The amount of freight transported by rail in the u.s was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then.a. write a function representing the amount of freight, in billions of ton-miles, transported annually. ( 1960 = year 0 )b. graph the functionc. in what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1,000 billion)?
Answers
The amount of freight transported by rail was 580 billion ton-miles in 1960.
The amount increased at a rate of 2.32% per year.
a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is
[tex]y=a(1+r)^x[/tex]Where
y represents the final number after "x" periods of time
a represents the initial number at x=0
r represents the growth rate, expressed as a decimal value
x represents the number of time intervals that have passed
For this example, the initial amount is a=580 billion
The growth rate is r=2.32/100=0.0232
You can determine the equation as follows:
[tex]y=580(1+0.0232)^x[/tex]b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞
To graph it, you have to determine at least two points of the graph, I will determine 3
For x=-100
[tex]\begin{gathered} y=580(1+0.0232)^{-100} \\ y=58.53 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} y=580(1+0.0232)^0 \\ y=580 \end{gathered}[/tex]For x=10
[tex]\begin{gathered} y=580(1+0.0232)^{10} \\ y=729.51 \end{gathered}[/tex]The points are
(-100,58.53)
(0,580)
(10,729.51)
Plot the points and then draw an increasing line from -∞ to +∞
c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000
This value is approximate x=23.57
This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.
Add the number of years to the initial year to determine the date:
[tex]1960+23=1983[/tex]By 1983 the number of ton-miles transported will exceed the trillion.
Related Questions
please help me thank you
Answers
The basic wage earned by a truck driver for a 40 - hour week is $560 How can I calculate the hourly rate for overtime, the driver is paid one and a half times the basic hourly?
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First, find the hourly rate by dividing the total wage of $560 by the amount of time worked, which is 40 hours:
[tex]\frac{\text{\$}560}{40h}=\text{ \$}14\text{ per hour}[/tex]To find the hourly rate for overtime, multiply the basic hourly rate by 1.5:
[tex](\text{\$}14\text{ per hour})\times1.5=\text{ \$}21\text{ per hour}[/tex]Therefore, the hourly rate for overtime is $21.
960 watts hour per how many watts hour does it consume in 4 days and 6 hours
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Answer:
Explanation:
[tex]undefined[/tex]a large human population of both globally and within individual countries has been a concern since the time of Thomas Malthus. country X is 95% desert. the government of country X is concerned about not having enough arable land (land capable of being used to grow crops) in the country to produce the food needed to feed its population without increasing food imports the demographic for Country X for the year 2020 is provided in the table below. 1. calculate the national population growth rate for a country X 2. using the rule of 70 calculate the doubling time for this population
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Firstly, we want to calculate the growth rate of the population
While birth would increase the population, death and migration will decrease the population
So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;
Thus, we have;
[tex]\begin{gathered} \frac{38}{1000}\text{ - (}\frac{24}{1000}\text{ + }\frac{2}{1000}) \\ \\ =\text{ }\frac{38}{1000}\text{ - }\frac{26}{1000} \\ \\ =\text{ }\frac{12}{1000} \end{gathered}[/tex]The national population growth rate for a country X is 12/1000
Secondly, we are to use the rule of 70 to calculate the doubling time for the population
Mathematically;
[tex]\begin{gathered} No\text{ of years to double = }\frac{70}{\text{annual growth rate}} \\ \\ No\text{ of years to double = 70 divided by }\frac{12}{1000} \\ \\ No\text{ of years = 70 }\times\frac{1000}{12}=5833\frac{1}{3}years^{} \\ \\ \frac{1}{3}\text{ years is same as 4 months} \\ \\ So\text{ it will take 5833 years and 4 months for the population to double} \end{gathered}[/tex]David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
Answers
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
Given,
The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.
Explain what each part of the expression represents in the context of the problem.
Now, According to the question:
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
What each part of the expression represents in the context of the problem include the following:
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
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In circle D with the measure of minor aré CE = 162 degrees, find m of CFE
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SOLUTION
Step 1: Make a more comprehensive sketch of the question.
The measure of CFE is 81 degrees.
simplify the following expression:7^-6 × 7^3
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To solve this question, we will apply the knowledge of exponents and indices
The values have the same bases (7) but different powers and they are separated by a multiplication sign.
So we can use the law:
[tex]a^{x\text{ }}\text{ x a}^{y\text{ }}=a^{x\text{ + y}}[/tex]so that
[tex]7^{-6}\text{ x 7}^3=7^{-6\text{ + 3}}[/tex]on simplifying will give
[tex]7^{-3}[/tex]=>
[tex]7^{-3}\text{ =}\frac{1}{7^3}[/tex]Find the point-slope equation for the line through (0,-2) and (4,1)
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ANSWER:
STEP-BY-STEP EXPLANATION:
We can calculate the value of the slope using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we replace each value and we will be left with the following:
[tex]undefined[/tex]how many drahms areequivalent to 300 grains?
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hello
to solve this question, we need to know how many grains is in 1 gram
[tex]\begin{gathered} 1\text{grams}=15.43\text{grains} \\ \end{gathered}[/tex]now let 300 grains be equal to x grams
[tex]\begin{gathered} 1\text{grams}=15.43\text{grain} \\ \text{xgrams}=300\text{grains} \\ \text{cross multiply both sides and solve for x} \\ x\times15.43=1\times300 \\ 15.43x=300 \\ \text{divide both sides by 19.44} \\ \frac{15.43x}{15.43}=\frac{300}{15.43} \\ x=\frac{300}{15.43} \\ x=19.44 \end{gathered}[/tex]300 grains will weigh 19.44g
Solve the following expression when
r = 22
r
11+3+r
Answers
11 +3 + r
11+3 = 14
So 14 + 22 is 36
Ans:36
Hope this helps!
represent the following expressions as a power of the number a (a≠0):
(a^-1*a^-2)^-2
Answers
By using some exponent properties, we will see that the expression can be written as:
a^6
How to simplify the expression?
Here we need to use some exponent properties, these are:
(x^n)^m = x^(n*m)x^(-n) = (1/x)^nx^n*x^m = x^(n + m)Here we have the expression:
(a^(-1)*a^(-2))^(-2)
Using the third property we can write:
(a^(-1)*a^(-2))^(-2) = (a^(-1 - 2))^(-2) = (a^(-3))^(-2)
Now we use the first property:
(a^(-3))^(-2) = a^(-3*-2) = a^6
That is the expression simplified.
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simply
i^3+i^20
show work
Answers
==================================================
Explanation:
Recall that
i = sqrt(-1)
Squaring both sides gets us
i^2 = -1
Now let's multiply both sides by i
i*i^2 = i*(-1)
i^3 = -i
Repeat the last step
i^3 = -i
i*i^3 = i*(-i)
i^4 = -i^2
i^4 = -(-1)
i^4 = 1
----------------------------
Here's a summary so far
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.
20/4 = 5 remainder 0
Therefore i^20 = i^0 = 1
Or we can think of it like this
i^20 = (i^4)^5 = 1^5 = 1
----------------------------
This means we can then say
i^3 + i^20 = -i + 1 = 1 - i
so, the order is i -1 -i 1.
if you have an exponent of 1, the answer is i.
if you have an exponent of 2, the answer is -1.
if you have an exponent of 3, the answer is -i.
if you have an exponent of 4, the answer is 1.
if you have an exponent of 5, the answer is i.
this repeats in this pattern. so one way to solve it is to count, or you can simply divide the exponent by 4.
if the answer has .25, it’s i.
if the answer has .50, it’s -1.
if the answer has .75, it’s -i.
if the answer has a whole nunber, any, such as 4 or 7, it’s 1.
3/4=.75. so i^3= -i.
20/4= 5. so i^20=1.
(-i) + (1) = 1-i
convert 85 degrees to radians
Answers
To convert 85 degrees to radians, consider:
[tex]\pi=180^o^{}[/tex]Let
[tex]x=85^o[/tex]Then
[tex]\begin{gathered} 180x=85\pi \\ x=\frac{85\pi}{180} \\ \\ =\frac{17}{36}\pi \end{gathered}[/tex]distance between (11,-5) and (0,1)
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Here,point can be written as:
[tex]\begin{gathered} x1=11, \\ y1=-5 \\ x2=0 \\ y2=1 \end{gathered}[/tex]The formula for the distance between the points as follows;
[tex]\begin{gathered} d=\sqrt{(x1-x2)^2+(y1-y2)^2} \\ d=\sqrt{(11-0)^2+(-5-1)^2} \\ d=\sqrt{121+36} \\ d=\sqrt{157} \\ d=12.53 \end{gathered}[/tex]Thus, the distance between the point is 12.53.
Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?
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1) Problems like these, we can solve by writing an equation.
2)Since that tomato plant grew 150% after three weeks we can write the following
[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5
3) Thus, the answer is:
[tex]10\:inches[/tex]hello! i need help on this question and the (select) questions have the options of 1997 to 2006
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To find the average rate of change, we use the following formula
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 1998, f(a) = 856, b = 2001, and f(b) = 1591.
[tex]r=\frac{1591-856}{2001-1998}=\frac{735}{3}=245[/tex](a) The average rate of change between 1998 and 2001 is 245.We use the same formula between 2002 and 2006, where a = 2002, f(a) = 1483, b = 2006, and f(b) = 745.
[tex]r=\frac{745-1483}{2006-2002}=\frac{-738}{4}=-184.5[/tex](b) The average rate of change between 2002 and 2006 is -184.5.(c) As you can observe, the population was increasing from 1997 to 2001.(d) The population was decreasing from 2001 to 2006.The table below shows distance as it relates to how many seconds have passed.1510time(seconds)distance, y =y = f(x)(meters)30150 300Write a formula to describe the distance as a linear function of time.
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Find the x- and y-intercepts of the graph of the equation.5x + 3y = 15x−intercept (x, y) = ( ) y−intercept (x, y) = ( )
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Consider that the intercept form of equation of a line whose x-intercept is (a,0) and y-intercept is (0,b), is given by,
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]The equation of the line is given as,
[tex]5x+3y=15[/tex]Convert this equation into intercept form,
[tex]\begin{gathered} \frac{5x}{15}+\frac{3y}{15}=1 \\ \frac{x}{3}+\frac{y}{5}=1 \end{gathered}[/tex]Comparing with the standard equation,
[tex]\begin{gathered} a=3 \\ b=5 \end{gathered}[/tex]Thus, the x-intercept and y-intercept of the equation, respectively, are,
[tex](3,5)\text{ and }(0,5)[/tex]A pendulum swings through an angle of 14° each second. If the pendulum is 14 cm in length and the complete swing from right to left last two seconds what area is covered by each complete swing?
Answers
Answer;
[tex]\text{Area = 47.90 cm}^2[/tex]Explanation;
Firstly, we need a diagrammatic representation to get what is described in the question.
We have this as follows;
Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees
To get the area, we simply need to find the area of the sector formed by the by pendulum
Mathematically, we have the area of a sector calculated as follows;
[tex]A\text{ = }\frac{\theta}{360}\times\pi\times R^2[/tex]theta is the angle made by the pendulum in one complete swing which is 28 degrees
pi is 22/7
R is the length of the pendulum which is 14 cm
Substituting these values in the formula above, we have it that;
[tex]\begin{gathered} A=\frac{28}{360}\times\frac{22}{7}\times14^2 \\ \\ A=47.90cm^2 \end{gathered}[/tex]Two buses leave a station at the same time and travel in opposite directions. One bus travels 16(km)/(h) slower than the other. If the two buses are 1040 kilometers apart after 4 hours, what is the rate of each busSolve using a system of linear equations
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Let x be the velocity (rate of change ) of one of the buses. We know that the other one travels 16 km/h slower; this means that the second velocity is:
[tex]x-16[/tex]Now the combined velocity would be:
[tex]2x-16[/tex]We know that the distance is equal to time by velocity, then we have that:
[tex]4(2x-16)=1040[/tex]Solving for x we have:
[tex]\begin{gathered} 4(2x-16)=1040 \\ 2x-16=\frac{1040}{4} \\ 2x-16=260 \\ 2x=260+16 \\ 2x=276 \\ x=\frac{276}{2} \\ x=138 \end{gathered}[/tex]Therefore the rate of the faster bus is 138 km/h and the rate for the slower bus is 122 km/h.
In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $1595.
Answers
Let
x ----> amount deposited at 4.5%
y ----> amount deposited at 5%
we have that
y=2x----> equation A
4.5%=0.045
5%=0.05
so
0.045x+0.05y=1,595 ----> equation B
solve the system
substitute equation A in equation B
0.045(x)+0.05(2x)=1,595
solve for x
0.045x+0.10x=1,595
0.145x=1,595
x=11,000
Find y
y=2(11,000)=22,000
The amount deposited at 4.5% was $11,000 and the amount deposited at 5% was $22,000One thousand Charity raffle tickets are sold for $1 each. Winning tickets will be drawn in order,1st,2nd,3rd. First prize is $500. Second prize is $300. Third prize is $150. Tickets are replaced after each drawing so the probability of being draw for each prize is 1/1000. What is the expected value? I am stuck on this question and need help
Answers
Answer:
-$0.05
Explanation:
The expected value can be calculated as the sum of each possible prize multiplied by its probability. You will buy a ticket for $1 and there is a probability of 1/1000 to win the $500, a probability of 1/1000 to win $300, and a probability of 1/1000 to win $150, then the expected alue is
[tex]\begin{gathered} E=-1+500(\frac{1}{1000})+300(\frac{1}{1000})+150(\frac{1}{1000}) \\ E=-1+0.5+0.3+0.15 \\ E=-0.05 \end{gathered}[/tex]Therefore, the expected value is -$0.05.
-Зе - 10 - 4Solve and graph the inequality
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The given inequality is expressed as
[tex]\begin{gathered} -\text{ 3e - 10 }\leq-4 \\ \end{gathered}[/tex]We would add 10 to both sides of the inequality. It becomes
[tex]\begin{gathered} -\text{ 3e - 10 + 10 }\leq-\text{ 4 + 10} \\ -\text{ 3e }\leq6 \end{gathered}[/tex]We would divide both sides by - 3. This would cause the inequality symbol to reverse. It becomes
[tex]\begin{gathered} \frac{-3e}{-3}\text{ }\ge\frac{6}{-3} \\ e\text{ }\ge-2 \end{gathered}[/tex]The graph would be
The shaded circle at the position of - 2 indicates that- 2 is inclusive
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
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The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]Solve for w.4w²-24w=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution".W =0U08Nosolution
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ANSWER
[tex]\begin{equation*} w=0,\text{ }w=6 \end{equation*}[/tex]EXPLANATION
We want to solve the given equation for w:
[tex]4w^2-24w=0[/tex]To do this, we have to factorize the equation and simplify it.
Let us do that now:
[tex]\begin{gathered} (4w*w)-(4w*6)=0 \\ \\ 4w(w-6)=0 \\ \\ \Rightarrow4w=0\text{ and }w-6=0 \\ \\ \Rightarrow w=0,\text{ }w=6 \end{gathered}[/tex]That is the answer.
which equation represents the function modeled by the graph? (picture of graph below)
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Answer:
The parent function of the graph is given below as
[tex]y=\sqrt[3]{x}[/tex]The parent function has undergone transformation
Hence,
Using a graphing calculator, we will have the graph be
Hence,
The final answer is
[tex]\Rightarrow f(x)=\sqrt[3]{4x+2}[/tex]The FIRST OPTION is the right answer
Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
Answers
In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
Need help determining if h. F(x)= 3^x is even, odd or neither
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Recall that:
1) f(x) is an even function if:
[tex]f(-x)=f\mleft(x\mright).[/tex]2) f(x) is an odd function if:
[tex]f(-x)=-f(x).[/tex]Now, notice that:
[tex]\begin{gathered} f(-x)=3^{-x}\ne3^x=f(x), \\ f(-x)=3^{-x}\ne-3^x=-f(x). \end{gathered}[/tex]Therefore f(x)=3^x is neither an even function nor an odd function.
Answer: Neither an even function nor an odd function.
The difference between the graph of a radical function and the graph of a rational function
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The difference between the graph of a radical function and that of a rational function is:
A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.
But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.
The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).
An object moves at a rate of 9,400 inches each week. How many feet does it move per minute?
Answers
To answer this question, we need to transform each of the values into the corresponding other units:
• Inches ---> Feet
,• Week ---> minutes
And we also have here a ratio:
• Inches/week ---> Feet/minute.
Then we can proceed as follows:
Inches to FeetWe know that the conversion between inches and feet is:
[tex]1ft=12in[/tex]Then
[tex]1in=\frac{1}{12}ft[/tex]If we have 9,400 inches, then:
[tex]9400in=\frac{9400}{12}ft\Rightarrow9400in=783ft+\frac{1}{3}ft=783.33333333ft[/tex]Week to minutesWe know that:
[tex]1\text{hour}=60\min [/tex]In one day we have 24 hours, then:
[tex]24\text{hours}=24\cdot60\min =1440\min [/tex]Then we have 1440 minutes in a day. A week has 7 days. Therefore, we will have:
[tex]1440\frac{\min}{day}\cdot7days=10080\min [/tex]Therefore, we have that there are 10,080 minutes in one week.
Now, to find the ratio of feet per minute, we need to divide:
[tex]\frac{783\frac{1}{3}ft}{10080\min}=0.0777116402116\frac{ft}{\min }[/tex]In summary, we can say that the object moves:
[tex]0.0777116402116\frac{ft}{\min }[/tex]into the