Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is 
As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is 
. Thus, there are only 35 ways to distribute the blackboards in this case.
Answer:
Strong and Positive Relation
Step-by-step explanation:
Here, when we plot the graph of y = 0.4125x + 0.1576
Then we see that the graph has a positive correlation as we increase the value of x, the value of y is also increasing. So, Life of Car's Engine and Number of Times the Oil is Changed has a Positive relation.
And if our scatter plot is horizontal, vertical or we unable to draw the line of best fit then it has no or little correlation but here we see that line is not lie in either case. So, the relationship is strong but not very strong.
2.8 meter= 2800cms
To solve this, we can create a simple algebraic equation:
45x=2800
Divide both sides by 45.
(45x)/45=(2800)/45
x=62.222
You can make 62 full pieces.
To find the waste, multiply the numbers of pieces by the length of each.
62*45
=2790
2800-<span>2790
=10 centimeters
There would be 10 centimeters of wasted linen.
Hope this helps!
-Benjamin</span>
Answer:
The length and width of the pool = 24 ft and 16 ft
Step-by-step explanation:
Let length of pool be l and width of pool be w.
A pool in the shape of a rectangle has a perimeter of 80feet.
Perimeter of pool = 2 x ( l + w ) = 80 feet
That is
l + w = 40 ft -----------------------------------eqn 1.
The pool is 8 feet less wide than it is long.
l = 8 + w
l - w = 8 ft -----------------------------------eqn 2.
eqn 1 + eqn 2
2 l = 48
l = 24 ft
Substituting
24 + w = 40
w = 16 ft
The length and width of the pool = 24 ft and 16 ft
Answer:
, 
Step-by-step explanation:
First, the vector must be transformed into its polar form:
Let assume that vector is rotated counterclockwise. The new angle is:
Which is coterminal with 
. The reflection across y-axis is:
The equivalent vector in rectangular coordinates is:
