Answer: y= -2/3 + 8/3
Step-by-step explanation:
-2/3 is the slope so you just need the y-intercept to write the equation in general form or slope intercept form
4= -2/3(-2) +b
4 = 4/3 + b
-4/3 -4/3
b= 8/3
general form is y= -2/3 + 8/3
A tank contains 5,000 L of brine with 13 kg of dissolved salt. Pure water enters the tank at a rate of 50 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
Required:
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 20 minutes?
Answer:
a) [tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
b) 10.643 kg
Step-by-step explanation:
Solution:-
- We will first denote the amount of salt in the solution as x ( t ) at any time t.
- We are given that the Pure water enters the tank ( contains zero salt ).
- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.
- The ODE is mathematically expressed as:
[tex]\frac{dx}{dt} =[/tex] ( salt flow in ) - ( salt flow out )
- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.
- So any time ( t ) the concentration of salt in the 5,000 L is:
[tex]conc = \frac{x(t)}{1000}\frac{kg}{L}[/tex]
- The amount of salt leaving the tank per unit time can be determined from:
salt flow-out = conc * V( flow-out )
salt flow-out = [tex]\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\[/tex]
salt flow-out = [tex]\frac{x(t)}{100}\frac{kg}{min}[/tex]
- The ODE becomes:
[tex]\frac{dx}{dt} = 0 - \frac{x}{100}[/tex]
- Separate the variables and integrate both sides:
[tex]\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)[/tex]
- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:
[tex]13 = C*e^0 = C[/tex]
- The solution to the ODE becomes:
[tex]x(t) = 13*e^(^-^\frac{t}{100}^)[/tex]
- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:
[tex]x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg[/tex]
- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg
what is the value of x in the equation 2x+3y=36 when y=6
Answer:
9
Step-by-step explanation:
[tex]2x+3y=36\\\\2x+3(6)=36\\\\2x+18=36\\\\2x=18\\\\x=9[/tex]
Hope this helps!
Answer:
X= 9
Step-by-step explanation:
2x+3y=36
2x+3(6)=36
2x+18=36
-18 -18
2x=18
----------
2
x=9
There are 225 students at March middle school. On Friday, 135 students wore spirit shirts. What percent of the students did Not wear spirit shirts on Friday?
Answer:
40%
Step-by-step explanation:
To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.
Please answer this correctly
Answer:
Opinion
Step-by-step explanation:
This is an opinion because it says "more exciting to visit than"
This implies the persons' own beliefs and is not a fact, because this is not true for everyone
what is 2043.666666 rounded to 2 decimal places
Answer:
[tex]2043.67[/tex]
Step-by-step explanation:
Hundredths is at 2 decimal places.
The thousandths place is higher than 5, so add 1 to the hundredths place.
Answer:
2043.67
Step-by-step explanation:
If you’ve ever rounded a number, you would know that if it’s 5 or higher, round it up, and if it’s 4 or lower, round it down. In this case, the second decimal place reads ’6’ which is higher that 5, so we round up. The rest of the numbers stay the same
2043.67
Any help would be great
Answer:
88/57
Step-by-step explanation:
Answer: 88:57
Step-by-step explanation:
Length is 88 and width is 57
So the ratio is 88:57
A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.
Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.
Answer:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
Step-by-step explanation:
Info given
n=861 represent the random sample
[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer
[tex]p_o=0.81[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.81[/tex]
Alternative hypothesis:[tex]p < 0.81[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
What is the answer to this question–1 × –5?
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
Answer:
5
Step-by-step explanation:
Since the you are multiplying 2 minuses together they will cancel each other out to form a positive number. However if you have an example like this
-6 × 7
Then the answer will be -42 because there is only one negative
For an exam given to a class, the students' scores ranged from 34 to 99 , with a mean of 78 . Which of the following is the most realistic value for the standard deviation: -14,3,0,56,15?
Clearly explain what's unrealistic about each of the other values.
