7, 3⟩ and b =⟨–2, –12⟩, and c = a + b. What is the magnitude and direction angle of c?
Answer: direction angle of c is pi/4.
Step-by-step explanation: We can find c by adding the corresponding components of a and b:
c = a + b = ⟨–7, 3⟩ + ⟨–2, –12⟩ = ⟨–9, –9⟩
To find the magnitude of c, we can use the formula:
|c| = sqrt(c1^2 + c2^2)
where c1 and c2 are the x- and y-components of c, respectively. In this case, we have:
|c| = sqrt((-9)^2 + (-9)^2) = sqrt(162) = 9sqrt(2)
To find the direction angle of c, we can use the formula:
theta = atan(c2 / c1)
where theta is the angle between the positive x-axis and the vector c. In this case, we have:
theta = atan((-9) / (-9)) = atan(1) = pi/4
So the direction angle of c is pi/4.
Therefore, the magnitude of c is 9sqrt(2) and the direction angle of c is pi/4.
I don't know this I've tried but I just don't know.
Answer:the median is Q2 aka 105
Step-by-step explanation:
Angle & segment relationship
Area & Arc Length
Answer:
x = 4
Step-by-step explanation:
given 2 secants drawn from an external point to the circle, then the product of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is
x(x + 4x) = 8(8 + 2)
x(5x) = 8(10)
5x² = 80 ( divide both sides by 5 )
x² = 16 ( take square root of both sides )
x = [tex]\sqrt{16}[/tex] = 4
A surge function is a function of the form
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.
1Tarko, Olta (2021) ”Surge Functions and Drug Interactions,” Undergraduate Journal of Mathematical
Modeling: One + Two: Vol. 12: Iss. 1, Article 7
Need help on this please
Answer:
Step-by-step explanation:
(-50, -20), (-60, 40)
(40 + 20)/(-60 + 50) = 60/-10= -6
y - (-20) = -6(x - (-50))
At how many square feet will both companies be at the same amount
If the yard is 2000 feet², both companies will charge the same price.
What is amount?In mathematics, the word "amount" is a broad one that refers to the size or quantity of something, typically given as a numerical value.
It can be used in a number of circumstances where there is a concern with money, measurements, or the quantity of an item.
We must assume both organisations' expenses to be equal and then solve for the yard size to determine the point at which their costs are equal.
Let's assume that x is the yard size at which expenses are equal.
7.5x + 24.5 = 16x + 23.5
When we simplify this equation, we obtain:
0.5x = 1
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Suppose that the value of a stock varies each day from $9.82 to $26.17 with a uniform distribution. Find the third quartile; 75% of all days the stock is below what value? (Enter your answer to the nearest cent.)
The third quartile if the distribution is $22.08.
How to find the third quartileTo find the third quartile, we need to find the value of the stock that separates the top 25% of days from the bottom 75%.
Since the distribution is uniform, we can find the third quartile by taking 75% of the range and adding it to the minimum value.
The range of the stock is:
$26.17 - $9.82 = $16.35
75% of the range is:
0.75 x $16.35 = $12.26
Adding this to the minimum value gives us the third quartile:
$9.82 + $12.26 = $22.08
So the third quartile is $22.08.
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If (x -1) is a factor of the polynomial f(x) = 4x²- 4x² - x - K, where K is a Constant.
1. What is the Value of K?
2. What are the roots of the equation
Answer:
If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:
f(x) = (x-1)(ax + b)
where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:
f(x) = (x-1)(ax + b) = 4x² - 4x - K
Expanding the left side of the equation, we get:
ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K
Now we can equate the coefficients of the like terms on both sides of the equation.
The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:
a = 4
The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:
b - a = -4
Substituting a=4, we get:
b - 4 = -4
Solving for b, we get:
b = 0
So the polynomial can be written as:
f(x) = (x-1)(4x + 0) = 4x² - 4x
Therefore, K = 0.
To find the roots of the equation, we need to set f(x) = 0 and solve for x:
4x² - 4x = 0
Factor out 4x:
4x(x - 1) = 0
So the roots of the equation are x = 0 and x = 1.
Is (-2, 10) a solution to this system of equations?
y = -4x + 2
y = -6x - 2
yes
no
Answer:
Yes
Step-by-step explanation:
(-2, 10)
x = -2
y = 10
y = -4x + 2
Substitute or plug in the x and y values
10 = -4(-2) + 2
Multiply(remember a negative times a negative is a positive)
10 = 8 + 2
Add
10 = 10
Because ten is equal to ten (-2, 10) is a solution for this part
Now take your next equation and repeat the same steps
y = -6x - 2
10 = -6(-2) - 2
10 = 12 -2
10 = 10
(-2, 10) is a solution to this system of equations
Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Felipe trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
Plan A lasts for 2/7 hours or approximately 17.14 minutes, and Plan B lasts for 9/7 hours or approximately 1 hour and 17.14 minutes.
What is an equation example?In algebra, the definition of an equation in its simplest form is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two expressions separated by an equal sign.
Let's say plan A takes x hours and plan B takes y hours.
Based on the given data, we can create two equations:
Monday: 6x + 5y = 7
Tuesday: 2x + 3y = 3
We can solve this system of equations by elimination or substitution.
Eliminating, we can multiply the second equation by two and subtract it from the first equation:
(6x + 5 y) - 2 (2x + 3y) = 7 - 2 (3)
Simplifying this, we get:
2x - y = 1
Using substitution, we can solve an equation in one variable and replace it with another equation:
From the first equation we can solve for x:
6x + 5y = 7
6x = 7-5 years
x = (7-5 years) / 6
Substituting this into the second equation, we get:
2 ((7-5 years) / 6) + 3 y = 3
Simplifying this, we get:
7 y = 9
y = 9/7
Now that we know y, we can substitute it back into both equations to solve for x:
6 x + 5 (9/7) = 7
Simplifying this, we get:
x = 2/7
Therefore, Plan A takes 2/7 hours, or approximately 17.14 minutes, and Plan B takes 9/7 hours, or approximately 1 hour and 17.14 minutes.
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what are 3 differnt types of rocks
Answer:
Step-by-step explanation:
sedimentary, igneous, metamorphic
Answer: sedimentary, igneous, metamorphic.
have an amazing day and crush that homework/class!
branliest?
Find the surface area of the figure (on photo)
Answer:
208
Step-by-step explanation:
4*4(2)+11*4(2)+11*4(2)=208
Find the small squares.
4^2+4^2=32
4*11*4=176
176+32=208
ANSWER ASAPP!!!!!!
AAAA
To purchase $14,500 worth of restaurant equipment for her business, Debra made a down payment of $1300 and took out a business loan for the rest. After 2 years of paying monthly payments of $585.04, she finally paid off the loan.
(a) What was the total amount Debra ended up paying for the equipment (including the down payment and monthly payments)?
(b) How much interest did Debra pay on the loan?
The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60
(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.
Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200
Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments
Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]
Total amount paid = $1,300 + $13,200 + $14,041.60
Total amount paid = $28,541.60
Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.
(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.
Total interest paid = Total amount paid - Total amount borrowed - Down payment
Total interest paid = $28,541.60 - $13,200 - $1,300
Total interest paid = $14,041.60
Therefore, the amount of interest Debra paid on the loan was $14,041.60.
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A cow is tethered to one corner of a square barn, 8 feet by 8 feet, with a rope 130 feet long. What is the maximum grazing area for the cow?
The maximum grazing area for the cow is approximately 53,343.08 square feet.
How to Find the maximum Grazing Area?The maximum grazing area for the cow can be found by imagining a circle with radius equal to the length of the rope (130 feet) centered at the corner of the barn where the cow is tethered. The grazing area is the portion of the circle that lies outside the barn.
Since the barn is 8 feet by 8 feet, it covers a square area of 64 square feet. The radius of the circle is 130 feet, so the area of the circle is π(130)^2 square feet.
To find the maximum grazing area, we need to subtract the area of the barn from the area of the circle.
Area of circle = π(130)^2 square feet = 53,407.08 square feet
Area of barn = 64 square feet
Maximum grazing area = Area of circle - Area of barn
= 53,407.08 - 64
= 53,343.08 square feet (rounded to two decimal places)
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Pls help! Mr Douglass trains a group of student athletes. He wants to know how they are improvising in the number of sit ups they can do. The following dot plots show the number of sit ups each student was able to do last month and this month.
By how much did the mean number of sit ups increase from last month to this month?
7. Which statement is NOT part of a debt-reduction plan? a. Lower debts with the highest interest rates. b. Slow or eliminate credit card spending c. Only pay the minimum amount when possible. d. Use an online debt management calculator.
Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
–2p – 17 = 3(p – 5) {–2}
Starting with the original equation:
-2p - 17 = 3(p - 5)
Distributing the 3 on the right side:
-2p - 17 = 3p - 15
Subtracting 3p from both sides:
-5p - 17 = -15
Adding 17 to both sides:
-5p = 2
Dividing by -5:
p = -2/5
Now, we can substitute this value of p back into the original equation and check if it is a solution:
-2(-2/5) - 17 = 3((-2/5) - 5)
4/5 - 17 = 3(-27/5)
-136/5 = -81/5
The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.
Hope this helps :)
Select all statements that are true.
Answers:
A, B, D, E
Nearly everything except choice C is true.
====================================================
Explanation:
Choice A is true because sine = opposite/hypotenuse.Choice B is true as well because cosine = adjacent/hypotenuseTangent is opposite/adjacent. The 4/9 should be 9/4. Therefore, choice C is false. If beta was theta, then tan(theta) = 4/9 would be true.Choice D is true because of the pythagorean theorem a^2+b^2 = c^2.Choice E is true because tan = opposite/adjacent, and the 9 and 4 are in the correct order (see choice C).Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
The equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
How to solveWe can observe from the table that the number of books collected increases by 10 for each week.
Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:
b = mw + c
where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).
The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):
10 = 10 * 1 + c
c = 0
Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):
b = 10w + 0
b = 10w
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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 70 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Therefore , the solution of the given problem of percentage comes out to be 14 gallons of the first brand and 56 gallons of the second brand must be utilised.
What is percentages?In statistics, a figure or metric than may be presented as a percentage or 100 is denoted by the abbreviation "a%". Another unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this. Additionally, there are no indications or predetermined ratios of any component to the whole. Numbers are effectively integers since they frequently add up to 100.
Here,
Let's write "x" for the first brand's (35% pure antifreeze) number of gallons and "y" for the second brand's (60% pure antifreeze) number of gallons.
Given:
70 gallons of mixture are required in total.
Desired antifreeze content in the combination is 55%
Based on the information provided, we can construct the following system of equations:
=> Equation 1: x + y = 70
=> Equation 2: 0.5*70 = 0.55x + 0.60y
=> x = 70 - y
=> 0.35(70 - y) + 0.60y = 0.55 * 70
=> 24.5 - 0.35y + 0.60y = 38.5
=> 0.25y = 14
=> y = 56
=> x = 70 - 56
=> x = 14
In order to get 70 gallons of a mixture that contains 55% pure antifreeze, 14 gallons of the first brand and 56 gallons of the second brand must be utilised.
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Prism A is a dilation of Prism B. The height of Prism A is 6
Bis
31/12 ₁²
ft.
61/1/21 ft, and the volume of Prism A is
What is the volume of Prism B?
Enter your answer as a mixed number in simplest form by filling in the boxes.
ft
872/1 T
ft. The height of Prism
S
Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.
How should mixed numbers be done step-by-step?Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.
We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):
We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:
cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²
Using the scale factor equation for height, we get:
k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31
Using the scale factor equation for cross-sectional area, we get:
k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)
Solving for the cross-sectional area of Prism B, we get:
cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]
Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:
Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]
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(07.03 MC)
Given the function h(x)=-2√x +3-1, which statement is true about h(x)?
Given the function h(x) = -2√(x + 3) - 1, the statement that is true about h(x) include the following: B. the function is decreasing on the interval (-3, ∞).
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.
By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the interval (-3, ∞).
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1. A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 40 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot.
the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
How to solve the question?
To find the actual area of the base of the fountain, we need to convert the measurements from the blueprint to the actual measurements.
First, we need to find the radius of the circular base. The diameter of the base is given as 40 centimeters on the blueprint, so the radius is half of that, or 20 centimeters.
Next, we need to convert the scale of the blueprint from centimeters to feet. The scale is given as three centimeters to four feet, which can be simplified to a ratio of 3:4. To convert from centimeters to feet, we need to multiply by a conversion factor of 1 foot/30.48 centimeters, since there are 30.48 centimeters in a foot.
