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PolarNik [594]
3 years ago
15

Use the subway train schedule below to answer the question. Train ScheduleTrainArrives Every...Red line4 minutesBlue line5 minut

esYellow line6 minutes All three trains just arrived at the station. When will they next all arrive at the station at the same time? They will all arrive at the station in minutes.
Mathematics
1 answer:
Stolb23 [73]3 years ago
7 0

Answer:

60 minutes

Step-by-step explanation:

Given the schedule above :

Red line arrives every 4 minutes

Blue line arrives every 5 minutes

Yellow line arrives every 6 minutes

All three just arrives at the train station ; when next will they all arrive at the train station at the same time.

Obtain the lowest common multiple of each arrov time :

Lowest common multiple of 4, 5, 6

_2___4___5___6

_2___2___5___3

_3___1___ 5 __ 3

_5___1___ 5 __ 1

_____1 ___1 ___1

Hence, lowest common multiple :(2 * 2 * 3 * 5) = 60

Hemce, they all arrive at the train station at the same time after 60 minutes

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What is sin -1 (1/2) if the terminal side of 0 is located in quadrant 1
Lady_Fox [76]

Answer:

sin^-1 (1/2) = 30°

Step-by-step explanation:

* Lets explain how to find the trigonometry functions from the unit circle

- The unit circle is the circle whose radius is 1 unit

- It intersects the four axes at:

# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)

# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)

- The terminal of any angle intersect it at point (x , y) where x² + y² = 1

- If The angle between the terminal side and the x-axis is Ф , then

# The adjacent side of Ф = x

# The opposite side of the angle Ф = y

- In the problem the terminal side lies in the first quadrant

∴ all the trigonometry functions are positive

∵ sin Ф = opposite/hypotenuse

∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1

∴ sin Ф = 1/2 ÷ 1 = 1/2

- To find Ф use the inverse function sin^-1 Ф

∵ sin Ф = 1/2

∴ Ф = sin^-1 (1/2)

∴ Ф = 30°

* sin^-1 (1/2) = 30°

6 0
2 years ago
A sweater is on sale for 20% off. A jacket is on sale for 15% off. The sale price for each item is $34.00. Which item cost more
SashulF [63]

The sweater cost more originally. It costs $2.50 more from jacket.

Step-by-step explanation:

Given,

Discount rate of sweater = 20%

Sale price of sweater = (100-20)% = 80%

Discount rate of jacket = 15%

Sale price of jacket = (100-15)% = 85%

Sale price of each item = $34.00

Let,

x be the original price of sweater.

y be the original price of jacket.

80% of x = 34

\frac{80}{100}x=34\\0.80x=34

Dividing both sides by 0.80

\frac{0.80x}{0.80}=\frac{34}{0.80}\\x=42.50

The original price of sweater is $42.50

85% of y = 34

\frac{85}{100}y=34\\0.85y=34

Dividing both sides by 0.85

\frac{0.85y}{0.85}=\frac{34}{0.85}\\y=40

The original cost of jacket is $40

Difference = 42.50 - 40 = $2.50

The sweater cost more originally. It costs $2.50 more from jacket.

Keywords: subtraction, division

Learn more about subtraction at:

  • brainly.com/question/10557938
  • brainly.com/question/10600222

#LearnwithBrainly

4 0
3 years ago
Solve the system by elimination 1: x+5y-4z=-10, 2x-y+5z=-9, 2x-10y-5z=0 .. . 2. Solve the system by substitution: 2x-y+z=-4, z=5
Kryger [21]
1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x -  y    + 5 z = -9
---------------------------
       - 11 y + 13 z = 11  /  * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
   2 x - 10 y - 5 z = 0
-----------------------------
         - 20 x + 3 z = 20  /  * 11
        ----------------------------------
         220 y - 260 z = -220
        - 220 y + 33 z = 220
        ------------------------------
                       z = 0,      y = -1,        x = - 5
2 )  
       2 x - y + 5 = -4
       - 2 x + 3 y - 5 = - 10
       Substitution: y = 2 x + 9
       - 2 x + 3(2 x + 9 ) = -5
        4 x = - 32,          x = -8,    y = -7,   z = 5
3 )
      x + y + z = 11
   1.5 x+3 y +1.5 z = 21
      x = 2 y
   ------------------------
      3 y + z = 11  / * (-2)
      6 y + 1.5 z = 21
    ------------------------
     - 6 y - 2 z = -22
       6 y + 1.5 z = 21
      ------------------------
                 -0.5 z = -1,           z = 2,   y = 3,   z = 6
Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins. 
           
8 0
3 years ago
I would like to buy a sandwich and pancakes, which would be $8.50, with a 6% tax and 20% gratuity, how much would that be all in
Luda [366]

Answer:

9.01 maybe my math might be wrong

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th
OlgaM077 [116]

Answer:

Interval [16.34 , 21.43]

Step-by-step explanation:

First step. <u>Calculate the mean</u>

\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666

Second step. <u>Calculate the standard deviation</u>

\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}

\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}

\sigma=\sqrt{17.815}=4.22

As the number of data is less than 30, we must use the t-table to find the interval of confidence.

We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).  

We must then choose t = 1.476 (see attachment)

Now, we use the formula that gives us the end points of the required interval

\bar X \pm t\frac{\sigma}{\sqrt n}

where n is the number of observations.

The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43

6 0
2 years ago
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