The arena should be financed by selling $ 320 million in bonds and borrowing $ 480 million.
==========================================================
Work Shown:
x = amount (in millions of dollars) from bonds at 7% interest rate.y = amount (in millions of dollars) borrowed at 2% interest rate.Something like x = 27 means "27 million dollars of bonds were sold".
The variable x has the restriction of [tex]0 \le x \le 480[/tex] since $480 million is the ceiling for the bonds.
The variable y has the restriction of [tex]0 \le y \le 640[/tex] since $640 million is the ceiling for the money borrowed from the insurance company.
The two amounts, x and y, must add to 800 to represent the $800 million total that needs to be raised.
x+y = 800
y = 800-x
-------------------
Let's calculate the interest for each item. Use the simple interest formula.
Bonds at 7% interest rate:
i = P*r*t
i = x*0.07*1
i = 0.07x
Borrowed money at 2% interest rate:
i = P*r*t
i = y*0.02*1
i = 0.02y
Total annual interest = 0.07x+0.02y = 32
The 32 at the end represents the $32 million of interest payout. This amount of money is paid to the bondholders and to the insurance company, and is done so yearly.
-------------------
Apply substitution to solve for x.
0.07x+0.02y = 32
0.07x+0.02(800-x) = 32 ...... plug in y = 800-x
0.07x+16-0.02x = 32
0.05x+16 = 32
0.05x = 32-16
0.05x = 16
x = 16/(0.05)
x = 320
They should sell $320 million in bonds.
320 million = 320,000,000
Note how x = 320 is in the interval [tex]0 \le x \le 480[/tex]
y = 800-x
y = 800-320
y = 480
They should borrow $480 million at an interest rate of 2%
480 million = 480,000,000
Note how y = 480 is in the interval [tex]0 \le y \le 640[/tex]
Answer:
The arena should be financed by selling $320 million in bonds and borrowing $480 million.
Step-by-step explanation:
Simple interest is calculated by multiplying the principal by the interest rate (in decimal form) and the time (in years).
Let x be the amount raised by selling bonds that pay an annual simple interest rate of 7%.
Therefore:
Interest = 0.07x
As the total cost of the sports arena is $800 million, the amount raised from borrowing money from the insurance company at an annual simple interest rate of 2% is (800 - x). Therefore:
Interest = 0.02(800 - x)To determine whether the arena can be financed so that the annual interest is $32 million, equate the sum of the two expressions for interest to 32 and solve for x:
[tex]\implies 0.07x+0.02(800-x)=32[/tex]
[tex]\implies 0.07x+16-0.02x=32[/tex]
[tex]\implies 0.05x+16=32[/tex]
[tex]\implies 0.05x=16[/tex]
[tex]\implies x=320[/tex]
As x is the amount raised by selling bonds, then the amount in bonds that should be sold is $320 million.
To calculate the amount to borrow, subtract the amount in bonds sold from $800 million:
[tex]\implies 800-320=480[/tex]
Therefore, the amount to be borrowed from an insurance company is $480 million.
As both these amounts are less than the maximum limits set, they are both valid.
sithe shares his two sandwiches between himself and two friends.caculate the fraction of the sandwiches that sithe will get
FIND THE VALUE OF 1+2+3+....+47-48-49-50.
Answer:
1225 is what I got, not sure tho.
In the United States,
13
1313 out of every
20
2020 cans are recycled.
What percent of cans are recycled?
In the United States, 65% of cans are recycled.
What is the percentage?A number or ratio that can be expressed as a fraction of 100 is called a percentage. Divide the number by its whole number and multiply it by 100 if we have to figure out the percentage of that number. Consequently, the percentage represents one part per hundred.
Given In the United States, 13 out of every 20 cans are recycled.
total cans = 20
recycled cans = 13
percent of recycled can = 100*recycled cans/total cans
percent of recycled can = 100*13/20
percent of recycled can = 60%
Hence 65% of cans are recycled.
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Correct question is In the United States, 13 out of every 20 cans are recycled. What percent of cans are recycled?
If 9 times a positive number is equal to 91 more than twice the same number, what is the number?
Answer:
13
Step-by-step explanation:
Len n = number.
