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2 years ago

If there are 42 boys and 54 girls in a room, fill out all of the possible ratios of boys to girls that could be made.

Mathematics

1 answer:

Tju [1.3M]2 years ago

3 0

Answer:

42:54,54:42

Step-by-step explanation:

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A meal at a restaurant cost $34.50, before tip. You decide to leave the server an 18% tip. What is your total bill?

anastassius [24]

The tip is $6.21

with that being said, 34.50 + 6.21 = 40.71

the total cost is $40.71

3 0

2 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

2 years ago

I NEED HELP PRONTO PLZZZ HELP ME

forsale [732]

Answer:

12 ÷ 4

Step-by-step explanation:

Let's try to solve the given expression to see if it matches with any of the options guven..

$\frac{1}{4}*12$

$= \frac{1*12}{4}$

$= \frac{12}{4}$ (this is equivalent to 12 ÷ 4, which is given in the question)

Thus,

12 ÷ 4 equivalent to $\frac{1}{4}*12$

4 0

3 years ago

Andre drives a bike for 4 hours covering 160 km. Find the distance covered by him in 7 hours.

swat32

Answer:

I think is 280km :))))))

4 0

2 years ago

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The measurement of the width of a garden plot is 44 m. Its actual width is 45.5 m.

romanna [79]

Answer: -3.3%

By not knowing how i did it, means you will still not know how to do it next time you encounter a similar problem.

Knowing how to solve a problem is just as important or even more important than just knowing the solution.

5 0

2 years ago