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3 years ago

Which table shows exponential decay?

1 answer:

7 0

The answer should be A, as the numbers exponentially decrease by half instead of a set or random sum. For example, D is incorrect as 8 is half of 16, but 3 is less than half of 8, and then 1 is one third of 3.

Exponential decay is consistent.

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Jade used candle molds, as shown, to make candles that were perfect cylinders and spheres:

Fittoniya [83]

Answer:

The difference in the amount of wax needed is 84.78 in³ (84.78 cubic inches)

Step-by-step explanation:

Given

Cylinder

Radius = 3 inches

Height = 7 inches

Sphere

Radius = 3 inches

Required

The difference in the amount of wax needed to make a candle from each of these molds

The quantity or amount required to make a wax of candle from each molds can be calculated by getting the volume of both molds

The volume of a cylinder is calculated using

V₁ = πr²h

where r and h are the radius and the height of the cylinder, respectively.

r = 3 in and h = 7 in

The volume of a sphere is calculated using

$V_{2} = \frac{4}{3}\pi r^3$

where r is the radius of the sphere

r = 3 in

Calculating V₁

V₁ = πr²h

V₁ = π * 3² * 7

V₁ = π * 9 * 7

V₁ = π * 63

V₁ = 63π

Calculating V₂

$V_{2} = \frac{4}{3}\pi r^3$

$V_{2} = \frac{4}{3} * \pi * 3^3$

$V_{2} = \frac{4}{3} * \pi * 27$

$V_{2} = \frac{108}{3} * \pi$

V₂ = 36π

Having calculated the volume of each molds, the difference in the amount of wax needed can then be calculated.

Difference = V₁ - V₂

Substituting 63π for V₁ and 36π for V₂

Difference = 63π - 36π

Difference = 27π

(Taking π = 3.14)

Difference = 27 * 3.14

Difference = 84.78

Hence, difference in the amount of wax needed is 84.78 in³

8 0

3 years ago

Read 2 more answers

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

Anna71 [15]

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

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