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Evgesh-ka [11]
2 years ago
5

The ratio of boys to girls in a local choir is 7:10. If there are 35 boys in the choir, how many girls are there?

Mathematics
1 answer:
erica [24]2 years ago
3 0

Answer:

50 girls

Step-by-step explanation:

Given data

We have the ratio as

7:10

The total part = 7+10= 17

let the number of boys and girls be x

applying the part to all method

7/17= 35/x

cross multiply

7x= 35*17

7x=595

x=595/7

x= 85

Hence the number of girls is

=85-35

=50 girls

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Answer:

\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}

Then, given the sides a=2, b=9, and c=8.

\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}

For B:

\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}

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The volume of a cone is 3rx? cubic units and its height is x units. Which expression represents the radius of the cone's base, i
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Answer:

It is given that the volume of a cone = 3\pi x^3 cubic units

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Therefore, r^2x=9x^3

r^2=9x^2

Therefore, r=3 x

So, the expression '3 x' represents the radius of the cone's base in units.

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