Answer:

Step-by-step explanation:
We can find the total amount of ways at least a woman receives a coupon by calculating the total amount of possibilities ot distribute the coupon and substract it to the total amount of possibilities to distribute 10 coupons to the 15 men (this is the complementary case that at least a woman receives a cupon).
- The total amount of possibilities to distribute the coupons among the 20 shoppers is equivalent to the total amount of ways to pick a subset of 10 elements from a set of 20. This is the combinatiorial number of 20 with 10, in other words, 
- To calculate the total amount of possibilities to distribute the coupons among the 15 men, we need to make the same computation we made above but with a set of 15 elements instead of 20. This gives us
possibilities.
Therefore, we have
possibilities to distribute the coupons so that at least one woman receives a coupon.
I hope that works for you!
Answer:
cos(52°) = 18/x
x = 18·sec(52°)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
In this geometry, that means ...
cos(52°) = 18/x
You can use the relation sec(x) = 1/cos(x) to rewrite this as ...
x = 18·sec(52°)
_____
You can also use the complementary angle and the complementary trig function.
sin(90° -52°) = 18/x
Answer:
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
24
−
16
√
2
Decimal Form:
1.37258300
…
subtract lowest time from highest time for each kind
129-29 = 100
320-210 = 110
the ranges are about the same but the times are higher for the dark chocolate