9n = 2n + 91
7n = 91
n = 13
Answer: 13
Mr. Rivera wants to know which of the classes that he teaches works the hardest. How many populations does he need to answer this question?
(Please help it's 50 points thank you!)
The number of populations that he needs to answer this question is the number of classes that he teaches.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
Hence in this problem each population is the set of all students in each class, hence the number of populations that he needs to answer this question is the number of classes that he teaches.
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uestion 5 (1 point) Find the following Quadratic Regression for the following set of data
(-1,8), (5,-4), (7,8), (2,-6)
A. y= = 2x² - 6x + 2 2
B. y = .96x² - 5.77x + 1.38
C. y = -5.77x² + 1.38x+.96
D. y = 5x + 10
The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96
How to determine the quadratic regression equationFrom the question, we have the following parameters that can be used in our computation:
(-1,8), (5,-4), (7,8), (2,-6)
Using a graphing calculator, we have the following summary:
function value
mean of x 3.25
mean of y 1.5
correlation coefficient r 0.9990171837
A 1.380577428
B -5.769028871
C 0.9553805774
The equation is represented as
y = ax^2 + bx + c
So,, we habe
y = 1.38x^2 - 5.77x + 0.96
Hence, the equation is y = 1.38x^2 - 5.77x + 0.96
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Please help me ans this question
After simplification, the value of expression is, (x + 1) / (2x - 1).
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The expression is,
⇒ 10x² + 10x / 20x² - 10x
Now, We can simplify as;
⇒ (10x² + 10x) / (20x² - 10x)
⇒ 10x (x + 1) / 10x (2x - 1)
⇒ (x + 1) / (2x - 1)
Thus, The value of expression is, (x + 1) / (2x - 1).
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Carlos wants to finish a 7.5 mile trial
walking at a constant rate the distance that
Carlos has left
to finish the trial after h hours
walking is represented by the fuction 1h+2d=15
The domain of the function 5h + 2d = 15 is [0, 3].
What is domain and range of a function?
The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x).
The collection of numbers that the function assumes is known as its range. The values that the function outputs when we enter an x value are in this set.
5h + 2d = 15
2d = 15 - 5h
d = (15 - 5h)/2
For h = 0, d = 15/2 = 7.5
For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.
For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.
For h = 3, d = (15 - 15)/2 = 0 miles
The domain of the function is [0, 3].
Thus,
The domain is [0, 3].
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If 6% of a number equals one, find 24% of that number.
A, B and C are currencies of different countries. Three As are worth four Bs and five Bs are worth one C. How many As are two Cs worth?
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
what is equation ?Its precise nature is understood to be the figure is probably smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the median and excess. A fractional number can always be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the intermediate is referred to as a linear expression. Every variable's classes are listed in lowest to highest in the general form of any formula. The formula for a linear function is x + b = 0. The simplified version of a two-variable mathematical expression is an x + b y + c = 0. (or something similar). Either conditioned equations or identities provide categories for equations. An identity holds true because of whatever value of the variables.
given
The aforesaid issue is easily resolved by doing the following:
Considering that,
Four Bs are worth three As.
It can be written as;
3A = 4B
determining B's value
B = 3A/4 (Equation 1) (Equation 1)
Now,
A B is worth five Cs.
So, 5B = C (Equation 2) (Equation 2)
Calculating B's value in equation 1
= 15A/4 = C
= 4C = 15A
2C = (15/2)A
2C = 7.5A
Therefore, the solution is 2C = 7.5A
When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.
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Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U={f, g, h, p, q, r, x, y, z)
A={f,g,r, x}
B={r, x, y, z)
C={g, h, q, r, z}
Find (BU A)'n C.
Write your answer in roster form or as Ø.
(BUA)'n C = {}
Using the properties of sets, (BU A)'n C = {h,q}
What kinds of Sets are there?Null set or an empty set There isn't even one element in it. Finite Set: It only has a finite number of components. The element count of an infinite set is infinite. Two sets with the same members are said to be equal sets.
An object collection that is taken into account as a whole is referred to as a set. The elements or members of the set are the things that make it up. A set's components can be any type of object, but for our purposes, they are most frequently mathematical components like integers, functions, or other sets.
