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irina1246 [14]
3 years ago
13

Simplify: Cube root of (128a^13b^6)

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
7 0
\sqrt[3]{128a^{13}b^{6}} \\\sqrt[3]{64a^{12}b^{6} * 2a} \\\sqrt[3]{64a^{12}b^{6}}\sqrt[3]{2a} \\4a^{4}b^{2}\sqrt[3]{2a}
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A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind. Find the speed of the wind
Lunna [17]

Given:

A pilot can travel 450 miles with the wind in the same amount of time as 360 miles against the wind.

Pilot's speed in still air is 315 miles per hour.

To find:

The speed of the wind.

Solution:

Let the speed of wind be x miles per hour.

Speed with wind = 315+x miles per hour

Speed against wind = 315-x miles per hour

We know that,

Time=\dfrac{Distance}{Speed}

According to the question,

\dfrac{450}{315+x}=\dfrac{360}{315-x}

Divide both sides by 90.

\dfrac{5}{315+x}=\dfrac{4}{315-x}

By cross multiplication, we get

5(315-x)=4(315+x)

5(315)-5x=4(315)+4x

5(315)-4(315)=4x+5x

(5-4)315=9x

Divide both sides by 9.

\dfrac{(1)315}{9}=x

35=x

Therefore, the speed of wind is 35 miles per hour.

4 0
3 years ago
Suppose that P(A)=0.5, P(B)= 0.4 and P(B/A) =0.6. Find each of the following.
Lady_Fox [76]

Part (a)

P(A) = 0.5

P(B) = 0.4

P(B/A) = 0.6

P(A and B) = P(A)*P(B/A)

P(A and B) = 0.5*0.6

P(A and B) = 0.3

<h3>Answer: 0.3</h3>

==========================================

Part (b)

We'll use the result from part (a)

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.5 + 0.4 - 0.3

P(A or B) = 0.6

<h3>Answer: 0.6</h3>

===========================================

Part (c)

A and B are not independent since P(B) does not equal P(B/A). The fact that event A happens changes the probability P(B). Recall that P(B/A) means "probability P(B) based on event A already happened". A and B are independent if P(B) = P(B/A).

Events A and B are not mutually exclusive since P(A or B) is not zero.

<h3>Answer: Neither</h3>
7 0
3 years ago
If X is a normally distributed random variable with mean .30 and standard deviation .06 : (draw appropriate diagrams) a) Find P(
Ierofanga [76]

Answer:

0.34  x 0.38

=0.1292

Step-by-step explanation:

Hopefully this helps, if not HMU and I will try my best to get you a better answer! :)

Good luck! <3

7 0
3 years ago
Simplify the expression 2x - 7 + 4x
bija089 [108]

Answer:

6x−7

Step-by-step explanation:

2x−7+4x

=2x+−7+4x

Combine Like Terms:

=2x+−7+4x

=(2x+4x)+(−7)

=6x+−7

3 0
3 years ago
Read 2 more answers
You are selling candy bars for the school to
Strike441 [17]

Answer:

200 bars

Step-by-step explanation:

$300 - $50 = the amount of money you still need, $250

250 dollars/$1.25 per bar = 200 bars you need to sell to get 300 dollars

7 0
4 years ago
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