Answer:
i) 960 , ii) 10 cm
Step-by-step explanation:
V of rectangular carton = 80 · 60 · 40 = 192 000
V of a packet of soap = 10 · 5 · 4 = 200
192 000 / 200
1920/2
960
ii)
960 : 1200 = 192 000 : x
x = 192 000 · 1200 / 960
x = 192 000 · 120 / 96
x = 240 000
80 · 60 · x = 240 000
4800 · x = 240 000
x = 240 000/4800
x = 2400/48
x = 200/4
x = 50
50 - 40 = 10
Answer:
i) 960 packets of soap
ii) 10 cm
Step-by-step explanation:
volume of cuboid = l*w*h
volume of carton = 80*60*40 = 192000 cm³
i)
volume of a packet of soap = 10*5*4 = 200 cm³
192000/200 = 960 packets of soaps
ii)
I am assuming the height is 40 cm
volume of carton/volume of a packet of soap = number of soap
x = volume of carton
x/200 = 1200
x = 1200*200 = 240000 cm³
80*60*h = 240000
4800h = 240000
h = 240000/4800 = 50 cm
50cm (desired height) - 40cm (current height) = 10cm
pat radigan wants to purchase a new home for $312,500. pat puts 20% down and will finance the remainder of the purchase. compare the following two mortgage options he has: 20 years at 6.5% or 25 years at 7.0%.
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
According to the given information
A.
Monthly payment for 20 year mortgage [tex]& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \[/tex]\
Monthly payment for 25 year mortgage [tex]& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B
Total cost of interest for 20 year mortgage [tex]& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\[/tex]
Total cost of interest for 25 year mortgage [tex]$=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &[/tex]
C.
Difference in interest paid [tex]& $=\mathrm{B} 7-\mathrm{B} 6$ &[/tex] = Total interest for 25 year loan-total interest for 20 years
A.
Monthly payment for 20 year mortgage [tex]& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\[/tex]
Monthly payment for 25 year mortgage [tex]& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B.
Total cost of interest for 20 year mortgage = [tex]& $\$ 197,343.88$ & $=$[/tex] total monthly payments-loan taken
Total cost of interest for 25 year mortgage = [tex]& $\$ 280,084.40$ & $[/tex] = total monthly payments-loan taken
C.
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
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What is the probability of flipping a coin 50 times and getting tails 22 times or fewer? Round your answer to the nearest tenth of a percent.
The probability of flipping a coin 50 times and getting tails 22 times or fewer is given as follows:
A. 24%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are given as follows:
n = 50, p = 0.5.
Hence the mean and the standard deviation are obtained as follows:
[tex]\mu = 50 \times 0.5 = 25[/tex][tex]\sigma = \sqrt{50 \times 0.5 \times 0.5} = 3.54[/tex]Using continuity correction, the probability of 22 or fewer tails is the p-value of Z when X = 22.5, hence:
Z = (22.5 - 25)/3.54
Z = -0.71
Z = -0.71 has a p-value of 0.2709.
Which is closest to 24%.
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A local movie theater has a movie lovers club. After paying a membership fee,
all ticket purchases are discounted. The cost after buying 5 movie tickets is $48.75. The
cost after buying 7 movie tickets is $58.25. Write an equation in slope-intercept form to
represent the data. Describe what the slope and intercept mean. Use the equation to
find the total cost after buying 12 tickets.
Answer: 57 dollars, hope this helps!
Write the systems of equations from the table below and find the solution?
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
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DIRECTIONS: Use this information to answer Parts A and B.
A faucet supplies water at a constant rate. After 3 minutes, the faucet supplies 12 liters of water.
Part A
Use the Line Tool to graph the proportional relationship that gives the number of liters of water the facet supplies, y, after x minutes.
The required proportional relationship is given as y = 4x and shown in the graph.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
According to the question,
The proportional relationship gives the number of liters of water the facet supplies, y, after x minutes,
y = kx - - - - - (1)
Put x = 3 so y = 4
12 = k[3]
k = 4
From equation 1,
y = 4x
Thus, the required proportional relationship is given as y = 4x and shown in the graph.
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Need help, please!