What subgroups of ABCD are there?The list of all subsets of a,b,c,d is ϕ ,{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}
(B U A) = {f,g,r,x,y,z}
(BU A)'n C = {h,q}
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how water changes its state in each part of the water cycle 1 paragraph
Answer:
The water cycle involves the continuous movement of water on, above, and below the surface of the Earth. In the cycle, water can exist in three states: liquid, solid, and gas. During evaporation, liquid water changes into water vapor, the gaseous state of water, as it heats up and turns into steam. When water vapor cools, it can condense back into liquid form, such as when it forms clouds. Precipitation, such as rain or snow, occurs when water droplets in the clouds become heavy enough to fall from the sky. When precipitation reaches the ground, some of it may flow into rivers and streams and eventually make its way to the ocean. Some of it may also be taken up by plants or seep into the ground, becoming part of the groundwater system. Eventually, the water in the groundwater system may evaporate back into water vapor and start the cycle over again.
Simon took out an unsubsidized student loan of $43,000 at a 2.4% APR,
compounded monthly, to pay for his last six semesters of college. If he will
begin paying off the loan in 33 months with monthly payments lasting for 20
years, what will be the amount of his monthly payment?
OA. $240.58
OB. $225.77
O C. $241.16
D. $225.23
As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.
what is interest rate ?By dividing initial principal by the risk premium, the time it has been and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the technique used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating this is as a portion of the principal amount. For example, if he borrowed $100 from a buddy and agrees to pay back the loan at 5% interest, he will just pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must lend money when you lend it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.
given
Assuming a specific interest rate (r), principal (p), and number of times the interest is compounded annually (n), we can calculate the total amount owed on a loan (A) as follows:
A = p(1+ r/n) nl
Because in our example, n = 12 (monthly), p = $43,000, r = 2.4% = = 0.024, and t = 20 years.
A = $69457.89.
$289.41 per month for a 20-year term.
As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.
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There were 160 boxes of biscuits in a shop at first. Each box contained 30 packs of biscuits. There were 2800 packs of strawberry biscuits and the rest were chocolate biscuits. The shopkeeper sold an equal number of packs of chocolate biscuits each month over a period of 5 months. How many packs of chocolate biscuits did the shopkeeper sell each month?
Using the concept of multiplication and division, the number of chocolate sold each month is 400 packs.
How many chocolate biscuit was soldTo determine the number of chocolate biscuits in the shop, we have to determine how many is contained in each box and then multiply it by number of days in a month and then subtract the number of chocolate in the shop. This tasks involves the use of basic arithmetic operations to determine the number of packs sold.
The total number of packs of biscuits in the shop was 160 * 30 = 4800.
So, the number of packs of chocolate biscuits was 4800 - 2800 = 2000.
The shopkeeper sold 2000 packs of chocolate biscuits over 5 months, so he sold 2000 / 5 which will give us 400 packs of chocolate biscuits each month.
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Roman cuts a sheet of poster paper into 10 equal parts. His mom uses some of the paper and leaves 8/10 for Roman. He wants to make some posters with the leftover paper, how many posters can he make
Therefore , the solution of the given problem of fraction comes out to be Roman can thus perform 8 poster.
A fraction is what?Any number of equal amounts or fractions can be used to represent a whole. In standard English, the quantity of a certain size is stated as a fraction. 8, 3/4. Wholes also include ratio. Numbers are represented in mathematics by the fraction to numerator ratio. These are all straightforward integer fractions. There is a fraction in the denominator of a difficult fraction. because the calculations, numerators, and numerators of actual fractions vary.
Here,
Given :
Roman divided a poster board sheet into ten equally sized pieces.
The entire sheet should be x.
then, one part of sheet= 1/1 0 of the sheet
Currently, only 8/10 of the poster is left after his brother used portion of it.
Roman can therefore use each remaining piece of the poster to create a sign if he so chooses.
The number of indications he is capable of making is then
=> 8/10/1/10
= > 8/10 * 10 = 8.
Roman can thus perform 8 signs.
Therefore , the solution of the given problem of fraction comes out to be
Roman can thus perform 8 poster.
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A new is being built in Safety Harbor. The perimeter of the rectangular playing field is 582 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
The dimensions of the rectangular field are given as follows:
Length: 232 yards.Width: 59 yards.How to obtain the perimeter of a rectangle?The perimeter of a rectangle is given by twice the sum of the length and the width of the rectangle, as follows:
P = 2(l + w).
