Answer: the cyclist must wait for 25 minutes until the hiker catches up.
Step-by-step explanation:
Distance = speed × time
The Cyclist was travelling in the same direction along the same path
as the hiker at a constant rate of 20 miles per hour. If the cyclist stops to wait for the hiker 5 minutes after passing her, then the distance that the cyclist travelled in 5 minutes(5/60 hour) is
20 × 5/60 = 100/60 miles
For the hiker to catch up with the cyclist, she would cover 100/60 miles at a speed of 4 miles per hour.
Time = distance/speed
Time required by hiker to catch up with the cyclist is
(100/60)/4 = 100/240 hour
Converting 100/240 hour to minutes, it becomes
100/240 × 60 = 25 minutes
f(x) = x2 + 2x + 1, g(x) = 11x − 19 x<span>2 </span>+ 2x + 1 = 11x - 19 x2 - 9x + 20 = 0 (x-4)(x-5) = 0 x = 4, 5
Using the combination formula, it is found that:
a) 180 different starting lineups can be created.
b) The probability that mary and alice will get on the lineup is .
The order in which the players are chosen is not important, hence the <em>combination formula </em>is used to solve this question.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
Item a:
The lineup is composed by:
- 2 guards from a set of 5.
- 2 forwards from a set of 4.
- 1 center from a set of 3.
Hence the number of lineups is given by:
Item b:
The number of lineups with Mary and Alice are given as follows:
- 2 guards from a set of 5.
- Mary and 1 other forward from a set of 3.
Hence:
Hence the probability is given by:
The probability that mary and alice will get on the lineup is .
More can be learned about the combination formula at brainly.com/question/25821700
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Okay, just break it up so you're not overwhelming yourself or anything :)
So here, do it in steps-
Let's do 5(3 + t) first:
Distribute the 5, or in non-mathematical terms, just multiply 5 by 3 and t. This will give you 15 + 5t.
Now onto -3(t + 1):
Again, just multiply -3 by t and 1. This will come out to: -3t - 3.
*Note: the 3 is negative because it's "MINUS 3" in the original equation and remember that any number times a negative, if it isn't negative itself, will turn out to be negative.... (aka "-" x "-" = "+" | "+" x "+" = "+" | "-" x "+" = "-")*
ANYWAY
Now just put both answer together and you get:
15 + 5t -3t - 3. You can only add and minus the LIKETERMS (which are the things that are the same) - in this case, the liketerms are 15 and -3 ,,,, AND 5t and -3t.
15 - 3 = 12
5t - 3t = 2t
12 + 2t is your final answer. Hope that helps! :)
The Length of the Given Sign = 90 inches
The Side of the Triangle can be found by Pythagorean Theorem
⇒ (Side of the Triangle)² = 40² + 30²
⇒ (Side of the Triangle)² = 1600 + 900
⇒ (Side of the Triangle)² = 2500
⇒ (Side of the Triangle) = 50
⇒ Perimeter of the Given Sign = (4 × Side of Triangle) + (2 × Length)
⇒ Perimeter of the Given Sign = (4 × 50) + (2 × 90)
⇒ Perimeter of the Given Sign = (200 + 180) = 380 in