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forsale [732]
2 years ago
14

A committee must be formed with 4 teachers and 5 students. If there are 11 teachers

Mathematics
1 answer:
Ivenika [448]2 years ago
7 0

Answer:

11C4 × 11C5

\binom{11}{4}   \times  \binom{11}{5}  =  \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1}   \times  \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2 \times 1}  = 330 \times 462 = 152460

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Janet can plant nine feet of carrots in 15 minutes while her daughter Amy can plant 17 feet of carrots in half an hour.
Lena [83]

Answer:

Step-by-step explanation:

In order to find who is more efficient at planting carrots, we want to put both ratios in terms of the same amount of time.

For simplicity, lets see how many carrots each can make in 1 hour.

Janet:\\9ft \: in \: 15 \:minutes

\frac{9ft}{15min} = \frac{xft}{60min}\\x = \frac{60*9}{15} = 36

Janet can plant 36 feet of carrots in one hour

Amy:\\\frac{17ft}{30min} = \frac{xft}{60min}\\x = \frac{17*60}{30} = 34

Amy can plant 34 feet of carrots in one hour

So, Janet can plant carrots more quickly

6 0
3 years ago
Which expression is equivalent to 7a^2b + 10a^2b^2 + 14a^2b^3?
vladimir1956 [14]
7a^2b + 10a^2b^2 + 14a^2b^3 =
a^2b (7 + 10b + 14b^2) <==
3 0
4 years ago
Read 2 more answers
This math question is hard. Help Me Pls
devlian [24]

Answer:

solution is: plus -2

6 0
3 years ago
If an angle is 40 , then it is acute
Firdavs [7]

Yes, an angle less than 90 degrees is acute.

5 0
3 years ago
Hello everyone, could you please solve this problem step by step. I don't have the exact solution and there are no options for i
lara31 [8.8K]

Answer:

<em>The area of the shaded part  = 61.46</em>

<em />

Step-by-step explanation:

Assume the hypotenuse of the triangle is c (c>0)

As the triangle inscribed in the semi circle is the right angle triangle, its hypotenuse is equal to the diameter of the circle.

The hypotenuse of the triangle can be calculated by Pythagoras theorem as following: c^{2} =a^{2} +b^{2} =(2\sqrt{5}) ^{2} + (4\sqrt{5}) ^{2} = 20 + 80 = 100

=> c = 10

So that the semi circle has the diameter = 10 => its radius = 5

  • The total area of 2 semi circles is equal to the area of the circle with radius =5

    => The total area of 2 semi circles is: \pi x 5^{2} = 25\pi

  • The area of a triangle inscribed in the semi circle is: 1/2 x a x b = 1/2 x 2\sqrt{5\\ x 4\sqrt{5} = 20

    => The area of 2 triangles inscribed in 2 semi circles is: 2 x 20 = 40

  • The area of the square is: c^{2} = 10^{2} =100

It can be seen that:

<em>The area of the shaded part = The area of the square - The total area of 2 semi circles + The total are of 2 triangles inscribed in semi circles </em>

<em>= 100 -  25</em>\pi<em> + 40 = 61.46</em>

6 0
3 years ago
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