Mathematics College

There were three trains made of the cars with exactly the same number of passenger's seats. The first train had 418 seats, the second 456, and the third 494. How many cars were in each train, if it is known that each train had not more than 50 cars?

1 train=?

2 train=?

3 train=?

Answers

Answer 1
1 train=418  2 train=456  3train=494 add them all together and divide by 3      418+456+494=1368/3=456 i hope this helps you and each train has more than 50 cars
Answer 2
You apparently need to find the greatest common divisor of (418, 456, 494). You can start by looking at the differences between these numbers. They are
.. 456 -418 = 38
.. 494 -456 = 38
So, if 38 divides these numbers evenly, that is the number of seats in each car. (It does).

train 1 had 418/38 = 11 cars
train 2 had 456/38 = 12 cars
train 3 had 494/38 = 13 cars

_____
The number of seats in each car could be a sub-multiple of 38, say 19. In that case, the number of cars in each train would be twice the number shown above. It is slightly unusual for a train car to have an odd number of seats, but is not unheard of.

Related Questions

The circumference of a circle is 31.4 inches. What is the circle's diameter? C=31.4 in Use 3.14 for ​.

Answers

We will use the circumference formula to find the radius and then multiply it by 2 to find the diameter.

C = 2πr
31.4 = (2)(3.14)(r)
31.4 = 6.28r
5 = r

So our radius is 5 in.

We can multiply it by 2 to get the diameter.

5*2 = 10

So the diameter is 10 inches

49.3
this can be calc for a form

What is the best measure of the center for the data set: 2,2,2,4,4,5,5,5,7,7,15,17

Answers

5,5 are in the middle. So it is 5+5\2 which is 10\2 which is 5

Kieran is making a birthday card with construction paper. He wants to cut a circle out of a square piece of construction paper. The circle will have a radius of 6 inches. In square inches, what is the area of the smallest piece of construction paper Kieran could use?

Answers

when cutting a circle from a square piece of paper, to use the minimum piece of square paper, midpoints of the edges of the square should be touching the edges of the circle.
For this the length of the square paper should be equal to the diameter of the circle.
If so the the area of the square piece of paper needed;
area = length * length 
length of the square = diameter of the circle 
diameter = 2 radii 
               = 2 * 6 inches 
               = 12 inches 
Therefore length of square = 12 inches 
area of the square = 12 inches * 12 inches 
                              = 144 sq.inches

What is the value of z in the equation 5z − 9 = 36?

4
5
6
9

Answers

You answer is 9.
5 x 9 = 45
45 - 9 = 36

In this question, you have to solve the equation.

5z – 9 = 36

You transpose the 9 to other side so the equation would look like this:

5z = 36 + 9

5z = 45

Divide 5 in both sides to solve the value of z:

z = 9

Divide. 3.2 ÷ 0.8 help me e pleaseeeeeeeeeeee !!!!!!

Answers

[tex] \frac{3.2}{0.8} = \frac{32}{8} = \frac{4\times 8}{8} = 4[/tex]
The answer is 4. simply move the deimal to create 8 and 32. this gives you 4 or 0.4

The expression 52x – 169 is equivalent to 13

Answers

4x - 13 it is the last answer choice

What is the solution of the system?


Use the elimination method.

4x+2y=18
2x+3y=15

Answers

{4x+2y=18
{2x+3y=15           -divide both sides by -2
                                 -2x-y=-9
                                  2x+3y=15
                            -sum the equations vertically to
                              eliminate at least one variable
                               2y=6 divide both sides of the equation
                                         by 2
                               y=3
             -substitute the given value of y into the simplest equation
                               2x+3*3=15
                                    -solve for x
                                         x=3
                  -the solution of the system is the ordered pair (x,y)
                                   (x,y)= (3,3)
                                         Check √
-check if the given ordered pair is a solution of the system of equations
{4*3+2*3=18
{2*3+3*3=15
simplify the inequalities 
{18=18
{15=15
-since all of the equalities are true the ordered pair is the solution of the system 
                           

Answer:

 -divide both sides by -2

                                -2x-y=-9

                                 2x+3y=15

                           -sum the equations vertically to

                             eliminate at least one variable

                              2y=6 divide both sides of the equation

                                        by 2

                              y=3

            -substitute the given value of y into the simplest equation

                              2x+3*3=15

                                   -solve for x

                                        x=3

                 -the solution of the system is the ordered pair (x,y)

                                  (x,y)= (3,3)

                                        Check √

-check if the given ordered pair is a solution of the system of equations

{4*3+2*3=18

{2*3+3*3=15

simplify the inequalities  

{18=18

{15=15

-since all of the equalities are true the ordered pair is the solution of the system

Step-by-step explanation:

Assume you have a poker chip set containing blue, red, and white chips, all of the same size. you place 15 blue chips, 10 red chips, and 25 white chips in a bag. as you are about to randomly draw a chip from the bag, you bet your friend you will pick a red chip from the bag because you feel that red is your lucky color.

