The dimensions that will minimize the total cost to enclose the rectangular parking area are x = 500 ft and y = 1000 ft, and the minimum cost is $6500.
Let x be the length and y be the width of the rectangular parking area. The area of the rectangular parking area is given by the equation A = xy, where A is the area in square feet.
The given area of the rectangular parking area is 2000 ft^2, so we have the equation A = xy = 2000.
The three sides of the parking area that are enclosed with chain-link fencing will have a cost of $5.50 per foot. Since there are two sides with length x and one side with length y, the total cost for the chain-link fencing will be 2x + y multiplied by the cost per foot, which is $5.50. So the cost for the chain-link fencing is 5.5(2x + y).
The fourth side of the parking area, which is the wooden fence, will have a cost of $6 per foot. Since the length of the fourth side is y, the total cost for the wooden fence will be 6y.
The total cost to enclose the parking area, C, is the sum of the cost for the chain-link fencing and the cost for the wooden fence, which can be expressed as:
C = 5.5(2x + y) + 6y.
We want to minimize the total cost C, subject to the constraint A = 2000. We can use the constraint equation A = xy = 2000 to express one of the variables in terms of the other, and then substitute it into the cost equation C = 5.5(2x + y) + 6y.
Solving the constraint equation for y, we get y = 2000/x.
Substituting this into the cost equation, we get C = 5.5(2x + 2000/x) + 6(2000/x).
Now, we can take the derivative of C with respect to x, and set it equal to 0 to find the critical points where the minimum cost occurs. Taking the derivative of C with respect to x, we get:
dC/dx = 5.5(2 - 2000/x^2) - 6(2000/x^2).
Setting dC/dx equal to 0 and solving for x, we get:
5.5(2 - 2000/x^2) - 6(2000/x^2) = 0.
Simplifying, we get:
11 - 11000/x^2 - 12000/x^2 = 0.
Combining like terms, we get:
11 - 23000/x^2 = 0.
Multiplying both sides by x^2 to get rid of the fraction, we get:
11x^2 - 23000 = 0
Solving for x, we get x^2 = 23000/11, or x ≈ 36.81 ft.
Plugging this value of x back into the constraint equation y = 2000/x, we get y ≈ 54.20 ft.
So, the dimensions that will minimize the total cost to enclose the rectangular parking area are x ≈ 36.81 ft and y ≈ 54.20 ft. The minimum cost, which can be found by plugging these values of x and y into the cost equation C = 5.5(2x + y) + 6y, is $6500.
For more questions like Equation click the link below:
https://brainly.com/question/29657983
#SPJ11
may i have some help with 9? thanks :)
#9. C
A negative sign on the outside of the function indicates a reflection in the y-axis.
A negative sign on the inside of the function (attached to the x) indicates a reflection in the x-axis.
Hope this helps!
Find the measure of KM¯¯¯¯¯¯¯¯¯¯.
Answer:
12
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
( 7+x+2) * 7 = ( 6+8) * 6
Combine like terms
(9+x) *7 = 14*6
Distribute
63 +7x = 84
Subtract 63
63 +7x -63 = 84-63
7x =21
Divide by 7
7x/7 = 21/7
x = 3
KM = x+2+7
= 3+2+7
=12
Answer:
\(\huge\boxed{KM = 11}\)
Step-by-step explanation:
According to secant - secant theorem:
(MK)(ML) = (MR)(MN)
Where
MK = 7 + x+ 2 = x + 9
ML = 7
MR = 8 + 6 = 14
MN = 6
=> (x+9)(7)= (14)(6)
=> 7x + 63 = 84
Subtracting both sides by 63
=> 7x = 84 - 63
=> 7x = 21
Dividing both sides by 7
=> x = 3
Now,
KM = x + 9
KM = 3 + 9
KM = 11
81 + 9 = 9+81
true or false
Answer:
true
----------------------------------
it says I have to use the Pythagorean theorem and trig to find the perimeter and area. but I don't know how to apply that correctly to get the right answer. help is very appreciated!
Answer:
Let h be the height of the triangle.
Set your calculator to degree mode.
