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postnew [5]
3 years ago
6

**WILL MARK BRAINLIEST!!!** At a train station, freight trains depart at a rate of 2 trains every 30 minutes and passenger train

s depart at a rate of 1 train every 90 minutes. At this rate, how many total trains will depart from the station in a 12-hour period? Show your work.

Mathematics
1 answer:
lyudmila [28]3 years ago
7 0
Top is the passenger train
bottom is the freight
make sure you add 48+8=56
there are 56 trains that went to the station in a 12 hour period.

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Hi so this question is super confusing! I can't even figure it out
frutty [35]

Answer:

i think it's n/2 may be even and 3n+1 is odd. They succumb to 3n if that helps.

Step-by-step explanation:

hope it helps, have a good day/night

6 0
2 years ago
I will give lots of points please help
aalyn [17]

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

The cake can be modeled as a <u>cylinder </u>with:

  • diameter = 9 in
  • height = 4 in

\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in

\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}

<h3><u>Part (b)</u></h3>

\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}

<h3><u>Part (c)</u></h3>

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}

<h3><u>Part (d)</u></h3>

Probability is approximately 10.6%  (see above for calculation)

<h3><u>Part (e)</u></h3>

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

3 0
2 years ago
Write an equation of the line that passes through the points (0,4)(0,4) and (2,10)(2,10). $y=
lutik1710 [3]
I am going to guess you want to find a line which passes through the points (0,4) and (2,10)...

y₂-y₁ / x₂-x₁
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6 / 2
3....slope
(0,4) .....b

y = 3x + 4
3 0
3 years ago
Mike's biweekly salary is $2345.00. How much does he make<br> each week?
Aloiza [94]
He makes 1,172.50. you find this by dividing 2345 by 2 (since that’s his BI weekly salary which means every 2 weeks he gets paid) when you divide by 2 you get 1,172.50
8 0
3 years ago
Read 2 more answers
The length of a rectangular book is 2 times its width. The perimeter of the book is 42 inches. Write a system of
wel

Answer:

Mark me as brainlist

Step-by-step explanation:

P = Perimeter            

L = Length          

W = Width

Perimeter of rectangle = L + L + W + W        

or P = 2L + 2W

You know:

P = 36 inches

L = 2W          [length is(=) 2 times it's width]

W = ?

P = 2L + 2W    

Substitute/plug in what you know, plug in 2W for L since L = 2W

36 = 2(2W) + 2W         Simplify

36 = 4W + 2W

36 = 6W        Divide 6 on both sides

6 = W              Now that you know the width, you can find the length:

L = 2W

L = 2(6)

L = 12

L = 12 in

W = 6 in

PROOF

P = 2(12) + 2(6)

P = 24 + 12

P = 36

7 0
2 years ago
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