Round 545,999 to the nearest hundred thousand

Gael and Torin don't want to take the garbage out, but their mom said one of them had to. Gael suggests they flip 2 coins to det

Alexandra [31]

Possible outcomes :

Heads Heads

Heads Tails

Tails Tails

Tails Heads

Probability of matching : 2/4 = 0.5

Torin should agree since the proposal is fair

3 0

2 years ago

Captain Emily has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band

LenaWriter [7]

Answer:

The probability that the pirate misses the captain's ship but the captain hits = 0.514

Step-by-step explanation:

Let A be the event that the captain hits the pirate ship

The probability of the captain hitting the pirate ship, P(A) = 3/5

Let B be the event that the pirate hits the captain's ship

The probability of the pirate hitting the captain's ship P(B) = 1/7

The probability of the pirate missing the captain's ship, P'(B) = 1 - P(B)

P'(B) = 1 - 1/7 = 6/7

The probability that the pirate misses the captain's ship but the captain hits = P(A) * P(B) = 3/5 * 6/7

= 0.514

5 0

2 years ago

The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.1 in/s. At

kow [346]

Given:

$\dfrac{dr}{dt}=1.4\text{ in/s}$

$\dfrac{dh}{dt}=-2.1\text{ in/s}$

To find:

The rate of change in volume at $r=120\text{ in. and }175\text{ in.}$

Solution:

We know that, volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

Differentiate with respect to t.

$\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]$

Substitute the given values.

$\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]$

$\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]$

$\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560$

$\dfrac{dV}{dt}=29920$

Therefore, the volume of decreased by 29920 cubic inches per second.

6 0

2 years ago

Samara is adjusting a satellite because she finds it is not focusing the income radio waves perfectly. The shape of her satellit

gogolik [260]

Answer:

$\boxed{\text{(6, 3)}}$

Step-by-step explanation:

The conic form of the equation for a sideways parabola is

(y - k)² = 4p(x - h)

The focus is at (h + p, k)

The equation of Samara's parabola is

(y - 3)² = 8(x - 4)

h = 4

p = 8/4 = 2

k = 3

h + p = 6

So, the focus point of the satellite dish is at

$\boxed{\textbf{(6, 3)}}$

8 0

1 year ago

Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company pi

yKpoI14uk [10]

Alright, lets get started.

If Matthew wants to complete packages at an average rate of at least 39 packages per hour.

And they worked 4 hrs only due to picnic, yesterday, it means they have to make $39*4 = 156$ packages.

But they made only 112 packages means they are short of $156 - 112 = 44$ packages.

Suppose they are working today t hrs, and his department will complete 43 packages per hour today.

It means they are going to make 43 t packages today.

This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.

So, average will be

$\frac{43 t - 44}{t} = 39$ (39 average given in question)

Cross multiplying

$39 t = 43 t - 44$

Adding 44 in both sides

$39 t + 44 = 43 t - 44 + 44$

$43 t = 39 t + 44$

Subtracting 39 t in both sides

$43 t - 39 t = 39 t + 44 - 39 t$

$4t = 44$

Dividing 4 in both sides

t = 11 hrs

Hence they have to woth 11 hrs today : Answer

Hope it will help :)

3 0

2 years ago

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