Answers

Is the question what is the probability that you draw a red chip? If it is, the answer is 10/50, which can be simplified to 1/5, 0.2 or 20%.

Kate ran 6 miles. How far did she run in kilometers?

Answers

Final answer:

Kate ran approximately 9.66 kilometers after converting her distance run in miles to kilometers using the conversion factor of 1 mile equaling 1.60934 kilometers.

Explanation:

Kate ran 6 miles and we need to convert that distance into kilometers. To do this, we use the conversion factor that 1 mile is approximately equivalent to 1.60934 kilometers. By multiplying 6 miles by this conversion factor, we get:

6 miles × 1.60934 km/mile = 9.65604 kilometers

So, from the above calculation Kate ran roughly 9.66 kilometers, considering we usually round the result to two decimal places when dealing with distances unless high precision is required.

A sample of cigarette smoke contains 2.09% carbon monoxide. the u.s. national ambient air quality standard for co in a 1−hr period is 35 ppm. how many times greater than this standard is the co concentration in cigarette smoke?

Answers

For a gas, 35 ppm means that there are 35 units of carbon monoxide in a totla of 1,000,000 units of gas in total. This is equivalent to: 35/1,000,000 = 3.5 x 10^-5.

The actual sample, which has 2.09%, can also be written as 0.0209. Then we divide 0.0209 / 3.5 x 10^-5, which gives 597.14. So the sample of cigarette smoke has CO concentration nearly 600 times more than the standard allows.

What is the a-value of the function, then determine if the graph opening up or down f(x)=−5(x+7)2+6?

Question 4 options:

a = -5, opens down


a = -5, opens up


a = 7, opens up


a = 7, opens down

Answers

we know that
the equation of the vertical parabola in the vertex form is
y=a(x-h)²+k
where 
(h,k) is the vertex of the parabola
if a> 0 then
 the parabola opens upwards

if a< 0
then the parabola open downwards

in this problem  we have
f(x)=−5(x+7)²+6
a=-5
so
a< 0 -------> the parabola open downwards

the vertex is the point (-7,6) is a maximum

the answer is the option
a = -5, opens down 

see the attached figure

Answer:
a = -5, opens down

Explanation:
The general form of the quadratic equation is:
f(x) = a(x-h)² + k where (h,k) is the vertex of the parabola.

The value of the "a" determines whether the parabola is open upwards or downwards:
1- if the value of "a" is positive, this means that parabola opens upwards
2- if the value of "a" is negative, this means that the parabola opens downwards

Now, for the given:
f(x) = -5(x+7)² + 6
By comparison, we can note that:
a = -5
The value of "a" is negative which means that the parabola opens down.

The attached image shows the graph of the given function

Hope this helps :)

A rancher wants to fence in a rectangular area of 14900 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do this?

Answers

Suppose the length of the fence perpendicular to the central partition is x. Then the total length of the fence (L) for enclosed area A is
.. L = 2x +3*A/x
The derivative of this with respect to x is
.. L' = 2 -3A/x²
L will be minimized when this is zero.
.. 0 = 2 -3A/x²
.. x² = 3A/2
.. x = √(3A/2)

For this value of x, the total length of fence is
.. L = 2√(3A/2) -3A/√(3A/2)
.. L = 4√(3A/2) = 2√(6A)

For this problem, A = 14,900 ft², so
.. L = 2√(6*14,900 ft²) ≈ 597.997 ft

The smallest length of fence required to fence the rectangular area is 598 ft.

the slope of the line passing through (-9,-6) and (-15,y) is 2/3. what is the value of y

Answers

The value of y is -10

Sir, please show your work

which of the following expressions is equivalent to the expression below ?

Answers

The correct answer is C

Read the statement, and identify the expressions that are equivalent. the product of a number minus 17 and 5

Answers

Answer:

The expressions equivalent to 'the product of a number minus 17 and 5' are (n - 17) x 5 and 5(n - 17), where n is the unknown number. These cannot be simplified further without additional information.

Step-by-step explanation:

The statement 'the product of a number minus 17 and 5' can be translated into an algebraic expression. This expression would look like (n - 17) × 5 or 5(n - 17), where n represents the unknown number. Both expressions are equivalent and represent the same mathematical operation.

When simplifying algebraic expressions, it is important to eliminate terms wherever possible to get a more straightforward expression. However, in this case, since we don't have a specific value for n, we cannot simplify the expression further without additional information.

Always remember to check your answer to ensure that the expression makes sense and is reasonable within the context of the problem.

in the following figure find a deg,2adeg and bdeg

Answers

From the figure. a and b are equal because the lines are parallel. The jargon is alternate interior angles are equal.