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of
pairs of data in and the significance level a
n=14,a=0.01
A: r=0.661
B: r= +- 0.532
C: r= 0.684
D: r= +- 0.661
Answer:
c or b
Step-by-step explanation:
use an appropriate taylor series to find the first four nonzero terms of an infinite series that is equal to ln(5/3).
The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......
What is taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.
The formula is:
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
Here,
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
at n=1,
=0/1!
at n=2,
=0/2!
at n=3,
=0/3!
at n=4,
=0/4!
Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......
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Departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. Make the mathematical model for the given problem
Answer:
510
Step-by-step explanation:
1200-860x3 /2 = 510
Given the equation v over 9.4 equals 13.7, solve for v.
4.3
23.1
128.87
128.78
Therefore the solution to the given question is option d)128.78 for this particular equation.
What is Equation?Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Here,
=> v/9.4 = 13.7
=> v = 13.7*9.4
=> v= 128.78
Therefore the solution to the given question is option d)128.78 for this particular equation
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In a random sample of 125 people, 42 of them owned two vehicles. The sample proportion of people who own two vehicles is
In a random sample of 125 people, 42 of them owned two vehicles. The sample proportion of people who own two vehicles is 0.336
The percentage of people in a sample that exhibit a particular attribute or trait is expressed by the sample proportion (p).
Divide the total number of individuals (or things) in the sample by the number of individuals (or items) who share the characteristic of interest to obtain the sample proportion.
p = x/n, where x stands for the sample's success rate and n for sample size, gives the sample proportion p.
According to the question,
Sample size = 125
Number of people owned two vehicles = 42
Sample Proportion (p) = x/n
=> p = 42 / 125
=> p = 0.336
Therefore , The sample proportion of people who own two vehicles is 0.336
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what is the solution for
an= -3an-1-3an-2-an-3, a0=1, a1=0, a2=5
a) (-1-4n+3n^2)(-1)^n
b) (1-4n-3n^2)(-1)^n
c) (1+4n+3n^2)(-1)^n
Answer:
none of the above
(1 -4n +3n^2)(-1)^n
Step-by-step explanation:
You have the recursive relation {a[0]=1, a[1]=0, a[2]=5, a[n]=-3a[n-1] -3a[n-2] -a[n-3]} and you want to know the explicit relation.
Test a fewThe given initial value a[0] = 1 rules out choice A.
The value a[1] = 0 rules out choices B and C.
Actual solutionWe observe that changing the sign of the constant in the first choice will make it match the sequence:
(1 -4n +3n^2)(-1)^n . . . . . . the solution for the recursive equation
Carmen made $209 for 11 hours of work.
At the same rate, how much would she make for 8 hours of work?
Answer:
Step-by-step explanation:
First find the hourly rate Carmen makes. You can find it by dividing the amount she made by the number of hours she worked
209 / 11 = 19
Now multiply that rate by the amount of hours you want to figure out.
19 * 8 = 152
Answer: $152
Step-by-step explanation:
Divide 209 by 11 to find how much money she gets for 1 hour of work ($19) then multiply that value by 8.
Suppose you can afford to pay $ 325 a month for 9 years towards a new car with no down payment. If the current interest rates are 4.75%, how expensive a car can you afford?
Car sticker price =
Based on the given parameters, the car would be $497.9 expensive in 9 years
How to determine the amount in nine years?The given parameters about the compound interest are
Principal Amount, P = $325Interest Rate, R = 4.75%Time, t = 9 yearsCompound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R)^t - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this case, we introduce the variable n
So, we have
A = P(1 + R/n)^nt
Where n is the number of times in a year
i.e. n = 12
Substitute the known values in the above equation
A = 325 * (1 + 4.75%/12)^(12 * 9)
Evaluate the percentages and the quotients
A = 325 * (1 + 0.0039583)^(108)
Evaluate the sum
A = 325 * (1 .0039583)^(108)
Evaluate the exponent
A = 325 * 1.532
Evaluate the product
A = 497.9
Hence, the value of the investment after 9 years is $497.9
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Gina changes the amount of milk she purchases depending on whether it costs $1,$1.50, or $1.75 a pound. What other information do we need to come up with her demand curve for milk?
