You are planning a three-day trip to seattle, washington, in october. use the fact that on each day, it could either be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question. what is the probability that it rains on exactly one day?

Step-by-step explanation:

In this case, we can put all the scenarios and then, count the scenario which can be rainy at least one day (it doesn't matter if it's day 1, day 2 or day 3 because it's asking for exactly one day). With this, we can also assume that the rest of the days will be sunny so:

We have this scenarios:

S: Sunny

R: Rainy

Now, let's do the scenarios:

If day 1 begins sunny:

SSS, SSR, SRS, SRR

If day 1 begins with Rain:

RRR, RRS, RSR, RSS

So, we have 8 possible scenarios, now let's see which ones we have one day of raining and the rest of the days, are sunny.

SSR, SRS and RSS

We have 3 scenarios, which can be rainy exactly one day.

So the probability is:

3/8 = 0.375 or simply 37.5%

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.