The two remote interior angles are equal to the exterior angle. That interprets to
b + 2a = 84o But b = a
a + 2a = 84o
3a = 84
a = 84/3
a = 28 <<<< answer
b = 28 <<<< answer
2a = 56 <<<< answer.


Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find ||u+v||

a. sqrt32

b. 2

c. 5

d. 8

Answers

[tex]\bf \begin{cases} u=-4i+1j\implies & \ \textless \ -4,1\ \textgreater \ \\ v=4i+1j\implies &\ \textless \ 4,1\ \textgreater \ \end{cases}\qquad u+v\implies \ \textless \ -4,1\ \textgreater \ +\ \textless \ 4,1\ \textgreater \ \\\\\\ \ \textless \ -4+4~,~1+1\ \textgreater \ \implies \ \textless \ 0,2\ \textgreater \ \\\\ -------------------------------\\\\ \stackrel{magnitude}{||u+v||}\implies \sqrt{0^2+2^2}\implies 2[/tex]

Given the exponential function A(x)=P(1+r)^x, what value for r will make the function a decay function

Answers

The function will be a decay function for
.. |1 +r| < 1
.. -1 < 1 +r < 1
.. -2 < r < 0

Any value of r in the interval (-2, 0) will make the function a decay function.

_____
If x can have non-integer values, then you probably want r ∈ (-1, 0).

Answer:

To make the function a decay function the rate of change in the function A(x) is r<0.              

Step-by-step explanation:

Given : The exponential function [tex]A(x)=P(1+r)^x[/tex]

To find : What value for r will make the function a decay function?

Solution :

The exponential function is [tex]A(x)=P(1+r)^x[/tex],

where,  P is the initial value

and r is the rate of change

The condition of rate of change is

1) The function is an exponential growth if their is positive rate of change i.e r>0.

2) The function is an exponential decay if their is negative rate of change i.e. r<0.

Therefore, To make the function a decay function the rate of change in the function A(x) is r<0.

Jordan had $10.00 if each drawing pen costs $1.49, how many can he buy

Answers

He can by 6 pens. 6.7 to be exact.

Hope this helps!!
Hey there!

To solve this, you can multiply different numbers with 1.49 til you get 10.00 or very close to 10.00.

1.49 x 2 = 2.98 (that's too small)

1.49 x 3 = 4.47 (that's also too small)

1.49 x 4 = 5.96 (again, too small)

1.49 x 5 = 7.45 (close, but still not exactly 10 or close enough)

1.49 x 6 = 8.94 (correct answer)

It wouldn't be 7 because 1.49 x 7 = 10.43 and Jordan will not have enough money.

Final answer:
Jordan can buy 6 pens <-----

Hope this helps you.
Have a great day!

In a sale Gameboys are reduced by two-fifths. What is the sale price if the original price was $50.00?
(PS: Please write how you got the answer)

Answers

Two-fifths equals 0.4 or 40 percent off, this will help us later. So if the Gameboy was $50.00, then two-fifths off of that or 40 percent would mean that the Gameboy sale price is now $20.00. Quite a steal if you ask me! Multiply the decimal by the original price to find the new sale price for the future. Hope I helped! :)
You would divide $50 by 2/5 which equals $5

So, the Gameboys were sold for $5

Please mark as brainliest.

Please completely factor the following expression. e. 3x^2+5xy-2y^2

Answers

3x^2 + 5xy - 2y^2

Simplifying:

3x^2 + 5xy + - 2y^2


Reorder Terms:
5xy +3x^2 + - 2y^2


Factor a Trinomial.
(3x + - 1y)(x + 2y)


Final Result:
(3x + - 1y)(x + 2y)


Hope this helps!!!

A basketball player practices free throws by shooting 50 free throws a day. she records the number of free throws made each day. her number of free throws made is normally distributed with a mean = 34 free throws and standard deviation = 5 free throws. using appropriate rule learned in lesson 10, approximately what percent of the days does she make less than 29 free throws?

Answers

46 percent on free throws

Answer: 46%

Step-by-step explanation:

What is the mean of the data set?

10, 15, 14, 8, 18, 11, 12, 12, 10, 10, 17, 16


12.00

12.25

12.75

15.50

Answers

The answer is 17.75 :D
I just had this question on a test and that's the answer!!!
u just add then all together and divide them by how any numbers there are!!
10 + 15 + 14 + 8 + 18 + 11 + 12 + 12 + 10 + 10 + 17 + 16 = 153/12 = 12.75

Answer:

the answer is 12.75

Step-by-step explanation:

btw if you need the median is 12 :>

A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11 pounds of salt per gallon flows into the tank at the rate of 44 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 11 gallon per minute. set up a differential equation for the amount of salt a(t)a(t) in the tank at time tt. how much salt is in the tank when it is full? (round your answer to the 2 decimal places).

