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!
Solving inequalities is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here if the coefficient in front of x is positive when you divide!
Also remember:- To add/subtract fractions, you have to turn all mixed numbers into improper fractions (if needed), <span>find a common denominator on both fractions (if needed), add/subtract the numerators, put the sum/difference over the common denominator, and
simplify if needed.
- To multiply fractions, multiply the numerators and multiply the denominators. Put the product of the numerators over the product of the denominators.
- To divide fractions, remember that dividing by a fraction is the same as multiplying by the inverse of that fraction (aka fraction flipped).
- To turn mixed numbers into improper fractions, multiply the whole number by the denominator of the fraction. Add the numerator of the fraction to the product you get, and put that final sum over the original denominator.
Back to the problem:
</span>You are told that
and you have to solve for x.
<span>
1) </span>Using the info for converting mixed numbers to improper fractions from above, you know that
and
and
. Now add/subtract using the info above, isolating the variable x by adding
to both sides and subtracting
from both sides.
2) Divide both sides by
to get the inequality for x. Remember the info for dividing from above:
Your final answer is x < 
or x < 
.
Answer:
Centimeters might be easier because they can be much more precise than inches when there isn't an ideal length. Kilometers might be easier because it would not require such large numbers to work with.
Step-by-step explanation:
:)
Answer:
6- Part A: 
Part B: 
Solution of the system: 
Step-by-step explanation:
<u>Part A:</u>
In words, the equation is formed like this:
Total kg of Arabica + Total kg of Robusta = Total kg of coffee
Now, the total of each yield is calculated by the product of kg/hectare and number of hectares. Thus, the equation is:
<u>Part B:</u>
In words:
Arabica's worth + Robusta's worth = plantation worth
Each yield's worth is given by the product of the price per kg and the corresponding production. So, the equation is:
400 in² = (20 in)²
The area of a square is the square of the side length.
The length of one of the sides is 20 inches.