Select the correct answer below:
whether her milk consumption goes up or down with price
how much milk she buys in total
whether or not she switches to a substitute when the price is high
how much milk she buys at each price point
The information that we need to come up with her demand curve for milk is D how much milk she buys at each price point
What is a demand curve?A demand curve is a graph that shows the relationship between a commodity's price and the amount that is desired at that price. Demand curves can be applied to the price-quantity relationship for either a specific consumer or for every consumer in a given market.
Individual demand curves and market demand curves are the two types of demand curves. It shows a graphic depiction of the demand schedule. It should be noted that based on the information, the quantity is needed. The correct option is D.
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A mural is feet long and is divided into 7 equal-length panels. How many feet long is each panel?
The required length of each panel would be 1 feet.
Given that,
A mural is 7 feet long and is divided into 7 equal-length panels. How many feet long is each panel to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The required length of each panel = total length of the panel / 7
= 7 / 7 = 1 feet
Thus, the required length of each panel would be 1 feet.
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Graph the line with y-intercept.....
Can you also mark the two points on the graph.
[tex]\lim_{n \to \pi/2} (tanx)^{2cosx}[/tex]
In 2010, a total of 2187 of the employees at Zoe's company owned a petrol
car.
In 2013, there were 1029 employees with petrol cars.
Assuming this number decreases exponentially, work out how many
employees owned a petrol car in 2017.
Give your answer to the nearest integer.
The number of employees with petrol cars is 423
Exponential Decay:In exponential decay, a quantity initially drops gradually before decreasing quickly. Finding the exponential drop of a fast reduction over time is made easier by the exponential decay formula.
The exponentially decreasing formula is used to calculate the radioactivity decay, population decay, and half-life.
The formula for Exponential Decay is given by
f(x) = a (1 - r)ˣHere we have
In 2010, a total of 2187 of the employees at Zoe's company owned a petrol car.
In 2013, there were 1029 employees with petrol cars.
The number of cars decreases exponentially,
As we know the formula for Exponential Decay, A = P (1 - r)^t
From the given data, a = 2187 and t = 3
The number of cars decreased = 2187 (1 - r)³
=> 2187 (1 - r)³ = 1029
=> (1 - r)³ = 1029/2187
=> (1 - r)³ = 343/729
=> (1 - r)³ = 7³/ 9³
=> 1 - r = 7/9
=> r = 1 - 7/9
=> r = 2/9
=> r = 0.2222
The Number of cars in 2017 i.e after 4 years from 2013
=> (1029)(1 - 0.2222)⁴
=> 423.0721516 ≅ 423
Therefore,
The number of employees with petrol cars is 423
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A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than three?
For many rolls of the die, the long- run relative frequency of a number less than three landing face app is 1/3.
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
What is relative frequency?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that, Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
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Dhara will be 26 years old when she graduates. If her mean bi-weekly wage over her career is $1,875.00, what will her lifetime earnings be when she retires at the age of 65?
Dhara's Lifetime earnings when she retires at the age of 65 is; $1,901,250
How to find the lifetime earnings?The first thing we will do here is to find the difference between Dhara's current age and the age he will be when he retires. Thus;
Difference in age = 65 - 26
Difference in age = 39 years old
Bi- weekly wage = 52 weeks/2
Bi- weekly wage = 26 paychecks per annum
Thus;
Lifetime earnings = $1875.00 × 26 paychecks per annum × 39
Lifetime earnings = $1,901,250
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Solve x2 = 36 for x.
Answer:
x=18
36/2=18
all good.
rectangle abcd is similar to rectangle wxyz what is the value of ab if wx is 8 feet ad is 12 feet and wz is 16feet
The value of AB is 6 units.
What are Similar Rectangles ?
Similar rectangles states that the corresponding sides are in proportion.Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.
As per the statement:
Rectangle ABCD is similar to rectangle WXYZ.
WX = 8 feet, AD = 12 feet and WZ = 16 feet.
Since. Rectangle ABCD and rectangle WXYZ are similar
then;
their corresponding sides are in proportion:
[tex]\frac{AB}{WX} =\frac{BC}{XY} = \frac{CD}{YZ} =\frac{AD}{ZW}[/tex]
To find the value of AB:
[tex]\frac{AB}{WX} =\frac{AD}{ZW}[/tex]
Substitute the given values we have;
[tex]\frac{AB}{8} =\frac{12}{16}[/tex]
Multiply both sides by 8 we have;
[tex]AB = \frac{12}{16} * 8 = 6[/tex]
Therefore, the value of AB is 6 units.