So, to find the actual radius of the circular base in feet, we multiply the blueprint radius (20 centimeters) by the conversion factor:
20 centimeters * (1 foot/30.48 centimeters) = 0.656168 feet
Now that we have the actual radius of the circular base, we can find the actual area of the base. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the actual radius we just found, we get:
A = π(0.656168 feet)^2 = 1.34977 square feet
Therefore, the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
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The length of a rectangle is 2 inches more than 2 times the width. If the area of the rectangle is 40
square inches, find the length and the width.
The length of the rectangle is 10 inches and the width is 4 inches.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Let's assume that the width of the rectangle is "x" inches.
From the given information, we can write an equation for the length "L" in terms of the width "x":
L = 2x + 2
We also know that the area of the rectangle is 40 square inches:
A = L * x = 40
Substituting the expression for "L" in terms of "x" into the area equation, we get:
(2x + 2) * x = 40
Expanding the left-hand side of the equation and simplifying, we get:
2x² + 2x - 40 = 0
Dividing both sides by 2, we get:
x² + x - 20 = 0
This is a quadratic equation that can be factored:
(x + 5)(x - 4) = 0
The solutions are x = -5 and x = 4. Since the width of the rectangle cannot be negative, the only valid solution is:
x = 4
Substituting this value for "x" into the equation for "L", we get:
L = 2x + 2 = 2(4) + 2 = 10
Therefore, the length of the rectangle is 10 inches and the width is 4 inches.
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What is 5a^2b + 15ab^2 factories fully
Answer:
[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]
[tex]5ab(a + 3b)[/tex]
NO LINKS!! URGENT HELP PLEASE!!!
Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB.
A(-6, 4), B(14, -12)
Answer:
The perpendicular bisector of a line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.
To find the equation of the perpendicular bisector of segment AB, we can follow these steps:
Find the midpoint M of AB. The coordinates of M are:M = ( (x1 + x2)/2, (y1 + y2)/2 )
where A = (x1, y1) and B = (x2, y2).
In this case, A = (-6, 4) and B = (14, -12), so the coordinates of M are:M = ( (-6 + 14)/2, (4 - 12)/2 ) = (4, -4)
Find the slope m of AB. The slope of AB is:m = (y2 - y1) / (x2 - x1)
In this case, the slope of AB is:m = (-12 - 4) / (14 - (-6)) = -16/20 = -4/5
Find the slope of the line that is perpendicular to AB. The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So, the slope of the line that is perpendicular to AB is:m_perp = -1/m
In this case, the slope of the line that is perpendicular to AB is:m_perp = -1/(-4/5) = 5/4
Use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. The point-slope form of the equation of a line is:y - y1 = m(x - x1)
We can use the midpoint M as the point (x1, y1) and the slope m_perp as the slope m:y - (-4) = (5/4)(x - 4)
Simplifying, we get:
y + 4 = (5/4)x - 5
Moving terms around, we get:(5/4)x - y - 9 = 0
So, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB is:
(5/4)x - y - 9 = 0
DETERMINE IF THE SEQUENCES ARE ARITHMETIC, IF SOFIND THE COMMONDIFFERENCE, THE 52 TERM, AND EXPLICIT FORMULA
31, -69, -169, -269
The common difference of the sequence is - 100.
The explicit formula of the sequence is 131 - 100n.
The 52 term of the sequence is -5069.
How to find the explicit formula of a sequence?Let's find the explicit formula of the arithmetic sequence as follows:
31, -69, -169, -269
We will find the common difference and the 52 terms.
Therefore,
a + (n + 1)d = nth term
where
a = first termd = common differencen = number of termsTherefore,
d = common difference = -69 - 31 = - 100
Therefore,
nth term = 31 + (n - 1)-100
nth term = 31 - 100n + 100
nth term = 131 - 100n
Let's find the 52 term
Hence,
52 term = 131 - 100(52)
52 term = 131 - 5200
52 term = -5069
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THE UNITE
VENOCH
Suppose you buy a $1000 bond with a 4.3% coupon that matures in 30 years.
1. First, how much do you earn off your bond every 6 months?
Type answer here...
SUBMIT
Every six months, you will receive $21.50 back from your bond.
The 4.3% coupon is the annual interest rate, which is paid semi-annually (twice a year).
To find the amount earned every 6 months, we need to divide the annual interest rate by 2:
(4.3% / 2) = 2.15%
Next, we need to calculate the dollar amount earned every 6 months. To do this, we need to find 2.15% of the bond's face value:
2.15% of $1000 = $21.50
Therefore, you will earn $21.50 off your bond every 6 months.
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