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Vinil7 [7]
3 years ago
13

Joe and Maxine are playing a game where they flip a fair coin four times and try to predict the outcomes. Joe thinks that the pr

obability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips. Maxine disagrees. She thinks that the two probabilities are equal.
Mathematics
2 answers:
timofeeve [1]3 years ago
8 0

Answer: Joe is right, the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips.

Step-by-step explanation:

First creating a sample space :

HHHH, HHHT, TTHT, HTTH, THHH, TTTT, TTTH, TTHH, HTHH, HTTT, HHTT, THTH, HHTH, THTT, HTHT, THHT

A fair coin (H - HEAD, T - TAIL)

Probability = (required outcome / possible outcome)

Probability getting exactly two heads in first four flips:

= 6/16 = 3/8

Probability of getting head on both the first and second flips :

= 4/16 = 1/4

Therefore Joe is right, the probability of getting exactly two heads in the four flips is greater than the probability of getting heads on both the first and second flips.

Nezavi [6.7K]3 years ago
6 0

Answer:

Maxine is correct.

Step-by-step explanation:

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$#4 find the value of x. Round answer to nearest tenth please
Sonja [21]

Answer:

12.9

Step-by-step explanation:

sin 59 = opposite/hypotenuse

opposite is x, the dimension facing the angle 59

hypotenuse is the longest side = 15

sin 59 = x/15

x = 15sin59 = 15 x 0.8572 =12.858 = 12.9 in the nearest tenth

3 0
3 years ago
Is 5768 divisible by 2
Alexandra [31]
Yes it is divisible by 2. The answer would be 2884.
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4 0
3 years ago
Read 2 more answers
Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2
Anastaziya [24]

Answer:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

Step-by-step explanation:

we would like to figure out the derivative of the following:

\displaystyle  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

to do so, let,

\displaystyle y =  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

By simplifying we acquire:

\displaystyle y =  3 -  \frac{2}{x}  -  \frac{1}{ {x}^{2} }

use law of exponent which yields:

\displaystyle y =  3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} }

take derivative in both sides:

\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  (3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} } )

use sum derivation rule which yields:

\rm\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  3 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

By constant derivation we acquire:

\rm\displaystyle  \frac{dy}{dx} =  0 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

use exponent rule of derivation which yields:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ - 1 -1} ) -     ( - 2 {x}^{  - 2 - 1} )

simplify exponent:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ -2} ) -     ( - 2 {x}^{  - 3} )

two negatives make positive so,

\displaystyle  \frac{dy}{dx} =   2 {x}^{ -2} +      2 {x}^{  - 3}

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

\displaystyle  \frac{dy}{dx} =   \frac{2 }{x^2}+       \frac{2}{x^3}

simplify addition:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

and we are done!

5 0
3 years ago
John made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length,
kati45 [8]
Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.

P = 28 ft.
Length = x
Width = (1/2)x + 2

So now we can plug in the little equations of length and width into a perimeter formula:
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2x + x + 4 = 28
3x + 4 = 28
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x = 8

To find the width, just plug in 8 for x in our little equation:
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So, the length is 8 feet and the width is 6 feet.
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