We have been given that a right triangle with integer sides has area equal to 30. We are asked to find the length of hypotenuse of right triangle.
We know that area of triangle is half the product of its base length and height.
Since our given triangle is a right triangle, so its base and height will be legs of right triangle.
This means that product of two bases is 60.
Now we need to find two multiples of 60 such that they are make a right triangle.
Multiples of 60:
1, 60
2, 30
3, 20
4, 15
5, 12
6, 10
We know that (5, 12 and 13) is a Pythagoras triplet.
Therefore, the hypotenuse of right triangle is 13 units.
Answer:
Step-by-step explanation:
If Thaddeus drives the whole 16 hours, the distance between them is ...
distance = speed · time
distance = 20 mi/h · 16 h
distance = 320 miles.
It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...
(45 mi)/(5 mi/h) = 9 h
The rest of the 16 hours is the time that Thaddeus drove: 7 hours.
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Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...
distance = speed · time
365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)
45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms
(45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x
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<em>Comment on the solution</em>
You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.
Solution :
It is given that P(x) is said to be complete or proper probability distribution if it satisfies the following two ways :
1. 
2. 
Now consider,
⇒ 
⇒ 
⇒ 
⇒ 
= 0.2
Therefore, the value of T is 0.2
Thus, option (c) is correct.
Answer:
Step-by-step explanation:
Ratio of businesses to cars= 3:5
Number of businesses= 30
Number of cars= Unknown
Let the number of cars be y
3/5 = 30/y
Cross multiply
3y = 30×5
3y = 150
y= 150/3
y= 50
Number of cars is 50
If Jenny made $315.25 for 8 hours of work:
Then it means that she made:
$312.25/8 hours = $39.41 per hour.
If Jenny works for 40 hours, then she will make:
40 hours × $39.41 = $1,576.25
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