For this problem, the perimeter is of 582 yards, hence:
2(l + w) = 582
l + w = 291.
The length of the field is 4 yards less than quadruple the width, hence:
l = 4w - 4.
Then the width is obtained as follows:
4w - 4 + w = 295
5w = 295
w = 295/5
w = 59.
The length is obtained as follows:
l = 4 x 59 - 4
l = 232 yards.
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D) What is the greatest common factor of 45 and 30?
Answer:15
Step-by-step explanation:
i did the math
Answer:
15
Step-by-step explanation:
15 x 2=30
15x3=45
Pankaj is a Biomedical Engineering student. He plans to deposit $600 that he earned as stipend, in
a bank account at 3% rate of interest compounded weekly for no more than 2 years. The total
amount of the money, A, that Pankaj will get back, is a function of time, t. Which is a reasonable
domain of the money that he may accumulate?
The correct answer is A: 600 <= money <= 2822.4.
This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.
Consider the logistic equation
y=y(1-y)
a.Find the solution satisfying 1(0)=14 and y2(0)=-3
y1(t)=
y2(t)=
b.Find the time t when y1(t)=7
t=
c.When does y2(t) become infinite?
t=
The solution satisfying y1(0)=14 and y2(0)=-3 are y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13))) and y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))
The time t when y1(t)=7 is 1.08y2(t) becomes infinite when t ⇒ +∝Find the solution satisfying y1(0)=14 and y2(0)=-3The logistic equation is a non-linear ordinary differential equation that models the growth of populations over time.
The solution to the logistic equation with initial conditions y1(0)=14 and y2(0)=-3 is given by (from a graphing tool):
y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13)))
y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))
Note: ln is the natural logarithm function.
Find the time t when y1(t)=7The time t when y1(t)=7 can be found by solving for t in the equation y1(t) = 7.
From the graphing tool, we have
t = 1.08 when y1(t) = 7
When does y2(t) become infinite?he solution y2(t) becomes infinite when the denominator of the equation becomes zero.
This occurs when -3/2 * e^(t * ln(-3/2)) = -∞.
This can be written as t * ln(-3/2) = ∞, which occurs when t approaches positive infinity.
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Which of the following is the equation that represents the graph
y = -2/3x -6
y = -3/2x -6
y = -3/2x -4
y = -3/2x -4
The equation of the graph is y = -2/3x - 4
How to determine the equation of the graphA linear equation is represented as
y = mx + c
Where
c = y when x = 0
From the graph, we have
c = -4
So, the equation becomes
y = mx - 4
From the graph, we have the following point
(-6, 0)
So, we have
0 = -6m - 4
Evaluate
m = -2/3
So, we have
y = -2/3x - 4
Hence, the equation is y = -2/3x - 4
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HELP PLEASE I WILL GIVE BRAINLIEST
answer the first 2 questions.
The total area of all the pieces would be: - x² + y² + 2xy = (x + y)².
What is the total area of all of the pieces?This tile collection is composed of four tiles: two squares, each with sides of length x, and two rectangles, each with sides of length x and y.
The total area of all of the pieces can be expressed algebraically as A = x² + 2xy.
This expression can also be written as A = x² + xy + xy.
This tile collection is an example of a two-dimensional shape composed of two squares and two rectangles.
By adding the areas of each of these shapes, we can calculate the total area of the tile collection.
The area of each square is x², and the area of each rectangle is xy.
Adding these three expressions together gives us the total area, A = x² + 2xy.
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Prove the Consecutive Interior Angles Theorem.
Given: p || q
By the given explanation it is proven that ∠1 and ∠3 are supplementary from this, it has proven the Consecutive Interior Angles theorem.
Consecutive Interior Angles theorem:According to the consecutive interior angle, if a transversal intersects two parallel lines each pair of consecutive interior angles is supplementary, meaning that the sum of the consecutive interior angles equals 180°
Here we have
Line p and line q are two parallel lines and line 't' is a transversal on Line p and line q
Theorem:
When a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary i.e added up to 180°.
