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Verizon [17]
3 years ago
14

Two trains leave towns 1250 km apart at the same time and travel toward each other. one train travels 10 km/hr slower than the o

ther. if they meet in 5 hours, what is the rate of each train?
Mathematics
1 answer:
Oksana_A [137]3 years ago
6 0
Here are the rates of the trains:
(n represents train A's speed)
A: n
B: n + 10
We know it is 5 hours, and total distance, so:
5(n) + 5(n + 10) = 1250
5n + 5n + 50 = 1250
10n = 1200
Divide:
n = 120
One train goes 120, the other goes 130
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It’s the product of three and nine.


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A master student is planning to take a qualifying exam in the coming summer. She has three chances. The first one is in June. If
Soloha48 [4]

Answer:

Step-by-step explanation:

Given

P_1=Probability of clearing exam in 1 st attempt=0.5

P_2=Probability of clearing exam in 2 nd attempt=0.7

P_3=Probability of clearing exam in 3 rd attempt=0.8

Probability that she passes the exam=P(1 st\ attempt)+P(1\ fail)\cdot P(2\ pass)+P(1\ fail)\cdot P(2\ fail)\cdot P(3 rd pass)

P=0.5+0.5\times 0.7+0.5\times 0.3\times 0.8=0.97

(b)P(Pass qualification on 2nd try|passes qualification)

P(Pass qualification on 2nd try|passes qualification)=\frac{P(fail\ on\ 1 )\cdot P(pass\ in\ 2nd)}{P(passes)}

P(Pass qualification on 2nd try|passes qualification)=\frac{0.5\times 0.7}{0.97}=0.3608

5 0
3 years ago
for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).
Schach [20]

Answer:

  • k = 18

=========

<h2>Given</h2>

<h3>Line 1</h3>
  • 3x - ky + 7 = 0

<h3>Line 2</h3>
  • Passing through the points (4, 3) and (5, - 3)

<h2>To find</h2>

  • The value of k, if the lines are perpendicular

<h2>Solution</h2>

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

<u><em>Info:</em></u>

  • <em>standard form is ⇒ ax + by + c = 0, </em>
  • <em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>

  • 3x - ky + 7 = 0
  • ky = 3x + 7
  • y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

  • m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

  • (3/k)*(- 6) = - 1
  • - 18/k = - 1
  • k = 18

So when k is 18, the lines are perpendicular.

4 0
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Four times the square of a non-zero number is equal to twelve times the number.
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5(-42/-7) + (-15) - (-3)​
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Answer:

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Step-by-step explanation:

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