Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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Explanation:
Let's factor 180 in such a way that exactly one factor is a perfect square.
I'll ignore the trivial factor of 1.
Here are the possible factorizations we could go with:
180 = 4*45
180 = 9*20
180 = 36*5
Those factorizations then lead to the following

Then we have
p+q = 2+45 = 47
p+q = 3+20 = 23
p+q = 6+5 = 11
The smallest value of p+q is 11 and it happens when p = 6 and q = 5.
Side note: p+q is smallest when we go with the largest perfect square factor.
Answer:
87.5 inches long
Step-by-step explanation:
250 x 0.35 = 87.5
<u>The probability that the marble will be blue if he shakes the bag and when you puts his hand into the bag, to move it around and probably he'll get the blue marble.</u>
<em>Hopefully, it correct.... :)</em>
If Ian uses 1/20 of the ketchup 4 times, this is equal to 4/20, or

.

can be simplified to

, which means we need to work out

of 12.2

is equivalent to 20%, which as a decimal is 0.2
0.2 x 12.2 = 2.44 - however, this is how much he has
used, and we need to figure out how much is left.
12.2 - 2.44 = 9.76
So, Ian has 9.76 oz remaining :)
He brought 4 children over 12, and 1 child under 12