The tunnel A will be damaged and truck can pass through tunnel B.
Given that, tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² – 30x + 16y – 95 = 0.
What is the standard form of parabola equation?The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y²= = 4ax.
Part A: x²+y²+30x+56=0
Add 15² on both the sides of a equation
That is, x²+30x+15²+y²=-56+15²
⇒ (x+15)²+y²=169
⇒ (x+15)²+y²=13²
Divide 13² on both the sides of the equation
⇒ (x+15)²/13² + y²/13² =1
Part B:
x²-30x+16y-95=0
Now, x²-30x+16y=95
Add 15² on both the sides of a equation
That is, x²-30x+15²+16y=95+15²
⇒ (x-15)²=320-16y
⇒ (x-15)²=16(20-y)
Part C:
Maximum height:
A: 13 feet
B: 20 feet
Width = 8 feet
A: x+15=8/2=4 y=12.37<13.5
B: x-15=8/2=4 y=19>13.5
Hence, the tunnel A will be damaged and truck can pass through tunnel B.
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A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,
(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.
(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.
As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.
We are required to determine the correct time domains for four different situations, by observing the plotted graph.
Part (A) is to determine the correct time domain where the water balloon's height remains the same.
From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
Part (B) is to determine the correct time domain where the height of the water balloon is increasing.
From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.
Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.
From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.
Since, [(30/1) > (10/0.5) > (30/3)],
Or, [30 > 20 > 10],
Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).
Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.
Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.
Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.
Time Domain: Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to the time interval over which, the function occurs.To learn more about Time Domain, click on the link below.
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Find the value of x.
Answer: 90 degree
Step-by-step explanation: the diameter of a circle compounds to an inscribed angle of 90 degree
Water is filling a swimming pool at a constant rate. After 4 hours, 2 inches of water have filled the pool.
C) Write an equation that gives the amount of water, w, after t hours.
Answer:
Step-by-step explanation:
u will have 1 niche of water in 2 hours
please help 5-7, thanks
Answer:
-2
Step-by-step explanation:
5-7 where be -2 because 7 is More powerful than 5 so 7 push 5 all the way back to -2
a random sample of 130 mortgages in the state of mississippi was randomly selected. from this sample, 20 were found to be delinquent on their current payment. what is the mean of the sampling distribution of the proportion of delinquent payments?
For a random sample of 130 mortgages with 20 delinquents on their current payment, the mean of the sampling distribution of the proportion of delinquent payments is not possible to say because population proportion is not known.
A random sample refers to a randomly selected subset of the population. In random sampling, each member of the population has an equal chance of selection, reducing the risk of selection bias. Random sampling ensures that the conclusion drawn from the sample should approximate the results obtained if entire population had been measured. The mean of the sampling distribution is the mean of the population from which results were sampled. As the population proportion (fraction of the population with certain characteristic) is unknown, the mean cannot be determined.
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The value of a machine. V at the end of years is given by V = C(1-r)^t, where C is the original cost of the machine and r is the rate of depreciation. A machine thatoriginally cost $13,500 is now valued at $10,419. How old is the machine if r= 0.12? Round your answer to two decimal places.AnswerHow to enter your answer (Opens in new window)KeypadKeyboard Shortcuts
The value of a machine at the end of t years with a rate of depreciation, r is given by the function:
[tex]V=C(1-r)^t[/tex]It is required to find the age of a machine that originally costs $13,500, but is now valued at $10,419 and has a rate of depreciation of 0.12.
To do this, substitute C=13500, V=10419, and r=0.12 into the function:
[tex]\begin{gathered} 10419=13500(1-0.12)^t \\ \Rightarrow10419=13500(0.88)^t \end{gathered}[/tex]Solve the resulting equation for t:
[tex]\begin{gathered} \text{swap the equation:} \\ \Rightarrow13500(0.88)^t=10419 \\ Divide\text{ both sides by 13500:} \\ \Rightarrow\frac{13500(0.88)^t}{13500}=\frac{10419}{13500} \\ \Rightarrow0.88^t=\frac{3473}{4500} \end{gathered}[/tex]Take the Logarithm of both sides:
[tex]\begin{gathered} \ln(0.88^t)=\ln(\frac{3473}{4500}) \\ \Rightarrow t\cdot\ln(0.88)=\ln(\frac{3473}{4500}) \\ \Rightarrow t=\frac{\ln(\frac{3473}{4500})}{\ln(0.88)}\approx2.03 \end{gathered}[/tex]Hence, the machine is about 2.03 years.
The machine is about 2.03 years.
a marine aquarium has a small tank and a large tank, each containing only red and blue fish. in each tank, the ratio of red fish to blue fish is 333 to 444. the ratio of fish in the large tank to fish in the small tank is 464646 to 555. what is the ratio of blue fish in the small tank to red fish in the large tank?
The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.
Ratio is the relationship between two quantities.
Let x : y = ratio of the blue fish in the small tank to red fish in the large tank
Hence, there are x blue fish in the small tank for every y red fish in the large tank.
If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:
small tank :
red : blue = 3 : 4 = (3/4)x : x
large tank :
red : blue = 3 : 4 = y : (4/3)y
If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
Simplifying the proportion,
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
(7/3)y : (7/4)x = 46 : 5
(161/2)x = (35/3)y
x/y = (35/3) / (161/2)
x/y = x : y = 10 : 69
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the sum of four times a number and six divided by the number squared
Answer: 4x+6/x^2
Step-by-step explanation:
100 pts for who solves
I have no : idea
Step-by-step explanation: WHat grade is this for I might be able to help you.
Autumn has a points card for a movie theater.
She receives 40 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 225 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Autumn can make to earn her first free movie ticket.
HURRY PLEASE!!!!!!!!!!!!!!!!!
On Solving inequality 40 + 12.5 v ≥ 225, we get solution v ≥ 14.8. It means Autumn can earn movie ticket from 15 visits.
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
When we multiply both sides of the inequality with a positive number then the sign of the inequality does not change, but when we multiply both sides by an negative number then the sign of inequality reverses.
Given that Autumn receives 40 points for signing up and 12.5 points for each visit to the theatre.
Let the number of visits to the theatre be v
Then points earned by v visits = v × 12.5 = 12.5 v
Total points earned = signing up points + points of v visits
⇒ Total points earned = 40 + 12.5 v
For earning a free movie tickets the total points must be at least 225 or greater than or equal to 225
Then the inequality becomes:
40 + 12.5 v ≥ 225
Subtracting 40 from both sides
⇒ 12.5v ≥ 225-40
⇒12.5v ≥185
Multiplying both sides by 1/12.5
⇒ v ≥ 185/12.5
⇒ v ≥ 14.8
∴ The number of visits must be greater than or equal to 14.8 or nearest integer 15
∴After 15 visits, Autumn will earn a free movie ticket
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How many solutions exist for the following system if m1 ≠ m2?
y = m1x + b
y = m2x + b
answers:
1.an infinite number
2.none
3. one
4. the number of solutions cannot be determined.
Answer:
3
Step-by-step explanation:
Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once
don’t know what to do
The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation for the function is:
f(x) = 3x⁵
The domain of the function: D = all real number
The range of the function: R = all real number
x-intercept = 0
y-intercept = 0
Increasing interval: x ∈ [0, ∞)
Decreaing interval: x ∈ (-∞, 0]
Symmetry = The function is not symmetric
End behavior:
x → ∞, y →∞
x → -∞, y → -∞
Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.
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5. Which of the following is parallel to the line y = 3/5x+1?
Answer:
y=3/5x-7
Step-by-step explanation:
when lines are parallel they have the same slope and the slope of the first line was 3/5
Hello!
Let's consider the equation given:
⇒the coefficient before the x is the slope
When lines are parallel:
⇒the slopes are equal
Since the line given has a slope of 3/5
⇒ the line parallel is [tex]y = \dfrac{3}{5} x - 7[/tex] <==Answer
Hope that helps!
Which answer choice correctly identifies the extraneous information in the problem?
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
A. The extraneous information is Samuel earned $40 and it took him 4 hours to mow the lawn.
B. The extraneous information is Samuel took 4 hours to mow the lawn and 2 hours to clean his room.
C. The extraneous information is Samuel is 10 years old and earned $40.
D. The extraneous information is Samuel is 10 years old.
Option D is correct.
Extraneous information means irrelevant or unrelated to the problem or issue.
In this question, Samuel's Age is not a matter of concern and totally unrelated to the money he earns by mowing the lawn and cleaning the room
A circular wimming pool has a radius of 15 ft. There is a path all the way around that pool that is three feet wideWhat is the circumference of the outer edge of the path around the pool? Use 3.14 for pi
Given:
Radius of circular swimming pool = 15ft
Radius of the path around the pool = 3ft
radius of outer edge of the pool = 15 + 3 = 18ft
To find the circumference of the outer edge of the path around the pool, use the formula below:
[tex]C\text{ = 2}\pi\text{ r}[/tex]where,
r = 18 ft
pi = 3.14
Thus, we have:
[tex]C\text{ = 2 }\ast\text{ 3.14 }\ast18\text{ = }113.04\text{ ft}[/tex]Therefore, the circumference of the outer edge of the path around the pool is 113.04 ft
ANSWER:
113.04 ft
How many flowers spaced every 6 inches are needed to surround a circle garden with a 125 feet radius. Use three. 3.14 pi.