\( \tan(71) = \frac{26}{h} \)
\(h \tan(71) = 26\)
\(h = \frac{26}{ \tan(71) } = 8.9525\)
So the area of this triangle is
(1/2)(26)(8.9525) = 116.3827 square feet
The length of the hypotenuse is
\( \ \sqrt{ {( \frac{26}{ \tan(71) } )}^{2} + {26}^{2} } \)
\( \sqrt{ {8.9525}^{2} + {26}^{2} } = 27.4981\)
So the perimeter of this triangle is
8.9525 + 26 + 27.4981 = 62.4506 feet
Amanda and Alexis live 4 miles apart. They decide to start walking toward each other’s houses at the same time. Amanda walks at a rate of 3.5 miles per hour and Alexis walks at a rate of 4 miles per hour. How long will it take for them to meet? Round to the nearest hundredth of an hour. [Remember: D = (r)(t)]
Answer:
0.53 hours
Step-by-step explanation:
D = (r)(t), Where
‘D’ is the distance covered
‘r’ is the approach rate
‘t’ is the total time spent
Distance covered, ‘D’ = 4 miles
Approach rate, “r” = 3.5mph + 4mph
r = 7.5mph.
t is unknown
Solving for t,
D = (r)(t)
4 = 7.5t
t = 4/7.5
t = 0.53 hours (to the nearest hundredth)
Therefore, it will take Amanda and Alexis 0.53 hours to meet
pls, help 30 points!! thank you so much!
The ability of typhoid to spread can best be attributed to bacteria in unclean water. the lack of good medicine. an unhealthy lifestyle. mosquito bites.
The ability of typhoid to spread can be best attributed to bacteria in unclean water. Unclean water contaminated with the bacterium Salmonella typhi is a primary source of transmission for typhoid fever.
Typhoid fever is caused by the bacterium Salmonella typhi, which primarily spreads through the consumption of contaminated food and water. Unclean water sources, such as those contaminated with fecal matter containing the bacteria, can serve as a breeding ground for the transmission of typhoid.
When individuals consume or come into contact with water contaminated by the bacteria, they become susceptible to the infection. Other modes of transmission, such as contaminated food, can also contribute to the spread of the disease. However, the main factor behind the ability of typhoid to spread is the presence of the bacteria in unclean water, highlighting the importance of clean water sources and proper sanitation practices in preventing the transmission of typhoid.
Learn more about Salmonella typhi here: brainly.com/question/7981522
#SPJ11
Find one value of x that is a solution to the
X
equation:
(x² − 8)² + x² − 8 = 20
X =
Answer: x = {+-sqrt(3), +-2*sqrt(3)}.
Step-by-step explanation:
(x^2 - 8)^2 + (x^2 - 8) = 20
▪︎ Let (x^2 - 8) be y.
Then,
y^2 + y = 20
y^2 + y - 20 = 0
D = b^2 - 4ac = 1 + 20*4 = 81 = 9^2
y1 = (-b - sqrt(D))/(2a) = (-1 - 9)/2 = -10/2 = -5
y2 = (-b + sqrt(D))/(2a) = (-1 + 9)/2 = 8/2 = 4
1) x^2 - 8 = -5
x^2 = 8 - 5
x^2 = 3
x = +-sqrt(3)
2) x^2 - 8 = 4
x^2 = 8 + 4
x^2 = 12
x = +-sqrt(12)
x = +-2*sqrt(3)
Would "approximately 3.24 billion gallons of water flow over niagara falls daily" be a discrete or continuous relationship?
The statement "approximately 3.24 billion gallons of water flow over Niagara Falls daily" describes a continuous relationship.
In a continuous relationship, the variable (in this case, the amount of water flowing) can take on any value within a certain range. In contrast, a discrete relationship involves distinct, separate values.
In this case, the amount of water flowing can vary continuously and is not limited to specific, separate values. Therefore, the relationship between the amount of water flowing over Niagara Falls daily and the given value is continuous.
To know more about continuous relationship visit:
https://brainly.com/question/11070105
#SPJ11
Which inequality has no solution?
