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4 years ago

Please help with question 1

Mathematics

1 answer:

sammy [17]4 years ago

5 0

Answer:

The volume of Solid A is 120 cm³.

Step-by-step explanation:

Given the area of the solids are in the ratio: 4 : 9

Let their actual areas be 4x² and 9x². We have assumed the common ratio as x² for easier computation.

We have area: $A_A : A_B =$ 4x² : 9x²

This implies, the length should have been of the ratio of the square root of these numbers.

Therefore, the ratios of the lengths is: $\sqrt{4x^2} : \sqrt{9x^2}$

$L_A : L_B = 2x : 3x$

Now, volume is cube of lengths. Therefore, the ratio of volumes would be:

$V_A : V_B = 8x^3 : 27x^3$

Given $V_B = 405 cm^3$

$\implies 27x^3 = 405 \hspace{1mm} cm^3$

$\implies x^3 = \frac{405}{27} = 15$

Hence, the volume of solid A, $V_A = 8x^3 = 8 \times 15 = \textbf{120} \hspace{1mm} cm^3$ .

Hence, the answer.

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Consider all angles whose reference angle is 45° with terminal sides not in Quadrant I.The angles that share the same cosine val

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Solution:

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As cosine 45 ° is always positive in first and fourth quadrant.

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As, Cos 45°, Cos (-45°) or Cos ( 360° - 45°)= Cos 315°are same.

So, Angles that share the same Cosine value as Cos 45° have same terminal sides will be in Quadrant IV having value Either Cos (-45°) or Cos (315°).

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3 years ago

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Find the derivative of the function. y = sin−1(6x + 1)

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If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:

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(true for <em>y</em> between -π/2 and π/2)

Now take the derivative of both sides and solve for it:

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3 years ago

Suppose that 80 percent of all statisticians are shy, whereas only 15 percent of all economists are shy. Suppose also that 90 pe

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Answer:

37.21% probability that the person is a statistician.

Step-by-step explanation:

We have these following probabilities:

An 80% probability that a statistican is shy.

A 15% probability that an economist is shy.

At the gathering, a 90% probability that a person is an economist.

At the gathering, a 10% probability that a person is a statistican.

If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?

This can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

What is the probability that the person is a statistican, given that he is shy?

P(B) is the probability of the person being a statistican. So P(B) = 0.1.

P(A/B) is the probability of a statistican being shy, so P(A/B) = 0.8.

P(A) is the probability of a person being a shy. This is 15% of 90%(economists) and 80% of 10%(statisticans). So

$P(A) = 0.15*0.9 + 0.8*0.1 = 0.215$