Answers

Let [tex]A(t)[/tex] denote the amount of salt in the tank at time [tex]t[/tex]. We're given that the tank initially holds [tex]A(0)=100[/tex] lbs of salt.

The rate at which salt flows in and out of the tank is given by the relation

[tex]\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}[/tex]
[tex]\implies A'(t)+\dfrac{11}{200+33t}A(t)=484[/tex]

Find the integrating factor:

[tex]\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}[/tex]

Distribute [tex]\mu(t)[/tex] along both sides of the ODE:

[tex](200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}[/tex]
[tex]\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}[/tex]
[tex]A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt[/tex]
[tex]A(t)=22(200+33t)^{2/3}+C[/tex]

Since [tex]A(0)=100[/tex], we get

[tex]100=22(200)^{2/3}+C\implies C\approx-652.39[/tex]

so that the particular solution for [tex]A(t)[/tex] is

[tex]A(t)=22(200+33t)^{2/3}-652.39[/tex]

The tank becomes full when the volume of solution in the tank at time [tex]t[/tex] is the same as the total volume of the tank:

[tex]200+(44-11)t=500\implies 33t=300\implies t\approx9.09[/tex]

at which point the amount of salt in the solution would be

[tex]A(9.09)\approx733.47\text{ lb}[/tex]

(1/3+9) x ( 8-3) tell me the steps help

Answers

Use PEMDAS to solve
(Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)

Solve parenthesis first
(1/3+9) x ( 8-3)
28/3 x 5

Use Multiplication 
28/3 x 5 ≈ 4.7
After rounding 4.7 should be your answer

How many pounds must a sand bag weigh to test if a safety net can absorb the proper amount of force?

Answers

 its 400lbs
hope i helped
Final answer:

To test if a safety net can absorb the proper amount of force, you would need to determine the weight of the sand bag. This can be done by using the concept of Newton's second law and calculating the mass of the sand bag using the equation F = mg, where F is the force required and g is the acceleration due to gravity.

Explanation:

To test if a safety net can absorb the proper amount of force, you would need to determine the weight of the sand bag. This can be done by using the concept of Newton's second law, which states that force equals mass times acceleration. You would first need to calculate the acceleration of the sand bag using the formula F = ma, where F is the force required to be absorbed by the safety net and a is the acceleration. Once you know the required force and acceleration, you can calculate the mass of the sand bag using the equation F = mg, where g is the acceleration due to gravity (approximately 9.8 m/s²).

For example, if the required force is 500 N and the acceleration is 5 m/s², you would calculate the mass of the sand bag as follows:

F = ma

500 N = m * 5 m/s²

m = 500 N / 5 m/s²

m = 100 kg

Therefore, the sand bag must weigh 100 kilograms (or approximately 220 pounds) to test if the safety net can absorb the proper amount of force.

Learn more about Weight of sand bag for safety net testing here:

https://brainly.com/question/31920126

#SPJ12

Prudence has 20 pairs of gold earrings and 4 pairs of silver earrings in a drawer in her jewelry box. If she randomly pulls six pairs of earrings out of the drawer to take with her on a trip, which of the following is the best prediction of the number of pairs of earrings that will be gold?

Answers

Final answer:

The best prediction of the number of gold earrings Prudence will pull out is 5 pairs.

Explanation:

To predict the number of pairs of gold earrings Prudence will randomly pull out of her drawer, we need to find the probability of selecting gold earrings from the total number of options.

Prudence has 20 pairs of gold earrings and 4 pairs of silver earrings, making a total of 24 pairs of earrings in her drawer.

The probability of selecting a gold earring is given by:

Number of gold earrings / Total number of earrings =  20 / 24= 5 / 6.

Therefore, the best prediction of the number of pairs of earrings that will be gold is 5 pairs.

Based on each applicant’s median credit score, to which client is Rachel likely to offer the best interest rates? a. Leslie b. Pat c. Sam d. Alex

Answers

Alex I think. it needs more information in it

Just got this question in a practice test on Edge. The answer is definitely Alex, or D.

What is the sum of (–2.1x + 3.7) and (5 + 4.9x)?
-7.0x + 8.7
-2.8x + 8.7
2.8x + 8.7
7.0x + 8.7

Answers

2.8x + 8.7

Hope this helps?

Answer

C.

2.8x + 8.7                  

Megan buys 3 bracelets and 3 necklaces. Each bracelet costs 5. Megan pays on 40 and gets 4 change. what is the cost of one necklace?

Answers

The necklaces cost $3 each. 
40-4=36 <-- that's how much she spent.
3x5=15 <-- that's how much the bracelets cost
36-15=21 <-- that's how much she had left over
21/3=7 <-- that's how much one necklace costs

One necklace costs $7.
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