You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.
First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:
C = 2πr
If we substitute 125ft for r and use 3.14 to approximate π
we get a circumference of:
C = 2 * 3.14 * 125
C = 6.28 *125
C = 785ft
We can now convert the circumference in feet to inches as follow;
As we know that 1ft = 12inches
∴ 785ft = 12(785) inches = 9,420 inches.
To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:
=[tex] 9,420in\ X \ \frac{1\ flower}{6 in} [/tex]
=[tex] \frac{9,420}{6 } \ flower [/tex]
=1,570 flowers
Hence You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.
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If f(x) = –3(1 – x – 2x squared by 2) give f-2.
The value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function is:
f(x) = 3(1 - x - 2x²)/2
It is required to find the value of f(-2)
Plug x = -2
f(-2) = 3(1 - (-2) - 2(-2)²)/2
f(-2) = 3(1 + 2 - 8)/2
f(-2) = 3(-5)/2
f(-2) = -15/2
Thus, the value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.
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Let’s say you want to borrow $500 for two weeks from a pay lender that charges a $100 fee for the loan. It’s takes you a year before your are able to pay them back
The interest rate for the loan is 20%.
What is the interest rate?The interest rate represents the percentage or the proportion of the interest over the total loan.
The interest is the finance charge for the credit extended by the pay lender.
The interest rate, R = Interest x 100/Principal x Time, where the simple interest equals principal x rate x time.
The total amount borrowed = $500
The total finance charge = $100
The period of the loan = 1 year
The interest rate
= $100 x 100/$500 x 1
= 20%
Thus, the pay lender is charging an interest rate of 20% per annum.
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Question Completion:What is the interest rate?
PLEASE HELP FAST!!!!
Answer: 0.01 more
Step-by-step explanation:
60% sure!
I NEED HELP ON THIS QUESTION. I CAN'T SEEM TO GET THE LAST MARK
The dimensions of this cuboid are 2 cm, 11 cm, and 17 cm respectively.
How to calculate the volume of a geometric figure?Mathematically, the volume of a cuboid can be calculated by using this following formula:
Volume = L × W × H
Where:
L is the length of a cuboid.W is the width of a cuboid.H is the height of a cuboid.Substituting the given parameters into the formula, we have;
Volume = 2 × (x + 3) × (x + 9)
374 = 2 × (x² + 9x + 3x + 27)
374 = 2 × (x² + 12x + 27)
Dividing both sides by 2, we have:
187 = x² + 12x + 27
Rearranging the equation, we have:
x² + 12x + 27 - 187 = 0
x² + 12x - 160 = 0
Next, we would solve the quadratic equation by using the factorization method as follows:
x² + 12x - 160 = 0
x² + 20x - 8x - 160 = 0
x(x + 20) - 8(x + 20) = 0
(x - 8)(x + 20) = 0
x = 8 or x = -20
Since the dimensions cannot be negative, the value of x is equal to 8.
Check:
x² + 12x - 160 = 0
8² + 12(8) - 160 = 0
64 + 96 - 160 = 0
160 - 160 = 0 (True).
For the dimensions, we have:
Width = x + 3 = 8 + 3 = 11 cm.
Height = x + 9 = 8 + 9 = 17 cm.
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find the rate of change of the volume of a cylinder when its radius is 6 feet if its height is always (3/2) times its radius and its radius is increasing at the rate of 2 feet per minute.
When the radius of a cylinder is 6 ft. and it is increasing at the rate of 2 feet per minute, its volume will change at rate of 509.14 ft³/minute.
Given a cylinder with:
r = radius
h = height = 3/2 . r
The volume of the cylinder is:
V = πr².h
Substitute h = 3/2 . r,
V = πr².(3/2 r)
V = 3/2 . πr³
Take the derivative with respect to t:
dV/dt = 9/2 . πr² . dr/dt
Substitute dr/dt = 2 ft./minute and r = 6 ft.,
dV/dt = 9/2 . π.6²
dV/dt = 9/2 . π.6² = 509.14 ft³/minute.