6(x+2) > x-3
3+4x2(1+ 2x)
-2(x+6)
X-9 <3(x-3)
Answer:
\(6(x + 2) > x - 3\)
\(6x + 12 > x - 3\)
\(6x - x > - 12 - 3\)
\(5x > - 9\)
\(3 + 4 \times 2(1 + 2x)\)
\(3 + 8(1 + 2x)\)
\(3 + 8 + 16x\)
\(11 + 16x\)
\( - 2(x + 6)x - 9 < 3(x - 3)\)
\( - 2( {x}^{2} + 6x) - 9 < 3x - 9\)
\( - 2 {x}^{2} - 12x - 9 < 3x - 9\)
Alex purchased a new car for $35,000. Cars decrease in value at a rate of 18% per year.
Show your work/explain your response for each part.
Part A: Write an exponential function to model the cost y, of the car after x years.
Part B: Use your function from Part A to determine how much the car is worth after 10 years. HURRYYY PLEASE!!
The y = 35,000(1 - 0.18)^x and car is worth approximately $4810.68 after 10 years.
How to find exponential equation?Part A:
Let the initial cost of the car be $35,000 and let the rate of decrease be 18% per year. We can use the formula for exponential decay:
y = a(1 - r)^x
where:
y is the cost of the car after x years
a is the initial cost of the car, which is $35,000
r is the rate of decrease, which is 18% or 0.18 in decimal form
x is the number of years since the car was purchased
Therefore, the exponential function to model the cost of the car after x years is:
y = 35,000(1 - 0.18)^x
Simplifying this expression, we get:
y = 35,000(0.82)^x
Part B:
To determine how much the car is worth after 10 years, we plug in x = 10 into the exponential function we obtained in Part A:
y = 35,000(0.82)^10
Using a calculator to evaluate this expression, we get:
y ≈ $4810.68
Therefore, the car is worth approximately $4810.68 after 10 years.
To know more about Exponential function visit:
brainly.com/question/14355665
#SPJ1
Nabhitha measure the volume of a sink basin by modeling it as a hemisphere. Nabhitha measures its radius to be 15 1/4
The volume of the sink basin is approximately 7430.9 cubic inches.
What is hemisphere?
A hemisphere is a three-dimensional geometric shape that is obtained by slicing a sphere into two halves along a plane passing through its center. A hemisphere is a half-sphere, meaning that it has one curved surface that is shaped like a circle and has a constant radius, and a flat circular base.
The volume of a hemisphere with radius "r" is given by the formula:
(2/3) x π x r³.
In this case, the radius of the sink basin is 15 1/4 inches, which is equivalent to 61/4 inches. Therefore, we can calculate the volume of the sink as follows:
Volume = (2/3) x (22/7) x (61/4)^3
= 2/3 x 22/7 x 3546.58
= 7430.9 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the sink basin is approximately 7430.9 cubic inches.
Complete question : Nabhitha measure the volume of a sink basin by modeling it as a hemisphere. Nabhitha measures its radius to be 15 1/4. find sink's volume in cubic inches. round your answer to the nearest tenth.
To learn more about hemisphere visit the link:
https://brainly.com/question/333717
#SPJ1
yall should add da ig prettyface.kalei ♀️
Answer:
the answer for this is yes I will try to follow you
Given that x is a nonnegative number, a student conjectured that x + 3 < x2.
Which value of x is a counterexample to the student's conjecture?
A: x= -1/3
B: x= -3
C: x= 2
D: 3
Answer:
C (x = 2)
Step-by-step explanation:
Since x is a non-negative number, A and B are eliminated.
This leaves C and D.
C: x = 2,
2 + 3 < 2^2
5 < 4 is false.
So C would be a counterexample.
Hope this helps!
The value of x is a counterexample to the student's conjecture (x = 2). The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that x is a non-negative number, a student conjectured that x + 3 < x².
Since x is a non-negative number, A and B are eliminated.
This leaves C and D at the value of x = 2,
2 + 3 < 2²
5 < 4 is false.
Therefore, the value of x is a counterexample to the student's conjecture (x = 2). The correct option is C.
To know more about an expression follow
https://brainly.com/question/29336033
#SPJ2
The average cost of producing x game disks for a computer is getting better 14 c(x)= 2.8+5200/x find the number of name is that must be produced for the average cost to be $5.40.
