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3 years ago

If the ratio of boys to girls in the school band is 2 to 3, which of these show possible numbers

Mathematics

1 answer:

Andru [333]3 years ago

8 0

Answer:

Step-by-step explanation:

Simply guess and check, meaning the boys category must be divisible by 2 and the girls category must be divisible by 3

A: 24 boys ÷ 2 = 12 (equals a whole number so it is divisible; not a decimal)

36 girls ÷ 3 = 12 (both of the boys and girls are divisible by their corresponding numbers)

Yes

Now make sure the boys are a lower count than the girls as the ratio says it should be 2 to 3, meaning there are more girls than boys

B: 20 ÷ 2 = 10 (divisible)

35 ÷ 3 = 11.666 (this is a decimal answer so it is not divisible)

C: 36 ÷ 2 = 18

24 ÷ 3 = 8

Yes, they are divisible

Now lets check if boys have a lower count than girls

36 boys > 24 girls

This is not the solution as it doesn't reflect the correct ratio of less boys than girls

D: 35 ÷ 2 = 17.5 (not divisible)

20 ÷ 3 = 6.66 (not divisible)

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Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?

bagirrra123 [75]

$\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\$

$\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}$

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus $\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]$

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3 years ago

You inherit $1000, but spends $8 each day at lunch. How many days until you have $768

schepotkina [342]

Answer:

29 days

Step-by-step explanation:

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3 years ago

Read 2 more answers

Solve the following problems : Given: S, T, and U are the midpoints of RP , PQ , and QR respectively. Prove: △SPT≅△UTQ.

AleksandrR [38]

Answer:

Hence Proved △ SPT ≅ △ UTQ

Step-by-step explanation:

Given: S, T, and U are the midpoints of Segment RP , segment PQ , and segment QR respectively of Δ PQR.

To prove: △ SPT ≅ △ UTQ

Proof:

∵ T is is the midpoint of PQ.

Hence PT = PQ ⇒equation 1

Now,Midpoint theorem is given below;

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

By, Midpoint theorem;

TS║QR

Also, $TS = \frac{1}{2} QR$

Hence, TS = QU (U is the midpoint QR) ⇒ equation 2

Also by Midpoint theorem;

TU║PR

Also, $TU = \frac{1}{2} PR$

Hence, TU = PS (S is the midpoint QR) ⇒ equation 3

Now in △SPT and △UTQ.

PT = PQ (from equation 1)

TS = QU (from equation 2)

PS = TU (from equation 3)

By S.S.S Congruence Property,

△ SPT ≅ △ UTQ ...... Hence Proved

6 0

3 years ago

A grounds crew is marking out a circular logo at the center of a football field. The logo will

patriot [66]

Answer:

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Step-by-step explanation:

then

141.3 = 2*pi * r

solve for r

141.3/ (2*pi) = r

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diameter is 2*r

2*22.48859= 44.9771 feet

divide by 3 because there are 3 feet in one yard

44.9771/3= 14.99239 yds.

it doesn't say to round off, but I would call this 15 yds.

Diameter is 15 yards ± .008 yds That's just about 1/4 of an inch

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2 years ago

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bixtya [17]

Answer:

y=4x and x+4y=12 are perpendicular because they have opposite reciprocal slopes

Step-by-step explanation:

y=4x slope is 4

x+4y=12 slope is -1/4

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