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LenaWriter [7]
2 years ago
8

Find the dimensions of a rectangle

Mathematics
1 answer:
gayaneshka [121]2 years ago
4 0
The length of the shorter side is 7 longer side is 12 7+7+12+12 is 38 and 7x12 is 84
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10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15
zmey [24]

Answer:

\, {20 \choose 10} - {15 \choose 10}

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, \, {20 \choose 10} = \frac{20!}{10!10!} .

- 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  \, {15 \choose 10} = \frac{15!}{10!5!} possibilities.

Therefore, we have \, {20 \choose 10} - {15 \choose 10} possibilities to distribute the coupons so that at least one woman receives a coupon.

I hope that works for you!

3 0
3 years ago
What is the distance between P(12, 4) and Q(-8, 2)
abruzzese [7]

\huge{\boxed{2 \sqrt{101}}}

The distance formula is \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, where (x_1, y_1) and (x_2, y_2) are the points.

Substitute in the points. \sqrt{(2-4)^2+(-8-12)^2}

Subtract. \sqrt{(-2)^2+(-20)^2}

Solve the exponents. \sqrt{4+400}

Add. \sqrt{404}

Now, we can simplify this square root just a little bit. 404 has a square factor of 4. \sqrt{404}=\sqrt{4}*\sqrt{101}

The square root of 4 equals 2. \boxed{2 \sqrt{101}}

6 0
3 years ago
Read 2 more answers
Find the value of X and a missing angel in this triangle
shepuryov [24]

Answer:

x=175

Step-by-step explanation:

4 0
2 years ago
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12. A scientist is observing a family of mice. There are four nice which are reproducing and doubling in number every month. Whi
Margaret [11]

Answer:

?

x = the number of months pass right

3 0
2 years ago
What is the solution to the system of equations?
Dvinal [7]
X = 4
y = 0
is the answer to the system of equation
8 0
3 years ago
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