To find the number of game disks that must be produced for the average cost to be $5.40, we can set up an equation using the given average cost function and solve for x.
The equation to solve is: 2.8 + 5200/x = 5.40
To isolate x, we can subtract 2.8 from both sides of the equation:
5200/x = 5.40 - 2.8
Simplifying further:
5200/x = 2.6
Next, we can cross-multiply:
5200 = 2.6x
To solve for x, divide both sides of the equation by 2.6:
x = 5200/2.6
Calculating the division:
x = 2000
Therefore, the number of game disks that must be produced for the average cost to be $5.40 is 2000.
To learn more about average click here:
brainly.com/question/24057012
#SPJ11
How many counterexamples does it take to show that a conditional statement is false
Answer:
A counterexample is sufficient, as long as it is well built and complete.
Step-by-step explanation:
A counterexample is a statement used to show that a previously spoken statement is false.
The counterexample must be direct, clear, simple, well constructed and concise to be effective. If the counterexample has all of these characteristics, only one counterexample is sufficient to show that a conditional statement is flawed.
As an example of this, we can use a square as a counterexample of a statement that states that every rectangle has 4 equal sides.
Suppose an insurance company wants to determine the average speed of cars passing through an intersection. They randomly selected 85 cars and found their average speed to be 42 miles per hour with standard deviation of 4.2 miles per hour. A 90% confidence interval for the average speed of all the cars passing through the intersection is
The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.
To calculate the confidence interval, we can use the formula:
Confidence interval = Sample mean ± (Critical value * Standard error)
Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.
Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.
The standard error is calculated as the standard deviation divided by the square root of the sample size:
Standard error = (Standard deviation) / √(Sample size)
Standard error = 4.2 / √85 ≈ 0.456
Now we can plug in the values into the confidence interval formula:
Confidence interval = 42 ± (1.66 * 0.456)
Confidence interval ≈ (41.29, 42.71)
Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.
Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.
To know more about intersection , visit :
https://brainly.com/question/12089275
#SPJ11
Which point is closest to -3 on the number line.
Answer: w
Step-by-step explanation:
A special duty vehicle has 26 tyres. Asumadu has 871 of these vehicles and his sister ,Afia has 639 vehicles if they want to import brand new tyres for all their vehicles, how many tyres will the siblings import.
Answer:
The answer to the given Question will be 39,260 tires .
Step-by-step explanation:
As we know Asumadu has 871 of these special duty vehicles and his sister Afia has 639 vehicles herself. In order to replace all the tires together, first we have to find out the total number of vehicle,
Total number of vehicle = No. of Asumadu's vehicle + No. of Afia's vehicle
= 871 + 639
= 1510
Total no. of vehicle is 1510.
We know there are 26 tires in a single vehicle.
In order to calculate the total no. of tires we have to do,
1510 * 26
= 39,260
Therefore, there are a total of 39,260 tires to be imported in order to change all the tires.
NB*- there is no answer to this question in the website so I am unable to upload any link.
An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
To know more about randomly:
https://brainly.com/question/13319968
#SPJ11
what is the radius of a circle in which a 30° arc is 2 inches long? 24 inches 12 inches 2 root 3
Answer:
Step-by-step explanation:
θ=l/r
where θ is in radians.
θ=30 =Π/180 ×30=π/6
π/6=2/r
πr=12
r=12/π≈3.82 in
2√3≈3.46
which is near to 3.82
Compute an expression for P{,m max B(s) 41 x} 7. Let M = {maxx, x}. Condition on X(t1) to obtain P(M) = PMXt) = y) 1 V2πf, –y?
The final expression would be: Φ((x-y - σ ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] - exp[-(y+x)^2/(2σ^2(1-t1/t))]))/(σ(1 - ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] + exp[-(y+x)^2/(2σ^2(1-t1/t))])))
First, let's start with some definitions. In this problem, we're working with a stochastic process B(t), which we assume to be a standard Brownian motion.
We want to compute the probability that the maximum value of B(s) over some interval [0,t] is less than or equal to a fixed value x, given that B(t1) = y.
In notation, we're looking for P{max B(s) <= x | B(t1) = y}.
To approach this problem, we're going to use the fact that the maximum value of a Brownian motion over an interval is distributed according to a Gumbel distribution.
Specifically, if we let M = max B(s) over [0,t], then the cumulative distribution function (CDF) of M is given by:
F_M(m) = exp[-exp(-(m - μ)/σ)]
where μ = E[M] = 0 and σ = Var[M] = t/3.
So, if we can compute the CDF of M conditioned on B(t1) = y, then we can easily compute the probability we're interested in.
To do this, we'll use a result from Brownian motion theory that says that the joint distribution of a Brownian motion at any finite collection of time points is multivariate normal. Specifically, if we let X = (B(t1), B(t2), ..., B(tn)) and assume that 0 <= t1 < t2 < ... < tn, then the joint distribution of X is:
X ~ N(0, Σ)
where Σ is an n x n matrix with entries σ^2 min(ti,tj).
In our case, we're interested in the joint distribution of B(t1) and M = max B(s) over [0,t]. Let's define Z = (B(t1), M). Using the result above, we can write the joint distribution of Z as:
Z ~ N(0, Σ')
where Σ' is a 2 x 2 matrix with entries:
σ^2 t1 σ^2 min(t1,t)
σ^2 min(t1,t) σ^2 t/3
Now, we can use the conditional distribution of a multivariate normal to compute the CDF of M conditioned on B(t1) = y. Specifically, we have:
P(M <= m | B(t1) = y) = Φ((m-μ')/σ')
where Φ is the CDF of a standard normal distribution, and:
μ' = E[M | B(t1) = y] = y + σ ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] - exp[-(y+x)^2/(2σ^2(1-t1/t))])
σ' = (Var[M | B(t1) = y])^(1/2) = σ(1 - ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] + exp[-(y+x)^2/(2σ^2(1-t1/t))]))
where ϕ is the PDF of a standard normal distribution.
So, putting it all together, we have:
P{max B(s) <= x | B(t1) = y} = P(M <= x | B(t1) = y)
= Φ((x-μ')/σ')
= Φ((x-y - σ ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] - exp[-(y+x)^2/(2σ^2(1-t1/t))]))/(σ(1 - ϕ((t1/t)^(1/2))(exp[-(y-x)^2/(2σ^2(1-t1/t))] + exp[-(y+x)^2/(2σ^2(1-t1/t))])))
Know more about expression here:
https://brainly.com/question/1859113
#SPJ11
Jacob wants to purchase a new computer, but he does not have enough money in his bank account to pay for one. Which of these is not an option for Jacob?
Responses
He can buy the computer using cash once he has saved enough money. He can buy the computer using cash once he has saved enough money. He can purchase the computer now using his his debit card. He can purchase the computer now using his his debit card. He can purchase the computer now using his his credit card. He can purchase the computer now using his his credit card. He can put more money in his bank account and use his debit card to purchase the computer at a later date. He can put more money in his bank account and use his debit card to purchase the computer at a later date
The option that is not available to Jacob is: He can purchase the computer now using his debit card, even though he does not have enough money in his bank account to cover the cost.
Using a debit card requires that there are sufficient funds in the linked bank account to cover the transaction. If there is not enough money available, the transaction will be declined. Therefore, Jacob cannot purchase the computer using his debit card unless he has enough funds in his account. The other options, including saving up to purchase the computer with cash, using a credit card, or putting more money in his bank account to use his debit card at a later date, are all valid options for Jacob.
Learn more about financing here: brainly.com/question/10024737
#SPJ4
How do I find the area?
Answer:
The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square, you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Answer:
Base x Width x Height
Step-by-step explanation:
60ft^3
I don't know if this is correct
Try using online volume calculator.
Can someone pls help me to solve 15 and 16 and answer 17 I will mark you the brainly pls I will really appreciate
Answer:
15) x = 20
16) y = 45°, z = 30°
17) all 4 corners = 90°, all 4 sides are equal length, diagonals are perpendicular, diagonals bisect the corner angles.
We can't do the extra credit because we do not have a relationship about the side lengths. We just have angle information.
Step-by-step explanation:
15) 2x + 8 = 3x - 12
x = 20
16) 2y = 90°
y = 45°
3z = 90°
z = 30°
asdasdasdsadasasdasd
Callie ha a rope that i 14. 7 inche long. She cut the rope into 3 piece. If each piece i the ame length, how long i each piece of rope?
the length of each rope would be 4.9 inches.
One of the four fundamental operations in mathematics is division; the other three are addition, subtraction, and multiplication. Simply put, division is the process of dividing a large group into smaller ones so that each group has the same number of items. In mathematics, it is a procedure for equal sharing and grouping.
Callies has a rope of length = 14.7 inches,
she cut the rope into pieces = 3
let 'x' be the length of each rope,
if each piece is of the same length, the length of the original rope would be 3x.
this implies, 3x = 14.7 inches,
x = 4.9 inches.
therefore, the length of each rope would be 4.9 inches.
know more about division here: https://brainly.com/question/14087177
#SPJ4
(complete question)
Callie has a rope that is 14.7 inches long. She cut the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?
3 Jo chooses 3 whole numbers between 1 and 40.
The first number is a multiple of 4.
The second number is 6 less than the first number.
The third number is half of the second number.
The difference between the first and third numbers is 21.
What are the three numbers? Show your working.
The three numbers are 36, 30, and 15.
Jo chooses 3 whole numbers between 1 and 40.The first number is a multiple of 4.The second number is 6 less than the first number.The third number is half of the second number.The difference between the first and third numbers is 21.
In order to solve the given problem, we have to use the information given in the problem. Let the first number be 4a. The second number is 6 less than the first number, so it is 4a - 6.
The third number is half of the second number, so it is (4a - 6)/2 = 2a - 3. The difference between the first and third numbers is 21, so 4a - (2a - 3) = 21. Simplifying this gives 2a + 3 = 21. Solving for a gives a = 9.So, the first number is 4a = 4(9) = 36.
The second number is 4a - 6 = 36 - 6 = 30.The third number is 2a - 3 = 2(9) - 3 = 15. Therefore, the three numbers are 36, 30, and 15.
For more such questions on numbers, click on:
https://brainly.com/question/25734188
#SPJ8
please help me asappppp
Answer:
48/x
6x²-24=0
Step-by-step explanation:
Pam has 228 ounces of lemonade. she pours the lemonade into
8-ounce cups, filling as many as she can until all the lemonade is
gone. the last cup is not completely full. how much lemonade is
in the last cup?
a: 4ounces
b: 8 ounces
c: 12 ounces
d: 3 ounces
The last cup contains 4 ounces of lemonade. Option (a) is correct.
Pam has 228 ounces of lemonade and she pours it into 8-ounce cups. To determine the amount of lemonade in the last cup, we divide the total amount of lemonade by the size of each cup.
228 ounces ÷ 8 ounces = 28 cups with a remainder of 4 ounces.
Since the last cup is not completely full, the remaining 4 ounces of lemonade are in the last cup. This means option (a), which states that there are 4 ounces in the last cup, is the correct answer.
By dividing the total amount of lemonade by the cup size and considering the remainder, we can determine the quantity of lemonade in the last cup, which in this case is 4 ounces.
To know more about ounces,
https://brainly.com/question/29374025#
#SPJ11
Barium Corp purchased a piece of equipment on September 30 for $27,000. It cost $400 to ship the go the company's facilities and another $1,000 to install the equipment. After the equipment was installed the company had to pay an additional $1,500 for increased insurance. The capitalized cost of the equipment was
Select one:
a $29,900
b $29,500
c $28,400
d $27.400
The capitalized cost of the equipment is $29,900 (option a).
How to find the capitalized cost of the equipmentTo determine the capitalized cost of the equipment, we need to sum up all the costs associated with its acquisition and installation.
The costs include:
- Purchase price: $27,000
- Shipping cost: $400
- Installation cost: $1,000
- Increased insurance cost: $1,500
To find the capitalized cost, we add up these costs:
Capitalized cost = Purchase price + Shipping cost + Installation cost + Increased insurance cost
= $27,000 + $400 + $1,000 + $1,500
= $29,900
Therefore, the capitalized cost of the equipment is $29,900 (option a).
Learn more about capitalized cost at https://brainly.com/question/25355478
#SPJ1