We can prove the above theorem as follows
Given p║q
Let's take angles 4 and 5 on line 'p' as shown below
Here ∠4 + ∠3 = 180° [∵ pair of linear angle ]
Now substitute ∠1 in place of ∠4
=> ∠1 + ∠3 = 180° [ ∵ Corresponding angles ∠1 and ∠4 are equal ]
Therefore,
By the given explanation it is proven that ∠1 and ∠3 are supplementary from this, it has proven the Consecutive Interior Angles theorem.
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I need help with this problem
Me ayudais por favor
Answer:
x= - 52
Step-by-step explanation:
we need to multiply both sides by 4 to leave the x alone
so
[tex]\frac{-x}{4} *4= 13*4\\-x= 52\\\frac{-x}{-1}=\frac{52}{-1}\\ x=-52[/tex]
Which number line represents x<-3??
Answer:
1st number linline
Step by step explanation:
x < -3 means x is less than -3
so it should be any number less than -3
In the 2nd number line represents
[tex]x \leqslant - 3[/tex]
so the answer is 1st one
Which interval on the graph could be described as linear decreasing? a A b B c C d D
Answer:
C
Step-by-step explanation:
Mr. Lopez is looking to fill a part of a park with sand. The shape below represents the part of the park being covered in sand. How many square yards of the park will Mr. Lopez cover in sand?
Mr. Lopez cover in sand by 50 yd².
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Mr. Lopez is looking to fill a part of a park with sand.
And, The shape below represents the part of the park being covered in sand.
Now, We will find the area of figure as;
The park is mix of two figure rectangle and triangle.
Hence, We get;
Area of rectangle = 5 × 8
= 40 yd²
And, Area of triangle = 1/2 × 4 × 5
= 10 yd²
Thus, The area of given figure is,
⇒ Area = 40 yd² + 10 yd²
⇒ Area = 50 yd²
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The
• The top of a second mattress has 1½ times as much area as
the first mattress. What is the area of the top of the second
mattress? Write an equation to model the problem.
The area of the top of the second mattress , 3/2x²
The equation to model the problem is y= 1.22x.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
let the side of mattress one be x
and, the side of Mattress 2 be y.
So, area of Mattress 2 / Area of Mattress 1 = 1 1/2
area of Mattress 2 / Area of Mattress 1 = 3/2
y²/ x² = 3/2
(y/ x)² = 3/2
y/x = √3/2
y /x = 1.22
Hence, the equation is y= 1.22 x .
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A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 50 feet and the slant height of each lateral side of the pyramid is 40 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
Step-by-step explanation:
The lateral surface area of the pyramid can be found using the formula for the area of an equilateral triangle:
A = (s^2 * √3) / 4
where s is the length of one side of the equilateral triangle base.
For this pyramid, s = 50 feet
A = (50^2 * √3) / 4 = (2500 * √3) / 4 = 1250 * √3 ≈ 2129.28 ft^2
The total surface area of the pyramid can be found by adding the area of the base to the area of the lateral surface:
A = base area + lateral surface area
A = (side length^2 * √3) / 4 + (3 * triangle area)
A = (50^2 * √3) / 4 + (3 * (50^2 * √3) / 4)
A = 2500 * √3 + 3750 * √3 ≈ 5884.28 ft^2
To paint 75% of the pyramid, the painter needs to paint 75% * 5884.28 ft^2 = 4413.71 ft^2
Since the painter can paint 100 ft^2 in 18 minutes, he can paint 4413.71 ft^2 in 4413.71 / 100 * 18 minutes ≈ 786.96667 minutes
Rounding to the nearest tenth, the painter will take 786.967 minutes to paint 75% of the pyramid, which is approximately 13.1 hours.
The total number of fence posts Edwin installs varies directly with the number of hours worked. He installs 40 fence posts in 8 hours.
Write a direct variation equation to represent this relationship.
Answer:
y = 5x
where
y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts
Step-by-step explanation:
Let y = number of fence posts that Edwin installs in x hours
We have the relation:
y ∝ x where ∝ is the symbol for is-proportional-to
We can rewrite this as an equation using the constant of proportionality,k:
y =kx
Given y = 40 fences, x = 8 hours we get
40 = k(8) = 8k
or, switching sides
8k = 40
k = 40/8 = 5
So Edwin can install 5 fences per hour
Plugging this into the equation of proportionality
y = 5x