Find the distance between points P and B.

Kaden, Keith, and Kipp compete in a series of daily 3-way races. For each race, the probability that Kaden wins is 1/6, the prob

BlackZzzverrR [31]

9514 1404 393

Answer:

3/5

Step-by-step explanation:

Let a, b, c represent the probability of a win by Kaden, Keith, and Kipp, respectively.

P(bc' | a') = P(a'bc')/P(a')

P(bc' | a') = (1/2)/(1 -1/6) = (3/6)/(5/6) = 3/5

The probability is 3/5 that Keith beats Kipp when Kaden doesn't win.

4 0

2 years ago

A boat can travel 496 km on 124 liters of fuel. How much fuel will it need to go 84 km?

Anika [276]

Answer:

A boat would need 21 liters to cover the distance of 84 km.

Step-by-step explanation:

Given

A boat can travel 496 km on 124 liters of fuel.

To determine

How much fuel will it need to go 84 km?

It is stated that:

Distance covered in 124 liters of fuel = 496 km

Thus,

Unit rate = 496 km / 124 liters

= 4 km per liter

Thus,

The distance covered in 1 liter = 4km

In order to determine the distance covered in 84 km, all we need is to divide 84 km by 4.

i.e.

The fuel needed to go 84 km = 84 / 4 = 21 liters

Therefore, a boat would need 21 liters to cover the distance of 84 km.

7 0

3 years ago

Find the surface area of the regular pyramid shown to the nearest whole number. plz help

Sav [38]

The surface area of the regular hexagonal pyramid is
SA = (1/2) pl + B
where p is the perimeter of the base, l is the slant height of the pyramid, and B is the area of the base
The area of a regular hexagon is 3 sh
where s is the length of the side and h is the length of the apothem.
So,
SA = (1/2)(6)(12) (11) + 3(12)(6sqrt3)
SA = 770 square meters

5 0

2 years ago

Read 2 more answers

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

There where 12 children at a party.of those 12 children 3/4 of them had an apple.how many children had an apple?

jonny [76]

Answer:

12×<u>3</u>

4

= 9

there 9 children had ana apple

3 0

3 years ago

Read 2 more answers