Create a probability model for the outcome of flipping a coin 3 times. what is the probability of landing on heads at least once

You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research

____ [38]

<span>The answer should be set up like so:

3125 = 3200*(d)^3
3125/3200 = d^3
3-root (3125/3200) = d
d = 0.992125657...

1 - d = 0.007874...
Therefore it depreciates at about 0.8% monthly

To find the depreciation 6 months from now, or 9 months from the beginning:
v = 3200 (d)^9
= 2980.232239...

So after 9 months the car would be about $2980.23</span><span>
</span>

6 0

3 years ago

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What is the height of the tree to the nearest tenth of a foot?

Ugo [173]

Answer:

The height of the tree is approximately 21.4 feet

Step-by-step explanation:

We list out the question parameters first as follows;

The distance from the base of the tree where the angle of elevation is measured, d = 10 feet

The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°

Let 'h' represent the height of the tree, then we have;

The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg

By trigonometric ratio, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{h}{d}$

∴ h = d × tan(θ)

Plugging in the given values, we get;

h = 10 feet × tan(65°) = 21 feet $5\frac{11}{32}$ inches

∴ By rounding to the nearest tenth of a foot, the height of the tree, h ≈ 21.4 feet.

3 0

3 years ago

Michael drove from home to work at an average speed of 45 mph. His return trip home took 45 minutes longer because he could only

Xelga [282]

The distance from his home to his work place is 118.125 miles

<h3>How to find the distance from his home to his work place?</h3>

He drove from home to work at an average speed of 45 mph. Therefore,

speed = 45 mph

let

time = x

speed = distance / time

distance = 45x

His return trip home took 45 minutes longer because he could only drive at 35 mph. Therefore,

45 minutes = 0.75 hours

distance = 35(x + 0.75)

distance = 35x + 26.25

Therefore,

45x = 35x + 26.25

45x - 35x = 26.25

10x = 26.25

x = 26.25 / 10

x = 2.625

Therefore,

distance = 45(2.625) = 118.125 miles

learn more on distance here: brainly.com/question/21329221

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3 0

2 years ago

Which system of equations corresponds to this matrix multiplication operation

faltersainse [42]

Answer:

Option (B)

Step-by-step explanation:

$\begin{bmatrix}5 & 2 & 1\\ 7 & -5 & 2\\ -5 & 3 & 1\end{bmatrix}\times \begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}16\\ 3\\ 12\end{bmatrix}$

By applying multiplication property of the matrices,

$\begin{bmatrix}(5x+2y+z)\\ (7x-5y+2z)\\(-5x+3y+z) \end{bmatrix}=\begin{bmatrix}16\\ 3\\ 12\end{bmatrix}$

Therefore, system of equations formed will be,

5x + 2y + z = 16

7x - 5y + 2z = 3

-5x + 3y + z = 12

Option (B) will be the correct option.

3 0

3 years ago

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Bobs supermarket sells red apples and green apples at the ratio of 5:3.

nika2105 [10]

Answer:

10 red apples and 6 green apples

Step-by-step explanation:

first you multiply 5×2 to get 10 apples

then you multiply 3×2 to get 6 apples

5 0

3 years ago