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Determine whether the equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.
log(x+3)-log(8x)=log(x+3)/log(8x)
if false make necessary changes to produce a true statement
So the RHS of the given equation is incorrect.
Solve equation with rational exponents. Check all proposed solutions.
8x^3/2-56=0
Answer: x=3√14
Step-by-step explanation:
a circular plate has a radius of 12 inches complete the table included a number and a unit in the last column
The area and the circumference of the circular plate is 452.16 in² and 75.36 in
What is area and circumference of circular plate?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle. It is typically expressed in units like cm or unit m.a closed circle geometric shape in space. A circle is a locus of a point moving around a fixed point at a defined distance from the point in mathematical terms. A circle is essentially a closed curve with an outer line that is equally spaced from the center.Area of circular plate , A = πr²
=3.14 * 12 * 12
= 452.16 in²
Circumference of the circular plate, C = π * 2r
= 3.14 * 2 * 12
= 75.36 in
Hence, the area and the circumference of the circular plate is 452.16 in² and 75.36 inches.
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a sample of 79 eggs yields a sample mean weight of 1.00 ounces. assuming that the population standard deviation
The margin of error for 16 eggs with sample means 2 ounce and standard deviation as 42 ounces is 18.407 .
In the question ,
it is given that ,
the number of eggs = 16
the sample means weight is = 2 ounce .
the standard deviation is = 42 ounces .
we have to find the margin of error .
degree of freedom is 16 - 1 = 15 .
and the t score for the 90% confidence interval is
t₁₅,₀.₀₅ = 1.753
So , the margin of error is = t₁₅,₀.₀₅×(standard deviation/√n)
Substituting the values ,
we get ,
= 1.753×(42/√16)
On simplifying further ,
we get ,
= 18.407
Therefore , the margin of error is = 18.407 .
The given question is incomplete , the complete question is
A sample of 16 eggs yields a sample mean weight of 2.00 ounces and a sample standard deviation = 42.0 ounces, find the margin of error in estimating a confidence interval estimate at the 90% level of confidence. Round your answer to three decimal places. You may assume that egg weights are normally distributed .
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
The compound interest is 61.342 years.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
To find the time period the interest must be compounded quarterly.
Calculated twelve times a year is interest that is compounded monthly. Interest is calculated on a quarterly compound basis, four times a year.
Given that;
A = 1700 P = 500
r = 2% n = 4
= 2/100
r = 0.02 /year
Using the formula A=P(1+r/n)ⁿt find the time period (t)
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )
t = 61.342 years
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Aunt Georgia agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
Kayan will have enough money in the bank to get the phone.
Will Kayan have enough money?It is important to note that percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Aunt Georgia has $1000 and bought a gadget for $300, the remaining amount will be:
= $1000 - $300
= $700
Therefore, since also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99, she will have money left. This will be:
= $700 - $649.99
= $50.01
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Complete question
Aunt Georgia has $1000 and bought a gadget for $300 She also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
6. Jesse roasted 12 marshmallows in 4 minutes. How many marshmallows could she roast in 7 minutes?
Answer: 21
Step-by-step explanation: 12 in 4 minutes means every minute 3 marshmallows are roasted, 4x3=12, so add three more minutes and you get 21. 7x3=21
Answer: 21 marshmallows
Step-by-step explanation:
4 minutes x 1.75 = 7 minutes
multiply marshmallows by 1.75 as well.
12 marshmallows x 1.75 = 21 marshmallows
Question 21 Suppose that 12 inches of wire costs 36 cents. At the same rate, how much (in cents) will 5 inches of wire cost?
Answer: To determine how much 5 inches of wire would cost at the same rate as 12 inches of wire, we can first determine the rate at which the wire is being sold by dividing the cost of the wire by the length of the wire:
36 cents / 12 inches = 3 cents/inch
We can then use this rate to determine the cost of 5 inches of wire by multiplying the rate by the length of the wire:
3 cents/inch * 5 inches = 15 cents
Therefore, 5 inches of wire would cost 15 cents at the same rate as 12 inches of wire.