Answer:
The most realistic value for the standard deviation is 15.
Step-by-step explanation:
The standard deviation of a distribution is a measure of dispersion. It is a measure of the spread of the distribution from the mean of the distribution. It expresses how far most of the distribution is from the mean.
Mathematically, the standard deviation is given as the square root of variance. And variance is an average of the squared deviations from the mean.
Mathematically,
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable (ranges from 34 to 99)
xbar = mean = 78
N = number of variables
Now taking the given possible values of the standard deviation one at a time,
-14
The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, it directly translates that the standard deviation cannot be negative.
3
A small standard deviation like 3 indicates that the distribution mostly centres about the mean, with very little variation. And the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence, 3 is too low to pass ad the standard deviation of this distribution described.
0
A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That is, the distribution only contains 1 number, probably multiple times. So, this cannot be the standard deviation for the distribution described.
56
This value represents a value that is too high to express the spread of the distribution described. The mean (78) is very close to the maximum value of the distribution, and far away from the lower value(s), indicating that most of the distribution is in and around the upper values with a few variables closer to the lower limit. A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of variables far from the mean, which isn't the case here.
Moreso, a simple add of the standard deviation to the mean or subtracting the standard deviation from the mean should give at least one of the results with values within the distribution.
(Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)
(Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)
15
This is the most realistic value for the standard deviation as it represents what the distribution described above is.
The mean (78) being close to the maximum value of the distribution, and far away from the lower value(s) indicates that most of the distribution is in and around the upper values with a few variables closer to the lower limit.
So, 15 indicates a perfect blend of small deviations due to the high values close to the mean and the very high deviation from the evidently few lower values.
(Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)
(Mean) + (Standard deviation) = 78 - 15 = 63 > 34 (also within the distribution)
Hope this Helps!!!
When The most realistic value for the standard deviation is 15.
Step-by-step explanation:
Standard deviation The standard deviation of a distribution is a measure of dispersion. also, It is a measure of the spread of the distribution from the mean of the distribution. when It expresses how far most of the distribution is from the mean. Then according to Mathematically, the standard deviation is given as the square root of variance. And also variance is an average of the squared deviations from the mean.mathematically,When Standard deviation is = σ = √[Σ(x - xbar)²/N]After that x = each variable (ranges from 34 to 99)then xbar is = mean = 78Now N is = number of variablesThen we take the given possible values of the standard deviation one at a time, -14 after that The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, also it directly translates that the standard deviation cannot be negative. After that 3 no when A small standard deviation like 3 indicates that the distribution mostly centers about the mean, with very little variation. And also the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence proof that is, 3 is too low to pass ad the standard deviation of this distribution described. Then 0 when A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That means is, the distribution only contains 1 number, probably multiple times. So that, this can't be the standard deviation for the distribution described. Now 56 This value represents a value that is too high to express the spread of the distribution described. when The mean (78) is very close to the maximum value of the distribution, and also far away from the lower value(s), indicating that most of the distribution is in and also around the upper values with a few variables closer to the lower limit. when A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of the variables far from the mean, which isn't the case here. More so, when a simple addition of the standard deviation to the mean or subtracting the standard deviation from the mean should have given at least one of the results with values within the distribution.After that (Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)Then (Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution) Now last digit 15 This is the most realistic and also a value for the standard deviation as it represents what the distribution described above is.When The mean (78) is close to the maximum value of the distribution, and also far away from the lower value(s) indicates that most of the distribution is in and also that around the upper values with a few variables closer to the lower limit.So that, 15 indicates a perfect blend of small deviations due to the high values close to the mean and also the very high deviation from the evidently few lower values.Then (Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution) After that (Mean) + (Standard deviation) =Thus, 78 - 15 = 63 > 34 (also within the distribution)
Find out more information about standard deviation here:
https://brainly.com/question/25309029
How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 98% confidence that the sample mean is within 4 minutes of the population mean, and the population standard deviation is known to be 12 minutes. 25 35 49 60
Answer:
49
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
The critical value at 98% confidence is z = 2.326.
Standard error is SE = σ / √n.
4 = 2.326 × 12 / √n
n = 49
please help!! Select the two reasons which fit best in lines 1 and 2 of the proof (given and details in photo)
A: 1.) Vertical Angles are congruent
2.) SSS Congruence Postulate
B: 1.) Definition of Angle Bisectors
2.) SAS Congruence Postulate
C: 1.) Vertical Angles are congruent
2.) AAS Congruence Postulate
D. 1.) Vertical Angles are congruent
2.) SAS Congruence Postulate
Answer:
D
Step-by-step explanation:
Line 1: Since these angles are vertical, they are congruent
Line 2: We have 2 sides and an angle in between them so it is SAS
This means the answer is D.
Answer: The correct answer is this set:
1.) Vertical Angles are congruent
2.) SAS Congruence Postulate
14 fewer than 12 times the
number of people in my
family is 46.
Answer:
538
Step-by-step explanation:
12 times 46 is 552 then 552 minus 14 is 538
:D
A street performer earns 40% of all his daily earnings at the barclays center subway station.He earns about $60 at that station. Assuming he works everyday and earns the same amount, how much does he earn in two weeks?
Answer:
He earns $2,100 in two weeks.
Step-by-step explanation:
We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:
[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]
If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:
[tex]W=14\cdot\$\,150=\$\,2100[/tex]
Which is the graph of f(x) = 2(3)^x?
Answer: The graph is:
Breakfast Bar’s scrambled egg recipe uses 8 eggs to feed 5 people. How many eggs are they going to need to serve 100 people on Saturday morning?
Explain the steps you would use to solve the problem.
Answer:
800 eggs
Step-by-step explanation:
You would first thing about the starting numbers, Then look at the number 100 and multiply by 8. This would give you 800. This means that you will need 800 eggs to serve 100 people.
Brainliest is greatly appreciated
Answered by: Skylar
6/8/2020
9:59 AM (Eastern Time)
Answer:
the answer is 12.5 i know because i divided 100 by 8 and got 12.5 then multiply then got 100
Step-by-step explanation:
got it right just did the test
Write a quadratic function f whose zeros are −6 and −1.
Answer:
y = (x+6) (x+1) or in quadratic form: y = x² + 7x + 6
Step-by-step explanation:
The diameter of a circle is 5 ft. Find its area to the nearest tenth.
Answer:
A = 19.6 ft²
Step-by-step explanation:
A = πr² Use this equation to find the area of the circle
A = π(2.5)² Multiply
A = π(6.25) Multiply
A = 19.6 ft²
g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high
Answer:
0.3537 feet per minute.
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.
[tex]\dfrac{dV}{dt}=10$ ft^3/min[/tex]
[tex]\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h[/tex]
If the Base Diameter = Height of the Cone
The radius of the Cone = h/2
Therefore,
[tex]\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}[/tex]
[tex]\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}[/tex]
Therefore: [tex]\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10[/tex]
We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.
[tex]When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute[/tex]
When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
Complete question:
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
a. How much cheese does Mai use per Pizza
b. At this rate how much cheese will she need to make 15 Pizza's
Answer:
a. ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. amount of cheese to make 15 pizzas= 2.5 × 15 = 37.5 ounces of cheese
Step-by-step explanation:
Mai is making a personal pizzas .For 4 pizza she uses 10 ounces of cheese. This means Mai uses 10 ounces of cheese in weight to make just 4 pizzas.
a. How much cheese does Mai use per Pizza
Not she uses 10 ounces of cheese to make 4 pizzas. Therefore,
If 4 pizzas requires 10 ounces of cheese
1 pizza will require ? ounces of cheese
cross multiply
ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. At this rate how much cheese will she need to make 15 Pizza's
Since she requires 2.5 ounces of cheese to make 1 pizza
? ounces of cheese will be required to make 15 pizzas
cross multiply
amount of cheese to make 15 pizzas = 2.5 × 15 = 37.5 ounces of cheese
please see attachment
Answer:
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Step(i):-
Given function
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex] ...(i)
Differentiating equation (i) with respective to 'x'
[tex]f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }[/tex] ...(ii)
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }[/tex]
Equating Zero
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]2 x^{2}-1 = 0[/tex]
[tex]2 x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{2}[/tex]
[tex]x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }[/tex]
Step(ii):-
Again Differentiating equation (ii) with respective to 'x'
[tex]f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }[/tex]
put
[tex]x = \frac{1}{\sqrt{2} }[/tex]
[tex]f^{ll} (x) > 0[/tex]
The absolute minimum value at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step(iii):-
The value of absolute minimum value
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex]
[tex]f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}[/tex]
on calculation we get
The value of absolute minimum value = - 0.3536
Final answer:-
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13
Answer:
√x+3-13
Step-by-step explanation:
This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?
Answer:
24
Step-by-step explanation:
That would be:
(3/8)(30)
---------------
(15/16)(1/2)
This can be reduced in various ways. First, divide that 30 by 15, obtaining:
6/8
-----------
1/32
Now invert the divisor (1/32) and multiply:
(6/8)(32/1)
This reduces to 6*4, or 24.
Simplify the quotient shown 3480 divided by 29
Answer:
120
Step-by-step explanation:
3480/29=120
120
Simplify ———
1
final result is 120
The line y = kx + 4, where k is a constant, is
graphed in the xy-plane. If the line contains the
point (c,d), where c ≠ 0 and d ≠ 0, what is the slope
of the line in terms of c and d ?
Answer:
(d - 4) / c
Step-by-step explanation:
The slope of the line in terms of c and d is (d - 4) / c.
Here, we have,
To find the slope of the line in terms of the coordinates of the point (c, d), we can use the slope-intercept form of a line, y = mx + b, where m represents the slope.
In the given equation, y = kx + 4, we can see that the coefficient of x is k, which represents the slope of the line.
Since the line contains the point (c, d), we can substitute these values into the equation:
d = kc + 4
To isolate the slope term, we rearrange the equation:
d - 4 = kc
Now, divide both sides by c:
(d - 4) / c = k
Therefore, the slope of the line in terms of c and d is (d - 4) / c.
To learn more on slope click:
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The sum of two consecutive integers is −19. Find the integers.
Answer:
-9 and -10
Step-by-step explanation:
x + x+1=-19
2x+1=-19
2x=-19-1
2x=-20
x=-10
x+1
-10+1=-9
Answer:
[tex]-9[/tex]
[tex]-10[/tex]
Step-by-step explanation:
[tex]x+x+1=-19[/tex]
[tex]2x+1=-19[/tex]
[tex]2x=-19-1[/tex]
[tex]2x=-20[/tex]
[tex]x=-20 \div 2[/tex]
[tex]x=-10[/tex]
[tex]x+x+1=-19[/tex]
[tex]x+1=-19-x[/tex]
[tex]-10+1=-19-(-10)[/tex]
[tex]-9=-19+10[/tex]
[tex]-9=-9[/tex]
Suppose you want to buy a new car and are trying to choose between two models: Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year. Model B: costs $24,500 and its gas mileage is 40 miles per gallon and its insurance is $450 per year. If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:
1. Find a formula for the total cost of owning Model A where the number of years you own the car is represented by x.
2. Find a formula for the total cost of owning Model B where the number of years is the independent variable.
3. Find the total cost for each model for the first five years. If you plan to keep the car for 4 years, which model is more economical?
4. Find the number of years in which the total cost to keep the two cars will be the same.
5. Identify the number of months where neither car holds a cost of ownership advantage.
6. What effect would the cost of gas doubling have on cost of ownership?
7. If you can sell neither car for 40% of its value at any time, how does the analysis change?
Answer:
1. CA=16,500+5,050x
2. CB=24,500+3,450x
3. CA(x=5)=CB(x=5)=41,750
If keeped 4 years, Model A is more economical.
4. 5 years
5. From month 49 to 61.
6. The cost of ownership of Model A increases more than Model B, as it is less gas efficient. The break-even point for x is reduced from x=5 to x=2.35.
7. The fixed cost are reduced by a 40%, so the variable cost, the ones that depend on time of ownership, are increased in importance.
Step-by-step explanation:
We can express the cost of ownership as the sum of the purchase cost, gas cost and insurance cost.
1. For model A we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$4,800x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$5,050x[/tex]
2. For model B we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$3,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$3,450x[/tex]
3. If x=5, the costs for each car are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(5)=16,500+25,250=41,750\\\\\\\text{CoOwn B}=24,500+3,450\cdot(5)=24,500+17,250=41,750[/tex]
5 years is the break-even point for the cost of ownership between these two cars.
If you plan to keep the car for 4 years, the costs are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(4)=16,500+20,200=36,700\\\\\\\text{CoOwn B}=24,500+3,450\cdot(4)=24,500+13,800=38,300[/tex]
For a 4 year period ownership, the model A is more economical ($36,700).
4. This happens for 1 year, the fifth year, in which the two models have the same cost of ownership.
5. At the 5th year, the cost for both models are the same.
Then, this corresponds to the months 4*12+1=48+1=49 and 5*12+1=61.
6. If the cost of gas doubles, the cost of ownership would rise for both model, but more for the Model A, which is less gas efficient and hence has a higher gas cost.
Model A
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$9,600x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$9,850x[/tex]
Model B
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$6,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$6,450x[/tex]
The breakeven point goes from x=5 (for $3 per gallon) to x=2.35 (for $6 per gallon).
[tex]16,500+9,850x=24,500+6,450x\\\\(9,850-6,450)x=24,500-16,500\\\\x=8,000/3400=2.35[/tex]
7. If we can sell any car for 40% of its value at any time, the cost of ownership becames:
Model A:
[tex]\text{Cost of ownership}=16,500+5,050x-0.4\cdot16,500\\\\\text{Cost of ownership}=9,900+5,050x[/tex]
Model B
[tex]\text{Cost of ownership}=24,500+3,450x-0.4\cdot24,500\\\\\text{Cost of ownership}=14,700+3,450x[/tex]
The fixed costs are lowered by 40%, so the variable costs (the ones that depend on time) became more important.
Identify which type of sampling is used random, systematic, convenience, stratified, or cluster To determine customer opinion of their inflight service, Continental Airlines randomly selects 30 flights during a certain week and surveys all passengers on the flights. Which type of sampling is used?
A. Stratified
B. Cluster
C. Systematic
D. Random
E. Convenience
Answer:
B. Cluster
Step-by-step explanation:
Samples may be classified as:
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Each Continental Airlines flight is a group.
30 of them are chosen, and in each group chosen, every passenger is surveyed.
So cluster sampling was used.
Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of whole cheese sandwiches that can be prepared from 32 slices of bread and 51 slices of cheese. g
Answer:
Only 16 whole sandwiches can be produced
Step-by-step explanation:
From the question, we know that we will need two slices of bread to make a full sandwich.
We can divide the number of slices of bread by two to check how many full sandwiches can be made.
Number of complete sets of bread = 32/2 = 16 sets
Similarly, we can divide the number of slices of cheese by 3 to find out the number of complete sets of cheese that will be there:
Number of complete sets of cheese = 51/3 = 17 sets
Since we have more cheese than bread, the number of whole sandwiches that can be made will be limited to the number of sets of bread available. (in this case, the ingredient smaller in quantity will be used to limit the production) which is = 16
Therefore only 16 whole sandwiches can be produced
Use the following equation to answer the questions below:
y − 2 = 1 /3 (x + 4)
Find the equation of the line that is passing through (8, 2) and is perpendicular to the given line.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped you plz don't forget to thank me...