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Paloma made a list to track the number of minutes she spent practicing piano.
24, 18, 23, 25, 30, 32, 35, 28, 25, 32, 28, 24
What was her median practice time? please help me
Paloma's median practice time would be = 26.5
What is median?Median is defined as the middle of a set of data which will be selected after the data has been grouped in an ascending or descending order.
The list to track the number of minutes Paloma spent practicing piano in ascending order include the following:
18, 23, 24, 24, 25, |25, 28,| 28, 30, 32, 32, 35
The middle figures are 25 and 28 which should be added and divided into two.
That is;
25 + 28 = 53/2
= 26.5
Therefore, the median practice time for Paloma = 26.5
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please help will give brainliest
The correct answer to the question would be:
D. The manufacturer tests every 500th smartphone off the production line.
WILL GIVE BRAINLEIST
Which steps show how to use distributive property to evaluate 5 x 38
Answer:
A
Step-by-step explanation:
When distributing, you multiply the outside number to each number in the inside as well as looking at the operation inside the parenthesis. Hope this helps!
explain how to solve
2(4x-3)=2
Answer:
x=1
Step-by-step explanation:
1. distribute through the parentheses
8x-6=2
2. Combine like terms
8x=8
3. Divide by 8
x=1
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\2(4x-3)=2\\\\\text{Multiply 2 into the equation in the parentheses}\\8x - 6 = 2\\\\\text{Add 6 to both sides of the equation}\\8x-6+6=2+6\\8x=8\\\\\text{Divide by 8 on both sides}\\\dfrac{8x}{8} =\dfrac{8}{8} \\\\x=1[/tex]
Answer: x = 1
Hope that helps!
a random variable x follows the continuous uniform distribution with a lower bound of −5 and an upper bound of 7. a. what is the height of the density function f(x)? (round your answer to 4 decimal places.)
Using the uniform distribution:
a) The height of the density function which is f(x) is [tex]\frac{1}{12}[/tex]
We know that for a uniform distribution we have two bounds, namely a and b. The probability or likelihood of finding a value of at lower than x is given by the following formula:
P (X < [tex]x[/tex]) = [tex]\frac{x-a}{b-a}[/tex]
Now where we have been mentioned that the two bounds are as follows:
a = - 5 (lower bound)
b = 7 (upper bound)
a) To find the height (h) of the density function we use the below given formula:
h = [tex]\frac{1}{b-a}[/tex]
Putting here the values of a and b we get the height as,
∴ h = [tex]\frac{1}{7-(-5)}[/tex]
⇒ h = [tex]\frac{1}{7+5}[/tex]
⇒ h = [tex]\frac{1}{12}[/tex]
Hence, the height of the density function f(x) is [tex]\frac{1}{12}[/tex]
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Starting with the letter A and counting left
to right,
write the second letter
write the eighth letter
write the third letter
The second letter is B, the eighth letter is H and the third letter is C
When we start to count from left to right starting from letter A,
1st letter is A
2nd letter is B
3rd letter is C
4th letter is D
5th letter is E
6th letter is F
7th letter is G
8th letter is H
9th letter is I
10th letter is J
11th letter is K
12th letter is L
13th letter is M
14th letter is N
15th letter is O
16th letter is P
17th letter is Q
18th letter is R
19th letter is S
20th letter is T
21st letter is U
Thus,
Second letter is B
Eighth letter is H
Third letter is C
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Click and drag like terms onto each other to simplify fully.
-3y³-5y²+7x³+y²-5x²+7y³+5y²
You must answer all questions above in order to submit.
Answer:
+11y³ +y² -5x²
Step-by-step explanation:
-3y³-5y²+7x³+y²-5x²+7y³+5y²
= +11y³ +y² -5x²
9. the school district is served by four buses, each of which delivers students to three different schools. you know the cost of transporting each of the students to each of the schools, and you want to determine the least expensive way to get all of the students to their schools. if you use excel solver for this analysis, how many different variable cells should you use?
If you use excel solver for this analysis, the number of different variable cells should you use are 12
Option- C
The right answer is 12.
Given that,
There are four buses that transport children to the district's three main schools. You are aware of the price of transporting each student to each school.
Since there are four buses and three schools according to the supplied description, each bus has three school alternatives, thus 4*3=12, bearing in mind that there must be the least expensive route to transport all of the students to their schools.
There must therefore be 12 separate variable cells employed.
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write the midpoint formula
Answer:
[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
Step-by-step explanation: