A freight train traveling along a certain route uses 12 units of fuel per mile plus an additional 2.2 units of fuel per mile for each railcar on the train. Let N represent the number of railcars on the train. What is an expression for f(N), the total number of units of fuel used per mile? find f(12). How many railcars does the train have if f(N)=34?
Answer:
[tex]38.4\ \text{units of fuel/mile}[/tex]
10
Step-by-step explanation:
Let [tex]N[/tex] represent the number of rail cars on the train
Each rail car adds 2.2 units of fuel per mile.
Fixed fuel consumption is 12 units of fuel per mile
The function of fuel consumption per mile is
[tex]f(N)=12+2.2 N[/tex]
when
[tex]N=12[/tex]
[tex]f(12)=12+2.2\times 12\\\Rightarrow f(12)=38.4\ \text{units/mile}[/tex]
[tex]\boldsymbol{f(12)=38.4\ \text{units/mile}}[/tex]
[tex]f(N)=34\\\Rightarrow 12+2.2N=34\\\Rightarrow N=\dfrac{34-12}{2.2}\\\Rightarrow N=10[/tex]
So, the number of rail cars when [tex]f(N)=34[/tex] is 10.
While traveling in Canada, a police officer pulls you over for speeding. The posted speed limit is 100
km/hr. She asks you if you know how fast you were driving. You suddenly realize that your
speedometer's "100" measures miles/hr, not km/hr. How fast were you going?
Answer:
Speeding at 160.934 km/hr
Step-by-step explanation:
1 mile = 1.609344 kilometers
1.609344 * 100 = 160.934 kilometers
please help asap! it’s 1-10!
Answer:
1. yes, 3:2
2. no, population has an unproportional rate of change.
3. no, miles have an unproportional rate of change.
4. yes, 8:1
5. no, questions have an unproportional rate of change.
6. yes, 5:2
7. yes, 9:1
8. no, pounds have an unproportional rate of change.
9. no, days have an unproportional rate of change.
10. yes, 3:1
Chet started to slow his eating speed down later in the evening. He was
now eating only 1/4 of a turkey every 2 hours. What was his unit rate
later in the evening?
Answer:
The unit rate is:
1/8 turkey/per hour.Step-by-step explanation:
As Chet was eating 1/4 of a turkey every 2 hours.
This tells us that every two hours, Chet will eat 175 1/4 of a turkey.
Unit rate basically means 'how much of something per 1 unit of something else'.A unit rate is a rate with a denominator of 1 unit.
This means, in 1 hour, Chet will eat half of what he eats every 2 hours.
so Chet will eat [tex]\frac{\frac{1}{4}}{2}=\frac{1}{8}[/tex] of a turkey in 1 hour.
i.e.
[tex]\frac{\frac{1}{4}}{2}=\frac{1}{8}[/tex]
Therefore, the unit rate is:
1/8 turkey/per hour.54÷6+0.42×(9×8÷2+82)
Answer:
58.56
Step-by-step explanation:
Mr.West bought merchandise totaling $3,500. His overhead was $1,200. He sold the merchandise for $5,000. Find his percent on the profit based on the cost, to the nearest whole percent.
plz answer fast i rlly need it now
Answer:
17.647 = 18%
Step-by-step explanation:
I hope this helps also pls rate brainliest
please help with this question!
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
a ) Two matrices cannot be multiplied.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
b )
The answer is | 20 - 4 - 12 |
| 8 2 19 - |
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
I need help big time
The dimensions for a rectangular prism are x + 7 for the length, x + 9 for the width, and x for the height. What is the volume of the prism? Enter your answer as a polynomial in standard form. The volume of the prism can be expressed as _____.
Answer:
The volume of the prism is x^3 + 16x^2 + 63x
Step-by-step explanation:
Mathematically, the volume of the prism is the area of the base multiplied by the height of the prism
The area of the base is l * w
= (x + 7)(x + 9) = x^2 + 7x + 9x + 63 = x^2 + 16x + 63
The volume is now; x(x^2 + 16x + 63)= x^3 + 16x^2 + 63x
Steven is comparing the cost of a fresh lobster dinner at two different restaurants. The first
restaurant charges $51 for the meal, plus $2 per pound for the lobster he picks. At the
second restaurant, Steven would pay $4 per pound for the lobster, in addition to $19 for the
meal. Steven realizes that, in theory, dinner at both restaurants could cost the same amount
if the lobster had a certain weight. How much would Steven pay for his dinner? What is the
weight?
Answer:
Step-by-step explanation:
2x+51=4x+19
32=2x
x=16. The weight is 16 pounds
plug it back in to find the cost
32+51=83. 64+19 = 83. The cost is 83 dollars
Assume that y varies directly with x. If y= 2/5 when x= 1/3, find y when x = 1/4
Step-by-step explanation:
y1/x1=y2/x2
2/5÷1/3=y÷1/4
y=3/10=0.3
0.409 +0.681
can you add this with the repeating decimals?
Answer:
Yes, you can and the answer would be 1.09.
Step-by-step explanation:
jules loses a golf ball
Answer:
Ok. I'm sorry Jules lost a golf ball. Is there a question?
Answer:
jus buy a new one
Step-by-step explanation:
they lost the golf ball so they need to buy a new one cuh
Greta offers to buy a team photo for 15 of her teammates, but 6 of them don't want one. If a team photo costs $2, how much will Greta spend on her teammates? Choose the correct expression and solution to this problem .
Answer:
$18
Step-by-step explanation:
i have a question can someone help me!!
−7+m/2=−12
Solving Two-Step
Answer:
m=-10
Step-by-step explanation:
Answer: m = -10
[tex]-7+\frac{m}{2} =-12\\\\<=>\frac{m}{2}=-5\\\\<=>m=-5.2=-10\\[/tex]
Step-by-step explanation:
State the slope and y-intercept of the graph of y - x = -2.
Answer:
the slope is 1
the y-int is -2
Answer:
Slop=1 y-intercept=-2
Step-by-step explanation:
What’s it the slope of the line
Answer:
3/4
Step-by-step explanation:
the graph point starts at the y-intercept 1 and then moves 4 digits forward and 3 digit upward
Answer:
Since the slope doesn't go down we can safely ignore -3/4 and -4/3.
The slope goes up 3 and 4 to the right.
y = 3
x = 4
y/x
so the answer is 3/4
2 2 7 :(0.6x)= 4 21 :0.25
lol my phones taken away until i finish this question help
Answer:
i don't exactly know what the question is but based off what i understand x=140
Step-by-step explanation:
Answer:
what are you trying to solve, be more elaborate on your question
Step-by-step explanation:
PLEASE HELP ME! I NEED YOU TO HELP ME! WHOEVER ANSWERS CORRECTLYWILL GET A BRAINLEST AND POINTS!!!
On a chapter test, Stephanie uses the rules of equation solving and inverse operations to solve the cubic equation below. The directions on the test are not very specific, however, they do say to give an exact solution. Stephanie is not sure if she should submit a decimal approximation or a simplified radical as the answer.
4x3 = 756
What recommendation can you make to Stephanie regarding her answer to the cubic equation above? In your recommendation, explain what the term "exact" indicates with regards to the solution.
Solve the cubic equation from Stephanie’s test. Submit two solutions for the equation- a) your answer as a decimal approximation, rounded to the nearest hundredth, and b) as a simplified radical. Use substitution to check each version of your solution in the original equation.
After solving the test question and checking both the decimal solution and the simplified radical form, would you change your recommendation (in Part 1) to Stephanie regarding the format of her answer? Use complete sentences to explain your reasoning.
Answer:
Since, we are asked to present an exact solution, we are not able to give approximations.
The term exact means that you need to give the answer like this:
If we were asked to give an approximate result it would be like this x = 5,738.
f=4x%5E%7B3%7D%20%3D%20756%5C%5Cx%5E%7B3%7D%20%3D%20%5Cfrac%7B756%7D%7B4%7D%20%5C%5Cx%5E%7B3%7D%20%3D%20189%5C%5Cx%20%3D%20%5Csqrt%5B3%5D%7B189%7DHence, our answer is
Step-by-step explanation:
Gabriella ran several laps around a 1/4-mile track. Then she ran 2 1/2 miles on a trail. In all, she ran 4 miles. Write and solve an equation to find l, the number of laps Gabriella ran.
9514 1404 393
Answer:
1/4×l +(2 1/2) = 4l = 6Step-by-step explanation:
For l laps around a 1/4 mile track, the total distance is ...
l×(1/4)
After adding 2 1/2 miles to that, Gabriella's total distance was 4 miles:
l×(1/4) +(2 1/2) = 4 . . . . an equation to find l
__
We can solve this equation by subtracting 2 1/2, then multiplying by 4.
l×(1/4) = 1 1/2
l = 4(1 1/2)
l = 6
Gabriella ran 6 laps on the track.
Lisa puts $8,000 in an account that earns 12% simple annual interest. If she leaves her money in the account for 4 years, how much interest will she earn?
Answer:
392000
Step-by-step explanation:A=p(1+
Help! I Greatly appreciated it.
it is proportional
cause it is trust me
Answer: it's proportional
Step-by-step explanation:
A bag contains 5 red marbles, 3 blue marbles, 7 yellow marbles, and 2 green marbles. Which ratio can be used to compare the yellow marbles to the blue marbles?
Answer:
7:3
Step-by-step explanation:
The number of yellow marbles: the number of blue marbles
Answer:
7:3
Step-by-step explanation:
there are 7 yellow marbles and 3 blue marbles
The pair of points lies on the same line with the given slope. Find x.
(4,6). (x, 12); slope = 2
Answer:
x=7
Step-by-step explanation:
I got this because it is rise over run
[tex]\frac{rise}{run} =\frac{6}{?} =2[/tex]
The missing number would be 3, and if you add that three to 4 you get 7. which means that the answer is...
(7,12)
Hope this helps you!!!f(x)=2x+3 g(x)=x-4 Find (fg)(x) (Hint use FOIL)
Answer:
2x^2-5x-12
Step-by-step explanation:
using foil this should be the answer, do you need the solution values?
Change each radian measure to degree measure
Answer:
13)60°
14)90°
15)-270°
16)-180°
17)30°
18)150°
19)120°
20)300°
21)210°
22)-315°
23)450°
24)720°
25)-1260
26)-810°
27)45°
28)135°
29)-300°
30)15°
31)1170°
32)-240°
Step-by-step explanation:
Gavin has $50,000 with which to start a new business. He wants to maintain a cash balance of more than $26,000.
If w is the amount Gavin withdraws to pay for expenses, the inequality representing the situation is BLANK. The amount he can withdraw is given by BLANK.
Answer: the answer is $76,000 dollars.
Step-by-step explanation:
$50,000 + $26,000= $76,000
Please answer this..........
Answer:
The answer would be 126
Step-by-step explanation:
you add 28+35 which is 63, then you multiply by 8 which is 504 and you multiply by 1/4 which is 126 :)
If a person walks 1/4 of a mile in 1/8 of an hour. Determine how many miles they are running per hour.
Answer:
1&1/8 m/h
Step-by-step explanation:
2/8 of a mile = 1/8 of an hour
add 7/1 to both sides thats 1 and 1/8 of a mile in 1 hour
What is the equation of in line slope intercept from that has a slope of 4 and goes through the point -8 -16
Answer:
Step-by-step explanation:
is your qustion like -8-16 because its -24
Answer:
y = 4x + 16
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4, thus
y = 4x + c ← is the partial equation
To find c substitute (- 8, - 16) into the partial equation
- 16 = - 32 + c ⇒ c = - 16 + 32 = 16
y = 4x + 16 ← equation of line